Dust around Main-Sequence and Supergiant

Stars

A Thesis submitted for the Degree

of

Doctor of Philosophy of the University of London by Roger James Sylvester

UCL

Department of Physics & Astronomy

University College London

University of London

1995 ProQuest Number: 10044337

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ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 A bstract

This thesis is a study of the properties of the dust around two rather different types of star. The first part is concerned with the mid-infrared emission from a sample of

16 M-type supergiants. As weU as silicate emission features, seven of the stars showed the UIR (unidentified infrared) emission bands, associated with carbonaceous material.

According to standard theory, aU the carbon in the outflows from these oxygen-rich stars should be bound up in CO molecules, preventing the formation of carbonaceous dust.

The results were interpreted in terms of a non-equilibrium chemical model, which invoked chromospheric UV photons to dissociate CO, allowing carbonaceous material to form, and to excite the observed UIR-band emission. The larger part of the thesis considers Vega-excess stars — main sequence stars with excess infrared emission from circumstellar dust discs. Photometric and spectroscopic observations were carried out. A number of the stars displayed excess near-IR emission, indicating the presence of hot material. Mid-infrared spectroscopy enabled the grain composition to be identified: both silicates and carbona­ ceous species were detected. Millimetre and submiUimetre photometry indicated that large grains are present around many of our sources, implying that significant grain coagulation has occurred. Most of the sources were modelled using a radiative transfer code, with disc geome­ try and multiple grain sizes. Two grain materials, astronomical silicate and amorphous carbon, were considered. Successful fits to the spectral energy distributions at mid-IR and longer wavelengths were found. The temperatures needed to produce near-IR excess emission were too high for grains in thermal equilibrium to survive. A model was therefore developed with very small grains undergoing thermal spiking due to single-photon absorp­ tion, which provided satisfactory fits for the hottest stars; the others had insufficient UV flux to excite the small grains. Acknowledgements

First, I would like to thank my supervisor, Professor Mike Barlow, for all his help and guidance thoroughout the course of my PhD work, and for his useful comments on the actual text of this thesis. Mike is a co-author of Chapter 2, which appeared in a slightly different form in Monthly Notices. Chris Skinner also helped me a great deal, particularly with observing and the dust-disc modelling.

I would also like to thank my family for their constant interest and encouragement throughout this period.

I am grateful to SERC and PPARC for three years’ funding, to the Department of

Physics and Astronomy for funding during (what I believed would be) my final term, and to the staff at UKIRT, JCMT and La Palma for their assistance, and for making Service observations. And finally, a big thanks to all the inhabitants at various times of the Corridor of

Gloom, which is no more... Mike H., Robin, Bill, Bill, John, Kay, Raul, Alex, Sean,

Annelie, Sarah, Vince, Ian, Ian, Xiao-Wei, Richard, Martin, Martin, and everyone I’ve forgotten. C ontents

Title Page 1

A bstract 2

Acknowledgements 3

Table of Contents 4

List of Tables 8

List of Figures 10

1 Introduction 13 1.1 Overview ...... 13

1.2 Stardust...... 14

1.3 Infrared and Submillimetre Astronomy ...... 15

1.4 Circumstellar D ust...... 17

1.5 Vega-Excess Stars ...... 18

1.5.1 The Prototypes ...... 18

1.5.2 (3 P ic to r is ...... 20

1.5.3 Other sources ...... 22

1.6 Evolutionary Status of Vega-excess System s ...... 24

1.6.1 Target Selection ...... 27

2 Dust Emission from M-type Supergiants 29 2.1 Introduction...... 29

2 . 2 Spectroscopy with CGS3 ...... 30 2.3 The Observed Spectra ...... 33

2.4 Mass loss ra te s ...... 42

2.5 Discussion...... 44

2.5.1 Non-Equilibrium Dust Formation...... 46

2.5.2 Incidence of UIR-Band Emission in the Sam ple ...... 48

3 Observations of Vega-Excess Stars 54

3.1 Introduction...... 54 3.2 Optical Photom etry ...... 55

3.2.1 Results ...... 56

3.3 Near-Infrared P h o to m e try ...... 60

3.3.1 UKT 9 ...... 60 3.3.2 IRCAM ...... 62

3.3.3 Results ...... 62

3.4 Mid-Infrared Spectroscopy with CG S 3 ...... 67

3.4.1 Results ...... 6 8 3.4.2 Spectral Features...... 77 3.4.3 Notes on Individual Sources...... 82 3.5 Near-Infrared Spectroscopy with CGS4 ...... 87

3.6 Millimetre-Wave Photometry using UK T 14 ...... 8 8

3.6.1 Results ...... 91

3.6.2 Spectral Indices ...... 97

3.7 Spectral Energy Distributions ...... 102

3.8 Tabulated D ata ...... 118

4 Radiative Transfer Modelling of Vega-Excess Systems 122 4.1 The Model ...... 122

4.2 The Central Stars ...... 122

4.3 The G rains ...... 124

4.3.1 Size Distribution...... 124

4.3.2 Radiative Equilibrium and Dust Temperature...... 126

4.3.3 Grain Optical Properties ...... 127

4.4 Spatial Distribution of the D ust...... 131 4.5 Model Output...... 132

4.6 Effects of the Input Parameters ...... 132

4.7 Modus Operand] ...... 141

5 Small Grains around Vega-excess Stars 143

5.1 Reasons for Considering Small G rain s ...... 143

5.2 The Small Grain Hypothesis ...... 144

5.3 Calculating the Temperature Distribution...... 145 5.4 Solving for the Steady State ...... 153

5.5 Results...... 155

5.5.1 Effects of Grain Size ...... 156

5.6 Effects of the Radiation Field ...... 162

5.6.1 Hardness ...... 162

5.6.2 Intensity ...... 163

6 Results of Modelling 170 6.1 Stars with a Near-infrared Excess ...... 172

6 . 1 . 1 SAO 77144 (HD 35187) ...... 172

6 . 1 . 2 SAO 131926 (HD 43282) . . . . , ...... 175

6.1.3 SAO 183956 (HD 142666) ...... 180

6.1.4 SAO 183986 (HD 143006) ...... 187

6.1.5 SAO 184124 (HD 144432) ...... 192

6.1.6 SAO 186777 (HD 169142) ...... 196 6.1.7 SAO 206462 (HD 135344)...... 200

6.1.8 SAO 226057 (HD 139614) ...... 204

6.2 Stars with mid-IR excess but no near-IR Excess ...... 208

6 .2 . 1 SAO 26804 (HD 233517) ...... 208

6.2.2 SAO 112630 (HD 34700)...... 210

6.2.3 SAO 140789 (HD 141569) ...... 214

6.2.4 SAO 158350 (HD 123160) ...... 219

6.2.5 SAO 179815 (HD 98800) ...... 225

6.3 Stars with no mid-IR excess ...... 229

6.3.1 SAO 91022 (HD 218396)...... 229 6.3.2 SAO 93601 (HD 23680) ...... 233

6.3.3 SAO 111388 (HD 23362) ...... 238

6.3.4 SAO 147886 (49 Get) ...... 241

6.4 Summary of Modelling R esults ...... 245

7 Conclusions and Future Work 254

7.1 M Supergiants ...... 254

7.2 Vega-excess stars ...... 255

References 260 List of Tables

2.1 The programme stars ...... 32

2.2 Positions and widths of the narrow emission features ...... 39

2.3 M supergiants: derived quantities ...... 41 2.4 Comparison of calculated mass loss rates ...... 44

3.1 Stars observed photometricaUy in the optical region ...... 56 3.2 Optical magnitudes from JKT Service photom etry ...... 57

3.3 The adopted zero-magnitude flux calibration ...... 58

3.4 Distances and reddenings derived from JKT Service optical photometry . . 58 3.5 Distances and reddenings from published optical photom etry ...... 59

3.6 Log of UKT9 observations ...... 61

3.7 New near-IR photometry ...... 63

3.8 Magnitude and colour temperatures of the near-IR excesses ...... 65

3.9 Log of the CGS3 observations ...... 69

3.10 CGS3 spectra: derived quantities ...... 80 3.11 Proposed assignments of some of the UIR bands (see AUamandola et al.

1989) ...... 81

3.12 Individual JCMT measurements ...... 92

3.13 Weighted mean JCMT fluxes ...... 95

3.14 IRAM 1.2 mm fluxes from Bockelee-Morvan et al...... 96

3.15 Spectral indices for different conditions ...... 98

3.16 Observed submiUimetre spectral indices ...... 99 3.17 Spectral indices for prototype Vega-excess sta rs ...... 99

3.18 Usage of IRAS catalogues ...... 103

3.19 Fractional luminosities of Vega-excess s ta r s ...... 105 3.20 Sum mary of observational data: O p tic a l...... 119

3.21 Summary of observational data: Near-IR and C G S 3 ...... 120

3.22 Summary of observational data: IRAS and sub-mm ...... 1 2 1

6.1 Models for SAO 77144 (HD 35187) ...... 173

6 . 2 Models for SAO 131926 (HD 43282) ...... 178

6.3 Models for SAO 183956 (HD 142666) ...... 182

6.4 Models for SAO 183986 (HD 143006) ...... 189

6.5 Models for SAO 184124 (HD 144432) ...... 193

6 . 6 Models for SAO 186777 (HD 169142) ...... 198

6.7 Models for SAO 206462 (HD 135344) ...... 201

6 . 8 Models for SAO 226057 (HD 139614 ...... 206 6.9 Models for SAO 112630 (HD 34700) ...... 212

6 . 1 0 Models for SAO 140789 (HD 141569) ...... 216 6.11 Models for SAO 158350 (HD123160) ...... 220

6 . 1 2 Models for SAO 158350 (HD123160) as a G5V s ta r ...... 223

6.13 New models for SAO 179815 (HD 98800) ...... 225

6.14 Models for SAO 91022 (HD 218396) ...... 231 6.15 Models for SAO 93601 (HD 23680) ...... 234

6.16 Further models for SAO 93601 ...... 236

6.17 Models for SAO 111388 (HD 23362) ...... 240

6.18 Models for SAO 147886 (49 G e t) ...... 242

6.19 Presence of silicate and UIR-band em ission ...... 247

6.20 Best-fitting model param eters ...... 249 List of Figures

2.1 CGS3 spectra of M supergiants ...... 34

2.2 ‘Excess’ spectra after subtraction of blackbodies ...... 38

2.3 Silicate feature strength versus mass loss r a te ...... 42

2.4 Excess flux profiles for stars with IRAS 1 2 -/xm fluxes less than 2 1 Jy . . . . 50

2.5 Excess flux profiles for stars with IRAS 1 2 -/im fluxes greater than 2 1 Jy . . 51

2.6 Comparison of observed and model silicate features ...... 52

3.1 Near-IR colour-color diagram for Vega-excess stars ...... 65

3.2 Colour-colour diagram for Herbig Ae/Be stars. From Hillenbrand et al. 1992 6 6 3.3 CGS3 spectra of Vega-excess s ta r s ...... 70

3.4 20-/im spectra enlarged for clarity ...... 79

3.5 CGS4 Service spectrum of SAO 186777 8 8

3.6 Spectral energy distributions ...... 106

4.1 Comparison of blackbodies and model atmospheres ...... 123

4.2 Mie theory results for silicate g ra in s ...... 129

4.3 Mie theory results for amorphous carbon grains ...... 130

4.4 Effects of varying 7 ...... 134 4.5 Effects of varying (3 ...... 135

4.6 Effects of varying the inner radius ...... 136

4.7 Effects of varying the outer radius ...... 138

4.8 Effects of varying the minimum grain siz e ...... 139

4.9 Effects of varying the maximum grain size ...... 140

5.1 Temperature evolution of grains in a radiation field ...... 145

5.2 Different types of matrix elem ent ...... 155

10 5.3 Effects of grain size on probability distribution function ...... 157

5.4 High-temperature behaviour of small grains ...... 160

5.5 Spectral energy distributions of small grains ...... 161

5.6 Effects of stellar temperature on probability distribution ...... 164

5.7 UV-visible portions of stellar radiation fields ...... 165

5.8 Effects of radiation field intensity on small grains ...... 167

5.9 SEDs for different intensities ...... 168

6 . 1 Results of modelling SAO 77144 ...... 176

6 . 2 1 0 -/im region of SAO 77144 m odels ...... 177

6.3 Results of modelling SAO 131926 ...... 179

6.4 Results of modelling SAO 183956 ...... 183 6.5 Fit to CGS3 spectrum of SAO 183956 ...... 184

6 . 6 Mid-IR portion of various SAO 183956 models ...... 185 6.7 Results of modelling SAO 183986 ...... 190

6 . 8 Fit to CGS3 spectrum of SAO 183986 ...... 191 6.9 Results of modelling SAO 184124 ...... 194

6 . 1 0 Fit to CGS3 spectrum of SAO 184124 ...... 195 6.11 Results of modelling SAO 186777 ...... 197

6 . 1 2 Fit to CGS3 spectrum of SAO 186777 ...... 199

6.13 Results of modelling SAO 206462 ...... 203

6.14 Fit to CGS3 spectrum of SAO 206462 ...... 204

6.15 Results of modelling SAO 226057 ...... 207

6.16 Model of SAO 26804 ...... 209

6.17 Results of modelling SAO 112630 ...... 213

6.18 Results of modelling SAO 140789 ...... 217

6.19 Results of modelling SAO 158350 ...... 221

6.20 Models of SAO 158350 as a G-type s t a r ...... 224

6 . 2 1 Results of modelling SAO 179815 ...... 226

6 . 2 2 Fit to CGS3 spectrum of SAO 179815 ...... 227

6.23 Results of modelling SAO 91022 ...... 232

6.24 Results of modelling SAO 93601 ...... 235

6.25 Results of modelHng SAO 111388 ...... 239

11 6.26 Results of modelling SAO 147886 ...... 243

12 C hapter 1

Introduction

1.1 Overview

Dust around stars is of great importance, given that the Earth itself is composed of materials that were once in circumstellar grains, and was formed by the accretion of circumstellar dust.

This thesis is concerned with circumstellar dust at the beginning and end of its ex­ istence. Dust is formed in the atmospheres of massive, cool stars, and expelled into the interstellar medium, enriching it with heavy elements. The properties of dust around cool stars of one particular type, the M supergiants, are the subject of Chapter 2. After a long sojourn in the interstellar medium, some fraction of the dust ejected by a cool star can be involved in the condensation of discs around young main-sequence stars, forming larger grains and, at least in the case of our Solar System, planets. Eventually, solar-type stars evolve off the main sequence and become red giants. These undergo mass loss, leading to the formation of new dust, and thus completing the cycle of stellar and dust evolution.

The major part of this thesis deals with observations (Chapter 3) and modelling (Chap­ ters 4-6) of dusty main-sequence stars. Conclusions and possibilities for future work are presented in the final Chapter.

Observations of the two types of dusty circumstellar environment discussed in this thesis show that grains of similar chemical composition are present around both cool supergiants and main-sequence Vega-excess stars.

The discovery, made in the course of this work, of aromatic hydrocarbons in the dust around both M supergiants and Vega-excess stars provides a further link between the two

13 types of object. This discovery was unexpected in the case of the supergiants; for the

Vega-excess systems it is consistent with an interstellar origin for the dust, as well as with the fact that substantial amounts of carbonaceous material are found in the Solar System.

1.2 Stardust

Astronomical dust was first noticed due to the extinction of starlight. William Herschel discovered small regions of the sky where the number of stars in a given telescope field- of-view dropped by around a factor of 10 from the surrounding areas. He interpreted this phenomenon as being due to an actual absence of stars, an “opening in the heavens”

(Herschel 1785). The detection of structure in the dark regions of various Galactic star- helds, observed in early photographic surveys (e.g. Barnard 1907), led to the starless regions being ascribed to obscuration by foreground material.

Trumpler (1930) calculated the distances to a number of open clusters based on two methods, one geometrical and one based on the luminosities of the stars in the clusters. The two methods systematically gave different distances, which Trumpler showed to be evidence for an extinguishing layer in the plane of the Galaxy, indicating that interstellar extinction was not just confined to the dark nebulae.

The dynamical calculations carried out by Oort (1932) found an upper limit to the density of interstellar matter of 3 X 10“^' kg m~^. This strongly suggested that the extinguishing material was composed of dust grains, since other candidates, such as gas- phaise atoms or free electrons, would have required far more mass to produce the observed amount of extinction. Multi-band photometry showed that the amount of extinction was inversely propor­ tional to wavelength in the optical region, implying that the interstellar grains were of size comparable to the wavelength of visible light (e.g. HaU 1937). This A”' behaviour implies that blue light wiU suffer greater extinction than red Ught, hence the phenomenon of ex­ tinction is also known as reddening. In photometric terms, extinction produces a ‘colour excess’, where the observed difference in magnitudes between two photometric bands is greater for a reddened star than would be expected in the absence of extinction.

Observations have shown that the extinction varies with wavelength in a similar fash­ ion for many different lines of sight, and that the colour excess between the B and V

14 photometric bands, E(5 — V), is proportional to the total extinction in the V band, A y-

This makes it possible to correct, or ‘deredden’, the observed spectral energy distribution

of a reddened star if its expected {B — V ) colour is known, a technique which is exploited in Chapter 3.

Extinction comprises two components: absorption, where incident light is converted into internal energy (i.e. heat) within a grain, and scattering, where the light is deviated from its original path by processes analogous to refraction and diffraction. For grains

substantially larger than the wavelength of interest, geometrical optics and diffraction can

be used to determine the scattering and absorption properties of the grain, but for grains of

size comparable to the wavelength, geometrical optics do not predict the observed results,

and a more sophisticated treatment of the interaction of electromagnetic radiation with

small particles, known as Mie theory, must be used (see e.g. Bohren & Huffman 1983). Scattering makes it possible to observe dust directly, in the form of reflection nebulae, such as the well-known nebulosity around the star Merope in the Pleiades. Reflection nebulae are typically bluish in colour, as would be expected given that light of shorter wavelengths is scattered more efficiently than longer-wavelength light. Reflection nebu­ lae and reddened starlight are often found to be polarised, indicating that a substantial fraction of interstellar grains are elongated, rather than spherical, and are aligned by the

magnetic field of the Galaxy.

The principle of conservation of energy tells us that grains which absorb light will

undergo an increase in temperature. Absorbing grains wiU therefore emit radiation, with

a spectral energy distribution (SED) which depends on the grain temperature. Solid materials evaporate at temperatures around 1500 K, so the SED of the emission from dust grains (treated as blackbodies) must peak at wavelengths longer than about 2 /xm. Most of the energy radiated by grains wiU therefore lie in the infrared spectral region.

1.3 Infrared and Submillimetre Astronomy

Infrared radiation was discovered by W. Herschel in 1800, who found that a thermometer placed just beyond the red end of a spectrum of the Sun showed an increase in temperature compared with a reference thermometer located some distance away from the spectrum.

In an elegant series of experiments, he went on to show that the heat-producing rays

15 could be reflected and refracted in the same way as visible light, and that the rays from

hot terrestrial objects, such as stoves and hot pokers, were of the same nature as the solar rays.

A lack of sensitive detectors limited astronomical infrared observations to the Sun,

Moon and some of the brighter stars until the mid-20th century, when devices such as lead sulphide photo-resistors and germanium-gallium bolometers became available.

The infrared (IR) spectral region is generally taken to extend from approximately

1 fim to 400 fim (the region immediately short wards of 1 /xm is sometimes known as the photographic IR or the ‘far-red’). Beised on the techniques used for observing, the IR can be subdivided into three wavelength regions: the near-, mid- and far-IR, with approximate wavelength coverages of 1-5, 5-40 and 40-400 /xm respectively. Near- and mid-IR observations can be made from ground-based observatories, while atmospheric absorption leads to the far-IR being only accessible to high-altitude aircraft, balloons or satellites.

Even within the near- and mid-IR, the atmosphere is opaque at some wavelengths, due mainly to absorption by CO 2 and water molecules, giving a set of discrete atmospheric

‘windows’ through which observations are possible. The J, H, K, L, Af, photometric bands were chosen to lie within the near-IR windows, and the wavelengths in Table 3.3 give an indication of the central wavelengths of the windows. The two main mid-IR windows lie at approxim ately 7-13 and 17-25 /xm, and are known as the 10-/xm (A ) and 20-/xm (Q) windows.

The millimetre and sub miUimetre wavelength region, which lies at approximately

0.4-2 mm, is also divided into a number of atmospheric windows, to which the filter band passes used for photometry have been matched (see e.g. Matthews 1993).

In the mid-IR and (sub)mm regions, the sky is several orders of magnitude brighter than typical astronomical sources. To overcome this, the techniques of chopping and nodding are employed (see e.g. AUen 1975) to cancel the foreground sky emission by subtracting the flux due to a nearby patch of sky.

As mentioned above, warm dust wiU radiate in the infrared. If a star surrounded by dust is observed in the IR, it wiU therefore be found to emit more radiation than would be expected from the photosphere alone, i.e. it would display an ‘infrared excess’.

16 1.4 Circumstellar Dust

Just as for interstellar dust, circumstellar dust was first detected in absorption. The hydrogen-poor carbon star R Coronae Borealis was long known to exhibit variations in brightness of up to 9 magnitudes, with no discernible periodicity. The variations take the form of transient events where the star becomes fainter, before returning to its usual mag­ nitude. During these events, the optical spectrum of the star does not change, suggesting that the variation is not caused by changes in the star’s photosphere, but is due to some obscuring material entering the line of sight to the star. The lack of periodicity ruled out an Algol-type behaviour, where a fainter binary companion eclipses the brighter star. Loreta (1934) and O’Keefe (1939) proposed that the events were due to graphitic grains condensing in the atmosphere of the star.

With the advent of sensitive IR instruments, observers were able to detect excess IR emission from a number of stars (see e.g. GiUett et al. 1968, Woolf & Ney 1969), including R CrB (Stein et al. 1969). The stars which showed excess IR emission were cool giants and supergiants, such as Betelgeuse, Mira and /x Cephei.

Spectroscopy in the 1 0 -/xm region showed that oxygen-rich stars displayed an emission feature that resembled that of the silicate mineral olivine ([Mg,Fe] 2 Si0 4 ), while carbon stars did not show this feature (e.g. Woolf & Ney 1969). Gilman (1969) showed, on the basis of molecular equilibrium calculations, that0 -rich stars would indeed be expected to produce silicate dust, while C-rich stars would produce carbon and silicon carbide dust.

This is because the highly stable CO molecule forms in preference to any other molecule, until aU of the less-abundant of carbon and oxygen is bound up into CO, leaving only the more-abundant species to form dust.

The first exception to the rule that 0-rich and C-rich dust cannot form together around a single star came with the observations of Nova Cen 1986, where silicate emission and the so-called Unidentified Infrared (UIR) bands, ascribed to carbonaceous media, were detected contemporaneously in mid-IR spectra (Bode 1989, Smith et al. 1994). Smith et al. suggested that this could come about if there were inhomogeneities in the outflow, with abundance gradients in the gaseous outflow leading to C-rich and 0-rich dust condensing in spatially distinct regions, such as shells or clumps. A more widespread occurrence of this phenomenon is detailed in Chapter 2, where the mid-IR spectra of a number of oxygen-rich cool supergiants are shown to display both silicate and UIR-band emission.

17 Due to their high dust mass-loss rates, typically M©yr“' (Justtanont &

Tielens 1991), cool evolved stars are important sources of dust and heavy elements for the interstellar medium (see e.g. Bode 1988). Combined with their high luminosities, large mass-loss rates from oxygen rich giants and supergiants mean they can have strong silicate features, which can be observed with high signal-to-noise, and the feature profiles used in modelling other objects. At the other end of the stellar evolution process lie the pre-main sequence stars, another type of dusty star. T Tauri stars, the precursors of solar-mass main sequence stars, and

Herbig Ae/Be stars, their intermediate mass counterparts, display large infrared excesses, believed to be due to discs or envelopes of circumstellar dust (see e.g. Rydgren 1978,

Hillenbrand et al. 1992). Unlike the cool giants and supergiants, pre-main sequence stars

do not produce dust, but are surrounded by dust from the molecular clouds in which they form.

1.5 Vega-Excess Stars

1.5.1 The Prototypes

Vega (a Lyrae) is a bright (zero-magnitude) photometric standard star, and so was a

natural choice to be one of the reference stars used in the IRAS mission. At wavelengths

longer than a few microns, this star was expected to emit like the Rayleigh-Jeans portion

of a blackbody spectrum.

Special slow-scan observations were made by IRAS to determine accurate fluxes of Vega

at 1 2 , 25, 60 and 1 0 0 /xm, as part of the effort to calibrate the satellite’s detectors. Much to their surprise, the IRAS Science Team found that although Vega gave good agreement

with the predicted flux at 12 /xm, the observed fluxes at 25, 60, and 100 /xm were in excess

of the predicted values by factors of 1.3, 7, and 16 respectively (Aumann et al. 1984).

Aumann et al. (1984) found that the diameter of the region emitting at 60 /xm was

approximately 20 arcsec, and that an 85-K blackbody gave a reasonable fit to the spectral

energy distribution of the excess emission. They deduced that the best explanation for the IR excess was emission from a shell or ring of solid particles of radius ~1 mm, located

some 85 AU from the star, and they discussed four alternative explanations for the origin

of the dust: ( 1 ) it is continuously produced by mass loss from a Lyr; (2) it was produced

18 in the past by mass loss in a process which has subsequently ceased; (3) the dust grains were captured from the interstellar medium; and (4) the dust is left over from the original cloud of gas and dust from which the star was formed. The first possibility could be discounted because there is no observational evidence for mass loss from Vega, and the upper limit of 10“^^ M© yr~' (quoted by Aumann et al.) is lower than the rate required to produce enough dust to explain the observed excess flux.

The second and third possibilities would imply quite small grain sizes ( 0.5/im), typical of dust in the interstellar medium (ISM) and in the outflows of mass-losing stars. Such grains would rapidly be ejected from the environs of a Lyr by radiation pressure (Aumann et al. 1984). ISM-size grains also emit inefficiently at IR wavelengths, and so would be hotter than larger grains for a given distance from the star (Chapter 4). Backman &

Paresce (1993) have shown that if ISM grains around Vega were producing the observed IR excess emission, the apparent diameter of the dust shell would be almost 2000 arcsec. The remaining possibility is therefore that the dust formed in the cloud from which the star was formed. During the IRAS mission, three other bright stars were found to display excess infrared emission: a PsA (Fomalhaut), e Eri, and /3 Pic. Additional (pointed) observations were m ade with IRAS to obtain accurate photometry of all four stars (GiUett 1986). As weU as Vega, Fomalhaut and Pic were resolved by IRAS. The four stars are taken as the prototypes of the class of Vega-excess stars.

The energy distributions of the excess emission from the four stars are qualitatively similar, with the notable exception that /5 Pic shows significant excess emission at 12 /xm, unUke the other three sources. The 25-100/xm fluxes of aU four stars can be reasonably weU fitted with blackbodies of temperatures ~100 K (e.g. Walker & Wolstencroft 1988), but the 13 Pic 12-/xm flux is greater than th at of the combination of steUar flux and cool blackbody, indicating the presence of dust at higher temperatures.

The faU-off in excess emission towards shorter wavelengths impUes the presence of relatively dust-free regions close to the Vega-excess stars, with (model-dependent) sizes similar to the orbits of planets in the Solar System (e.g. GiUett 1986). The fractional excess luminosity, Lir/Z/* of the four prototypes are in the range

10“^-10“^, with (3 Pic having the largest value, compared with ~ 10“^ estimated for the zodiacal dust in the inner solar system (Backman & GiUett 1987, Backman & Paresce

19 1993). However, Backman & Paresce show that the Sun could have a dust cloud similar to that of Vega without it being detected ‘from inside’ by IRAS.

Observations of the prototype Vega-excess stars were soon made at longer wavelengths.

Harper et al. (1984) showed that the flux of Vega at 193 /xm was significantly lower than that expected for an 85 K blackbody which fits the IRAS 25-100 /xm data.

Becklin & Zuckerman (1990, also Zuckerman & Becklin 1993) and Chini et al. (1990,

1991) observed the four prototypes at wavelengths between 0.8 and 1.3 mm, and found that the mm-wave flux of Vega and (3 Pic (but possibly not Fomalhaut) were also below the extrapolated blackbody fluxes. These observations suggest that the dust around Vega and (3 Pic is dominated by grains smaller than 1 mm radius, in contrast to the grain size originally postulated for Vega by Aumann et al. (1984). However, Zuckerman & Becklin noted that the emission could nevertheless be due to mm-size grains with low emissivity at long wavelengths. The difficulties of submiUimetre astronomy manifest themselves in the apparent in­ consistencies between the sub-mm fluxes measured by the Zuckerman and Chini groups (acknowledged by both authors), and in the spurious detection of an extended disc-Uke structure around Fomalhaut (Stern et al. 1994a), which was subsequently retracted (Stern et al. 1994b).

1.5.2 /? Pictoris

An extended disc-like structure unquestionably has been detected about the A5V star

P Pictoris. Soon after the discovery of the P Pic IR excess was announced. Smith h Terrile

(1984) observed P Pic at 0.89 /xm with a coronagraph designed to observe satellites around bright planets. They found an edge-on disc visible in scattered Ught, which extended out to at least 400 AU from the star. Further observations with coronagraphs (Paresce h

Burrows 1987, GoUmowski et al. 1992) and with an anti-blooming CCD (LecaveUer des

Etangs et al. 1992) were able to observe the disc down to approximately 30 AU from the star, and detected a change in the surface brightness gradient at about 80 AU. This change is in agreement with the predictions of models by Backman et al. (1992).

The P Pic disc has also been spatially resolved in the mid-infrared. Telesco et al. (1988) used a 2 0 -element bolometer array to observe P Pic at 10.8 and 19.2 /xm, with a resolution of approximately 5 arcsec. The emission from the star was centred on one pixel, and it was

20 found that for /? Pic, a greater amount of the total flux was observed by the surrounding pixels than in the case of the point-source calibrator star. The opiission was not distributed evenly among these pixels, but was located in an elongated structure, oriented with a position angle in good agreement with that of the optically imaged scattering disc. This demonstrated that the material responsible for the excess emission detected by IRAS is related to the material visible in scattered light.

Lagage & Pantin (1994a) used a more sophisticated 64x64 pixel mid-IR camera, with sub-arcsecond resolution, and a broad band 10.5-13 /im filter. Their image clearly shows the edge-on disc, which extended to at least 4 arcsec from the star and was found to be asymmetric. The asymmetry appears to be a real feature of the disc, not an artifact of the data reduction. From their data, Lagage & Pantin inferred a partially-cleared zone in the innermost 30 AU of the disc, and discussed an explanation in terms of the gravitational effects of a planet orbiting the star. The mid-infrared emission from (3 Pic has also been studied spectroscopically. Spec­ trophotometry at four wavelengths by Telesco & Knacke (1991) showed evidence for a 10-/im silicate feature in the (3 Pic emission, which was confirmed in medium-resolution spectra obtained by Aitken et al. (1993) and Knacke et al. (1993). Both groups found that the silicate feature was rather broad, and clearly different from those of massive cool stars such as Cep, but that the silicate features found in the spectra of some comets did give a good fit to the (3 Pic spectrum. Knacke et al. (1993) inferred from this that the (3 Pic dust is not composed of unaltered interstellar grains, but that the grains have undergone substantial processing in the /? Pic system, and were possibly formed in the disc from the fragmentation of larger bodies, such as comets or asteroids.

As well as the dust seen in scattering and emission, substantial quantities of gas have been detected in absorption around (3 Pic, whereas for Vega, Fomalhaut and e Eri, no gas has yet been detected (see e.g. Lagrange-Henri 1995). In fact, circumstellar gas had been detected in lUE ultraviolet spectra of (3 Pic, causing it to be classified as a shell star, before it was known to have an infrared excess (Slettebak & Carpenter 1983). Several different elements have been detected in the CS lines, in neutral and ionised states: iron, carbon, magnesium, calcium and aluminium (see Lagrange-Henri 1995 for a recent review).

There are two types of component contributing to the circumstellar lines: a stable component, centred on the heliocentric velocity of the star, and variable components.

21 with time-scales sometimes as short as a few hours, and velocities of up to several hundred km s~'. Observations of the stable component have shown that the gas giving rise to the CS lines lies mainly within 1 AU of the star (Hobbs et al. 1988) and so may not be related to the dust disc, which has an inner radius that is probably of the order of 10 AU

(Backman & Paresce 1993).

The strong variable components are always red-shifted with respect to the stable com­ ponent, implying that the absorbing gas is falling in towards the star; some blue-shifted features have been observed, but they are always much weaker than the red-shifted features

(Beust et al. 1994). The variable features have been attributed to material evaporating from comets falling in towards the star (Lagrange et al. 1987).

In a long series of papers, Beust et al. (1994 and references therein) have developed the cometary hypothesis further with detailed modelling of the dynamics of ionised material released from a comet nucleus. The comets are modelled as moving towards the star on near-parabolic orbits, a few tens of stellar radii from the star. As a mass of such material passes into the line of sight, it produces a transient, red-shifted absorption feature, which closely matches the observed spectral features.

1.5.3 Other sources

After the discovery of the prototype Vega-excess stars, a number of searches were made of the IRAS data for stars with infrared excesses. Aumann (1985) searched the IRAS Point

Source Catalog (PSC) for sources positionally associated with main-sequence stars within

25 pc and situated at least 10° from the Galactic plane. He found 1 2 stars that fitted

these criteria and had a 60-/im excess such that [ 1 2 ] —[60]> 1 . 0 (square brackets indicate magnitude at a given wavelength). This set of twelve stars, which included the four prototypes, contained six A-type stars, and no double or multiple stars. The seemingly high proportion of A stars was recognised as a luminosity selection effect.

Sadakane & Nishida (1986) took the Bright Star Catalogue (Hoffleit 1982) as their

starting point, and found a further 1 2 IRAS PSC stars which satisfied Aumann’s criteria for 60-/xm excess and Galactic latitude. Again, the sample was dominated by A-type stars,

but Sadakane & Nishida found several binary stars with IR excess, demonstrating that

binarity is not an obstacle to the existence of a Vega-excess dust cloud.

One of the stars in Sadakane & Nishida’s list was A Boo, which is known to be metal-

22 deficient. This, together with the discovery that Vega itself is slightly metal-deficient, led

Venn & Lambert (1990) to suggest that such metal deficiency was due to the accretion of

(metal-depleted) circumstellar gas, while the metal elements, in the form of dust grains, remain in orbit around the star.

Walker & Wolstencroft (1988) and Stencel & Backman (1991) both produced useful lists of stars with infrared excesses; these lists formed the basis of the sample of Vega-excess stars studied in this thesis, and are discussed in some detail below. Backman h Paresce

(1993), as part of their extensive review of the “Vega Phenomenon”, compiled a ‘master list’ from the published lists of known Vega-excess stars. None of these more recently- discovered Vega-excess stars have received as much attention as (i Pic, but observations have been made of a number of them after they were recognised as Vega-excess stars.

51 Oph, optically classified as a Be star, has a large infrared excess, which extends to wavelengths as short as 2.2 ^m (Waters et al. 1988), implying the presence of hotter dust than that around ^ Pic. Narrow band ( 6 A % 1 /xm) photom etry in the 10-/xm spectral region (Fajardo-Acosta et al. 1993) showed a prominent silicate emission feature, similar to that of (5 Pic.

Ultraviolet spectra (Grady et al. 1991) of 51 Oph showed variable absorption features, interpreted ais due to infaUing material. This suggests that the 51 Oph disc, like that of

(3 Pic, is seen edge-on. Observations with the same infrared camera used to image the

(3 Pic disc (Lagage & Pantin 1994b) found that the 10-/xm emission from 51 Oph was unresolved (FWHM 1 arcsec), implying that the dust seen at 10 /xm lies within roughly

70 pc of the star, a result consistent with the observed size of the (less distant) 13 Pic disc at 10 /xm (Lagage & Pantin 1994a).

SAO 179815 (HD 98800) was observed by Skinner et al. (1992) with the mid-IR spec­ trometer CGS3, and was found to have a broad silicate feature, the first such feature in a Vega-excess spectrum to be fully resolved, rather than just detected by narrow band photometry. Using radiative-transfer modelling, Skinner et al. determined some of the physical parameters of the disc, and showed that SAO 179815 could be detected at mm wavelengths. These observations aroused considerable interest in this star, and new op­ tical observations were made of it. Fekel Sz Bopp (1993) demonstrated the youth of the star from the presence of strong lithium lines, rotational broadening and Ha emission.

Fekel and Bopp attributed the Ha profile to a high level of chromospheric activity, and

23 predicted that SAO 179815 is variable with an amplitude of at least 1 magnitude at visible wavelengths, due to emission from star-spots, modulated by the rotational period of the star. Time-series photometry by Henry & Hall (1994) showed that SAO 179815 is indeed variable, with a period of 14.7±0.2 days, and an amplitude of 0.07 mag. SAO 179815 was also imaged at 10 /xm (Lagage h Pantin 1994b), and was found to be unresolved compared to the 1 arcsec point-spread function. A large number of Vega-excess candidates (approximately 100) were observed by Smith et al. (1992), using a coronagraph. The result of this survey was that no discs were detected in scattered light — /? Pic is still unique in this regard. The possible explanations and implications of this result are discussed in the review by Lagrange-Henri (1995).

Another survey was undertaken by Zuckerman et al. (1995), who observed 30 candi­ date Vega-excess stars to search for CO emission, in order to determine the amounts of circumstellar gas around these stars. A number of the stars observed by Zuckerman et al. are members of the sample selected for this thesis, observations and models of which are described in Chapters 3-6. From their estimates of the gas masses and ages of the stars, Zuckerman et al. claimed that the gas dissipates rapidly enough to inhibit the formation of

Jupiter-like planets, unless they form with a shorter time-scaie than predicted by present theories.

1.6 Evolutionary Status of Vega-excess Systems

As soon as the dust around Vega was discovered, it was discussed in terms of planetary systems. Aumann et al. (1984) pointed out that the age of Vega (3 x 10® years) is less

than that of the Solar System (4.5 x 10® yr), and is bracketed by the time scale of active planetary formation (10^-10® yr). They suggested that the disc around Vega is in an

intermediate stage between the final phases of star formation and the present state of the

solar system.

T Tauri stars, the precursors of main-sequence solar-like stars, have massive circum­

stellar discs, as can be inferred from their SEDs (e.g. Strom et al. 1989). Some T Tauri

discs have been directly imaged at mm wavelengths (e.g. Sargent & Beckwith 1987) and

display evidence for Keplerian rotation (e.g. Skrutskie et al. 1993). Herbig Ae/Be stars,

the intermediate-mass counterparts of T Tauris, show large infrared excesses, similar to

24 those of T Tauris. The spectral energy distributions of some Herbig Ae/Be stars are in­ terpreted as implying that the excess emission arises from a combination of a disc and a surrounding envelope (e.g. HQenbrand et al. 1992). There is evidence for evolution oc­ curring in the circumsteUar environments of T Tauri stars, with the disc mass and optical depth decreasing with time; this progression can be traced backwards in time to include optically invisible protosteUar objects (André & Montmerle 1994), which form from the collapse of molecular cloud cores. Extrapolating the disc-dissipation process forwards in time should lead to main-sequence stars with smaller amounts of circumsteUar dust, and most of the solid material either accreted on to the star, expeUed from the system, or bound up into planets.

Among the Vega-excess sources, (3 Pic is younger than Vega (100 and 400 Myr re­ spectively; Hackman & Paresce 1993. Heap et al. 1995 suggest that (3 Pic may be even younger), and has a larger infrared excess. It is tempting to ascribe this to disc clearing with time, but the possibility cannot be excluded that Pic’s circumsteUar environment had a higher initial dust mass. SAO 179815 has an infrared excess larger than that of (3 Pic, and is considerably younger (<10 Myr; Fekel & Bopp 1993), lending weight to the suppo­ sition that younger Vega-excess stars have more substantial discs, however, SAO 179815 is a K star, and so has no evolutionary Unk with Vega or (3 Pic, which are both A-type stars. A number of authors have suggested that planets are present in Vega-excess systems.

Smith & Terrile (1984) proposed that the (3 Pic disc is associated with planet formation.

Given the youth of the star, any planetary formation would either be stiU occurring, or recently-completed. Weissman (1984) noted that the lack of dust hotter than approxi­ mately 85 K in the Vega system could indicate that the inner part of the disc had been swept clear of dust by an orbiting planet. Hackman et al. (1992) tentatively suggested that a “large object” orbiting /? Pic could be responsible for the clearing particles from the innermost part of the disc, while Lagage h Pantin (1994a) interpreted their mid-IR image of Pic (mentioned above) as indicating the possible presence of at least one planet in orbit around the star. Beust et al. (1991) suggested that perturbations due to a planet on an eccentric orbit around (3 Pic are responsible for the star-grazing comets suggested to be causing the variable absorption features seen in Pic’s spectrum.

As well as the evolutionary status of the Vega-excess discs themselves, one can also

25 consider the status of the individual dust grains. As mentioned above, spatially-resolved observations show that the grains are not products of mass-loss from the Vega-excess stars, nor are they unaltered interstellar grains. The two remaining possibilities are that the grains are remnants of the star-formation process, i.e. that they formed (by agglomeration of interstellar grains) in the molecular cloud in which the star formed; or that they are fragments of larger bodies, such as asteroids or comets, and are liberated from these parent bodies in collisions. The two scenarios are similar in that they both involve accretion from small ISM grains, but the second scenario requires the accretion process to go further, with the formation of large objects. Unless they are very numerous, asteroid- or comet-sized bodies would be very difficult to detect compared with grains, since grains have a much higher surface area per unit mass, so the two scenarios would probably appear identical to the observer. However, time-dependent processes, as discussed by Hackman & Paresce 1993 and Zuckerman & Becklin (1993), allow the two possibilities to be distinguished in principle. Detection of the silicate emission feature from the /3 Pic dust (Telesco & Knacke 1991, Aitken et al. 1993) and spatially-resolved IRAS observations (e.g. GiUett 1986) show that micron­ sized grains are present in the discs of Vega-excess stars. Such particles would rapidly be removed by radiation pressure ‘blowout’ and Poynting-Robertson drag. They could also be eroded by dust grains in the ISM (Lissauer & Griffith 1989) on time scales shorter than main-sequence stellar lifetimes. It therefore seems clear that the grains observed in

Vega-excess discs are short-lived, and therefore not merely remnants of the star-formation process, but must be replenished during the stellar lifetimes, unless the stars are very young.

In view of the importance of Vega-excess stars as possible sites of planetary formation, and as an important stage in the postulated stellar evolutionary sequence that begins with collapsing molecular cloud cores and progresses via the T Tauri and Herbig Ae/Be phases towards main-sequence stars, it was decided to undertake a major study of Vega-excess stars. This programme, comprising multi-waveband observations and modelling, forms the major part of this thesis. The overall aims of the project were to confirm the circumsteUar nature of the excess emission, and determine the physical parameters of the discs, such as their dimensions and density distributions and the composition and sizes of the dust grains.

26 1.6.1 Target Selection

In selecting candidate Vega-excess systems to observe, the overall aim was to define a set of objects for which the nature and physical parameters of the discs could be observa- tionally determined. In practice, this required selection of those sources with the greatest amounts of excess emission, in order that they could be detected over a wide range of wavelengths, especially the submillimetre region, to look for evidence of large grains, and so that reasonable signal-to-noise infrared spectra could be obtained.

We excluded the four ‘prototype’ Vega-excess stars, a Lyr (Vega), (3 Pic, a PsA (Foma-

Ihaut) and e Eri, because they had already been observed in the sub-mm region (Becklin

& Zuckerman 1990, Chini et al. 1990, 1991). ^ Pic, the only prototype with an excess at 12 /zm, is too far south to be observed from UKIRT.

Several authors have published lists of Vega-excess candidates, e.g. Aumann et al

(1984), Aumann (1985), GiUett (1986), Sadakane & Nishida (1986) Stencel & Backman (1990). One of the most useful was found to be that of Walker & Wolstencroft (1988), who selected objects from the IRAS Point Source Catalog using the foUowing criteria:

1 . They must be associated by the IRAS processing with the SAO catalogue

2. They must have ratios of 60/zm/100/zm flux densities (in Janskys) similar to those of

the prototypes, i.e. between 0 . 8 and 2 . 0 (corresponding to a blackbody temperature range of 60K to 150K).

3. There must be evidence that the objects are extended in one or more IRAS bands

(determined from the IRAS Working Survey Database).

Objects were relegated to a secondary Ust (‘Section B’) if their spectral classification contained an “e”, denoting the presence of emission fines, if they had a binary companion, or if they had spectral classes indicating they were late-type giants or supergiants.

We selected all nine of the primary (‘Section A’) candidates (SAO 26804, 77144,112630,

147886, 183956, 184124, 186777, 206462, 226057), and three (SAO 179815, 140789 and

183986) from the secondary list. The remaining sources were rejected either because they were M stars or cool giants/supergiants, and so were likely to be losing mass and producing dust of their own, or they were too far south to be observable from Mauna Kea.

SAO 87856, another Section B star, was also initially in our source list, but a literature

27 search showed that it had an M-type companion (see e.g. Lee 1970, Bidelman 1988).

Optical and near-infrared photometry in the literature (Lee 1970) showed that the M star dominates the infrared spectral energy distribution of the system, so this source too was rejected. We also selected one star, SAO 208591, from the Walker & Wolstencroft list of asso­ ciations with the Gliese (1969) catalogue which met the first two criteria, but were not required to show extension. SAO 208591 is the only star in that list which showed a large excess in the IRAS bands. Stencel & Backman (1991) published the results of a survey for infrared excess emission in a flux-limited sample of stars, which was not limited to main-sequence stars, but also included evolved stars. They required that stars meet the foUowing criteria:

1. They must have a measured flux density at 12 ^m, and in one or more of the longer-

wavelength bands.

2. They must have a high galactic latitude, | 6 | > 25°

3. The IRAS source must be positionaUy associated with an SAO star of spectral type B-M.

4. they must show excess emission in at least one of the IRAS 25, 60 or 100 fim bands, compared with the 12^m band flux. The 12fim flux was (conservatively) assumed

to be photospheric in origin.

This produced 379 stars with excess emission, out of a total of 5706 stars which satisfied

criteria 1-3 above.

Seven of these stars, with spectral types B-K and luminosity class V (if known) were

selected for ground-based observation (SAO 75532, 91022, 93601, 111388, 131926,140845,

158350). They were chosen to have sufficient 100/xm flux to be good candidates for suc­

cessful JCMT observations.

Three stars not listed by Walker & Wolstencroft or Stencel & Backman were also

included. HR 890 (SAO 23763) and HR 2522 (SAO 151962) are included in Backman &

Paresce’s (1993) list of main-sequence Bright Star Catalog stars having infrared excesses,

while 51 Oph had been suggested to be a Vega-excess star by Waters, Coté & GebaUe

(1988).

28 C hapter 2

Dust Emission from M-type Supergiants

2.1 Introduction

M supergiants are bright (L ~ lO^L©), cool (Teff 3000K) stars. They deserve the supergiant appellation, having radii typically ~ 10^i2©, equivalent to approximately 5 AU. Their masses lie in range 10-60 M©(AUen 1973, Maeder 1981, Jura & Kleinmann 1990).

Such large radii imply very low surface gravities, log g % 0.2, which give rise to highly extended stellar atmospheres, that are susceptible to instabilities and mass loss. It is therefore no surprise that M supergiants are generally variable — in fact, of the sixteen stars studied in this chapter, fifteen have variable-star designations. They are typically semi-regular variables with periods of 1 0 0 - 1 0 0 0 days. Red supergiants are a post-main-sequence stage in the evolution of massive stars. A main-sequence 0 star, of initial mass roughly 15-60 M©, after exhaustion of its core hydrogen, expands rapidly at nearly constant luminosity, crossing the ‘Hertzsprung Gap’ in the HR diagram and becoming a cool supergiant. After exhaustion of the core helium, the star heats up, and may pass through the Wolf-Rayet stage before ending its life as a

Type II supernova (see Chiosi and Maeder 1986 for a detailed discussion of the evolution of massive stars).

They undergo significant mass loss, as demonstrated by such phenomena as blue-shifted optical absorption lines, sub-millimetre lines due to CO gas, and excess infrared emission due to circumsteUar dust. Many also show maser emission from molecules such as OH

29 H 2 O. Some, such as a Ori, are also known to have chromospheres, as evidenced by the presence of ultraviolet emission lines, e.g. the Mg I I h and k doublet at A «2800 Â (e.g.

Kondo et al 1972). According to the standard scenario for dust grain formation around cool stars (e.g.

Gilman 1969), the great stability of gaseous CO should lead to the less abundant of the elements carbon and oxygen being locked up by that molecule, so that only oxygen-rich grains should form in environments where C /0<1, by number, while only carbon-rich grains should condense when C /0>1. Observations have largely confirmed this scenario, although a number of apparent exceptions have been found. Carbon stars have been found whose IRAS Low Resolution Spectrometer (LRS) spectra exhibit silicate emission features (Willems & de Jong 1986; Skinner et al. 1990; Lloyd-Evans 1990) - all these objects have been found to be J-type carbon stars, whose optical spectra exhibit high 13Q/12Q ratios. Skinner & Whitmore (1988b) and Skinner et al. (1990) discussed two oxygen-rich M supergiants, AD Per and MZ Cas, whose LRS spectra appeared to show the 11.5-/im silicon carbide emission feature, in addition to the silicate emission feature. As part of a survey of the mid-infrared spectral characteristics of circumsteUar dust around cool evolved stars, higher resolution 10-/im spectra of these two stars, and of 14 further

M supergiants in the h and % Per association were obtained. These spectra reveal that emission features arising from carbon-rich material are indeed present in the 1 0 -/zm spectra of a number of M supergiants, although the new spectra indicate that the carbon-rich material is not silicon carbide but is instead composed of hydrocarbons of the polycyclic aromatic hydrocarbon or hydrogenated amorphous carbon type.

2.2 Spectroscopy with CGS3

AU the stars were observed on the nights of 1992 October 4-7 using the United Kingdom

Infrared Telescope (UKIRT) with the common-user spectrometer CGS3, a 10- and 20- /xm grating spectrometer built at University CoUege London. CGS3 contains an array of 32 discrete As:Si photoconductive detectors, and three interchangeable, permanently mounted gratings covering the 7.5-13.5 and 16.0-24.5 /xm wavebands. Two grating settings give a fuUy sampled 64-point spectrum of the chosen waveband. 7.7-13.3 /xm spectra

were obtained with a 5.5-arcsec circular beam, yielding a spectral resolution of 0.17 /xm.

30 Wavelength calibration was with respect to observations of a Kr arc-lamp. The telescope secondary was chopped east-west at 5 Hz using a 30-arcsec throw. Further details of

CGS3 observing techniques may be found in Chapter 3. The observed sample comprised 15 M-type supergiants in the h and \ Per association, 14 of them chosen from the list of Cohen & Gaustad (1973), plus XX Per, an M3.6Ib

supergiant listed by Humphreys (1978) as being in the same association. In addition, the

M 1 .3 Iab supergiant MZ Cas was observed since, as noted above, its IRAS LRS spectrum

had been found by Skinner h Whitmore (1988b) to be similar to that of AD Per in

appearing to show an 11.5-/xm silicon carbide feature. Three of the Cohen & Gaustad stars

were referred to in that paper, and also by Sylvester et al (1994a), by catalogue number,

but have since been pointed out to have variable-star designations (W.P. Bidelman, 1994,

private communication). They are HD 14826 = V441 Per; HD 14404 = PR Per; HD 14242

= V605 Cas; and BD-|-56°595 = V439 Per. Five stars, a Tau, a Cet, ft Peg, e Cyg and ot Aur, were used as standards, and sky

spectra obtained using a rotating sector chopper were used for flat-fielding all spectra. The spectra of sources taken using a Tau as the standard star were flux-calibrated using the absolutely calibrated spectrum of a Tau constructed by Cohen, Walker & Witteborn

(1992), whilst some sources were calibrated using a similarly constructed /? Peg spectrum

provided by M. Cohen (1992, private communication). The other spectra were calibrated with respect to a Cet, e Cyg and a Aur, which were assumed to emit as blackbodies in the

10-/im region, with effective temperatures of 3730, 4790 and 4880 K and 10.0-/xm fluxes

of 226.7, 40.5 and 228.8 Jy, respectively. The blackbody assumption is likely to be reasonable for the lO-fim region of the G5III

standard a Aur, but the possible presence of SiO absorption bands between 8 and 9 fim

in the spectra of the standards a Cet (spectral type M2III) and e Cyg (spectral type KOIII) was cause for concern. The validity of the blackbody assumption was tested by

normalizing the Cohen spectrum of j3 Peg, which has a similar spectral type (M2.5II-III),

to the lO.O-fim flux of a Cet, and then calibrated the target spectra with this synthetic ‘standard’. The discrepancy between the spectra reduced in this fashion and those reduced

by treating the standard as a blackbody was found to have a peak value of approximately

8 per cent, occurring at 8 fim.

Two stars, RS Per and BD-f56°595, were observed through broken cloud. This meant

31 Table 2.1: The programme stars.

Source Spectral K Fi2 D ate of Type (Jy) Observation

S Per M4.5Iab 1.45 329.5 1992 Oct 4

SU Per M3.3Ib 1.39 45.1 1992 Oct 4

RS Per M4.4Ib 1.63 68.3 1992 Oct 6

XX Per M3.6Ib 1.83 57.1 1992 Oct 6

HD 14826 M3.1Ib 1.94 18.1 1992 Oct 7 YZ Per M1.91a 2.03 32.9 1992 Oct 7

AD Per M 2.4Iab" 2.06 20.3 1992 Oct 4

KK Per M1.9Ib 2.13 17.6 1992 Oct 7

BU Per M3.7Ib 2.24 39.8 1992 Oct 4

HD 14404 MG.TIab 2.34 1 2 . 0 1992 Oct 7

FZ Per M 0.3Iab“ 2.53 10.7 1992 Oct 7

HD 14242 M 5.7Iab 2.56 1 1 . 8 1992 Oct 7

T Per M2.1Iab 2.58 9.7 1992 Oct 4

BD+56°595 M5.8Iab 2.80 7.5 1992 Oct 7

HD 13658 M5.4Iab 3.21 3.3 1992 Oct 7

MZ Cas M1.3Iab 2.65 2 0 . 6 Oct 7

32 that some of the 1 0 -s integration cycles were obtained whilst the source was obscured by cloud. However, by monitoring the integrated flux level for each cycle, it was possible to determine which were the most badly affected cycles, and then to discard them. It is possible that the 7.5-13 fim slopes of the spectra obtained for these two objects could differ from the true slopes, if there were some residual thin cloud present with non-grey extinction.

Table 2.1 lists the stars observed. Spectral types are taken from White & Wing (1978).

Table 2.1 also lists K (2.18 fim) magnitudes for the stars, from Johnson (1966), along with their colour-corrected IRAS 12-fim fluxes. The colour-correction factors were obtained in the same way as those for the Vega-excess stars, by convolving the CGS3 spectra with the

IRAS l2-fim band spectral response curve {IRAS Explanatory Supplement) to give the 12-fim in-band flux. This in-band flux was then used to derive a nominal 12.0-/im flux, making the normal A“^ spectral assumption used for the IRAS Point Source Catalog.

Comparison of this flux with the actual 1 2 .0 -^m flux in the CGS3 spectrum gives the colour-correction factor for each star, which was then used to correct the published IRAS \2-fim flux. The derived colour-correction factors all lie in the range 1.03-1.24.

2.3 The Observed Spectra

The calibrated CGS3 spectra are displayed in Figures 2 . 1 (a)-(p) along with the colour- corrected IRAS l2-fim fluxes (filled circles). Due to imperfect cancellation of the time- varying atmospheric ozone band, the error bars of the CGS3 spectra are larger at approx­ im ately 9.6-fim, whilst the larger error bars associated with the first few points in each spectrum are due to the high opacity at the short-wavelength edge of the 1 0 -/im atm o­ spheric window. The two shortest-wavelength points of each spectrum were discarded due to the high noise levels, and hence the spectra presented in Figures 2.1 and 2.2 contain only 62 points. There is very good agreement between the 12.0-/im flux levels of the cal­ ibrated CGS3 spectra and the IRAS 12-fim photometry, with the only sources for which there is substantial disagreement being RS Per and BD-|-56°595, the two sources that were observed through broken cloud. The dashed lines in Figure 2.1, which are normalized to the S-fim region of each spectrum, are blackbody functions corresponding to the effective temperatures listed as a function of spectral type by Schmidt-Kaler (1982; these were

33 (a) S P er 2x10"

T g 1.5x10-“ I r “ ?

a 10-“ — \ a 6x10

I 5 x 1 0 “ > 1 —

J 1----- 1----- 1----- 1----- 1----- 1----- 1----- 1___ I___ I----- 1----- L 8 10 12 14 8 10 12 14 W avelength Gum) Wavelength (/xm)

(c) RS Per (d) XX Per 2.5x10 4x10" 1 — I— I— I— T— I— I— I— r

2x10 g 3x10"“ . I B 1.6 x10 V- 7 B 2x10"“ e \ 10 ►

3 10-“ I 5x10

j I 1___ 1___ I___ I___ I___ I___ I___ I___ I— I— I 8 10 12 14 Wavelength (/im) Wavelength (^m)

(e) HD 14826 (f) YZ Per 1.2 x10 -1# 10 2 x10

8x10 I 1.5x10 7 8x10 I* B

-u 4x10' s E 2x10

0 8 10 12 14 10 12 Wavelength (jim) Wavelength ( / i m )

Figure 2 .1 ; CGS3 spectra of M supergiants. Error bars: observed spectrum; dashed line: normalized blackbody continuum (see text); filled circles: colour-corrected IRAS fluxes.

34 (g) AD Per (h) KK Per 1.2 x1 0 "

10 ^ 10” “ T

i. BxlO I 8X 10-" ? B 8x10 B 6x10"“

4x10 I ; ^ 2x10 ^ 2 x 1 0 ""

0 -1___1___I___L J I I I I I L 8 10 12 14 Wavelength (pim) Wavelength (/im)

(i) BU Fer (j) HP 14404 8 x10 2x10

T g 6x10 1.5X10' ? Ë 4x10

H 0 2x10 5x10 k

10 12 Wavelength (/im) Wavelength ( / i m )

(k) FZ Per (1) HP 14242 8x10

Y g 6x10 g 6x10 3. ? ? 0 4x10 0 4 x 1 0

d 2x10 0 2 x10 E E

8 10 12 14 Wavelength (/im) Wavelength (/im)

Figure 2.1: continued

35 (m ) T Per (n) BD+56 595 6x10 4x10

T

^ 4x10 ? B 2x10 ► 2 x10 X ê

14 6 10 12 14 Wavelength (/im) Wavelength (/im)

(o) HD 13656 (p) MZ Cas 3x10 1.5x10 I 3. 10 'a 'b -!• I# 10 X 5x10 3 k

0 0 8 10 12 14 8 10 12 14 Wavelength (/im) Wavelength (/im)

Figure 2.1: concluded

36 between 2700 and 3600 K). The normalized blackbody functions were found also to pass through the A'-band continuum fluxes corresponding to the photometry listed in column 3 of Table 2.1 [a zero-magnitude üf-band (2.18-/xm) flux of 655.5 Jy was adopted]. Apart from RS Per and BD-|-56®595, the exception to this was S Per, whose 7.5-8 /im ‘contin­ uum’ lies well above a ‘photospheric’ 2900-K blackbody extrapolated from 2.18 fim. A blackbody of 750 K was found to give a good fit to the observed 3-8 fim excess of S Per after subtraction of a 2900-K blackbody normalized to 2.18 ^m. The sum of the 2900- and 750-K blackbody spectra is plotted as the dashed line in Figure 2.1(a).

It should be noted that the long-wavelength ends of the spectra displayed in Figure 2.1 aU lie well above the extrapolated blackbody continua. Laboratory silicate emissivities nor­ mally fall to very low values longwards of 13 fim (e.g. Kratschmer & Huffman 1979) and, although astronomical silicate emissivities have been proposed for which the emissivity trough between the 10- and 18-//m features does not fall to such low values (e.g. Draine

& Lee 1984), these emissivities are themselves based partly upon the spectra of sources similar to those presented here. Skinner & Whitmore (1987, 1988b) have attributed a large fraction of the mid-infrared continuum emission observed from M supergiants such

as a Ori and S Per to chromospheric free-free emission. However, for the purposes of this work, no attempt has been made to model the contribution made by chromospheric free-free emission to the mid-infrared continuum of each star.

The spectra of the more luminous sources, such as S Per and SU Per, show large

amounts of excess emission, due to a strong silicate feature, as is often observed in the

spectra of M supergiants. The fainter sources show a weaker silicate feature, but in

addition a number of narrow emission features are present. The ‘excess’ spectra (i.e.

after subtraction of the normalized blackbodies) of six of the sources that displayed these

features - MZ Cats, KK Per, AD Per, HD 14404, HD 14242 and FZ Per- are displayed in

Figure 2.2.

The peak wavelengths and FWHM of the various narrow features were determined by

subtracting a smooth continuum, representing the underlying silicate emission, and fitting

Gaussian profiles to the features using the e l f suite of subroutines, written by Dr P.J.

Storey, within the Star link package DIPSO (Howarth & Murray 1991). These wavelengths

and widths are presented in table 2 .2 .

The strongest of the features, at approximately 11.3 fim, was well-defined in aU six

37 .-1: .-13 1 .2 x 1 0 6 x 1 0 MZ Cas HD 14404

,-1 3 ,-13 0 X1 0 4x10 7 KK P er I I 11 hD 14242 - 7 a ,-13 ,-13 6 x 1 0 3x10 I

-1 3 ,-13 4x10 2 x 1 0 n ^ % f I I AD Per % FZ Per

2x10,-13 ,-13

14 6 10 12 14 Wavelength(/im) Wavelength(yum)

Figure 2.2: ‘Excess’ spectra after subtraction of blackbodies which were normalized to the flux at 8 /im (see text).

38 Table 2.2: Positions and widths of the narrow emission features

Star band ‘1 0 .6 -/zm ' band

Wavelength FWHM W avelength FWHM

MZ Cas 8 .6 6 ± 0 . 0 1 0.1410.03 10.6110.01 0.1710.10 KK Per 8.63±0.03 0.2610.07 10.5810.02 0.2310.06

AD Per 8.62±0.11 0 .2 2 1 0 . 1 0 10.5510.02 0.1710.05

HD 14404 8.48±0.16 0.510.3 ——

HD 14242 8.710.2 0.510.3 10.5710.03 0.3310.08 FZ Per 8.6010.01 0.2510.05 10.5310.02 0.2410.04

‘11.3-^m ' band T2.6-^m ' band

Wavelength FWHM Wavelength FWHM

MZ Cas 11.2310.03 0.3910.07 12.710.1 0 .2 1 0 . 1

KK Per 11.2510.03 0.3210.06 12.5710.04 0.3610.08

AD Per 11.3110.04 0.2710.08 12.7510.01 0 . 1 2 1 0 . 0 1

HD 14404 11.3010.07 0.2610.16 12.6310.01 0.2210.03

HD 14242 11.2610.05 0.2710.11 12.910.1 0.1510.05

FZ Per 11.2610.05 0.2610.12 12.5210.01 0.1310.01 All wavelengths and FWHM are in ^m.

39 spectra, with a central wavelength varying between 11.23±0.03 and 11.31±0.04 /xm, and

a FWHM of between 0.27±0.08 and 0.32±0.06 /xm.

A feature at approximately 8.65 /xm is most obvious in the excess spectra of MZ Cas,

KK Per and FZ Per, but can be seen in all six sources, despite the presence of significant noise in the excess spectra of HD 14404 and HD 14242. The peak wavelength of this feature was found to lie between 8.62 and 8 . 6 6 /xm. The width of the feature was not

well-constrained in most cases, but FWHM values of 0.17±0.06 /xm (i.e. unresolved) and

0.26±0.07 /xm were obtained for MZ Cas and KK Per, respectively. A weak emission feature at about 10.6 /xm is most evident in the spectrum of HD 14242, where it stands out clearly above the broad underlying silicate profile. In some of the other spectra, notably those of HD 14404 and KK Per, the feature appears at first glance to be confined

to just a couple of data points with slightly enhanced fluxes. However, a close inspection of the spectra of AD Per and KK Per reveals that there is a definite change in the spectral

slope between those points immediately short ward of the ‘isolated’ maximum point, and

those longward of it. The possibility that the 1 0 .6 -/xm feature was an artefact produced by the instrument or by the data-reduction process was investigated by inspecting the spectra of the standard stars, as well as those of other objects observed on the same

nights. No indication was found of a 10.6-/xm absorption feature in the raw spectra of

the standards, or of 1 0 .6 -/xm emission features in the spectra of oxygen-rich asymptotic giant branch (AGB) stars observed on the same nights; it is therefore justified to conclude

that the 10.6-/xm emission is a real feature in the spectra of the M supergiants shown in

Figure 2 . 2 Measurements of the peak wavelength of the feature gave values ranging from

10.53±0.02 to 10.61±0.01 /xm, with their FWHM ranging from 0.17±0.05 /xm (unresolved)

to 0.33±0.08 /xm.

A fourth feature is detected in the excess spectra, at approximately 12.6 /xm. Again,

this is a weak feature; it is readily seen in the spectra of HD 14404 and MZ Cas but is not

as clearly present in the spectra of the other four stars in Figure 2.2.

Table 2,3 gives measurements of the strengths of the silicate and narrow emission-band

features. The silicate contrast, Fio,obs/^io,cont, is defined as the ratio of the observed flux

at 1 0 . 0 /xm to that of the underlying blackbody continuum normalized at 8 /xm, also

measured at 10.0 /xm. The derived silicate contrasts are listed in column 2 of Table 2.3;

column 3 lists A^ax, the wavelength at which each silicate excess flux distribution peaks;

40 Table 2.3: M supergiants: derived quantities Source ^max FWHM ^sil M E W n.3 /(11.3) 7(8.65)

w {fim) (fim) (M © yr-i) (A) (W m -2) 7(11.3)

S Per 4.0 9.7 3.3 8.5 5.9 X 10"® < 1 0 0

SU Per 3.7 1 0 . 0 2.7 5.5 5.2 X 10-® < 1 0 0

RS Per 3.8 9.8 2 . 6 7.1 1.0 X 10"® < 1 0 0

XX Per 2 . 6 9.7 2.5 6.5 7.9 X 10-® < 1 0 0

HD 14826 1.5 1 0 . 6 >3.8 1 .1 4.2 X lO -’’ 2 1 0 l.OxlO-^4

YZ Per 4.7 9.8 2.4 9.5 6 . 6 X 10-® < 1 0 0 AD Per 1.9 10.4 3.1 3.0 1.3 X 10-® 320 1.5x10-^^ 0.28

KK Per 1 . 8 10.3 3.4 3.1 1.2 X 10-® 610 2 .8 x 1 0 - '^ 0.64

BU Per 6 . 1 9.9 2.5 1 1 9.3 X 10-® < 1 0 0

HD 14404 1.7 10.5 >3.8 1.3 3.3 X 10-^ 2 1 0 O.OxlO"''* 0.67: FZ Per 1.7 10.9 3.3 1.3 2.9 X 10-^ 380 l.lxlO-^'* 0.77

HD 14242 1.5 1 0 . 8 3.7 0.9 2.2 X 10-^ 380 1 .1 x 1 0 -^^ 0.55:

T Per 1.5 10.4 3.6 0.5 9.2 X 10-® < 1 0 0

BD-l-56°595 1 .1 -11.3 -3.3 < 0 > 1 0 -® ?

HD 13658 1 . 2 - 1 0 . 8 -3 .1 < 0 > 1 0 -® ?

MZ Cas 1.7 9.9 3.0 3.4 2.4 X 10-® 350 1.7x10-'^* 0.77 and column 4 lists the FWHM measured for each silicate excess flux distribution.

The strength of the 11.3-//m band was determined by measuring its equivalent width with respect to the underlying photospheric plus silicate emission. The derived values of

EW{11.3) are listed in column 7 of Table 2.3, while column 8 lists the integrated flux in the 11.3-^m feature. Finally, column 9 of Table 2.3 lists the ratio of the integrated fluxes in the 8.65- and 11.3-^m features, /(8.65)//(11.3), for those stars where both features are reasonably well-defined.

41 0

LO - 11 0 9 —

i/1 ^ 10 0

Ü CO 9 10

% S ' s ’V)

' 10 - 7 10 10"' 10"' 10^' Mass Loss Rate (Mso,yr )

Figure 2.3: Silicate feature strength, Fsii, versus mass loss rate for cool giants and super­ giants. From Skinner & Whitmore, 1988a.

2.4 Mass loss rates

M supergiants synthesise heavy elements and lose mass at prodigious rates, and so play an important part in injecting processed material into the interstellar medium. Their evolution and ultimate fate are strongly affected by the amount of mass lost in cool supergiant phase (Chiosi & Maeder, 1986). Ma.ss loss rate is therefore an important parameter describing these stars.

Skinner and Whitmore (1988a) demonstrated that there was a strong correlation be­

tween the mass loss rates, determined using the CO J= 2 - l and J =1-0 lines (Knapp et al. 1982, Knapp & Morris 1985), and the power radiated in the 9.7-/im silicate feature for

a sample of oxygen-rich red giants and supergiants (see Figure 2.3), and thus devised a

method for calculating mass-loss rates using the silicate band strength. In a subsequent paper (Skinner & Whitmore 1988b) they used this method to derive mass loss rates (M)

for a sample of 31 M-supergiants with IRAS LRS spectra.

The Skinner & Whitmore method was used to calculate mass loss rates for the present sample of M supergiants, seven of which are also included in the Skinner & Whitmore

(1988b) sample. In order to to determine M using this method, one must first calculate

42 the band strength, Bsiu of the 9.7-/im silicate feature. This was done in the same way as for the CGS3 spectra of Vega-excess stars (Chapter 2 ). Values of Bs\i are presented in

Table 2.3. B^ih as mentioned in Chapter 2, measures the ratio of the power emitted in the silicate band to that emitted by the continuum. Skinner & Whitmore therefore define a quantity, Pgil» which is proportional to the total power radiated in the 9.7-/xm silicate feature:

Pail = BsiiFudl where F\2 is the 1 2 /zm IRAS PSC flux and d* is the distance to the star in parsecs. Psi\ is the quantity which Skinner & Whitmore found to vary linearly with M, according to the relation:

M = 4.0 X IQ-'^Psil where M is measured in M©yr“ ^. For the present sample of M supergiants, M was calculated using this formula, with Bsii derived from the CCS3 spectra, rather than from IRAS LRS data. The distance to the h and % Per stars was taken to be 2.3 kpc, while that to MZ Cas was taken to be 2.9 kpc (Humphreys 1978). Calculated mass loss rates are presented in Table 2.3.

Two of the stars with the weakest excess emission, BD-f56°595 and HD 13658, gave negative values of BsH. This is because they show strong excess emission at 13.3 /im compared with that at 9.8 /im. Since the expression for Bsii treats the 13.3-/im point as continuum, this leads to an overestimate of the continuum flux at 9.8-/im; in the extreme cases of these two stars, the continuum flux is estimated as being higher than the observed flux at 9.8 /im. Since there clearly is some excess emission, an upper limit of 10“® M©yr“^ is quoted in Table 2.3.

Mass-loss rates have been calculated by other authors for a number of the stars in this sample. Skinner & Whitmore (1988b) used their method to determine M for seven of them. The new results are generally in fairly close agreement with those of Skinner

&: Whitmore (Table 2.4); with the exception of MZ Cas (see below) all agree to within a factor of two. The discrepancies can be attributed to the use of different estimates of the distances to the stars, as well as the different values of Bsü derived from the CCS 3 and

LRS observations. Skinner Sz Whitmore interpreted the 11.5-/im emission feature seen in the LRS spectra of MZ Cas and AD Per as a SiC feature, and so calculated M for these

43 Table 2.4: Comparison of calculated mass loss rates Star New M S&W

AD Per 1.3 X 1 0 “ ® 1.9 X 1 0 “ ®

BU Per 9.3 X 1 0 “ ® 5.8 X 1 0 “ ®

RS Per 1 . 0 X 1 0 “ ® 1 . 6 X 1 0 “ ®

S Per 5.9 X 1 0 “ ® 3.6 X 1 0 “ ®

SU Per 5.2 X 1 0 “ ® 5.2 X 1 0 “ ®

XX Per 7.9 X 1 0 “ ® 7.5 X 1 0 “ ®

MZ Cas 2.4 X 1 0 “ ® 8 . 6 X 1 0 “ ®

two stars using the relation they derived for carbon stars — the large discrepancy between the calculated mass loss rates for MZ Cas is therefore not surprising.

Gerhz & Woolf (1971) also used a method based on the contrast of the 1 0 -/xm silicate feature to derive a mass loss rate for S Per. The value they obtained, 2.7 X 10“® M©yr“', is slightly lower than that presented here. Hagen, Stencel & Dickinson (1983) fitted models to observations of circumsteUar ab­ sorption lines in the UV (to determine expansion velocities and gas masses) and to infrared photometry (to determine dust masses), and hence calculated mass loss rates for a num­ ber of stars, including three in the present sample. They obtained values of 6 X 1 0 “ ® ,

1 X 10“ ® and 6 x 10“® M©yr“^ for SU Per, AD Per and KK Per respectively. Their values for SU Per and AD Per are very close to those presented here, whereas that for KK Per is somewhat higher, but stiU within the factor-of-ten accuracy estimated by Hagen et al. for their results.

2.5 Discussion

The narrow emission features in Figure 2.2 are the unidentified infrared (UIR) bands.

These are usuaUy attributed to hydrocarbon vibrational modes in species such as hy­ drogenated amorphous carbon (HAG; Duley h WiUiams 1981) or polycycUc aromatic hydrocarbons (PAHs; Léger & Puget 1984). Both AD Per and MZ Cas, the objects whose

IRAS LRS spectra appear to show the SiC feature in emission (Skinner & Whitmore

44 1988b), exhibit narrow UIR bands in their CGS3 spectra. The lower spectral resolution and poorer signal-to-noise ratio of the LRS spectra seems to have resulted in the blending of the narrow 11.3-/xm UIR band and the silicate feature, making it appear that a broad

SiC feature is present.

The 11.3-/im UIR-band feature has been associated with out-of-plane C-H bending modes, versus in-plane bending modes for the 8.65-^m feature (AUamandola et al. 1989, see also Chapter 3). AUamandola et al. attribute a 12.7-//m feature sometimes discerned in astronomical UIR-band spectra to a C-H out-of-plane bending mode of triply adjacent H-atoms - the feature peaking at about 12.6 fim seen in several of the spectra presented in Figure 2.2 appears to be the same feature.

The 10.6-/im emission peak seen in several of the spectra is probably the same feature as the 10.6-10.75 fim band first detected by Justtanont et al. (1993) in CGS3 spectra of a number of carbon-rich F- and G-type post-AGB objects that had been found by Kwok,

Volk & Hrivnak (1989) to exhibit a 2\-fim emission band in their IRAS LRS spectra. It is worth noting that a feature at about 10.5 fim is evident amongst the transitions of PAHs such as chrysene, pyrene and coronene that are iUustrated in Figure 1 of AUamandola et al. (1989).

Among the family of UIR-band features, a strong feature attributed to aromatic C-C stretching modes is usuaUy prominent at 7.6-8.0 fim (AUamandola et al. 1989). Because of the choice of 8.0 fim for the normaUzation of the steeply rising steUar continuum, and the effect of the short-wavelength atmospheric cut-off, such a feature is difficult to identify positively in the present spectra. However, it is noticeable that the two stars with the most prom inent 8.65-fim bands, namely KK Per and MZ Cas, appear to show excess emission shortwards of 8 fim (Figures 2.1 and 2.2).

A CGS3 lO-fim spectrum of AD Per had been obtained by the UCL group on 1990

O ctober 6 (reproduced in the review by Barlow 1993), and agrees with the 1992 October

4 spectrum shown in Figures 2.1 and 2.2. Because of the lack of a prominent 8.65-/zm emission feature in AD Per’s spectrum, the possibiUty had been entertained that the

11.3-fim band in the spectrum of AD Per might be attributable to crystaUine oUvine, as had been proposed by Bregman et al. (1987) and Campins & Ryan (1989) for a similar narrow emission feature seen superposed on a broad siUcate feature in the spectrum of

Comet P/HaUey. However, the clear presence of the 8.65-fim UIR band in the spectra of

45 a number of the other M supergiants that show the 11.3-/im feature, such as MZ Cas and

KK Per, counts strongly against this interpretation, since none of the crystalline olivine spectra illustrated by Campins & Ryan exhibits a feature near this wavelength. In view of the fact that carbonaceous emission features peaking at about 3.36 /xm were clearly present in the spectrum of Comet Hailey (Baas, GebaUe & Walther 1986; Knacke, Brooke

& Joyce 1987), the possibility of a UIR-band contribution to Comet HaUey’s 11.3-//m feature should be taken into account.

2.5.1 Non-Equilibrium Dust Formation

An explanation must be sought for the strange combination, in a signihcant number of the M supergiant 10-/im spectra, of silicate emission (normally indicative of oxygen-rich material) and UIR-band emission (normally indicative of carbon-rich material). One pos­ sibility is that the UIR-band emission does not arise from the stars themselves, but from material distributed in surrounding nebulosity. Nebulae exhibiting UIR-band emission as strong as that seen here are normally very bright, whereas there is no obvious nebulosity to be seen in the environs of h and % Per. Further, a plot of the positions of the h and % Per M supergiants reveals no spatial correlation between the stars that exhibit UIR-band emission. Finally, the fact that aU the stars were observed by chopping between object and reference beams separated by 30 arcsec on the sky implies that, if the UIR-emitting material were distributed independently of the M supergiants, the features should have appeared equally often in the object and reference beams, so that UIR bands in apparent absorption should occasionally have been seen, which was not the case. The UIR-band emission must therefore originate from the same stellar outflows as do the silicate emission features.

Equilibrium theories of dust formation do not predict the presence of carbon-rich particles in the winds of classical oxygen-rich objects such as M supergiants. Such stars are expected to have C /0 ratios close to or less than solar, so that only silicates and other oxygen-rich materials should condense if CO molecules were locking up most carbon atoms. The chemical equilibrium condensation calculations of Sharp (1989) showed that weakly oxygen-rich mixtures, namely those with initial C /0 ratios larger than about 0.83, could have sufficient oxygen removed from the gas phase by oxide and silicate condensation that the remaining gas becomes carbon-rich, enabling the formation of hydrocarbons and

46 carbon particles.

However, this scenario is not expected to be applicable to environments such as M su­ pergiant winds, whose C /0 ratios should be solar (0.5) or less. Unlike AGB stars, dredge- up to the surface of carbon synthesized in helium-burning layers is definitely not predicted for the massive stars that evolve into M supergiants. If anything, their C /0 ratios are expected to be less than solar, due to the exposure of CN- and CN0-cycle-processed ma­ terial at the surface by the effects of convective dredge-up and prior mass-loss stripping.

For example, Lambert et al. (1984) derived a C /0 ratio of 0.4 for the M2Iab supergiant a Ori. The optical photospheric spectrum of AD Per, one of the M supergiants exhibiting UIR-band emission, shows no sign of carbon species (Skinner et al. 1990).

A possible explanation for the simultaneous presence of oxygen-rich and carbon-rich particles in the outflows from 0-rich M supergiants is provided by the work of Beck et al. (1992), who investigated the chemistry of the circumsteUar gas and dust around M- type stars by solving a fuUy time-dependent chemical reaction network in oxygen-rich circumsteUar outflows. They found that the strong ultraviolet emission from a warm chro­ mosphere causes the chemistry to enter the regime of kinetic equiUbrium, rather than chemical equiUbrium. Carbon is not completely locked up as carbon monoxide molecules, unUke under chemical equiUbrium conditions, due to the photodissociation of CO by suf­ ficiently energetic (hi/ > 11.2eV) ultraviolet photons. This produces a non-negUgible population of free carbon atoms, a situation not al­ lowed under the assumption of chemical equiUbrium. The partial pressure of atomic C reaches nearly one-third of that of CO in the case of their model for the conditions around the M supergiant a Ori. Beck et al. predicted that this could enable the formation of carbon dust alongside the expected oxygen-rich siUcate dust. Species containing nitrogen were not included in the chemical reaction network of Beck et al., but presumably the photodissociation of CN molecules, whose abundance may be enhanced by the mixing up of nitrogen from material processed by the CNO cycle, would also aid the formation of carbon particles. Since hydrogen is predicted by Beck et al. to be in the atomic form, a reasonable degree of surface hydrogenation should occur for any carbon particles that

are formed. FinaUy, chromospheric emission may also provide the UV photons that are

thought to be required to stimulate UIR-band emission from PAHs or similar carbonaceous

species (AUamandola et al. 1989).

47 2.5.2 Incidence of UIR-Band Emission in the Sample

In the context of this model for the origin of the observed UIR-band emission, there are a number of possible reasons as to why not all the M supergiants in the present sample exhibit detectable UIR bands. Among the h and % Per supergiants, UIR-band emission is not detected from any stars with IRAS 12-fim fluxes larger than 21 Jy or lower than

10 Jy, but is detected from all the stars with fluxes within these limits. The two faintest stars in the sample, BD-f-56°595 and HD 13658, have significantly weaker silicate excesses (Figs 2.In and 2.1o) than any of the other stars - the lower signal-to-noise ratios of their

CGS3 spectra leave open the possibility that UIR-band emission could be present at the same contrast as in the excess spectra shown in Figure 2.2. However, any 11.3-//m band emission from T Per is at least three times weaker than that from FZ Per and HD 14242.

Since no UIR-band emission was detected from any of the three stars in Table 2.3 with mass-loss rates equal to or below the 9 x 10~® M@ yr“^ derived for T Per, one might envisage that any C atoms liberated by the UV photodissociation of CO are present at such low number densities that they fail to associate into carbon species in sufiiciently large numbers to yield detectable UIR-band emission. The six stars brighter than 21 Jy at 12 //m (Table 2.1 and Figure 2.1) possess such strong silicate features that the equivalent width of the 11.3-/zm feature would be below the upper limits listed in Table 2.3 if 11.3-//m band emission were present at the same flux levels, 7(11.3), listed in Table 2.3 for aU but one of the h and % Per supergiants with detected 11.3-/xm bands. However, KK Per has a very strong 11.3-/xm band flux which would have been easily detectable if it had been emitted by SU Per, YZ Per or

BU Per. Another possible reason for the absence of UIR-band emission from the stars with the strongest silicate bands therefore suggests itself. Since the strength of the silicate band is believed to be proportional to the mass-loss rate (Skinner & Whitmore 1988a), these stars may have sufficiently large dust columns that they are optically thick to any chromospheric UV photons emitted underneath. This could lead to a failure to liberate carbon via photodissociation of CO and/or an inability to excite any emission from PAH- type particles that might exist.

In this regard, it is noteworthy that none of the M supergiants in the present sample with derived mass-loss rates in excess of 5 X 10~® M@ yr“^ exhibits UIR-band emis­ sion, whereas aU the supergiants whose derived ma^s-loss rates lie between 2 x 1 0 “ ^ and

48 1.3 X 10“® M@ yr“' do exhibit UIR-band emission.

It should be noted that since the method of Skinner & Whitmore (1988a) makes use of the strength of the silicate feature at 9.8 /xm relative to a baseline between 7.9 and 13.3 /xm, as originally defined for classification in the IRAS LRS catalogue, the mass-loss rates of these stars could be somewhat underestimated, due to their silicate features peaking at, and extending to, longer wavelengths than do the silicate features of the brighter stars (see below).

The incidence of UIR-band emission amongst M supergiants with mass-loss rates in the range (1-5) X 10“® M© yr“^ is less certain. MZ Cas exhibits 8.65- and 11.3-/xm UIR- band emission, and has a mass-loss rate of 2.4 x 10“® M© yr“' according to Table 2.3.

On the other hand, the mid-infrared spectrum of a Ori published by Treffers & Cohen (1974) did not reveal UIR-band emission at 11.3 /xm or elsewhere, and yields a mass-loss rate of 1.1 x 10“® M© yr“^ for a distance of 200 pc. However, since they are at different distances, a comparison of the mass-loss rates of these two stars with those in h and % Per is less reliable than the considering only the relative values of the mass-loss rate for the h and x Per stars, which are aU at effectively the same distance.

AU of the h and % Per stars with IRAS 1 2 -/xm fluxes less than 21 Jy appear to have similar silicate feature profiles, their excess flux profiles peaking between 10.3 and 10.9 /xm, with a FWHM of between 3.0 and 3.9 /xm (see Figure 2.4 and columns 3 and 4 of Table 2.3).

On the other hand, the stars with 12-/xm fluxes exceeding 21 Jy, none of which exhibits the narrow UIR-band features, have silicate profiles differing notably in shape and width from those of the fainter stars, their excess flux profiles being similar to each other and peaking between 9.7 and 10.0 /xm, with a FWHM of between 2.4 and 2.7 /xm (see Figure 2.5 and

Table 2 . 1 ), apart from the extreme object S Per, whose silicate profile has a FWHM of

3.3 /xm and shows clear evidence for additional broad components in the 11.0-11.5 and 12.7-13.2 /xm regions. In this regard, S Per’s silicate profile is similar to that belonging to the ‘Sil"*"’ category defined by Little-Marenin & Little (1990; LML) for the IRAS LRS spectra of some oxygen-rich Mira variables, while the excess flux profiles of the remaining M supergiants that are brighter than 21 Jy at 12 /xm are more consistent with the basic

‘Sir category of LML. The broad silicate feature associated with the fainter supergiants

(Figure 2.4) has some resemblance to spectra of LML’s ‘broad’ category for Mira variables, although the M supergiant excess flux distributions peak at a shorter wavelength than the

49 1.3

1.2

1.1

1.0

9 I . 8 Ti m 93 7 9) 6 I 5 & .4

3

2

.1

0 ^ 8.0 9.0 10.0 11.0 12.0 13.0 Wavelength (jim)

Figure 2.4: Excess flux profiles for stars with IRAS l2-^m fluxes less than 21 Jy: AD Per

(solid line), KK Per (dashed line), FZ Per (dotted line), T Per (dash-dotted line), MZ Cas

(dash-double-dotted line). The spectra are normalized to unity at 10.3 //m.

50 1.2

1.1 /V 1.0

.9

.8 I .7

0) . 6

.5 % .4

.3

.2

.1

G ^ 8.09.0 10.0 11.0 12.0 13.0 Wavelength (/im)

Figure 2.5: Excess flux profiles for stars with IRAS 1 2 -/zm fluxes greater than 2 1 Jy: S Per

(upper solid line), SU Per (dashed line), RS Per (dotted line), XX Per (dash-dotted line),

YZ Per ( dash- double- dot ted line), BU Per (lower solid line). The spectra are normalized to unity at 1 0 . 0 //m.

51 2.0

1.8

1.6 cP ■. 1.4

I o 1.2

1.0 I .8

I . 6 I .4

.2

0

-.2 7 6 9 10 11 12 13 14 Wavelength(j^m)

Figure 2.6: Comparison of the silicate profiles of BU Per (filled squares), AD Per (open squares) and the Draine & Lee (1984) ‘astronomical silicate’ model. AU spectra are nor­ malized to the BU Per flux at 10.0 ^m.

11-12 /im quoted by LML for ‘broad’-featured Miras. During the same nights that the current M supergiants were observed, lO-fim CGS3 spectra were obtained of 60 0-rich

AGB stars, including seven classified by LML as having ‘broad’ features, but none was found to exhibit narrow emission features at 11.3 /xm or elsewhere.

The observed silicate feature profiles can also be compared with model dust emissiv- ities. Figure 2.6 shows the excess spectra of two M supergiants, BU Per and AD Per, representing both types of observed silicate profile. These can be compared with the spectrum of 0.5-/xm grains of Draine & Lee (1984) ‘astronomical silicate’ shown on the same figure. The silicate feature of BU Per peaks at approximately the same wavelength

52 as that of astronomical silicate, but is considerably narrower. Draine & Lee constructed the optical constants for astronomical silicate such that they would give a good fit to the spectrum of the Trapezium region of the Orion Nebula, and noted that a number of stars had narrower silicate features than this. The silicate feature of AD Per peaks at longer wavelengths than the astronomical silicate, and falls off more steeply in the 11-13 fim. region. A shift to shorter wavelengths of the silicate peak is indicative of a decreasing sili­ cate Mg/Si ratio, with enstatites, (FenMgi_„)Si 0 3 , peaking at shorter wavelengths than olivines, (FenMgi_n) 2 Si0 4 (Day k Donn 1978; Stephens k Russell 1979). Enstatites have somewhat lower condensation temperatures than do olivines (Tielens 1990), implying that they should form at larger radii than do olivines and thus, if the critical densities for condensation are similar, that higher mass-loss rates are needed for significant enstatite formation. The observed shift of the M supergiant excess flux peak to shorter wavelengths with increasing mass-loss rate is consistent with this expectation.

53 C hapter 3

Observations of Vega-Excess Stars

3.1 Introduction

A large sample (over 20 objects) of Vega-excess stars have been observed at wavelengths spanning over three orders of magnitude from the optical to the millimetre-wave region. Each type of observation is complementary in that it can provide information about the sources that could not be gleaned from the other observations. In addition to their individ­ ual contributions, the new data, when assembled together with the IRAS data, define the optical-mm spectral energy distribution (SED) of the system, against which the results of modelling can be compared. Optical photometry enables the stellar photospheric contribution to the observed flux to be defined at all wavelengths since, given the dereddened optical magnitudes and the spectral type, a suitable model atmosphere can be selected. This can then be normalised in the optical region where photospheric emission dominates over any dust excess. The model atmosphere then provides the baseline to discriminate between normal and excess emission.

Near-infrared photometry can also determine photospheric fluxes, and define the short- wavelength limit of any excess emission. Such emission would be produced by the hottest components of the circumsteUar material. Sublimation temperatures for typical refractory materials lie in the range of approximately 1000-2000 K. Emission from grains at these temperatures would peak in the near-IR, so J-M band photometry can detect dust at the highest possible temperatures at which it can exist.

Spectroscopy in the near-IR indicates the nature of any excess emission in this wave­

54 length region and the relative importance of line and continuum emission. Some informa­ tion on the composition of the dust can be gained from near-IR spectral features, such as the 3.3-/xm UIR band. Mid-infrared spectroscopy is a powerful tool for diagnosing the composition of cir- cumstellar dust, since several of the most important constituent materials have mid-IR spectral features. Silicates display peaks in emission or absorption at wavelengths of 9.7 and 18 /im, while silicon carbide has a broad peak at 11.2/im. In addition, the suite of

‘Unidentified Infra-Red’ emission bands at 7.7, 8.65, 11.3 and 12.7 /xm are associated with emission by carbonaceous species, such as polycyclic aromatic hydrocarbons.

3.2 Optical Photometry

Service photometry in the U, B, V, R, and I bands was obtained for the stars SAO 26804,

111388, 112630, 131926, 158350, 183956 and 184124, at the 1.0-metre Jacobus Kapteyn Telescope (JKT), part of the Isaac Newton Group of telescopes of the Roque de los Mucha- chos Observatory on La Palma. The observations were made as part of the JKT Service programme, between 1993 December and 1994 June (see Table 3.1 for details of the observations).

The detector used was the EEV7 charge-coupled device, which comprises a 1280 x

1180 array of 22.5-/xm square pixels, giving an image scale of 0.31 arcsec per pixel at the f/15 Cassegrain focus of the telescope. Because the stars were known to be fairly bright

(typically V ~8.5), the telescope was de-focussed slightly to avoid saturating the detector.

The data were reduced by Dr V. Mannings using the I RAF package; standard data reduction procedures of bias subtraction, flat-fielding etc. were followed. AU observations were corrected for atmospheric extinction. The corrections were determined using a the­ oretical extinction curve, calculated for the atmosphere above La Palma (Argyle et al.

1988), together with the actual visual extinction measured by the Carlsberg Automated

Meridian Circle for the nights of our observations, obtained from the RGO archive.

Photometric standard stars were taken from the catalogues of Landolt (1983, 1992).

For the nights where there were observations of several standards, we were able to assess the quality of the observations by calibrating the standards against each other and comparing the magnitudes found in this way with the values quoted in the JKT CCD Handbook

55 Table 3.1: Stars observed photometrically in the optical region

D ate (U T) Stars Observed

1993 Dec 2,3 Targets SAO 26804,SAO 111388, SAO 112630, SAO 131926 Standards HD 39402, G1 239, 980653, 950134, 990358

1994 April 6 Targets SAO 183956, SAO 183986 Standards 108148, PG1323-086A

1994 May 26 Target SAO 184124 Standard 109Z747

1994 June 10 Target SAO 158350 Standard HD 121968 Note: Catalogue numbers without prefixes are from the Landolt (1983, 1992) catalogues.

(Argyle et al. 1988). These tests showed the photometric data to be of good quality, with typical deviations of less than a few hundredths of a magnitude.

3.2.1 Results

The derived magnitudes are presented in Table 3.2, and included in the compendium of data in Table 3.20. Good agreement was found with the photographic magnitudes quoted in SIMBAD.

The values of (B — V)o as a function of spectral type from Schmidt-Kaler (1982) together with the observed B — V colours were used to calculate the reddening, F,{B — V).

The photometry could then be dereddened, using a ‘standard’ Galactic reddening law based on the data of Seaton (1979) and Howarth (1983). The data were converted from magnitudes to flux densities using the flux calibration of Deacon (1991). The adopted zero-magnitude flux densities are presented in Table 3.3. The dereddened photometry could then be compared with Kurucz (1991) model atmosphere fluxes. The appropriate model atmospheres were selected using the Schmidt-Kaler (1982) calibration of Teff and log g against spectral type, together with the spectral types of the Vega-excess stars taken

56 Table 3.2: Optical magnitudes from JKT Service photometry

HD SAO U BV R I

(m ag)

23362 111388 1 1 . 6 6 9.53 7.85 6.98 6.07

34282 131926 10.16 10.05 9.88 9.79 9.68

35187 77144 8 . 1 1 8.08 7.80 7.62 7.41

123160 158350 1 2 . 2 0 1 0 . 1 2 8.62 7.81 6.94

142666 183956 9.35 9.20 8.65 8.36 7.98

143006 183986 11.30 1 1 . 0 2 10.18 9.73 9.22 144432 184124 8.65 8.50 8.17 7.93 7.71

233517 26804 12.39 1 1 . 0 2 9.67 9.02 8.35

from the literature (given in Table 3.20). Good agreement was found between the dereddened photometry and the model atmo­ spheres, indicating that the stars do not grossly deviate from normal main sequence stars at optical wavelengths.

Values of E(B — V) are tabulated in Table 3.4, along with the distances to the stars derived from the photometry. These were calculated using the well-known relation

My = TUy — Ay -f 5 — 5 log d (3.1)

where My and my are, respectively, the absolute and apparent visual magnitudes, d is the distance in parsecs, and Ay is the visual extinction in magnitudes. Absolute magnitudes and intrinsic colours for the various spectral types were taken from Schmidt-Kaler (1982).

The corresponding quantities for the stars with photoelectric photometry available in the literature were calculated, and are presented in Table 3.5.

The observations of SAO 111388 indicate that it is highly reddened and remarkably close, at 6.5 pc. No parallax data are available to confirm this result, but SAO 111388 is in the Hipparcos Input Catalogue (as number 17473), so an independent distance mea­ surement should be available in the near future, once the data from that satellite have been analysed. Another possibility is that the spectrum was misclassified in the HD cat­ alogue, and is really of type M, and hence has redder intrinsic colours. If this were the

57 Table 3.3: The adopted zero-magnitude flux calibration for optical and near-infrared pho­ tometry, taken from Deacon (1991)

Filter X\so F\

(/im) W m“^/im~^

- 8 u 0.376 4.183 X 1 0

-8 B 0.453 6.239 X 1 0 -

-8 V 0.547 3.602 X 1 0 -

-8 R 0.680 1.869 X 1 0 -

-9 I 0.898 9.254 X 1 0 -

-9 J 1.215 3.314 X 1 0 -

-9 H 1.654 1.151 X 1 0 -

10 K 2.179 4.139 X 1 0 -

10 L 3.545 6.608 X 1 0 -

1 0 Lf 3.761 5.263 X 1 0 -

10 M 4.769 2.107 X 1 0 - Note: Ajso = isophotal wavelength, F\ = flux density at zero magnitude.

Table 3.4: Distances and reddenings derived from JKT Service optical photometry

HD SAO Sp. Type {B-V)o my E{B-V) Mv d(pc)

23362 111388 K2 0.91 7.85 0.77 6.4 6.5

34282 131926 AO -0 . 0 2 9.88 0.19 0 . 6 547

35187 77144 A2 0.05 7.80 0.23 1.3 2 0 2

123160 158350 K5 1.05 8.62 0.36 7.4 1 0 . 6

142666 183956 A 8 V 0.25 8.65 0.31 2.4 114

143006 183986 G5V 0 . 6 8 10.18 0.16 5.1 82

144432 184124 A9/F0V 0.30 8.17 0.03 2.7 119

233517 26804 K2 0.91 9.67 0.44 6.4 28

58 Table 3.5: Distances and reddenings derived from photoelectric optical photometry in the literature

HD SAO Sp. Type {B-V)o mv E ( B - y ) Mv d(pc)

9672 147886 AIV 0 . 0 1 5.61 0.08 1 . 0 75

16908 75532 B3V -0 . 2 1 4.67 0.08 - 1 . 6 160

18537 23763 B7V -0.14 5.23 0.09 - 0 . 6 129

49662 151962 B7IV -0.14 5.40 0.04 -0 . 6 188

98800 179815 K5V 1.15 8.89 0 . 1 0 7.4 17

109085 157345 F2V 0.35 4.32 0.37 3.6 14

135344 206462 F 8 V 0.52 8.63 -0 . 0 1 4.0 84

139614 226057 A7V 0 . 2 0 8.27 0.03 2 . 2 157

155826 208591 GOV 0.58 5.96 0 . 0 0 4.4 2 1

158643 185470 AOV -0 . 0 2 4.81 0 . 0 2 0 . 6 6 8

169142 186777 B9V -0.08 8.13 0.37 0 . 2 227

218396 91022 A5V 0.15 5.99 0 . 1 1 1.9 56

59 case, however, the star would be even closer, since the effect of lower intrinsic luminosity

(i.e. larger My) would outweigh that of the smaller amount of extinction. Conversely, if SAO 111388 is actually a G-type star, its greater intrinsic luminosity would mean it is further away — for a G5V star, the revised distance would be approximately 26 pc. It would then be even more heavily reddened.

SAO 77144 is a double star, with the two components having equal V magnitudes

(Turon et al. 1992). The distance given in Table 3.4 was calculated assuming they are both of spectral type A2V.

The value of E{B — V) obtained for SAO 206462 is actually slightly negative, but for the purposes of the distance calculations was treated as zero. Since the accuracy of the photometry is of the order of 0 . 0 1 magnitude, the discrepancy can safely be neglected.

SAO 186777 and SAO 158350 have been reclassified as A5 by Dunkin (1995, private communication). Adopting these classifications, and assuming luminosity class V for both stars, gives a value of E{B — V) of 0.14 and a distance of 145 pc for SAO 186777, and an E{B — V) of 0.82 and a distance of 15.7 pc for SAO 158350. The dereddened photometric data are plotted in Figure 3.6.

3.3 Near-Infrared Photometry

3.3.1 UKT 9

Near-infrared photometry was obtained in the J, H, K, L, V and M bands for a total of 16 of our sources using UKT9, the UKIRT single-channel bolometer. UKT9 uses an

InSb detector, operating at pumped (solid) nitrogen temperatures (~55 K). Some of the observations were made by the authors in PATT time (1992 June 12, Table 3.6), the rest as part of the UKIRT Service programme. Circular apertures of 5 and 7.8 arcseconds were used, and the telescope secondary was chopped at 3.5 Hz to enable background subtraction. Several different standard stars, selected from the UKIRT list, were observed on each night (see Table 3.6). Data reduction was done by the automated facility at the Joint Astronomy Centre. Magnitudes were converted into flux densities using the isophotal wavelengths and flux calibration of Cohen et al. (1992), who define Vega to be zero magnitude at aU wavelengths short ward of 20 fim.

60 Table 3.6: Log of UKT9 observations

D ate (U T) Stars Observed A perture

1992 June 12 Targets SAO 140789, SAO 140845, SAO 158350, 7.8" {J-V),

SAO 183956, SAO 183986, SAO 184124, 5.0" (M) SAO 186777, SAO 208591, G1 471.2

Standards HD 161903, BS 6147, Y 4338

1993 Feb 10 Targets SAO 26804, SAO 77144 7.8"

Standards BS 2228, BS 3888, G1 390

1993 Sep 15 Targets SAO 75532, SAO 91022, SAO 93601, 5.0"

SAO 111388, SAO 147886, HR 890

Standards HD 3029, HD 18881, HD 162208,

HD 163754, HD 2019141, HD 203856,

BS 718, BS 1140, BS 8551

61 3.3.2 IRCAM

Imaging photometry was carried out using the UKIRT near-IR camera IRCAM (McLean et al. 1986), which was based on an SBRC 58x62 element InSb array (subsequently upgraded to 256x256), and uses a number of broad band and narrow band filters. The plate scale was 0.62 arcsec per pixel.

Observations were made on 1993 September 17 and 18 of eight Vega-excess stars, only three of which did not already have UKT9 near-IR photometry. The derived JHKLL'M magnitudes for these three stars are given in Table 3.21. From observations of standard stars and previously-observed Vega-excess stars, it was determined that September 18 was not a suitable night for photometry in the near-IR, so the magnitudes of SAO 112630 and HR 2522, indicated by colons in Tables 3.7 and 3.21, should be treated with caution, although the data are good enough to give an indication that neither of these two stars shows a near-IR excess. The September 17 data seem of higher quality, so the SAO 131926 magnitudes are probably reliable.

In order to determine if the emission from stars with near-IR excess is extended, cross­ cuts were taken of images of SAO 186777, using a narrow band filter centred on the 3.3/im

UIR emission band, and of SAO 131926 using a broad band K filter. Comparison images were also taken of the standard stars Y 4338 (through the K filter) and HD 22686 (through the 3.3/im filter).

3.3.3 Results

The derived near-infrared magnitudes are presented in Table 3.7 and included in Table 3.21

Their equivalent fluxes (dereddened by the appropriate amount) are shown on the spectral energy distributions plotted in Figure 3.6.

Comparing the observed fluxes with the Kurucz (1991) model atmospheres, we see that for the majority of our sources there is good agreement between observed and predicted fluxes, demonstrating that, as expected, a normal stellar photosphere is the dominant source of near-IR flux. However, nine of our twenty-three sources show excess emission in one or more of the near-IR photometric bands, clearly discernible by inspecting the SEDs or by comparing the observed near-IR colours with their theoretical values (presented in

Deacon 1991). This cannot be due to an abnormal reddening law, since dereddening using the standard value of R = Ay f E{B — V) = 3.1 produces a very good match between

62 Table 3.7: New near-IR photometry

HD SAO J H K L VM (mag)

9672 147886 5.54 5.51 5.51 5.53 - 5.51

16908 75532 4.91 4.94 5.00 5.05 - 5.06

18537 23763 5.37 5.38 5.41 5.43 - 5.46

23362 111388 4.89 4.05 3.85 3.72 - 3.98

23680 93601 6 . 0 1 5.37 5.24 5.16 - 5.29

34282 131926 9.02 8 . 2 0 7.44 6.53 - -

34700 112630 7.6: 7.8: 7.5: 7.0: -- 35187 77144 7.07 6.62 6.09 5.33 5.24 5.00 49662 151962 5.7: 5.5: 5.6: 5.8: --

109085 157345 3.69 3.57 3.54 3.51 3.55 3.59

123160 158350 5.86 5.07 4.87 4.73 4.76 5.33

141569 140789 6.87 6.84 6.80 6.69 6.67 6.50

142666 183956 7.32 6.70 6 . 0 2 5.04 4.95 4.85

142764 140845 6.41 5.58 5.35 5.20 5.21 5.49

143006 183986 8.35 7.65 7.06 6.14 6.06 6.18

144432 184124 7.16 6.57 5.95 5.00 4.91 4.52

155826 208591 4.93 4.64 4.58 4.55 4.59 4.52

169142 186777 7.44 7.05 6.61 5.79 5.73 5.49

218396 91022 5.46 5.30 5.28 5.28 - 5.26

233517 26804 7.38 6.80 6 . 6 6 6 . 6 6 6.63 6.62

63 optical photometry and the model atmosphere for all the sources. Attempts were made to deredden the SED of SAO 186777 using higher values of i2, appropriate for the more nearly

‘grey’ extinction caused by larger dust grains than those present in the interstellar medium.

No reddening law, even for values of A as high as 10, was able to increase sufficiently the optical flux so as to remove, even approximately, the near-IR excess without giving (U — B) and {B — V) colours that were far too blue.

The magnitudes of the excess in the various near-infrared wavebands are presented in

Table 3.8. They were calculated by fitting a Kurucz model atmosphere to the dereddened optical photometry, then determining the ratio of the observed fluxes to the values pre­ dicted by the model atmospheres, and then converting the ratios to magnitudes in the usual way. Subtracting the model atmosphere fluxes from the observed fluxes gave the energy distributions of the excess emission. To gain some idea of the temperature of the material responsible for the near-IR excess (assuming it is thermal in origin), blackbod- ies were fitted to these excess spectra. The temperatures which gave the best fits are recorded in Table 3.8. In most cases it was not possible to fit all the near-IR points with a single blackbody. In some cases, the observed excess energy distribution was broader than the Planck curve, suggesting that material at a range of temperatures contributed to the emission; in other cases, the observed distribution was narrower than the blackbody, possibly suggesting that the emissivity of the material was falling off with wavelength in the near-infrared region.

Further insight into the near-infrared properties of Vega-excess stars can be gained by plotting a colour-colour diagram. A {J — H) versus (H — K) diagram for the present sample is shown in Figure 3.1. It shows two distinct groups of objects. The stars with no near-IR excess tend to lie near the locus expected for main-sequence stars, starting near the {J — H) = {H — K) = 0 point and extending to {H — K) ^ 0.2, (J — H) ^ 0.9. The cooler stars have the redder colours, i.e. higher values of (J — H).

The stars which do have a near-IR excess lie further to the right of the diagram, in a

cluster centred on approximately {H - K) = 0.6, {J —K) = 0.5. The {J — H) colours of the

stars with an excess lie within the range spanned by the cooler of the stars without a near-

IR excess. This is consistent with the fact that near-IR excesses contribute a negligible

amount to the flux at J, and make only a small contribution at H. The net effect of

this is to produce colours that mimic those of a somewhat cooler stellar photosphere. The

64 Table 3.8: Magnitude and colour temperatures of the near-IR excesses

HDSAO Excess in magnitudes ÎBB

J HKL M (K)

34282 131926 0 . 2 1 .1 1.9 2 . 8 - 1700

35187 77144 0 0.4 1 . 0 1.7 2 . 0 1800

135344 206462 0.3 0 . 8 1.4 2.5 2.9 1500

139614 226057 0 0.4 0.9 1.9 1.7 1500

141569 140789 0 0 . 0 0 . 0 0 . 1 0.4

142666 183956 0 . 2 0 . 6 1 . 2 2 . 2 2 . 2 1800

143006 183986 0 . 6 0 . 8 1.3 2 . 2 2 . 2 1500

144432 184124 0 . 2 0 . 6 1 . 2 2 . 0 2 . 6 1500

158643 185470 0 0.3 0.5 1.4 2 . 2 2 0 0 0

169142 186777 0 0.4 0 . 8 1.5 1.7 1500

□□

X _l^

□ □

-.2

- . 4

- . 4 2 0 2 4 6 8 1.0 (H-K)

Figure 3.1: Near-IR colour-color diagram for Vega-excess stars. Open squares: stars without discernible near-IR excess, filled squares: stars with near-IR excess

65 2.5 1 I I i I I 1 I r ” j I I I I I I I 1 I I' I I 1 I ]' I ' l l ' I

• Group I * + Group II

C Group III

^ T-Tauri stars *

1.5 i . * • + ^ ^ .

- s L , , I , - O 5 1 1.5 2.5 (H - K).

Figure 3.2: Colour-colour diagram for Herbig Ae/Be stars. From Hillenbrand et al. 1992 observed excesses make a more significant difference to the flux at A' (see Table 3.8), giving rise to [H — K) colours which do not resemble the photospheric colours of normal main- sequence stars, therefore causing the points in the colour-colour diagram to be significantly displaced with respect to those of the stars which show only photospheric emission. Similar diagrams have been produced for protosteilar objects, T Tauri stars and Herbig Ae/Be stars (e.g. Hillenbrand et al. 1992, Lada & Adams 1992).

Comparing the diagram for Vega-excess stars with that produced by Hillenbrand et al. (1992) for Herbig Ae/Be stars (Figure 3.2), we see that the Vega-excess stars without near-IR excess lie close to the main-sequence line plotted in Figure 3.2, while the stars with a near-IR excess lie in an intermediate position between the region occupied by most of the Ae/Be stars and the main sequence. This may be more than coincidence, since it is thought that Vega-excess stars are in an intermediate evolutionary phase between young objects such as Herbig Ae/Be and T Tauri stars and mature main-sequence stars (see e.g. Backman & Paresce, 1993).

The observations made with IRCAM can give spatial, as well as photometric, infor­ mation. To determine if anything could be gleaned about the spatial distribution of the

6 6 material responsible for the near-IR excess, the full widths at half maximum of the IR­

CAM images of the two imaged stars with near-IR excess, SAO 186777 and SAO 131926, were measured. It was found that the FWHM for both targets and for the standard stars were similar. At 3.3/im, SAO 186777 had a FWHM of 2.2 pixels in the north-south di­ rection and 1 . 8 in the east-west direction, compared with 2 . 2 and 1.7 pixels for Y4338.

At K (2.2/im), SAO 131926 measured 2 . 1 pixels in the N-S direction and 1.6 pixels E-W , compared with 2.0 and 1.8 pixels for HD 22686. This would seem to imply that there is no evidence that the two target stars are extended in the near-infrared compared with the standard stars. Since both target stars show substantial excess emission at these wavelengths, the dominant source of emission is presumably hot circumsteUar matter, rather than the stel­ lar photospheres. The hot material must therefore be concentrated within a radius of approximately 0.6 arcsec of the exciting stars, which corresponds to 140 AU and 340 AU at the distances of SAO 186777 and SAO 131926 respectively. By contrast, the near-IR emission from reflection nebulae, attributed to thermaUy-spiking grains by SeUgren et al. (1983), is extended over a distance of 0.15 pc.

3.4 Mid-Infrared Spectroscopy with CGS3

We have obtained mid-infrared spectra in the 10- and 20-/im bands for 13 of our sources

(Table 3.9) in the course of three observing runs at UKIRT. The instrument used was the Cooled Grating Spectrometer No. 3 (CGS3), a common-user instrument designed and built at University CoUege London, and commissioned in July 1990. CGS3 contains three permanently-mounted diffraction gratings, cooled using Uquid heUum to 4.2 K. Two gratings were used for these observations: the moderate-resolution 1 0 and 2 0 -//m gratings, which give spectral resolutions of 0.17/im and 0.27/zm, respectively. The third grating, a high-resolution (R=330) 10-/zm grating, was not used for this project.

CGS3 uses a 32-element Unear array of Ga:As photoconductors cooled to 4.2K. To fuUy sample the observed spectrum, two sub-spectra were taken with the grating positions displaced by half a resolution element. The sub-spectra are then interleaved in the data reduction process to produce a fuUy-sampled 64-point spectrum. For our observations, the telescope secondary mirror was chopped east-west at 5Hz with a 30-arcsecond throw.

67 Sky spectra taken using a rotating sector chopper were used for flat-fielding aU spectra.

The of observed wavelength ranges were 7.5-13.5^m and 15.8-23.9^m. The gap in the spectral coverage between 13.5 and 16/xm is due to absorption by atmospheric H 2 O and

CO 2 , which renders this wavelength region unobservable from the ground, even from high- altitude sites such as Mauna Kea. Wavelength calibration was with respect to a Kr arc lamp. A log of the observations, with the standard stars used and the integration time per spectral point, is presented in Table 3.9. Allowing for the fact that two sub-spectra were

taken for each spectrum, and for the overheads associated with chopping and nodding,

the total observing time per spectrum was approximately 5.2 times the integration times per spectral point that are listed in Table 3.9.

The spectra were flux-calibrated by dividing the observed spectrum of a target source by that of a standard star, then multiplying by a model spectrum of the standard. Six standard stars were used, a Boo, a CMa, /3 Peg, a Lib, rj Sgr, and /x UMa. For a Boo,

a CM a and /3 Peg, we used absolutely-calibrated infrared spectra provided by Dr. M. Co­

hen, constructed in a similar way to the spectrum of a Tau described by Cohen, Walker & Witteborn (1992). The other standards, a Lib, rj Sgr, and /x UMa, were assumed to

emit as blackbodies with effective temperatures of 3640K, 3600K and 3895K, and 1 0 .0 -/xm

fluxes of 188.6 Jy, 208.7 Jy and 99.0 Jy respectively. Ratioing the target spectrum with that of a standard star during the data reduction

process removes most of the artifacts due to telluric absorption, but often some data points

remain contaminated. The spectral points most badly affected by atmospheric absorption

have been discarded, hence most of the spectra as presented contain fewer than 64 points

in either band (10 or 20 /xm). The discarded points tended to lie at approximately 9.8 /xm,

where there is a strong telluric ozone spectral line, and at the edges of the atmospheric

windows, where the atmospheric absorption is strongest. It is difficult to correct for the

very heavy atmospheric absorption suffered by these points unless the spectra of both

object and standard have very high signal-to-noise ratios.

3.4.1 Results

The observed CGS3 spectra are presented in Figure 3.3, along with the colour-corrected

IRAS flux densities at 1 2 and 25 /xm.

Colour correction of the IRAS data is necessary because the detector and optics com-

68 Table 3.9: Log of the CGS3 observations

HD SAO D ate (UT) Standard ^int (s)

1 0 fim 2 0 fiia 1 0 /im 2 0 /im 1 0 /im 2 0 /im

233517 26804 1/6/93 3 1/5/93 /i UM a a Boo 700 350

35187 77144 31/10/93 — a CM a — 1 2 0 —

141569 140789 1/6/93 30/5/93 a Lib a Boo 550 600

142764 140845 1/6/93 — (T Lib — 360 — 123160 158350 1/6/93 — a Boo — 600 —

98800 179815 29,30/5/93 30/5/93 a Boo a Lib 750 400

142666 183956 29/5/93 30/5/93 V Sgr a Lib 300 400 143006 183986 1/6/93 — (7 Lib — 600 —

144432 184124 29/5/93 30/5/93 T] Sgr T] Sgr 250 420

169142 186777 7/10/92 29/5/93 (5 Peg /? Peg 450 350

135344 206462 1/6/93 29/5/93 a Lib a Boo 510 600

155826 208591 1 /6/93 30/5/93 a Lib — 400 160

158643 158470 29/5/93 29/5/93 a Boo a Boo 260 300

69 CM

CM

CD LO O) CO OO

> %

O n n 2 O T o X X XX X X 0 0 CO CM CO CM 3_ui Nl) xnii

Figure 3.3: CGS3 10- and 20-^m spectra of Vega-excess stars. Errorbars: observed spec­ trum; filled squares: IRAS data; dashed line: model atmosphere (see text). -13 4 x 1 0

CO CO SAO 1 8 4 1 2 4 I 3 x 1 0

-13 10

10 15 20 2 5 Wavelength (/im)

-13 8 x 1 0 51 O ph I 6 x 1 0 "

Ë 4 x 1 0 "

-13 2 x 1 0

10 20 2 515 Wavelength (/im) m i OO -13 - 00 1 .5 x 1 0 SAG 1 8 6 7 7 7 § 3 3' Ë g -13 a. ^ 10

Ë ¥

f e S x l O X •ÆX èI k 0 .U I L J L 10 15 2 0 2 5 Wavelength (/im)

-13 1 .5 x 1 0 SAG 2 0 6 4 6 2

-13

-14 5 x 1 0

0 10 1 R 20 2 5 Wavelength (/im) T1

0 10 15 20 2 5 Wavelength (/im) -J w -14 4 x 1 0 1 r 1 r SAO 2 6 8 0 4

1 3 x 1 0

6 2 x 1 0

J I I L J L J L 15 2 0 25 Wavelength (/im) -13 <3 1 .5 x 1 0 I 1 r=\ 3 5 x 1 0 CO SAO 7 7 1 4 4 CO SAO 1 5 8 3 5 0 e - \ <1 § -13 4x10"^^ 3 10 - 3‘ g 3 x 1 0 " a. - -14 2 x 1 0 — 5 x 1 0 —

- 10"^^

0 0 J I I 1 I I I 1 L 8 10 12 8 10 12 14 Wavelength (/im) Wavelength (/im)

6 x 1 0 - ' ' ...... I I ... I

3 x 1 0 SAO 1 4 0 8 4 5 SAO 1 8 3 9 8 6 e -14 _ \ 4 x 1 0

2 x 1 0 "'^

-14 2 x 1 0 X 10 — PM 0 J __ I__ I__ L _ l __ I__ I T I__ L 0 8 10 12 14 8 10 12 14 W avelength (/im) W avelength (/im) —13 1 .2 x 1 0

-13 SAO 2 0 8 5 9 1

-14 8 x 1 0

-14 6 x 1 0 - \ -14 4 x 1 0 % :3 -14 2 x 1 0

0 8 10 12 14 W avelength (/^m)

Figure 3.3 concluded, binations used were sensitive to radiation over broad wavelength ranges: approximately 7.5-15/xm, 17-30/zm, 30-85/im and 70-140/xm for the ‘12’, ‘25’, ‘60’, and ‘100’-micron bands respectively {IRAS Explanatory Supplement). To obtain the flux density at the nominal wavelength of a particular band from the total in-band flux, requires knowledge of the shape of the energy distribution within the band. For the fluxes listed in the IRAS Point Source Catalog (PSC), aU sources were assumed to have an energy distribution with

constant flux per logarithmic frequency interval, which is equivalent to a flux density per

unit wavelength which varies with wavelength as f \ ex A“h If the source does not have

such an energy distribution, a correction factor must be applied to the quoted PSC flux

densities. The value of the correction factor depends on the shape of the source energy

distribution and on the combined wavelength response curve of the optics and the detector.

The flux F measured by a detector is {Supplement, p. VI-27):

F = Ao [actual] y*( A / Ao)[actual]Æ ^di/ (3.2)

= A, [quoted] /(/„/ /^, ) [quoted] d»/ (3.3)

_ /eo[actuaJ] J ) [ q u o t e d ] (3.4)

where uq is the effective frequency corresponding to the effective wavelength of a band, A

is the actual or quoted flux density of the source, (A/Ao) is the flux density normalised

to the effective frequency of the band and is the relative response of the system. The

75 relationship between the actual and quoted flux densities is therefore

[actual] = /^, [quoted]//if (3.5) where the correction factor, K is given by:

/if = )[actual]/It.di/j (fy jfy^)[q\ioteà]Ri,dv (3.6)

The procedure often employed in practice, where the energy distribution is not known in sufficient detail, is to use the values of K tabulated in the Supplement for various blackbody and power-law energy distributions, using the ratios of the uncorrected fluxes in adjacent bands as a guide to which energy distribution to assume when correcting a given band. (Typically, a different energy distribution is assumed for each band.)

However, a CGS3 1 0 -/im spectrum describes the shape of the energy distribution over a wavelength range that covers almost all of the IRAS 12-pm band. We could therefore calculate (/i//A,o)[actual], and convolve it with the system response profile, tabulated in the Supplement^ to determine an accurate value of the colour-correction factor, and hence a well-calibrated IRAS 1 2 .0 -/zm flux density. This can be compared with the flux density measured with CGS3 at 12.0 pm. Note that the above procedure is independent of the absolute flux level of the CGS3 spectra, so a truly independent comparison can be made.

Values of the 12/zm colour-correction factor, /fl2, derived in this fashion are presented in

Table 3.10

Also plotted in Figure 3.3 are the estimated mid-infrared photospheric energy distribu­ tions, based on Kurucz model atmospheres normalised to the optical/near-IR photometry.

For some of the sources, e.g. SAO 183956 or SAO 184124, the photospheric contribution to the mid-IR flux is negligible compared with the excess emission; the dashed line rep­ resenting the photospheric flux is barely visible above the abscissa, which represents zero flux. Conversely, for others, such as SAO 158350 or SAO 140845, there is no measurable excess in the 8-13-/im region, and the observed spectrum closely follows the predicted photospheric spectrum. This lends extra credibility to both the absolute flux calibration of the CGS3 spectra, and the photospheric spectra predicted using the model atmospheres. Further confirmation of the accuracy of the absolute flux calibration is provided by the excellent agreement with the IRAS PSC 1 2 /im flux in almost aU cases, independent of the shape of the mid-IR spectra and the level of excess emission.

76 The most notable exception is SAO 208591, for which the IRAS 1 2 /im point is a factor of 5.5 higher than the CGS3 flux at 1 2 .0 /im. This discrepancy is far too large to be accounted for by uncertainties in our estimate of the colour-correction factor, which we calculate as being 1.40, so some other explanation must be found. Pointing errors can be ruled out, as the star has an accurate SAO position and is optically bright (V = 5.96) and could easily be seen on the monitor screen of the UKIRT autoguider camera. Also, there were no problems with the pointing behaviour of UKIRT for the other sources observed the same night. The 10-13 fim portion of the CGS3 spectrum gives good agreement, in terms of both shape and overall flux level, with the predicted photospheric spectrum, so it would appear that the observed 1 0 -/xm spectrum gives an accurate representation of the emission from SAO 208591. We also attempted to take a 2 0 -/im spectrum of this source, but failed to detect it. The 3

CGS3 beam. The location of SAO 208591 close to the Galactic plane, in the direction of the Galactic bulge (co-ordinates / = 348.5°, 6 = —0.1°) support this argument, since this region of the Galactic plane is densely populated with infrared sources. The position of

SAO 208591 given in the SAO catalogue, with proper motion included up to 1993.0, is a = 17^12”^10"*.4, 6 = —38°31'57".7 (1950.0 coordinates), while the position of the IRAS source is a = 17^12"^09'.5, 6 = —38°32'23". The discrepancy is larger than the CGS3 beamsize, but smaller than the IRAS beam, so it is quite possible that the IRAS source is physically distinct from SAO 208591. Examination of the IRAS Sky Survey Atla^ image for the region around SAO 208591 shows significant Galactic emission at 1 2 /xm, of which the supposed SAO 208591 emission appears to form a part.

3.4.2 Spectral Features

The Vega-excess stars in our sample which show significant excesses at 10 /xm display spectral features which can be divided into two categories: either a broad emission feature centred on a wavelength of approximately 9.7 /xm, or a set of narrower bands, dominated by one at 11.3 /xm and one peaking shortward of 8 /xm, of which we see only the long-

77 wavelength wing.

It is harder to pick out features in the 20-/im spectra, partly because they tend to be noisier than their 1 0 -^m counterparts due to poorer atmospheric transmission than in the lO-fim window. In the case of SAO 183956, SAO 184124 and 51 Oph, plotting the combined 1 0 and 2 0 -/im spectra suppresses the contrast in the 2 0 -/im region due to the flux levels in the lO /zm spectra being significantly higher than at 20 ^m. For these three cases, the 2 0 -/zm spectra have also been plotted separately in order to emphasise any features (see Figure 3.4). The log-log scaling used on the spectral energy distribution plots (Fig 3.6) also helps emphasise weak 20 fim features. A feature that does appear to be present in some cases, e.g. SAO 184124, is a broad emission feature, peaking at around

18-19 fim.

The feature peaking at approximately 9-10 /^m in the mid-IR spectra of some of the stars has long been recognised as due to circumsteUar silicate grains (see e.g. Woolf and Ney 1969, Gilman 1969). The composition of the silicates is thought to be anal­ ogous to that of terrestrial minerals such as olivines, (Fe„Mgi_„) 2 Si0 4 or enstatites,

(FenMgi_„)Si 0 3 (Day & Bonn 1978; Stephens & RusseU 1979).

Silicate emission is clearly present in the 1 0 -/xm spectra of five of our sources; SAO

179815,183956,184124, 77144, and 51 Oph. It may be present in the spectra of two others,

SAO 26804 and SAO 183986, as a rather weak, narrow feature; these identifications are uncertain because the feature could be an artifact due to incomplete cancellation of the atmospheric ozone feature. The broad emission bump seen at 18 //m in the spectra of

SAO 179815, 184124, 186777 and 51 Oph is also due to silicate materials, but whereas the

9.7-fim silicate feature is associated with a Si-0 stretching resonance, the 18-/xm feature is due to an O-Si-0 bending mode (Forrest et al., 1979).

Many sources in the IRAS Low Resolution Spectrometer (LRS) atlaa (Neugebauer et al. 1986) show silicate emission features. For these, a measure of the strength of the silicate band is defined as:

Bsii = 10 X [\n fx(9.8fim) - (0.589 In/A(7.9/im)-f 0.411 In/A(13.3/im))] (3.7) where f\ is the flux density with wavelength. B^n is thus a measure of the ratio of the power emitted in the silicate band compared to that emitted in the underlying continuum.

For the five stars with obvious silicate emission, the derived values of Bsi\ are given in

Table 3.10.

78 1.5x10 -1 3 SAO 183956 I -1 3 1 0 ' b &

-1 4 I 5x10 y*

J I L _ l I I I I I I L J I L 16 18 20 22 24

,-13 1.5x10 51 Oph

B ,-13

X B

5x10 -1 4

16 20 22 24

-1 3 1.2x10 SAO 184124 ,-13 10

-1 4 B 8x10

-1 4 X 6x10

4x10 -1 4 16 18 20, ^ 22 24 Wavelength (/im) Figure 3.4: 20-fim spectra enlarged for clarity

79 Table 3.10: CGS3 spectra: derived quantities

HD SAO flO.exc K12 ^sil ■^10.phot

35187 77144 2.9 6 6 1 . 1 1

98800 179815 6.4 5.0 0.93

123160 158350 - 0 1.41 135344 206462 - 17 1.50

141569 140789 - 3.6 1.32

142666 183956 4.9 273 1.23

142764 140845 - 0 0.96

143006 183986 - 3 1.38

144432 184124 10.7 186 1.52

155826 208591 - 0 1.40

158643 185470 2.5 28 1 . 1 1

169142 186777 - 2 0 1.30

233517 26804 - 2 . 1 1.38

80 Table 3.11: Proposed assignments of some of the UIR bands (see Allamandola et al. 1989).

Band Transition

3.3/xm C -H stretch

7.7/xm C -C stretch

8.7/xm in-plane C-H bend

11.3/xm out-of-plane C -H bend (non-adjacent H atoms)

12.7/xm out-of-plane C -H bend

(triply-adjacent H atoms)

The values we obtain cover a wide range of silicate strengths, comparable to that found for a sample of 0-rich cool stars by Skinner & Whitmore (1988a). The value of JBsil = 10.7 for SAO 184124, is one of the highest known, as evidenced by the fact that the definition of Bsii was chosen so that the majority of stars with silicate emission would give values that lie between 1 and 9 (the maximum value quoted in the LRS atlas).

A set of narrow infrared emission bands were first discovered in the mid-infrared spec­ tra of the planetary nebulae NGC 7027 and BD-f36°3639 by GiUett et al. (1973), and have been subsequently observed in a wide range of astrophysical environments, including reflection nebulae, starburst galaxies, and the Orion Bar. Together with subsequently discovered emission bands at 3.3 /zm and 12.7 /xm, they are referred to as the Unidentified Infra-Red (UIR) bands, because for several years no convincing carrier of the bands was known. The presently-accepted hypothesis is that the bands are due to IR fluorescence by large aromatic molecules, such as polycyclic aromatic hydrocarbons (Leger & Puget 1984;

Allamandola et al. 1985), pumped by ultraviolet photons.

The individual bands have been associated with particular modes in aromatic molecules

(Allamandola et al. 1989). Some of these identifications are summarised in Table 3.11.

The two longest-wavelength bands are both due to modes involving out-of-plane C-H bending. They differ in the number of adjacent carbon atoms on the aromatic ring which are bonded to hydrogen. The 12.7-/xm band is due to C-H bonds where both of the carbon atoms adjacent to one with a C-H bond are also bonded to hydrogen atoms, while the

11.3/xm band is characteristic of aromatic rings where the two neighbouring carbon atoms

81 are not themselves bonded to hydrogen atoms. This can occur either if a C-H bond is broken, leaving a dehydrogenated molecule, or if the aromatic rings within the PAH are arranged in such a way that some of the carbon atoms have no adjacent C atoms available for bonding to hydrogen.

11.3-/zm UIR band emission is present in the 1 0 -/xm spectrum of SAO 186777 and probably present in the spectra of three other Vega-excess stars: SAO 140789, 183986, and 206462. A strong 7.7-//m feature is clearly present in the spectra of all four of these sources, and possibly also in the spectrum of SAO 26804. Although the peak of the 7.7-

/xm feature lies at a shorter wavelength than the short-wavelength extreme of the observed spectra, the fact that the 7.8-10 /xm slopes of the spectra of these five sources are steeper than a Rayleigh-Jeans energy distribution implies that a feature is truly present, rather than the emission being due to some combination of blackbodies. There is no correlation between the presence of UIR bands and spectral type: the five stars with UIR bands are distributed evenly across the range B9-K2. Since the UIR bands are thought to be excited by UV photons, it might have been expected that the incidence of UIR-band emission would be higher for the hotter stars. This would seem to imply that the later-type stars have excess UV flux above that expected from a normal photosphere.

3.4.3 Notes on Individual Sources

SAO 179815; The 10-/xm spectrum of SAO 179815 (Figure 3.3a) shows a fairly broad silicate feature superposed on a continuum rising towards longer wavelengths. The feature appears to peak at a wavelength slightly longwards of 1 0 /xm, whereas the ‘typical’ silicate feature peaks at around 9.7 /xm. In this respect, it is similar to the h and % Per M-type supergiants having IRAS 1 2 /xm fluxes less than 2 1 Jy, observed by Sylvester et al (1994a;

see Chapter 2).

The points at the short-wavelength end of the 10-/xm spectrum lie only slightly higher

than the expected photospheric spectrum — it would be interesting to extend the spectral

coverage to include the 5-8/xm region, where the changeover between the photospheric

and dust-dominated emission regimes is expected to take place. While this waveband

is unobservable from the ground, these observations could be made with ISO, and are

included in the ISO Short-Wavelength Spectrometer Consortium programme. It is not

clear whether the apparent sharp upturn in the spectrum at 13/xm is real or not; ISO

82 observations will also cover the 14-16/xm region and should resolve this question.

The 20-/xm spectrum seems to show a feature peaking at about 19 /im (most easily discerned in the overall energy distribution plot in Figure 3.61), presumably the ‘18-/im’ silicate feature, but the spectrum is rather noisy. The overall flux level in the 20-//m spectrum is higher than in the 1 0 -/xm spectrum, and the spectra are in accord with the

IRAS 1 2 and 25 /xm fluxes. SAO 183956: The spectrum of SAO 183956 (Figure 3.3b) is qualitatively different from that of SAO 179815. The 10-/xm region shows a falling continuum, upon which is superimposed a silicate feature peaking at about 9.5/xm. The peak itself is somewhat obscured by the noise due to the telluric ozone band, but its position can be interpolated from the uncontaminated points. Longwards of the emission peak, the spectrum starts to level off, until approximately 11.3/xm, where there is a point of inflection, after which the spectrum starts to fall more rapidly again. The 10-/xm excess is very large, with a ratio of excess flux to expected photospheric flux at 10.0 /xm of 273 — the largest value obtained for any of the sources. Agreement with the 1 2 -/xm IRAS point is not perfect, the discrepancy being about 20%, i.e. roughly three times the uncertainty of the PSC value.

SAO 184124: This star shows a remarkably strong 10-/xm silicate feature, (Fig­ ure 3.3c) peaking at about 9.5/xm. Again the peak is rather noisy due to ozone contami­ nation. As noted earlier, the BsH value, 10.7, is the highest for any source in the sample.

Also, as for SAO 183956, there is a secondary bump at about 1 1 /xm on the wing of the silicate feature; it is somewhat smoother than that of SAO 183956. The colour-corrected

IRAS flux is in excellent agreement with the CGS3 spectrum at 12.0 /xm. The gradient of the spectrum tends towards zero between 12 and 13 /xm, whilst there is a slight rise between the 13 and 16-/xm points at the respective ends of the 10 and 20-/xm spectra, so

the spectrum in the unobservable 13.5-16/xm region might be expected to rise slightly and

smoothly join the two observed spectra. The 18-/xm silicate feature is visible ais curvature in the 20-/xm spectrum (see the overall energy distribution in Figure 3.6o).

51 Oph: The 10-/xm spectrum of 51 Oph seems rather peculiar, composed of two

almost linear portions from 8-8.7 and 10-13/xm, with a bump at 9.0-9.5/xm (Figure 3.3d).

The bump is due to poor ozone cancellation — on reducing this spectrum it was found

that none of the standard star observations were fully able to cancel the ozone feature.

The slope of the short-wavelength part of the spectrum was also slightly dependent on the

83 choice of standard star. The value of Bsn found for this star (2.5) indicates a rather weak silicate feature. Subtracting a continuum At to the spectrum at8 and 13/im does leave a broad emission feature peaking at around 10 //m. The 20-/im spectrum clearly shows the

IS/xm silicate feature on a downward continuum (Figure 3.4).

The agreement between the colour-corrected IRAS 1 2 /zm Aux and the CGS3 spectrum is excellent, implying that the Aux calibration of the CGS3 spectrum is sound. Fajardo-

Acosta et al. (1993) obtained narrow band {X/6X ~ 1 0 ) photometry of 51 Oph from 7.8 to 21.9/xm. Their data are plotted in Figure 3.3(d) as open circles. Their spectrum has approximately the same shape as ours, but their points tend to be lower than the CGS3 data. Since the absolute Aux calibration of the CGS3 spectrum is in agreement with that of IRAS, it would appear that there is a slight discrepancy with the calibration of the

Fajardo-Acosta et al. data. The 7.8-8.7/xm slope in their photometry is slightly steeper than in the CGS3 spectrum, although both spectra have large errors shortward of 8 /xm— the 7.8/xm point is at the edge of the 1 0 -/xm atm ospheric window, so Aux calibration here is difficult.

SAO 77144: The spectrum of SAO 77144 (Figure 3.3i) has the same general structure as that of SAO 183956, with a silicate feature superposed on a very strong continuum which decreases to longer wavelengths. The silicate feature is rather broad, and peaks between

9.5 and 10.5 /xm, depending on how the continuum is deAned. The colour-corrected IRAS point does not agree within the uncertainties with the observed spectrum; the IRAS 1 2 -/xm

Aux is approximately 25% larger than the CGS3 1 2 .0 -/xm Aux.

SAO 186777: This was the Arst Vega-excess star to be shown to have UIR band emission in its 1 0 -/xm spectrum (Sylvester et al., 1994b). The CGS3 spectrum (reproduced in Fig 3.3e) shows the long-wavelength wing of a strong 7.7-/xm band. There seems to be a narrow 8.7-/xm UIR feature superposed on the wing of the 7.7-/xm band, but since it is only deAned by a couple of data points, it may be an artifact. Further mid-IR spectroscopy

(possibly with the CGS3 high-resolution grating) would help determine the reality of the feature. SAO 186777 is in the ISO SWS Consortium Guaranteed Time programme.

From 9-10.5 /xm, there is a smooth continuum with a slight downward slope to longer wavelengths.

There is a strong, well deAned emission peak extending from 11.0-11.6 /xm and peaking at 11.3 /xm, clearly the 11.3 /xm UIR feature. The spectrum starts to rise again at 12.3 /xm,

84 and seems to be levelling off at 12.6 /im, before breaking up and becoming noisy. This is probably the 12.7-/xm UIR band. The IRAS 1 2 -/im point lies significantly above the

CGS3 spectrum at 12.0 /xm. Since the colour-correcting technique takes into account the detailed shape of the spectrum, this cannot be ascribed to the fact that the spectrum is dominated by emission bands. The 20-/xm spectrum is somewhat noisy, but appears to show the 18-/xm silicate feature.

SAO 206462: The spectrum of this source shows the 7.7-/xm UIR band, with a subsidiary bump which is probably the 8.7-/xm band (Figure 3.3f). The 9.5-10.0 /xm region is noisy, due to ozone contamination. From 10-13 /xm, the spectrum shows a gently falling continuum, with a weak 11.3 /xm bump. The IRAS 1 2 -/xm point lies slightly above the CGS3 1 2 .0 -/xm point. The 20-/xm spectrum shows a general increase of flux with wavelength, but shows no obvious spectral features.

SAO 140789: The 10-/xm spectrum of this source bears a close resemblance to that of SAO 206462 in its overall shape. It has roughly one-third of the flux, and is somewhat noisier. SAO 140789 shows a broad ll-/xm bump, presumably the 11.3 /xm feature. Agree­ ment with the colour-corrected IRAS 12-/xm point is good. The 2 0 -/xm spectrum shows the 18-/xm silicate feature at low contrast. The overall energy distribution (Figure 3.6i) plot shows the 18-/xm silicate feature more clearly.

SAO 26804: The spectrum of SAO 26804 is rather noisy (Figure 3.3h). It is unlike any other Vega-excess spectrum in that the flux decreases with increasing wavelength between 8 and 9 /xm, but rises between 12 and 13 /xm. The 8-9 /xm slope looks as if it is due to the 7.7-/xm UIR feature. There appears to be a bump between 9-10 /xm, which could be a rather narrow silicate feature (Skinner et al 1995), but the spectrum is so noisy that it is difficult to be certain that this is not just the effects of telluric ozone. There is good agreement between the CGS3 and IRAS fluxes at 12/xm. The 20-/xm spectrum is noisy, and shows a generally constant flux level.

SAO 183986: The spectrum of this source shows an overall decrease in flux with wavelength (Figure 3.31). The shorter-wavelength part of this is due to the 7.7-/xm UIR feature. The 11.3 /xm band also appears to be present, as does a narrow silicate feature, although the spectrum is rather noisy around 9.5 /xm, due to telluric ozone.

SAO 140845: This is rather a faint source at 10 /xm, approximately 10 times fainter in the 1 2 -/xm band than SAO 184124, so its CGS3 spectrum is somewhat noisy (Figure 3.3k).

85 Nevertheless, it clearly agrees with the predicted photospheric spectrum, indicating there is a negligible dust excess in the 1 0 -/xm region. Convolving the observed spectrum with the

IRAS response curve yields a colour-correction factor of 0.96, which is approximately that expected for a 120 K blackbody {IRAS Explanatory Supplement)^ and so is unrealistic given the overall shape of the observed CGS3 spectrum. This value gives a colour-corrected flux that is slightly high compared with the photospheric spectrum (but still consistent within the errors of the CGS3 spectrum). This is presumably due to problems with interpolating between the noisy CGS3 points.

Since the spectrum is clearly photospheric in nature, a colour-correction factor of 1.42, appropriate for a 4000 K blackbody, was adopted. This more realistic estimate gives better agreement with the expected photospheric flux. Spline-fitting a smooth curve to the CGS3 spectrum, and using it for calculating the colour-correction factor, gives a similar result to the blackbody case.

W hile the IRAS PSC gives only an upper limit at 25/xm, the IRAS Faint Source Survey Catalog (FSSC) gives a flux of 0.11 Jy, which is consistent with photospheric emission, so it is unlikely that any excess would be detected in a 20-fim spectrum of this source.

SAO 158350: The spectrum of SAO 158350 (figure 3.3j) also shows photospheric emission only, but is less noisy than that of SAO 140845. Agreement between the observed spectrum, the model photospheric spectrum extrapolated from optical wavelengths and the IRAS 12-/xm point is reasonable. The IRAS 25-pm photometry of this source does show an excess, so a spectrum longwards of 2 0 /xm would be expected to show an upturn from the blackbody-like photospheric spectrum as the excess emission becomes important.

SAO 208591: The spectrum of SAO 208591 (Figure 3.3m) has already been men­ tioned in connection with the IRAS colour-corrected fluxes. As noted above, the 10-13 /xm region of the spectrum is in good agreement with the expected photospheric spectrum; however, there appears to be some excess between 8 and 9/xm. This is unique among the

CGS3 spectra of Vega-excess and cool stars in this thesis - in no other case does the 10-/xm spectrum show excess emission in the short-wavelength part, then revert to photospheric emission at longer wavelengths. Since, as shown above, the IRAS source is only associated with SAO 208591 by a chance positional coincidence, it is likely that the small amount of excess emission detected in the 5.5 arcsec CGS3 beam is not physically associated with the star, but is background emission from another Galactic source.

86 The good agreement found in almost all cases between the level of the CGS3 spectra and the colour-corrected IRAS 1 2 /zm fluxes provides useful confirmation of the accuracy of the flux calibration of the CGS3 observations. It also provides some spatial information, since if a source was significantly extended at 1 0 fim. with respect to the CGS3 beam,

CGS3 would have detected less flux than IRAS, which has a much larger beam. Since for the vast majority of our sources the CGS3 and IRAS 1 2 /xm fluxes are nearly identical, we can conclude that the objects are not extended compared with the 5.5 arcsec diameter

CGS3 beam. In the three cases where we see a large discrepancy between the IRAS and

CGS3 fluxes, the IRAS flux is always higher, as one would expect if the discrepancies are due to different beamsizes rather than faulty calibration.

For one of the three sources, SAO 208591, the large IRAS fluxes are probably due to source confusion, as discussed above. The other two sources, SAO 77144 and SAO 186777, probably could be extended with respect to the CGS3 beam. Mid-infrared imaging is required to confirm this hypothesis.

3.5 Near-Infrared Spectroscopy with CGS4

In order to determine the nature of the near-IR emission from some Vega-excess systems, a

3.2-3.4 /xm Service spectrum of SAO 186777 using the common-user spectrometer CGS4 at

UKIRT was obtained. CGS4 has a 58 by 62 pixel InSb array, and a number of interchange­ able gratings. For our observations, the 75 line/mm grating was used with a 1.5-arcsecond wide slit aligned east-west, to yield a spectral resolving power of approximately 1000. The

‘long’ (300 mm) focal length camera was used. Two overlapping subspectra were taken with slightly different central wavelengths, in order to produce a fully-sampled spectrum.

After removal of bad points (due to atmospheric absorption) the final spectrum contained

94 data points. The telescope secondary was chopped east-west with a 20-arcsec throw, and the A2V star BS 6378 was used as the standard star. The 3.2-3.4/xm wavelength range was chosen because of the well-known UIR emission feature at 3.3/xm; we intended to determine if it was present in the spectrum of SAO 186777, and how much of that star’s

T-band excess emission could be attributed to the feature.

The observed spectrum (Figure 3.5) does indeed show the 3.3/xm feature, but it is quite weak (having an equivalent width of 120 A), and is superposed on strong continuum

87 7x10

6x10

5x10

T

7

2x10,-13

,-13

3.24 3.26 3.28 3.3 3.32 3.34 3.36 3.38 3.4 Wavelength (/im)

Figure 3.5: CGS4 Service spectrum of SAO 186777 emission. The observed flux density at 3.3 /im is approximately 30% higher than the interpolated excess continuum at that wavelength, and approximately 10% of the 3.2-

3.4 /xm excess flux is due to the 3.3-/xm feature. This implies that we are justified in assuming that the near-IR photometric points are delineating a broad distribution of excess emission, rather than the broad band measurements being contaminated by flux from strong emission features, for instance.

3.6 Millimetre-Wave Photometry using UKT14

Millimetre and submillimetre wave photometry was obtained with the continuum receiver

UKT14 at the James Clark Maxwell Telescope, Mauna Kea, in 1992 February and August.

We were allocated six eight-hour shifts at the telescope on both occasions, but lost some nights due to poor weather on each run. A third observing run took place in 1994 August, again under less than optimum weather conditions. Further data were kindly obtained for us by Dr I.D. Howarth in 1992 March, by Dr. V.G. Mannings in December 1993, and in

JCMT Service time in 1994 April and May.

UKT14 (Duncan et al. 1990) uses a liquid-^He cooled composite GeilnrSb bolometer and a set of filters ranging in nominal central wavelength from 0.35mm to 2.0mm. Submil­ limetre atmospheric transmission is normally poor, due mainly to absorption by oxygen and water molecules. The filter passbands are chosen to match the semi-transparent at­ mospheric windows in the mm/sub-mm region. The observations presented here were made in the 0.45mm, 0 .8 m m, 1 . 1 and 1.3mm passbands. UKT14 has a variable iris for controlling the size of the input aperture where the beam enters the instrument dewar.

We kept this at its maximum size, 65mm, for our observations. This implies beamsizes of

18, 17, 19, and 21 arcsec for the 0.45mm, 0.8mm, 1.1 and 1.3mm passbands, respectively.

The accuracy with which the JCMT points at a source cannot be checked visually, in part because the telescope observes through a fabric membrane designed to protect it from exposure to the sun, wind and dust. This membrane is transparent to mm-wave radiation, but opaque to visible light. The pointing is therefore calibrated and checked by observing bright point sources of known position. Observations are first made on source, then offset to either side of the source in altitude and azimuth; such a set of observations is called a five-point for obvious reasons. A fit is made to the signal versus position results to determine the offset of the telescope pointing from its nominal position, which is then used to update the computer model of the pointing. Five-points and focus check observations were made at intervals throughout each observing shift. The pointing was found to be accurate to typically better than 3 arcsec. In the submiUimetre region, as in the mid-IR, sky background emission is significant compared with the signal from astronomical sources, so chopping and nodding techniques were employed to remove background emission. The typical chop frequency of the sec­ ondary mirror that was used was 7.8 Hz, with a throw of 60 arcsec (90 arcsec for the

February 1992 run) in azimuth.

We integrated for typically 10-30 minutes on our target sources. The Noise Equivalent

Flux Density, calculated from the observations of calibration sources, was of the order of

0.5-2 Jy/Vllz at 1 .1 mm, and 2-8 Jy/vHz at 0 .8 mm, compared with 0.7 and 5.0 Jy/\/Hz quoted in the JCMT User Guide for a night with ‘poor’ atmospheric conditions. The flux-calibration of submiUimetre continuum observations is difficult, especiaUy when the atmospheric conditions are unstable. In essence the aim of the calibration process is to determine the responsivity (Jy/mV) of the instrument and the zenithal optical depth {t\) of the atmosphere at the time the observations were made. Different

89 observers use a variety of techniques, ranging from adopting quoted values of the UKT14 responsivity and scaling the observed zenith optical depth to that measured at 1.3mm by the Caltech SubmiUimeter Observatory (CSC) radiometer, to sophisticated non-linear fits to calibration data sets extending over several nights (Matthews, 1993).

The weather conditions during the 1992 runs were very unstable, with the atmospheric opacity fluctuating markedly throughout each shift. In order to be able to calibrate the observations adequately, frequent observations were made of standard sources (see below), typically more than 2 0 separate observations per night in a single waveband, chosen to give a good match to the programme sources in time and airmass. Pairs of standard observations, obtained at times bracketing the target observations, allowed the zenith optical depth and the instrument responsivity to be determined. Typical responsivities derived in this way were 12 Jy/mV at 1.1 mm and 10 Jy/mV at 0.8mm, consistent with the values quoted in the JCMT Manual (Matthews 1993).

Weather conditions during the 1994 August run were slightly less troublesome. Atmo­ spheric transmission measurements at 1.3 mm, provided by the CSO radiometer located adjacent to the JCMT, indicated a poor but very stable zenithal optical depth of about 0.2 at 1.3 mm during each of the four nights. Such stability allows a rough determination of the instrument responsivity and the optical depth of the atmospheric extinction using a linear least squares fit to a secant plot — ie a plot of

log[F„/(signal voltage)] v. sec (zenith angle) for the observations of standard sources. By way of comparison, a second calibration method was used, employing the empirical ratios of ta/(CSO determined by

Stevens & Robson (1994) from observations made between 1992 and 1994, together with the calibration observation. The two methods were in good agreement; both indicated av­ erage UKT14 responsivities in the range 12.9 Jy mV“^ at 1.3 mm (aperture = 65 mm) to

35.4 Jy mV~' at 2.0 mm (same aperture). The average transmission at the zenith during each of the four shifts ranged from % 35% at 0.8 mm to % 85% at 2 mm; equivalently the zenith optical depths, r^, were 1.05 at 0.8 mm and 0.16 at 2 mm, compared with the

CSO value of 0 . 2 at 1.3 mm (see above). The 1 . 1 -mm noise equivalent flux density was typically 0.5 Jy. Little variation in sky opacity was observed between the four shifts of this run.

90 The primary calibration standard used at the JCMT is the planet Mars, the flux from

which can be calculated using a numerical model (Griffin et al. 1986, Orton et al. 1986)

available at the JCMT. Uranus is the next choice of calibrator, due to its brightness and

smaU angular size. Venus, Jupiter, Saturn and Neptune are also used (as with Mars, the

model fluxes from the other planets are available at the telescope). When no planets are

suitably positioned in the sky, secondary calibrators, such as ultra-compact HIT regions,

compact bipolar outflows, etc, are used. The fluxes from these objects have been observa-

tionally determined by comparison with the primary calibrators. In the three observing runs reported here, the calibrators used were Mars, Uranus, and the secondary standards 16293-2422, 2251-1-158, 3C279, G343.0, G45.1, GL490, K-350, N2071IR and W75N, the fluxes and positions of which are all given in the list published by SandeU (1994).

3.6.1 Results

The individual fluxes measured are presented in Table 3.12. We have 3

confidence in the calibrated fluxes.

The fluxes presented in Table 3.13 are the weighted means of the observed flux densities from all the runs. The weighting factors used, w,, were the squares of the signal-to-noise ratios of the individual measurements. The weighted mean fluxes were thus calculated as

^mean = (3.8)

while the errors on the mean values were calculated as

AFmean = imean (3 9)

Two Vega-excess stars, SAO 182956 and SAO 183986 were observed with the JCMT in May 1991 by van der Veen et al. (1994). Observations of both stars were made at 0.45

0 . 8 and 1 .1 mm, using similar techniques to those described above.

The fluxes measured by these authors for SAO 183956 were 1090±60 mJy, 287±10 mJy,

and 145±12 mJy at 0.45, 0.8 and 1 .1 mm respectively, while those for SAO 183986 were

91 Table 3.12: Individual JCMT measurements

HD SAO Date Filter Flux (mJy)

16908 75532 1992 Aug 1 .1 16±13

18537 23763 1992 Aug 1 .1 <34

23680 93601 1992 Aug 1 .1 33±15

34282 131926 1992 Aug 1 .1 183117

1993 Dec 0.45 13181254

1993 Dec 0 . 8 409 1 2 7

34700 112630 1992 Aug 1 .1 39113

35187 77144 1992 Aug 1 .1 80110

1993 Dec 0 . 8 115122

49662 151962 1992 Aug 1 .1 <42

98800 179815 1992 Feb 0 . 8 1 1 1 1 1 2

1992 Feb 1 .1 88111

1992 Mar 1 .1 6016

1994 Apr 0.45 123411272

1994 Apr 1.3 1113

123160 158350 1992 Feb 0 .8 <41

1992 Feb 1 .1 <47

1992 Mar 1 .1 <16

135344 206462 1992 Feb 0 .8 570121

1992 Feb 1 .1 209114

1994 Aug 1.3 142 1 19

1994 Aug 2 . 0 <76

92 Table 3.12 continued HD SAO Date Filter Flux (mJy)

139614 226057 1992 Feb 0 . 8 608±27

1992 Feb 1 .1 264116

1994 Aug 1 .1 287124 1994 Aug 1.3 242115

1994 Aug 2 . 0 80116

141569 140789 1992 Feb 1 .1 <44

1992 M ar 1 .1 <36

142666 183956 1992 Feb 0 . 8 351123

1992 Feb 1 .1 167117 1994 Apr 0.45 10221315

1994 Apr 1.3 118115

1994 Aug 0 . 8 < 795

1994 Aug 1 .1 190117

1994 Aug 1.3 131 111

1994 Aug 2 . 0 <63

142764 140845 1992 Feb 1 .1 <63

1992 Aug 1 .1 <45

93 Table 3.12 continued HD SAO Date Filter Flux (mJy)

143006 183986 1992 Feb 0 . 8 233±25

1992 Feb 1 .1 114±17

1994 Apr 0.45 720±340

1994 Apr 1.3 57±17

1994 Aug 1.3 65±9

1994 Aug 2 . 0 <132

144432 184124 1992 Feb 1 .1 58±19

1992 Aug 0 . 8 103±34

1992 Aug 1 .1 72±12

155826 208591 1992 Feb 0 . 8 < 2 2 0

1992 Feb 1 .1 <80

1992 Aug 1 .1 31±17

158643 185470 1992 Aug 1 .1 26±14

169142 186777 1992 Feb 0 . 8 504±48

1992 Feb 1 .1 302±19

1992 Aug 0 . 8 606±49

1992 Aug 1 .1 271±19

1992 Aug 1.3 197±15

1992 Aug 2 . 0 <213

1994 Aug 2 . 0 70±19

218396 91022 1992 Aug 1 .1 28±11

233517 26804 1992 Mar 1 .1 <36

94 Table 3.13: Weighted mean JCMT fluxes

HD SAO 0.45mm 0 .8 mm 1 . 1 mm 1.3mm 2 .0 mm

(m Jy) 16908 75532 -- 16±13 --

18537 23763 -- <34 - -

23680 93601 -- 33±15 --

34282 131926 1318±254 409±27 183±17 - - 34700 112630 -- 39±13 - -

35187 77144 - 115±22 80±10 --

49662 151962 -- <42 --

98800 179815 <3800 1 1 1 ± 1 2 63±6 11±3 -

123160 158350 - <41 <16 --

135344 206462 - 570±21 209±14 142±19 <76

139614 226057 - 608±27 272±13 242±15 80±16 141569 140789 -- <36 --

142666 183956 1022±315 351±23 180±12 127±9 <63 142764 140845 -- <45 --

143006 183986 720±340 233±25 114±14 64±8 <132

144432 184124 - 103±34 69±10 --

155826 208591 - < 2 2 0 <80 --

158643 185470 - - 26±14 --

169142 186777 - 554±34 287±13 197±15 70±19 218396 91022 -- 28±11 --

233517 26804 -- <36 - -

95 Table 3.14: IRAM 1.2 mm fluxes (in mJy) of Vega-excess stars from Bockelée-Morvan et al.

HD SAO 1 -channel 7-channel

9672 147886 12.7±2.3 -

18537 23763 - 3.8±1.5

98800 179815 59.1 ±5.4 26.5±3.1

158643 185470 - <28.2

142666 183956 161±5.5 78.6±5.4 169142 186777 - 178.5±0.6

218396 91022 4.0±2.7 -

1140±80 mJy, 162±14 mJy, and 87±17 mJy at the same wavelengths. These are in reasonable agreement with the values presented in Table 3.13, within approximately twice the formal error on the measurements.

Bockelée-Morvan et al. (1994) observed a number of Vega-excess stars at 1 .2 mm using the Institut de Radio Astronomie Millimétrique (IRAM) 30-m telescope. Observations were made in December 1993 using a single-channel bolometer, and in May 1994 using the MPIfR 7-channel bolometer array. The flux measurements with the two detectors are reproduced in Table 3.14.

As can be seen from Table 3.14, there are significant differences between the fluxes obtained in the December and May runs. Bockelée-Morvan et al. ascribe these to difficul­ ties in calibrating the May (7-channel) data, which were obtained under poor atmospheric conditions.

We have JCMT measurements of three of the stars for which Bockelée-Morvan et al. obtained detections above the 3-(t level with the single-channel bolometer: SAO 179815,

183956 and 184124. In aU three cases, the Bockelée-Morvan et al. measurements are in good agreement with the JCMT fluxes. For SAO 179815 and 183956, where we have

JCMT data at 1 .1 and 1.3 mm, the IRAM fluxes lie between the two JCMT values.

The IRAM beamwidth at 1.2 mm (10-12 arcsec) is about half that of the JCMT beam at 1 .1 mm (19 arcsec). The close agreement between the fluxes measured by the two telescopes suggests that the millimetre-wave emitting regions of these three objects are

96 not significantly extended with respect to the IRAM beam.

SAO 186777 was observed by Bockelée-Morvan et al. (1994) using only the 7-channel bolometer. The flux they measured was roughly 50% lower than the flux we measured with the JCMT. However, this cannot be taken as evidence of of extension of this source with respect to the IRAM beam, since for the three sources mentioned above (which had both 1-channel and 7-channel detections), the 7-channel flux was of the order of 50% lower than that measured with the single-channel detector. Scaling up the 7-channel flux by the average ratio of the single-channel to 7-channel fluxes gives a value of 340 mJy, in closer agreement with, and somewhat larger than, the JCMT 1.1 mm flux.

3.6.2 Spectral Indices

A spectral index can be calculated between any two flux densities at different wavelengths. The spectral index, a is defined as the index of the power-law spectrum which connects the two data points, i.e.

The long-wavelength Rayleigh-Jeans portion of a blackbody spectrum behaves as

F\ (X A"'* or Fy (X A“^, ie a = 2. The absorption (or equivalently emission) efficiency of a grain is approximately constant (‘grey’ emission) at wavelengths shortward of a turnover wavelength, Ay % 27ra, where a is the grain radius (e.g. Bohren & Huffman 1983). Long­ wards of At’, the grain emissivity e\ or absorption falls as A“^, where (3 is typically in the range 1-2 (see e.g. Pollack et al. 1994 for some computed values of /3). In real materials, the turnover does not occur abruptly, but over some wavelength interval (Figure 4.2). The observed spectral index for a grain emitting in the Rayleigh-Jeans domain will therefore be Q = 2 for X < Xt and 2 -f /? for A > A^.

The submiUimetre spectral index of a dust disc depends on three factors: the optical depth of the disc, the temperature distribution and the grain emissivity. Simplistically, we can describe these in terms of three pairs of possibilities — whether or not the disc is opticaUy thick in the sub-mm region, whether the emission from the dominant grains

(whichever they happen to be) is in the R-J regime in the sub-mm or not, and whether or not the emission from these grains has ‘turned over’. The expected spectral indices for

97 Table 3.15: Spectral indices for different conditions

R-J non R-J

Optically Turned-over 2 +/Î < 2 + /3

Thin Grey 2 < 2

Optically Thick 2 < 2

the varions combinations of these possibilities are presented in Table 3.15. Spectral indices have been derived for the observed Vega-excess stars, and are presented in Table 3.16. Uncertainties are calculated from the uncertainties on the flux measure­ ments, and on the quoted uncertainties in the IRAS PSC where appropriate. Where only upper limits to the mm-wave flux were obtained, lower limits to the value of a are quoted.

These observed values can be compared with those derived for three of the prototype Vega-excess stars: Vega, Pic and Fomalhaut. Some care needed to be exercised in selecting the observed fluxes to be used, since Fomalhaut is extended compared to the 11 arcsec beam of the 30-m IRAM telescope (Chini et al, 1991), but not compared to the

24 arcsec SEST beam (Chini et al, 1994, Stern et al, 1994b); while the 0.87 mm IRAM observations by Chini et al (1990) and the 0.8 mm JCMT observations by Zuckerman

& Becklin (1993) are admitted by both sets of authors to be inconsistent. Weintraub

& Stern (1994) raised the possibility that the two sets of measurements need not be inconsistent if the emitting regions were extended with respect to the largest beamsizes used. However, the observations of Chini et al. (1994) showed this was not the case for Fomalhaut, so the inconsistencies remain for this star, and assuming that calibration problems are responsible, for the other stars as well.

The optimum choice seemed to be to use the Zuckerman &: Becklin total flux measure­ ments of Vega (a Lyr), Fomalhaut (a PsA) and /? Pic at 0.8 mm, obtained by summing the contributions from a number of beams positioned on-source and offset by about a beamwidth, and the Chini et al (1991) 1.3 mm SEST measurements (of the same stars), which were made with a larger beam than the earlier IRAM observations. The spectral indices derived in this fashion are presented in Table 3.17.

There is clearly a difference between the spectral indices of the prototypes and those

98 Table 3.16: Observed submiUimetre spectral indices

HD SAO « 0 .1 - 0 .4 5 « 0 .1 - 0 .8 «0.1-1.1 «0.45-0.8 «0.45-1.1 «0.8-1.1 «0.8-1.3 18537 23763 -- > 2.5 --- -

23680 93601 -- > 2 .0 ----

34282 131926 1.4±0.2 1.61±0.06 1.70±0.06 2.0±0.4 2 .2 ±0 .2 2.5±0.4 -

34700 112630 - - 2 .2 ± 0 .1 ----

35187 77144 - 1 .8 ±0 .1 1.72±0.07 -- 1.1±0.7 -

49662 151962 - - > 2 .0 -- -- 98800 179815 - 1.82±0.07 1.78±0.06 -- 1.5±0.4 4.8±1.1 123160 158350 - > 2.3 > 2.3 -- --

135344 206462 - 1.83±0.05 2.01±0.05 -- 2 .8 ±0 .2 2.9±0.3

139614 226057 - 1.55±0.07 1.65±0.06 -- 2 .2 ±0 .2 1.89±0.2 141569 140789 -- > 1.9 ----

142764 140845 -- > 1.8 ----

142666 183956 1.07±0.05 1.35±0.04 1.05±0.05 2 .2 ±0 .2 2 .U 0 .1 2 .0 ±0 .2 2 .1±0 .2

143006 183986 0.96±0.08 1.49±0.07 1.56±0.04 3.0±0.2 2 .6 ±0 .2 1.9±0.4 2.7±0.3 144432 184124 - 1.7±0.2 1.59±0.08 -- 1.0±0.5 -

169142 186777 - 1.84±0.06 1.84±0.05 -- 1.78±0.08 2 .1±0 .2

233517 26804 - - > 2 .0 ----

Table 3.17: Spectral indices for prototype Vega-excess stars

Star «0 .1- 0.8 «0.8-1.3 a Lyr 2.7±0.3 3.9±1.2

(3 Pic 2.4±0.1 3.2±0.6

a PsA 2 .8 ± 0 .1 4.1±0.5

99 of our sources. The prototypes all show a > 2 in the 100 fim-O.S mm region, which from Table 3.15 indicates that the grain emissivity for these sources has already started to turn over, i.e. that the turnover wavelength occurs somewhere within the 1 0 0 /xm- 0 .8 mm region. The 60-100 /xm spectral indices of a Lyr, (3 Pic, and a PsA are 0.4, 1.1 and 0.4 respectively, suggesting that turnover has not occurred shortwards of 1 0 0 /xm.

The maximum grain size in these systems is therefore of the order of several tens to one hundred microns. Backman & Paresce (1993) estimated typical grain sizes of 80, 27, and

1 /zm for Vega, Fomalhaut and (3 Pic respectively, while Artymowicz et al. (1989) derived an upper limit of 15 /zm for the maximum grain size in the Pic disc. However, Zuckerman h Becklin (1993) found that grains of radius larger than 100 /zm must be present in the discs of Vega, Fomalhaut and (3 Pic based on the 800-/zm opacities calculated by Pollack et al. (1994), The 0.8-1.3 mm spectral indices, although having rather high uncertainties, show values consistent with turned-over emission in the Rayleigh-Jeans domain. In the cases of Vega and Fomalhaut, the values are close to 4, implying R-J emission and grain emissivity varying as A“^, consistent with the value expected for crystalline materials. Our own programme sources, on the other hand, have much lower spectral indices

(Table 3.16) — typically less than 2 . Only one system, SAO 206462, appears to show turned-over emissivity, while three others, SAO 112630, 131926 and SAO 226057, have

spectral indices larger than 2 , but values of2 would still be consistent within the errors.

Three stars, SAO 77144, SAO 179815 and SAO 184124 have very slightly lower 0 .8 - 1 .1 mm

than 1 0 0 /zm -0 .8 mm spectral indices, although they are consistent within the \-a errors.

This is more likely to be an artifact due to poor calibration of one of the sub-mm points than a real feature, since a real feature would imply a sudden increase in mass at cool

temperatures compared with the amount of mass at slightly higher temperature.

From Table 3.15, we see that a spectral index of less than 2 implies that the material

is not emitting in the R-J regime at the observed wavelengths, regardless of whether the

grain emissivity has turned over or not. There are thus three possible explanations for the

observed spectral indices:

• The grain emissivity has turned over, but the grain emission is far from the R-J

domain, and so the Planck function is falling very slowly (or even rising)

• The grain emissivity has not turned over - ie greybody emission

100 • The disc is optically thick at mm wavelengths, and so the emission is like that of a

collection of blackbodies

AU three situations require that the grain emission is not in the R-J domain.

If the grain emission has turned over, the slope of the equivalent blackbody spectrum must be very shadow and far from the Rayleigh-Jeans domain, implying very cool tem­ peratures. For example, an observed spectral index between 0.8 and 1.1 mm of sUghtly less than 2 with grains having an emissivity e\ oc A"' ® would require the Planck function to have a millimetre-wave spectral index of just under 0.5, implying the emission is dom­ inated by material at a temperature of 7 K. Since cool blackbodies emit less energy at aU wavelengths than do hotter ones, there needs to be more mass at low temperatures {i.e. in the cool outer parts of the disc) than at higher temperatures (further in towards the star).

This is contrary to the normal expectations of disc structure, according to which the outer parts of the disc are less densely-populated by the grains. Radiative transfer modeUing of the entire spectral energy distribution is needed in order to determine whether emission from grains with 2wa >C A can be responsible for the observed sub-mm spectral indices

(see Chapter 6 ).

OpticaUy thick emission behaves Uke blackbody radiation even for wavelengths longer than the turnover wavelength (see e.g. Adams, Lada & Shu 1988), and therefore gives rise to a spectral index indistinguishable from that due to emission by large greybody grains. One could calculate the optical depth of the emission from a model of the dust disc, and then determine whether optically thick conditions apply. It is worth noting that the millimetre-wave emission from a sample of Herbig Ae/Be stars (Mannings 1994), which are the possible precursors of Vega-excess stars, is optically thin (as judged from the mm/sub-mm spectral indices) in every case. The later stages of the standard evolutionary scenario have the large Ae/Be discs clearing by grains either falling onto the star or being expelled from the system, and by grain coagulation (e.g. Shu, Adams, & Lizano 1987).

Thus, one would expect a priori that the optical depth would not increase with time, but the maximum grain size would, so large grains could appear more plausible than opticaUy-thick emission.

In summary then, it can be said that unlike the prototype Vega-excess stars, the objects discussed here are not emitting in the Rayleigh-Jeans domain, and detailed modelling is required to determine whether turnover has been achieved, and whether the emission is

101 optically thick (see Chapter 6).

3.7 Spectral Energy Distributions

Combining all the new observations with the IRAS data enables the optical-miUimetre spectral energy distribution (SED) for each source to be defined. The SEDs for the present sample of Vega-excess stars are presented in Figure 3.6. The observations have been dereddened using the observed {B — V) colours and the tabulated intrinsic colours as a function of spectral type of Schmidt-Kaler (1982), assuming a typical Galactic reddening law of A y = 3.1E{B — V).

Two IRAS catalogues were used, the Point Source Catalog (PSC; see IRAS Explanatory

Supplement), and Version 2 of the Faint Source Survey Catalog (FSSC; Moshir et al. 1992).

The FSSC is more sensitive for faint sources, but is also more susceptible to contamination by infrared ‘cirrus’ emission. In general, the PSC fluxes in all four IRAS wavebands were used, unless the PSC data included an upper limit, or low-quality data (flagged with a colon in the PSC), in one or more wavebands. In this case, FSSC values were used for all four wavebands. However, if the FSSC data were suspected of being cirrus-contaminated, for instance if the FSSC flux in a given waveband wzis greater than the PSC upper limit, the PSC values would be retained for the wavebands in question. A summary of which catalogue was used for each source in the four wavebands is presented in Table 3.18. Fitting a model atmosphere to the dereddened optical photometry makes it possible to calculate the fractional luminosity of the dust, Ljptf Lgtar^ the ratio of the total energy radiated (in the infrared-submm) by the dust, L jr to the stellar luminosity, Z/*. LirJLi, gives a useful indication of the optical depth of the disc material. For optically thin emission, Lm lLi, is in fact equal to the fraction of the sky as seen from the star which is occupied by dust. For a flat opticaUy-thick disc, the maximum value of Ljr/L i, is 1/4, while for a ‘flared’ disc, i.e. one in which the azimuthal thickness increases with distance from the star, Lm fLi, can reach values of approximately 1/2 (Kenyon & Hartmann, 1987).

The prototype Vega-excess stars have Ljfi/Li, ~ 10“^-10“^ (e.g. for 13 Pic Lm /Li, =

2.6 X 10~^) — a very low value, which indicates that the dust discs have very low optical depths at aU wavelengths.

Table 3.19 presents the values of L/h /L* derived for the present sample of Vega-excess

102 Table 3.18: Usage of IRAS Point Source Catalog (F) and Faint Source Survey Catalog

(F) as a function of waveband

HD SAO 1 2 25 60 1 0 0

9672 147886 FFFF

16908 75532 FFFF

18537 23763 FFFF

23362 111388 FFFF

23680 93601 FFFF

34282 131926 FF FF

34700 112630 FFFF

35187 77144 F F F F 49662 151962 FF FF

98800 179815 FF FF

109085 157345 F FFF

123160 158350 F F F F 135344 206462 F FFF

139614 226057 FFFF

141569 140789 FFFF 142666 183956 FFFF

142764 140845 FFFF

143006 183986 F FF F 144432 184124 F F F F

155826 208591 FFFF

158643 185470 FFFF

169142 186777 FF FF

218396 91022 F F F F

233517 26804 F F F F

103 stars, which were calculated as foUows. First, a smooth curve representing the observed

(but dereddened) energy distribution is constructed by fitting a spline to the photomet­ ric points from the optical to the submiUimetre region. The photospheric contribution is represented by an appropriate Kurucz (1991) model atmosphere normalised to the dered­ dened optical photometry. The two curves were then plotted and inspected to ascertain at what wavelength the observed energy distribution diverges from that expected from the star, i.e. the shortest wavelength with excess emission. The total observed and expected

(photospheric) fluxes in the excess region are then determined by integrating under each curve longwards from this point with the photospheric continuum being subtracted from the observed flux to give the excess infrared luminosity, L jr .

Integrating under the model atmosphere over its complete wavelength range then gives the stellar luminosity, L*, finally allowing the ratio L/h /L* to be derived.

While several of the stars in Table 3.19 have values of Lm/Latar comparable to those of the ‘prototype’ Vega-excess stars (c.y.SAO 93601, SAO 140789 and SAO 158350), others show values substantially larger, some of which exceed the ‘flat disc’ maximum of 0 25. The largest values obtained is 0.64 for SAO 206462 (in good agreement with the results of Coulson & Walther 1995), implying that almost two-thirds of the stellar radiation is reprocessed before escaping from the stellar system. Zuckerman & Becklin (1993) found that for a number of Vega-excess stars, the emitting grains are not confined to a single thin plane, so the present sample of stars are not unique in this respect.

The observed values of LiRjLatar show a strong anti-correlation with the shortest wavelength at which an excess is discernible (Table 3.20).

For example, the stars with no excess at 12/zm have fractional luminosities of around

1 0 ~® - 10"3, while those with 1 2 /zm excess but no near-infrared excess have values from about 10~^ to nearly 10“^. The stars with near-IR excess have the largest values of

LmlLatari approximately in the range 0 . 1- 0 -6 . This is not surprising, given that stars emit more of their luminosity at visible and near-IR wavelengths than in the far-IR, so a short-wavelength excess, discernible above the photospheric flux, must necessarily be very luminous.

104 Table 3.19: Fractional luminosities of Vega-excess stars

HDSAO L i r ! L s t a r

9672 147886 8.7 X 10-4

16908 75532 1.8 X 10-5

18537 23763 8.7 X 10-4

23362 111388 7.9 X 10-4

23680 93601 3.0 X 10-3 34282 131926 0.39

34700 112630 0.15

35187 77144 0.14

49662 151962 1.1 X 10-3

98800 179815 0.084 123160 158350 4.4x10-3 135344 206462 0.64

139614 226057 0.39

158643 185470 0.028

141569 140789 8.4 X 10-3

142666 183956 0.34

142764 140845 1.7 X 10-3

143006 183986 0.56

144432 184124 0.48

169142 186777 0.26

218396 91022 1.8 X 10-4

233517 26804 0.077

105 SAO 26804 -10

-1 1 -12 -13

-18

-19

1 0 ° Wavelength (/zm)

SAO 75532 - 6 -9 -1 0 -1 1 -1 2

-19

1 0 ° Wavelength (/xm) Figure 3.6: Spectral energy distributions of Vega-excess stars. Large filled squares: dered­ dened photometry; small fiUed squares: CGS3 data; open squares: upper limits

106 SAO 77144

'î

I

1 2 3G Wavelength (/xm)

SAG 91022

I ■e

G 1 2 3 Wavelength (/xm)

Figure 3.6 continued.

107 SAO 03601

G 1 2 3 Wavelength (/xm)

SAO 111368

01 2 3 Wavelength (/xm)

Figure 3.6 continued.

108 SAO 112630 -10

-1 1 -12

-1 6

-1 9

-2 0 G 1 2 3 Wavelength (/xm)

SAO 131926 -1 0

- 1 1

-1 2

-1 3

—14

—18

-1 9

0 1 2 3 Wavelength (/xm)

Figure 3.6 continued.

109 SAO 140780 -9 -1 0

- 1 1

17 -1 8 -1 9 -2 0 G 1 2 3 Wavelength (/xm)

SAO 140845 -1 0

- 1 1

-1 2

-1 3

—14

-1 7

-1 8

-1 9 0 1 2 3 Wavelength (/xm)

Figure 3.6 continued.

110 SAO 147886

-1 0

-1 1

-12

-1 3

-1 7

-1 8 0 1 2 3 Wavelength (/xm)

SAO 158350 -1 0 -1 1 -12

-1 6

-1 9 -2 0 0 1 2 3 Wavelength (/xm)

Figure 3.6 continued.

I l l SAO 179615 -1 0

-1 1

-12

-1 3

-1 4

-1 8

-1 9 01 2 3 Wavelength (/im)

SAO 183956 -1 0

- 1 1

-12

-1 3

-1 4

-1 8

-1 9 0 1 2 3 Wavelength (/im)

Figure 3.6 continued.

112 SAO 183086 -1 1

-1 2

-1 3

-1 9

-2 0 G 1 2 3 Wavelength (/xm)

SAO 184124 -1 0

- 1 1 -12

-1 6

-1 9 -2 0 0 1 2 3 Wavelength (/xm)

Figure 3.6 continued.

113 SAO 186777

I 'a

0 1 2 3 Wavelength (/im)

SAO 206462 -1 0

- 1 1 -12 -1 3

-1 5 -1 6

-1 9 -2 0 0 1 2 3 Wavelength (/xm)

Figure 3.6 continued.

114 SAO 208591

-1 0 -1 1 -12 —13 ,—14

-1 8 -1 9 -2 0 G 1 2 3 Wavelength (/xm)

SAO 226057 -1 0

- 1 1 -1 2

-1 6

-1 9 -2 0 0 1 2 3 Wavelength (/xm)

Figure 3.6 continued.

115 HR 890

i I

0 1 2 3 Wavelength (/xm)

HR 2522

zl a

0 1 2 3 Wavelength (/xm)

Figure 3.6 continued.

116 51 Oph

I !a

10° 10 2 Wavelength (/xm)

Figure 3.6 continued.

117 3.8 Tabulated Data

The observational data, including values from the literature, are summarised in Ta­ bles 3.20-3.22. Sources of data in Tables 3.20, 3.21 and 3.22:

A = This paper

(1) Henry Draper Catalogue

(2)-(4) Michigan Spectral Catalog, vols 2-4

(5) SIMBAD database

(6 ) = Lesh, J.R., 1968. ApJS 17,371 (7) = Murphy, R.E., 1969. AJ 74, 1082

( 8 ) = Upgren, A.R., Grossenbacher, R., Penhallow, W.S., 1972. AJ 77, 486

(9) = van der Veen, W.E.C.J., Waters, L.B.F.M., Trams, N.R., Matthews H.E., 1994.

A&A 285, 551 (10) = Welty, D.E., Hobbs, L.M., Blitz, L., Penprase, B.E., 1989. ApJ 346, 232

(11) = Andrillat, Y., Jaschek M., Jaschek, C., 1990. A&A 233, 474

(12) = Cowley A. Cowley C., Jaschek M., Jaschek C., 1969. AJ 74, 375 (13) = Johnson, H.L., Mitchell, R.I., Iriarte, B., Wisniewski, W.Z., 1966. Comm. Lunar Planetary Lab. 63, 99

(14) = Crawford, D.L., Barnes, J.V., Colson, J.C., 1971. AJ 76, 1058 (15) = Gregorio-Hetem, J., Lepine, J.R.D., Quast, G.R., Torres, C.A.O., & de la Reza, R.

1992, AJ, 103, 449

(16) = van der Veen, W.E.C.J., Habing, H.J., Geballe, T.R., 1989. A&A 226, 108

(17) = Lindroos, K.P., 1985. A&AS 51,161

(18) = Mermilliod, J.P., 1986. UBV Catalogue, CDS.

(19) = Garcia-Lario, P., Manchado, A., Pottzisch, S R., Suso, J., Oiling, R., 1990. A&AS

82, 497

(20) = Coulson, I.M., Walther, D M., 1995. MNRAS, in press.

(21) = Waters, L.B.F.M., Coté, J., Geballe, T., 1988. A&A 203, 348

(22) = Zuckerman, B., For veille. T., Kastner, J.H., 1995. Nature 373, 494

(23) = Dunkin, S.K., 1995. private communication

118 Table 3.20: Summary of observational data: Optical Name HDSAO Sp. Ref U B V R I Ref

type (mag)

49 Cet 9672 147886 A IV (4) 5.78 5.70 5.61 - - ( 1 2 )

35 Ari 16908 75532 B3V (6 ) 3.91 4.54 4.67 4.69 4.82 (13)

HR 890 18537 23763 B7V (7) 4.76 5.18 5.23 - - (14)

23362 111388 K 2 ( 1 ) 1 1 .6 6 9.53 7.85 6.98 6.07 A

23680 93601 G5 ( 1 ) - 9.4 8 . 6 -- (5)

34282 131926 AO ( 1 ) 10.16 10.05 9.88 9.79 9.68 A

34700 112630 GOV (22) - 9.6 8 .8 - - (5)

35187 77144 A2/3IV/V (22) 8 .1 1 8.08 7.80 7.62 7.41 A

HR 2522 49662 151962 B7IV (4) 4.78 5.30 5.40 - - ( 6 )

98800 179815 K5V ( 8 ) 11.26 10.14 8.89 8 . 1 2 7.38 (15) G1 471.2 109085 157345 F2V (4) 4.71 4.69 4.32 3.94 3.76 (13)

123160 158350 K5 ( 1 ) 1 2 . 2 0 1 0 . 1 2 8.62 7.81 6.94 A G5 (23)

135344 206462 F 8 V (2 0 ) 9.14 9.14 8.63 8.16 7.83 ( 2 0 )

139614 226057 A7V (2 ) Wal. 8.50 8.27 8.14 7.99 (16)

141569 140789 AOVe ( 1 1 ) uvby 6.9 7.13 -- (17)

142666 183956 A 8 V (4) 9.35 9.20 8.65 8.36 7.98 A - 142764 140845 K5 ( 1 ) - 10.7 9.3 - (5)

143006 183986 G5V (9) 11.30 1 1 .0 2 10.18 9.73 9.22 A 144432 184124 A 9/F0V (3) 8.65 8.50 8.17 7.93 7.71 A

HR 6398 155826 208591 GOV (3) 6.61 6.54 5.96 -- (18)

51 Oph 158643 185470 AOV (4) 4.75 4.81 4.81 4.74 4.72 (13)

169142 186777 B9V (3)^ Wal. 8.42 8.13 7.96 7.75 (16) A5 (23)

HR 8799 218396 91022 A5V ( 1 0 ) 6 .2 1 6.25 5.99 - - ( 1 2 )

233517 26804 K2 ( 1 ) 12.39 1 1 . 0 2 9.67 9.02 8.35 A

119 Table 3.21: Summary of observational data: Near-IR and CGS3 HD SAO J H K L V M Ref CGS3 Start of

(mag) 1 0 /im 2 0 /im excess

9672 147886 5.54 5.51 5.51 5.53 - 5.51 A - - 1 2

16908 75532 4.91 4.94 5.00 5.05 - 5.06 A - - 60

18537 23763 5.37 5.38 5.41 5.43 - 5.46 A - - 1 2

23362 111388 4.89 4.05 3.85 3.72 - 3.98 A - - 25?

23680 93601 6 . 0 1 5.37 5.24 5.16 - 5.29 A - - 25

34282 131926 9.02 8 . 2 0 7.44 6.53 -- A - - J

34700 112630 7.6: 7.8: 7.5: 7.0: -- A - - 1 2

35187 77144 7.07 6.62 6.09 5.33 5.24 5.00 A - H

49662 151962 5.7: 5.5: 5.6: 5.8: - - A - - 1 2

98800 179815 6.44 5.82 5.66 -- 5.5 (19) y 1 2

109085 157345 3.69 3.57 3.54 3.51 3.55 3.59 A - - 1 2

123160 158350 5.86 5.07 4.87 4.73 4.76 5.33 A V - 25

135344 206462 7.31 6.67 5.97 - 4.89 4.54 (2 0 ) VV H? 139614 226057 7.71 7.32 6.74 5.72 - 5.89 (16) -- H

141569 140789 6.87 6.84 6.80 6.69 6.67 6.50 A VV L

142666 183956 7.32 6.70 6 . 0 2 5.04 4.95 4.85 A VV J

142764 140845 6.41 5.58 5.35 5.20 5.21 5.49 A V - 1 0 0

143006 183986 8.35 7.65 7.06 6.14 6.06 6.18 A V - J

144432 184124 7.16 6.57 5.95 5.00 4.91 4.52 A VV H

155826 208591 4.93 4.64 4.58 4.55 4.59 4.52 A VV 60?

158643 185470 4.61 4.53 4.31 3.46 - 2.60 (2 1 ) V V K

169142 186777 7.44 7.05 6.61 5.79 5.73 5.49 A y V H 218396 91022 5.46 5.30 5.28 5.28 - 5.26 A - - 25

233517 26804 7.38 6.80 6 . 6 6 6 . 6 6 6.63 6.62 A y 1 2

120 Table 3.22: Summary of observational data: IRAS and sub-mm

HD SAO Fi2 F25 Feo ^ 1 0 0 0.45mm 0.8mm 1.1mm 1.3mm 2.0mm

(Jy) (Jy) (m Jy)

9672 147886 0.34 0.38 2 . 0 2 1 . 8 8 — — - - -

16908 75532 0.41 <0.41 0.36: <1.87 - 16613 --

18537 23763 0.53 0 .6 8 : 3.12: 14.08 - <34 --

23362 111388 1.38 0.44 0.72 2 . 8 8 — — - - -

23680 93601 0.43 0.19 2.08 6 . 0 2 - 33615 --

34282 131926 0.70 1.63 10.80 10.72 1.3±0.3 409±27 183±17 - -

34700 112630 0.60 4.42 14.06 9.38 - 39613 --

35187 77144 5.39 11.50 7.95 5.00 - 115±22 8 0 6 1 0 - -

49662 151962 0.43 1.62 4.60 5.68 - <42 --

98800 179815 1.98 9.28 7.28 4.46 <3.6 111±12 6366 1163 - 109085 157345 2.24 0.77 0.31 0.80 --- -

123160 158350 0.62 0.37 3.11 4.41 <41 <16 --

135344 206462 1.59 6.71 25.61 25.69 3.8±1.521 570621 209±14 142±19 <76

139614 226057 4.11 18.14 19.30 13.94 - 608627 272613 242615 8 0 6 1 6

141569 140789 0.55 1.87 5.54 3.48 - <36 --

142666 183956 8.57 1 1 . 2 1 7.23 5.46 1.0960.06® 351623 180612 12769 <63

142764 140845 0.37 0.11 <0.44 3.52 - <45 --

143006 183986 0 . 8 6 3.16 6.57 4.82 1.1460.08® 233625 114614 6468 <132

144432 184124 7.53 9.36 5.77 3.29 - 103634 69610 - -

155826 208591 3.67 5.35 8.63 <260 - < 2 2 0 <80 - -

158643 185470 15.67 10.19 1.06 <5.97 - 26614 --

169142 186777 2.95 18.43 29.57 23.42 - 554634 287613 197615 70619

218396 91022 0.40 0.24 0.41 <2.59 - 2 8 6 1 1 --

233517 26804 0.50 3.60 7.60 5.10 - <36 --

121 C hapter 4

Radiative Transfer Modelling of Vega-Excess Systems

4.1 The Model

The modelling code used in this work for Vega-excess systems was a modification of the code used by Skinner, Barlow & Justtanont (1992) for SAO 179815. This in turn was based on the model of Skinner Sz Whitmore (1987) for the (spherical) dust shell around a Ori, and treated the dust disc as being optically thin. The main differences between the present model and that used by Skinner, Barlow & Justtanont (1992) are the use of Kurucz (1991) model atmospheres to represent the central stars, the facility to have multiple dust components (e.g. silicate and amorphous carbon), and the division of the disc into logarithmically-spaced elements.

4.2 The Central Stars

The central stars of Vega-excess systems were modelled using Kurucz (1991) model atmo­ spheres, as stored on the s t a r l i n k system. These models, for a wide range of effective temperatures and surface gravities, take much more complete account of line blanketing than did previous model atmospheres. It is important to use model atmospheres rather than blackbody models, since blackbodies do not accurately represent the photospheric emission from a star, as illustrated in Figure 4.1.

Model atmospheres thus give a better fit to optical photometry and, importantly, more

122 10®

10 8

10®

I 10®

.10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65 .70 Wavelength (/xm)

Figure 4.1: Comparison of the spectra of Kurucz (1991) model atmospheres with blackbod­ ies of the same effective temperature. Upper curves: Teff= 10500K, log g = 4.0, equivalent to a B9V star. Lower curves: Teff= 4250, log g = 4.5, equivalent to a K5V star.

123 realistically represent the stellar radiation field which is heating the grains.

The Kurucz models are specified by two parameters - the effective temperature, Teff, and the surface gravity, g. The choice of model atmosphere was determined by the observed spectral type of the star. Values of Teff and log g are tabulated by, e.g. Schmidt-Kaler

(1982) for various spectral types. Having determined the most suitable model atmosphere, only a further two parameters are required to describe the star — its radius and distance from the Earth. Stellar radii were derived from the effective temperature and stellar luminosity, both tabulated by Schmidt-Kaler (1982), using the simple relation between these three variables:

L^, = 4nRlaT^ (4.1)

The distances to the stars were then found by fitting the model atmosphere fluxes to the dereddened optical photometry.

4.3 The Grains

The dust grain population can be completely described by the the grain size distribution and the optical properties of the grains, which in turn depend on their size and composition. Several different species of dust could be included, each having identical spatial and grain-size distributions. The relative contribution of each species to the total grain pop­ ulation could be varied. The total mass of the disc was simply the sum of the masses of each species.

4.3.1 Size Distribution

AU grains were considered to be spherical, and the form of size distribution chosen was a single power law, i.e.

A(fl) CX û ^5 (^min ^ ^ — ® m a x ) (4.2) where A(a), the number of grains of radius a, is governed by three parameters: the power-law index 7 , and the minimum and maximum grain radii Omin &nd Omax-

Power-law grain size distributions have been predicted for asteroidal fragments and micrometeoroids by Dohnanyi (1969) and for grains in molecular clouds and in the outflows from red giant stars by Biermann and Harwit (1980). Power-law size distributions have been found to fit asteroids in the present-day Solar System (e.g. Safronov & Ruskol

124 1994), the particles in Saturn’s rings (e.g. Showalter & Nicholson 1990), and interstellar extinction curves (Mathis, Rumpl & Nordsieck 1977), and are a natural product of grain- grain collisions.

For these models, a discrete set of sizes was used, rather than the continuous distri­ bution which is likely to occur in a real dust disc. Since N{a) refers to the number of grains of a single size a, rather than the number in some size range (a, a -f da), it would not necessarily be correct to equate the power-law index 7 with the analogous index for a continuous distribution, i.e. n(a) oc a~°‘da. The exact relation between 7 and a de­ pends on the particular spacing used for the sizes in the discrete case. For the dust-disc modelling, the spacing increased linearly with size, so the number of grains per unit size interval varied as

n(a) (X (4.3) i.e. a = 7 + 1 . For example, the Mathis, Rumpl & Nordsieck, 1977 (MRN) size distribution n (a)

/•O m a x 4 o Mito t / -wa'^pgn(a) da (4.4) donriin /■Omax = (const) X / a a~°‘ da (4.5)

= ^ (4 6)

The total mass is therefore determined by the maximum grain size for distributions with a < 4 (or 7 < 3 in terms of the modelling parameters), as is believed to be the case for most Solar System and interstellar distributions. Omax is therefore an important parameter for Vega-excess systems.

A power-law size distribution can also be expressed as a power-law mass distribution:

n„i(m ) (X m~^dm (4.7) where nm{fn)dm is the number of grains with masses between m and m-\-dm. For spherical grains of density p, a size interval da corresponds to a mass interval dm = A'KO^pda. The corresponding size distribution index (a) for a power-law mass distribution with index q

125 is therefore

Q = 3g — 2 (4.8) for spherical grains.

4.3.2 Radiative Equilibrium and Dust Temperature

The temperature of each grain as a function of its size, composition and distance from the

central star was calculated by applying the condition of radiative equilibrium:

Em = Eout (4.9)

where

^inEi„ —= / F.(A, T)dX (4.10)

and

£out =j 4wa^Q,uWBx{T)dX (4.11)

where F* is the flux density emitted by the star, a is the grain radius, Qabs(<^) is the absorption efficiency of the grain at wavelength A ,F is the distance from the grain to the star, and E* is the stellar radius. Computationally the solution to this equation was found by using an iterative tech­

nique. An initial value of temperature was assigned to each grain. For the purposes of this

model an arbitrary temperature distribution was used such that Td{R) oc where the

dust temperature, Tj, is a function of the distance R of the grain from the central star,

but is independent of grain size and composition.

The energy absorbed and the energy emitted by each grain was then calculated, (i.e.

the two sides of the radiative ‘balance’), and a comparison made between the two. If

the energy absorbed, Fin, was greater than the energy emitted. Fout» the temperature of

the grain was increased by an amount dT, which was initially one-tenth of the assumed

dust temperature. If Fjn was less than Fout» the dust temperature was reduced by dT.

The radiative balance was then recalculated with the new temperature. These steps were

repeated iteratively to determine the equilibrium temperature. In order that the computed

temperature can reach the equilibrium value, the size of dT to be used in the subsequent

iteration was reduced by a factor of two whenever the sign of (Fin — Fout) changes. The

iterative process continues until the absorbed and emitted energies agree to within 1 %, or

1 0 0 iterations have been performed,

126 The dependence of the equilibrium temperature on distance from the star, grain size and composition can be understood from Equations 4.9-4.11. The dependence on R is straightforward — the amount of starlight absorbed by a grain is diluted by a factor of

R} as the distance R increases. The effects of grain size and composition are less explicit, but enter via their effects on the absorption efficiency, Qabs* Generally, smaller grains are hotter than their larger counterparts, because they are less efficient in absorbing (and therefore emitting) radiation at infrared wavelengths — the spectral region where they radiate away energy — compared with UV-visible wavelengths, where most of the energy from the star is radiated (see Figure 4.2).

In a similar fashion, amorphous carbon grains of a given size are usually found to be hotter than corresponding silicate grains, due to the shape of their Qaha curve. The abso­ lute values ofQahs &re less important for determining the equilibrium grain temperature than the relative magnitude of Qe,hs at the wavelengths where absorption and emission primarily take place.

4.3.3 Grain Optical Properties

The optical behaviour of a dust particle can adequately be described by three quantities: its absorption cross-section. Cabs? its scattering cross-section Csca. and the ‘asymmetry parameter’, g, which is the average cosine of the scattering angle, and describes the degree

of isotropy of the scattering. All three parameters are functions of wavelength for a given

particle, and also depend on the grain size and composition.

Absorption and scattering efficiencies (Qabs, Qsca) can be defined 2is the ratios of the absorption and scattering cross-sections to the geometrical cross section, i.e. for spherical

grains,

and

Qsca = (4.13)

Further parameters are needed to describe the polarization behaviour of the particle;

since polarization has been neglected in the modelling, no further mention shall be made

of them.

For a spherical grain, the parameters Qabs? Qsca and g can be calculated using Mie

theory, given the grain radius (a) and the real and imaginary components of the complex

127 refractive index, m = n ik of the bulk material, over the wavelength range of interest

( the ‘optical constants’). Optical constants can alternatively be specified in terms of the complex dielectric function € = €i -}-t€2 , which is related to the complex refractive index by the equations cj = and €2 = 2nk. Detailed treatment of Mie theory can be found in e.g. Bohren & Huffman (1983). Mie theory calculations were performed for the present work using a code similar to that of Bohren & Huffman (1983). The optical constants were calculated for a grid of approximately 70 wavelengths, ranging from the ultraviolet to the millimetre-wave region.

The absorption and scattering cross-sections are expressed under Mie theory in terms of infinite series which, in practice, must be truncated at some point to allow calculation in a finite time. The number of terms required to retain sufficient accuracy increases with the ‘size parameter’ (a/X). The very large ‘grains’ (a ~lcm) considered in the dust-disc models gave rise to large values of the size parameter, especially when attempting to calculate their ultraviolet properties. This in turn required more terms to be calculated

(~ 300,000) than was feasible on the VAX computers. For these situations, the code was modified to use relations derived from geometrical optics which are valid for a A, rather than Mie theory. For instance, Qsca Is calculated using the reflection coefficients of bulk material, integrated over the range of angles of incidence. Two grain materials were used in the dust-disc modelling. The oxygen-rich component of the dust was modelled using the optical constants for ‘astronomical silicate’ compiled by Draine & Lee (1984). Several other sources of optical constants for disordered silicates

(the type likely to be found in interstellar and circumstellar environments) are available, e.g. those of Kratschmer & Huffman (1978) and Day (1979). All the models presented in this thesis were calculated using Draine & Lee (1984) silicates, since, as discussed by

Skinner et al. (1995), other sets of optical constants tend to give very similar dust masses and related parameters to those derived using the Draine & Lee constants, but are not as well constructed at visible wavelengths as the Draine & Lee synthesis.

To model the carbonaceous dust component, the optical constants for amorphous car­ bon compiled from a number of sources by Hoare (1990) were used.

At long wavelengths where optical constants are not available, the efficiencies were extrapolated, and required to fall off as A“^, as expected for materials with an amorphous structure (e.g. Whittet 1988).

128 >N o c: i

G o -3 CL -4. o (/) _Q < -5

-6

W avcleiiiilh (/-/m)

Figure 4.2: Results of Mie theory calculations for silicate grains. Curves labelled 1, grain radius = 0.005/im; 2, radius = 0.01/zm; 3, radius = 0.05/im; 4, radius = 0.1/zm; 5, radius

= 0.5/im; 6 , radius = 1.0/im; 7, radius = 5.0/zm; 8 , radius = 10/zm; 9, radius = 50/xm; 10, radius = 100/xm; 11, radius = 500^m; 12, radius = 1.0mm; 13, radius = 5.0mm 14, radius = 10mm; 15, radius =50mm.

Sample results of Mie theory calculations for Draine & Lee silicate are presented in

Figure 4.2. The 9.7-/zm and 18-//m features are clearly visible in the Qabs curves for silicate grains of radii ^ 1/xm, but disappear for larger sizes. The increase in turnover wavelength with grain size can clearly be seen, aa can the approximately ‘grey’ behaviour at wavelengths shortward of the turnover point, (where At 27ra; Chapter 3) and the fall-off of emissivity with wavelength longward of At-

Amorphous carbon grains (Figure 4.3) show the same general properties as silicate grains, but are featureless in the infrared.

The largest grains are probably agglomerations of smaller particles, rather than ho­ mogeneous spheres, so the Mie theory and geometrical optics of homogeneous spheres are unbkely to be strictly applicable for such grains. However, they provide a useful first approximation to the optical properties of large grains.

129 -1

& g - 2 o S - 3

e* o M <

-6

- 7

W avelength

Figure 4.3: Results of Mie theory calculations for amorphous carbon grains. Same sizes as for silicate grains in previous Figure

130 4.4 Spatial Distribution of the Dust

The dust distribution is treated as optically thin, so the grains are heated only by the star, not by other grains. There is also assumed to be no shadowing of starlight by grains. In consequence, the temperature of a grain (of a given size and composition) depends solely on its distance from the star, not on position with respect to the disc midplane or similar constructions.

The dust density distribution was modelled as a power law, and so can be described by four param eters — the inner and outer radii (Æin, R o u t) of the disc, the power-law index,

/?, and the total mass of the disc, Mdisc- The definition of (3 is such that the number of grains lying between R and R-\- dR is given by

n(R) « R-l^+^dR (4.14) for Rin < R < Rout- This relation is general, and independent of the actual geometry of the distribution. In the case of a flat disc with constant (finite) thickness, the number density (number of grains per unit volume) therefore varies as R ~^, whereas in the case of a ‘wedge’ disc (one where the disc thickness increases linearly with distance from the star), the number density varies as R~^~^. For both the flat and wedge disc configurations, the surface mass density (i.e. the mass per unit area in a line of sight perpendicular to the disc plane) varies as S(/ 2 ) a R ~^.

The total mass in the disc can be obtained by integrating over all annular elements.

For values of j3 < 2, contributions from the outer portions of the disc dominate, so the total mass has a more sensitive dependence on Rout than Æi„. For (3 > 2, R\u is more important in determining the total mass.

For computational purposes, the disc is divided into 200 concentric annuli, whose widths (SR) increase logarithmically with radius {R). This is in order th a t the disc is

‘sampled’ more frequently close to the central star, where the dust temperatures are likely to vary more rapidly as a function of distance.

The model can simulate resolution of the disc by the telescope(s) used to obtain the observations. This is done by altering the instrumental beam-size used in the model. A circular beam is assumed, with a top-hat profile — all flux within the beam is included in the model output, whilst aU flux outside the beam is ignored. In practice, the beam-size was usually set to 20 arcsec diameter, to provide an approximate match to the JCMT

131 beam. In most cases, it was found that there was negligible model flux in the IRAS wavelength bands outside this beamsize. Re-running a model with the beamsize decreased to 5 . 5 arcsec, but all other parameters left unchanged made it possible to determine how much, if any, mid-IR flux was being excluded by the smaller CGS3 beam.

4.5 Model Output

After the temperature of the dust had been calculated as a function of position, grain size and composition, the emission from the dust could be computed. This provided the basis for the model output.

There were two main forms of output from the model. The first was a spectral energy distribution, produced by summing the emission from all the grains within the model beam and the contribution from the stellar photosphere. This is what is plotted in Figures 4.4-

4.9, and in Chapter 6 .

The other main form of output was a set of simulated IRAS fluxes at 1 2 , 25, 60

and 100 /xm, and JCMT 0.8-mm and 1.1-mm fluxes. The IRAS fluxes were derived by

convolving the model spectral energy distribution with the IRAS response profile, in a fashion analogous to that described in Section 3.4.1 for deriving IRAS colour-correction

factors from CGS3 1 0 -/xm spectra. The model IRAS fluxes are given in Janskys and

are not colour-corrected, which makes them suitable for immediate comparison with data

from the IRAS Point Source Catalog. The fluxes are accompanied by the derived colour-

correction factors at the four IRAS wavelengths. The model JCMT fluxes are simply the

model fluxes at 0.8 and 1 . 1 mm, expressed in milliJanskys (mJy).

The modelling code also provides an option to produce a map of the emission at a

wavelength selected by the user. This has yet to be put to much use, since at present,

only one of the sources in the sample (SAG 26804) has been imaged in the mid-infrared

(Skinner et al. 1995).

4.6 Effects of the Input Parameters

The effects of the various model input parameters are relatively easy to predict.

Increasing the value of 7 ‘steepens’ the power-law size distribution thereby increasing

the proportion of small grains relative to larger ones in the distribution. As Figures 4.2 and

132 4.3 show, smaller grains have a shorter ‘turnover’ wavelength, and in the case of silicate grains, more pronounced 9.7- and 18-;im emission features. Increasing 7 would therefore increase the contrast of any observed silicate features, while decreasing the relative amount of flux at longer wavelengths (see Figure 4.4).

From Figure 4.4, one can see that when 7 = 3.0, the contrast in the silicate feature is very large indeed — the flux at 9.7 /xm is increased by more than an order of magnitude compared with the estimated continuum flux at the same wavelength. For 7 = 1.0 , the excess emission is completely smooth and featureless — the ‘grey’ emissivity of grains larger than about 10 /xm (see Figure 4.2) dominates.

At long wavelengths, the effects of having a greater proportion of large grains again become apparent: there are more grains whose emissivity has not yet ‘turned over’ at the wavelengths shown, so the long-wavelength flux is greatest for 7 = 1 and least for

7 = 3. Also, since the area of a grain of radius ag varies as a^, but the volume (and hence the mass) varies as a^, smaller grains at a given temperature give rise to more emission per unit mass at wavelengths shorter than the turnover wavelength than do larger grains.

Increasing the value of 7 thus can be expected to decrease the dust mass required to produce sufficient flux at 12 /xm and 25 /xm.

Altering the value of /3 varies the density gradient in the disc and therefore varies the proportion of dust in the inner, warmer regions of the disc. This causes a change in the 12-/xm and 25-/xm fluxes relative to those at longer wavelengths, as illustrated in

Figure 4.5. The effect on the model spectrum of increasing — and thereby bringing relatively more material into the inner parts of the disc — is that the average temperature of the grain distribution goes up, and so the peak of the dust emission moves towards shorter wavelengths, without noticeably affecting the contrast of any silicate emission features (see Figure 4.5). The relative peak fluxes of the 9.7-/xm and 18-/xm features are, however, affected by the slope of the underlying emission in that region. Since hotter grains emit more at all wavelengths than cooler ones, the overall flux for a given dust mass increases with an increase in 13.

Since the hottest grains are those found closest to the star, increasing the inner radius of the disc has the effect of decreasing the maximum temperature attained by the grains; this reduces the flux at shorter wavelengths, while making little difference for wavelengths longer than ~ 60 /xm. (See Figure 4.6). By altering R\n, but re-normalising the 60 /xm

133 X

r— <

Wavelength

Figure 4.4; Effects of varying the size distribution index, 7 . Dashed line: 7=1, solid line:

7 = 2, dotted line: 7 = 3. Other parameters held constant. In Figures 4.4-4.9, parameters are held at the following values unless otherwise stated: 7 = 2 , /? = 2 , R\n = 3 AU,

Rout ~ 1500 AU, Urnin — 50 Â, Umax ~ 100 //m .

The total dust mass was varied to normalise the model fluxes at 60 /xm.

134 13X r H

Wavelength

Figure 4.5: Effects of varying the density power-law index, (3. Dashed line: /? = 1, solid line: (3 = 2, dotted line: P = 3

135 /\

X p

Wavelength

Figure 4.6: Effects of varying the disc inner radius. Dashed line: R\n = 1.5 AU, solid line:

Ain = 3. AU, dotted line: Ain = 10 AU

136 flux by changing the mass of dust present, one is effectively adding or removing dust from the inner edge of the disc, without greatly changing the amount of dust in the outer parts of the disc. The result of this is to alter the flux level in the shorter-wavelength parts of the excess energy distribution, where emission from the hottest grains reaches its peak, while slightly decreasing the flux long wards of about 60 /xm.

Conversely, increasing the outer radius of the disc effectively adds grains at the outer edge of the system, where the dust is coolest. This increases the flux at the very longest wavelengths, where the emission from cold grains peaks, while having little effect on the flux at wavelengths shorter than about 100 /xm (See Figure 4.7). Since the most distant grains are only weakly illuminated by the star, a large change in outer radius, and conse­ quently in the total mass of the disc, produces only a relatively minor change in the flux, even at the longest wavelengths. In practice, the disc outer radius was normally fixed so as to subtend an angle of 10 arcsec as seen from the Earth, to match the 20 arcsec diameter beam that was usually assumed.

Turning to the mid-infrared, increasing the minimum grain radius has the effect of decreasing the contrast in the silicate features, since small grains have a greater contrast in their absorption efficiency (see Figure 4.2). Since all plausible models have 7 positive, i.e. more small grains than large ones, a change in amin wiU have a noticeable effect, especially for grain sizes of between 1 and 5 /xm, where the silicate feature becomes ‘washed out’

(Figures 4.2,4.8 ). Small grains have very low emissivities at long wavelengths, so increasing the minimum grain size makes very little difference at long wavelengths (Figure4.8).

Altering the maximum grain radius affects the wavelength by which the emission from aU the grains has turned over. This affects the flux and spectral index at long wavelengths

(See Figure 4.9). It is worth comparing the effects of the outer radius of the disc and of the maximum grain size, both of which are greatest at long wavelengths. As we have already discussed, the amount of radiation emitted by a grain at a given wavelength is proportional to the product of the black-body emission and the grain absorption efficiency

(or emissivity), both measured at the wavelength of interest.

By varying the disc outer radius, one is changing the temperature of the coldest grains,

and hence the wavelength by which all of the grains are in the Rayleigh-Jeans region of the black-body curve. On the other hand, by altering the maximum grain size, one changes

the wavelength by which aU of the grains have left the ‘grey’ part of their emissivity curves.

137 X 0 r—Ik

Wavelength

Figure 4.7: Effects of varying the disc outer radius. Dashed line: Rout = 38 AU, solid line:

Rout = 1500 AU, dotted line: Rout = 15000 AU.

138 X rH k

1

Wavelength

Figure 4.8: Effects of varying the minimum grain size. Solid line: ümin = 50 Â, dotted line: «min = 1 dashed line: a^in = 5 fim

139 -12

X p f-H u.

-17

Wavelength

Figure 4,9: Effects of varying the maximum grain size. Dotted line: a^ax = 50 //m, solid line: a^ax = 100 //m, dashed line: Omax = 50 mm

140 and are radiating with an emissivity which varies as oc or A“^. In Figure 4.7, we see that from 60 ^m onwards, the curves diverge slowly, but by about 700 /xm, they are parallel to one another, indicating that more or less all of the grains’ emission is in the

Rayleigh-Jeans domain. In Figure 4.9, however, the curves diverge from one another at different wavelengths, depending on the turnover wavelength of the largest grains. The dotted curve is for a maximum grain radius of 50mm, so turnover is not reached in the wavelength region plotted.

The practical implication of this in terms of modelling observational data is that at least two photometric points are required longwards of 1 0 0 /xm to constrain these two disc parameters (Rout and Omax)- If, for instance, all one had were the IRAS 1 0 0 -/xm flux, and the flux at one submiUimetre wavelength, a range of models could be constructed that fitted the data points well, with a range of different values of these parameters. The models with a large outer radius, which tends to give large long-wavelength fluxes, would have a small maximum grain size — hence a short turnover wavelength and less long-wavelength flux — to compensate, and vice versa.

4.7 Modus Operand!

Faced with the daunting task of exploring a multi dimensional parameter space for each

Vega-excess system being modelled, the normal sequence of operations was to construct a grid of models, varying 7 and /5, after having run a few initial models to determine the distance to the star. Typically the values 1, 2, and 3 might be chosen for these two parameters.

For each point on this grid, the best-fitting values of the disc inner radius, Rin, and the disc mass, M j, were found. The disc mass was set to normalise the model output flux to the observed IRAS flux at (typically) 25 or 60 /xm, and the value of Ri„ which gave the best fit to the observational data short wards of the normalisation point was found. Upwards of ten executions of the model could be required to ascertain the best combination of R\n and Md for a given pair of ( 7 , 0 ) values.

Having sampled an area of parameter space in this manner, the best-fitting model(s) can be selected, and further refinements made. These might include varying the disc outer radius or the maximum grain size, or producing models with intermediate values of 7 and

141 to those in the initial grid of models. The initially-envisaged grid was occasionally left incomplete. For instance, if models with 7 = 2,/) = 1 and 7 = 1,/? = 2 were both found to underestimate the long-wavelength flux, it would not be necessary to calculate a model w ith 7 = 2 ,^ = 2 , as such a model would also underestimate the long-wavelength flux.

It is also possible to change the dust composition, for instance from purely silicate dust to a mixture of silicate and amorphous carbon grains. If this is done, an entirely new grid of models with the new composition must be produced, since the best-fitting values of 7 and for the new composition wiU not necessarily be the same as for the previous

composition.

142 C hapter 5

Small Grains around Vega-excess Stars

5.1 Reasons for Considering Small Grains

As mentioned in Chapters 3 and 4, several Vega-excess stars display excess emission in the near-infrared region. Simple inspection of the spectral energy distributions of SAG 183986 and SAG 206462, for example (Figure 3.6) is enough to make it clear that this excess is not merely the short-wavelength extension of the excess seen at mid- and far-infrared and millimetre regions, but rather that there is a double-peaked structure to the overall excess energy distribution.

This is confirmed by radiative transfer modelling (Chapter 4), which showed that no single spatial distribution of grains could simultaneously account for the excess in both the near-IR and longer-wavelength regions.

This implies that there is more than one distinct spatial distribution of dust, or that there is more than one type of grain behaviour taking place (or possibly both). The first scenario, that there are two (or more) populations of grains, aU in thermal equilibrium, immediately runs into the problem that the dust temperatures required to produce a near-infrared excess, approximately 1500 K, are higher than the sublimation temperature of circumstellar dust (approx. 1000 K). In other words, it would be impossible for dust to survive at the required temperatures for an extended period of time. Even if the evaporating dust was continuously being replenished, for instance by dust falling in from the cool outer regions of the disc, it would still be destroyed before reaching a temperature

143 oflSOOIC.

It is therefore necessary to consider the second possibility — that there is another

physical process at work to produce the observed near-IR excesses.

5.2 The Small Grain Hypothesis

One such process was suggested by the work of Greenberg (1968), who pointed out that

circumstances could arise whereby the energy gained by a small grain upon absorption of

a single photon could be comparable to the energy content of the grain. The grain would

therefore not be in thermal equilibrium, but would undergo temperature fluctuations.

This idea has been studied by a number of authors, e.g. Duley (1973), Purcell (1976),

Draine k Anderson (1985). An important connection between theory and observation

was made when thermally-spiking small grains were proposed by Sellgren (1984) to explain

observations of reflection nebulae which showed near-IR continuum and UIR-band emission

(Sellgren et al., 1983, 1985). These small grains (radius ~10Â) have a very low heat

capacity, and so can be heated to temperatures of the order of lOOOK by the absorption of

a single UV photon (energy 10 eV). Other possible grain-heating processes considered by Sellgren (1984) included chemical reactions between molecules on the grain surfaces,

collisions with atoms, molecules or other grains, and cosmic ray impacts; however she

found absorption of UV photons to be the most likely heating mechanism.

As indicated in Figure 5.1(a), taken from Léger k d'Hendecourt (1987), the temper­

ature of a small grain in a dilute radiation field is not constant — on absorption of a

photon, the grain more-or-less instantaneously heats up to a high temperature, then grad­

ually cools as it emits radiation (predominantly at infrared wavelengths). This behaviour

is known as thermal spiking. It is a discrete process: altering the intensity of the radia­

tion field changes the interval between spikes, but not the amplitude of the temperature

fluctuations, which is a function of the photon energy and the heat capacity of the grain.

Increasing the size of a grain increases both its heat capacity and its surface area,

so heating events become more frequent, but the amplitude of the temperature spikes is

reduced. Larger surface area implies that there is an increased probability th at another

photon will be absorbed before the grain has radiated away most of the energy from the

previous event, so the grain can spend long periods at elevated temperatures. The grain

144 T(

( a ) 3s

0

T (K) ( b ) 100

Figure 5.1: Temperature evolution of grains in a radiation field: (a) Small grain; (b) Large grain. From Léger & d’Hendecourt (1987)

can then be approximately in thermal equilibrium (Figure 5.1 b), with the amplitude

of the temperature fluctuations negligible compared with the time-averaged value of the temperature.

Small grains have been used to model the dust emission from the hydrogen-poor plan­ etary nebula AbeU 30, and were found to give a good fit to the near-infrared observations

(Borkowski et al., 1994). Natta et al., (1993) found that small grains could be responsible

for a significant fraction of the near-IR excess emission of Herbig Ae/Be stars, but were

unable to obtain better fits to the observed near-IR colours using small-grain models than

with models using only large grains in thermal equilibrium.

5.3 Calculating the Temperature Distribution

The thermal behaviour of a given small grain in a radiation field can be described by its probability distribution function f (T), where P{T)dT is the probability of finding the

grain in the temperature interval (T, T-\-dT). To determine this function, the method of

Guhathakurta h Draine (1989; GD89) was used, whereby the range of possible tempera­

145 tures is divided into a number of discrete bins, and the probability of a grain occupying each bin is calculated.

Upon absorption of a photon of frequency %/, the enthalpy (heat energy) of a grain increases by an amount hu. The change in temperature this produces depends on the heat capacity of the grain material, which is itself a function of temperature. It is therefore more convenient to work in terms of enthalpy rather than directly in terms of temperature, so the starting point of the Guhathakurta & Draine (1989) method is to define a set of temperature bins, and calculate the enthalpy of a grain in each one.

The data used by Guhathakurta & Draine to calculate grain enthalpy as a function of temperature were taken from experimental results using bulk materials. A correction factor was needed since the heat from a photon absorption event is distributed among only the internal vibrational modes of the grain, not the rotational and translational degrees of freedom. For a grain with A. atoms, there are thus SA. — 6 modes among which the energy of the photon can be distributed, whereas bulk enthalpies are derived on the basis of all

3Aa degrees of freedom being available. The bulk enthalpies were therefore multiplied by a factor (3A& — 6)/(3Aa) or (1 — 2/A&). This factor becomes important for small grains (radius a ;$ 5Â) which contain relatively few atoms.

For small carbonaceous grains, an analytic fit to the bulk graphite enthalpy data of Chase et al. (1985) was used:

“ (1 + 6.51 x lO - ^ r + 1.5 X l0-® r2 + 8.3 xlO-'^r2-3) where U^°™(T) is the enthalpy per atom of bulk material.

For silicate grains, suitable enthalpy values were not available, so values of heat capacity per unit volume, C^*(T), were substituted. A fit to experimental results for Si0 2 and obsidian was used for temperatures 10 < T < 300 K (Léger et al. 1985), extrapolated for

T >300 K:

C ^ \T ) = 1.40 X 10^ e r g s c m '^ K~^ (T <50 K)

2.16 X 10^ 3 ergs cm'^ (50 < T <150 K)

4.84 X 10® er g s cm " ^ (150 < T <550 K)

3.41 X 10^ ergs cm"^ (T >500 K)

For a grain of volume V with A& atoms, the enthalpy can be simply derived from the

146 heat capacity, since j.) ^ r c™l( J)iT (5.2) Jo A set of discrete enthalpy bins was defined to cover the temperature range of interest.

For the present work, typically 300 bins were used; experimentation showed that this was sufficient to avoid any problems due to having too coarse a spacing, and gave results that showed negligible differences compared with those obtained using a much larger number of bins (several thousand).

Having a relatively small number of bins is advantageous, giving considerable savings in the amount of computer time required, since the number of calculations performed by the algorithm scales as roughly where N is the number of bins used.

Guhathakurta & Draine found that for ease of computation, it was preferable not to have any grains reach a temperature of zero Kelvin. For this reason, some of the heating was treated as continuous, rather than discrete photon interactions. The heating due to long-wavelength (A > 1 mm) radiation was used for this, since the absorption of a single photon at these wavelengths would make little difference to the overall enthalpy of the grain because an individual mm-wave (or longer wavelength) photon carries very little energy (~ 1 0 "'* of the energy of a visible-light photon).

The minimum temperature a grain could achieve was therefore that at which the rate at which it radiates energy away is equal to the continuous heating rate. This is analogous to the state of radiative equilibrium discussed in Chapter 4, except that the energy input is restricted to long-wavelength radiation (the stellar radiation field for (A > 1 m m ). An iterative scheme similar to that used to find dust equilibrium temperatures (Chapter 4) was therefore used to find the minimum smaU-grain temperature, Tmin? before the enthalpy bins are set up. Typical values of Tmin were found to be of the order of 0.5 K.

The temperature for the highest enthalpy bin, Tmax? was usually set at 2000 K, as it was found that the probability of a grain being above this temperature was usually so small that grains hotter than 2000 K made a negligible contribution to the small-grain emission. Also, grains at temperatures substantially higher than 2000 K will lose energy by sublimation rather than by radiative cooling (GD89; Voit 1991) and so wiU not contribute significantly to the model emission.

In cases where the grains are near thermal equiUbrium (i.e. where multi-photon ab­ sorption is important), grains at low temperatures make a negUgible contribution to the

147 emission, because the probability of a grain being at a low temperature is very small, and because cool grains emit very weakly. In order not to ‘waste’ enthalpy bins on these unim­ portant temperatures, a third temperature parameter, Tbaw was introduced such that the temperature interval Tmin<^< is spanned by only ten equally-spaced enthalpy bins, allowing the bins in the range TbMe<î’<îmax to be more closely spaced (equally-spaced bins were also used in this regime). In such cases, it was also found that the maximum temperature could often be set considerably lower than 2000 K, as the probability of a grain being at ~2000 K was many orders of magnitude lower than the probability of it being near the thermal equilibrium temperature. For cases where single-photon events were important (i.e. the grain was far from ther­

mal equilibrium), and the probability of a grain being at low temperature was high, Tbase

was set so that the bins had a similar spacing for T < Tbase and T > Tbase- Having assigned the temperature to be used for each bin, its enthalpy U could be

calculated, along with its ‘width’, AC/, which for the kth. bin was defined as

A% = /(%+, - %_,) (5.3)

The exceptions to this were the first and last (iVth) bins, the widths of which were

AUi = ^{U2 - Ux) (5.4)

and

= -^{Un - Un -\) (5.5)

Guhathakurta & Draine noted that care is necessary in setting up the enthalpy bins

in order that the steep parts of the probability distribution function be well sampled. For

the work outlined in this Chapter, it was found that judicious choices of Tbase and T^ax

were sufiicient to give a well-sampled distribution (as determined by inspection of the output probability function), despite the somewhat unsophisticated bin spacing that was

employed (i.e. constant temperature intervals).

With the use of a more sophisticated bin spacing, with a concentration of bins at tem­

peratures where the probability distribution function varies rapidly, it would be possible

to achieve the same accuracy with a smaller total number of bins, thus reducing the com­

putational expense of the calculation. However, this improvement in efficiency would be

outweighed by the extra effort required in setting up a ‘customised’ distribution of bins

each time the model was used.

148 To determine the probability distribution function of the grain, it is first necessary to define a set of probabilities as the probability of the grain being in the fcth enthalpy bin at a time t. As its temperature fluctuates, a grain will move among the bins. An ensemble of identical small grains will soon reach a steady state, or dynamical equilibrium, where the number of grains in a particular bin remains constant with time, although each individual grain is making transitions among the bins as it absorbs photons and subsequently cools down. The steady state probabilities, will therefore be independent of time:

= 0 (5.6)

The ‘transition matrix’ A is defined such that the element A/,,- is the probability per unit time of a grain in state (bin) i making a transition to a state / ^ i. The diagonal elements of the matrix are defined to be

Ai.i = Aj,i (5.7)

Considering only transitions to enthalpies within the range Ui < U < Uni the rate of change of the probability P f is then

^Pf = T,A/,iPi-EA,.fPj (5.8)

«96 / N = (5.9) t=l

Three processes control the transitions that a grain can make:

• discrete heating events — absorption of a photon with energy comparable to, or

greater than, the energy content of the grain

• continuous heating by photons of low energy compared with the grain enthalpy

• cooling of the grain by emission of radiation

The grain cooling process is treated as continuous — in the interval between heating events, the grain cools by passing through successively lower-enthalpy states. Discrete cooling events, where a grain can go from one state to a cooler one without passing through

149 all the intermediate states, are not allowed in the Guhathakurta & Draine treatment.

This greatly simplifies the problem of solving the equations to determine the steady-state probabilities (see below). Siebenmorgen et al. (1992) pointed out that for real grains,

discrete cooling events could occur, and claimed that this would give rise to more far-IR

and sub-mm emission than predicted by the Guhathakurta & Draine method.

For the extreme example given by Siebenmorgen et al. of a 5-Â grain situated at a distance of 5 X 10^^ cm (0.16 pc) from a BIV star (Teff = 25000 K), the two methods give very similar results for wavelengths shorter than 40 /zm, but allowing discrete cooling events increases the sub-mm flux by a factor of approximately 20. However, for Vega- excess stars, such a discrepancy would make no appreciable difference to the total sub-mm fluxes, since the equilibrium emission of ‘normal’ large grains is typically 2-3 orders of magnitude stronger than the small-grain emission at sub-mm wavelengths. Since the continuous heating rate is constant and independent of grain temperature, it is convenient to define a net cooling rate as the difference between the cooling rate and the continuous heating rate. This quantity has the dimensions (energy tim e"'), and will be positive for all enthalpy bins, except of course for the lowest bin, where it is zero (from the definition of Thiini see above). Unless indicated otherwise, the cooling rate referred to below is this net cooling rate.

For the kth enthalpy bin, the net cooling rate is given by

cooling continuous heating

- ( ^ ) = 4wa^ J^Qa,hs{X)Bx{T)dX-Tra^c Qabs(A)uAdA (5.10) where Qabs is the absorption efficiency of the grain of radius a, c is the speed of light, and

u\ is the energy density of the radiation field per unit wavelength interval. The continuous

heating term above is equivalent to

T?2 roo Çab.(A)F.(A,7’)dA (5.11)

where F* is the flux density emitted by the star, Æ* is its radius, and R its distance. The

cut-off wavelength, Ac was set as 1 mm. For wavelengths longer than Ac, the emission from

the star can therefore safely be treated as being in the Rayleigh-Jeans domain. Since the

absorption efficiency of grains at wavelengths much larger than the grain size falls off as

A“^, taking /? = 1 (a conservative estimate) leads to a computationally simpler expression

150 for the continuous heating term:

R l ira "AeF*(Ae,T)Q,b.(Ac) (5.12) Æ2 4

An enthalpy state can be populated in two ways: by cooling from the state immediately above it, and by discrete heating from any of the bins below it. The matrix element for cooling into state / from the state immediately above it is

= --d jT i where (dU/dt)f^i is the rate of change of the enthalpy U due to cooling for a grain in the

(/+ l)th bin. This is the probability per unit time that a grain in state / + 1 will cool sufficiently to enter the (lower) state /, and is the reciprocal of the time a cooling grain would take to ‘traverse’ the (/+ l)th bin.

For discrete heating into / from a lower-enthalpy state t, the matrix element is

A/,, = Q«b8(A)7ra^UAAff/^ (5.14) for / ^ iV, where h is the Planck constant, and the photon that would cause the transition has wavelength

Discrete heating terms are only included for wavelengths shorter than the cutoff wavelength for continuous heating, A^. Guhathakurta & Draine also considered discrete heating due to collisions between the grain and other particles, and so included another term in the expression for A/,,-. CoUisional heating was ignored for the present work. Transitions which would give the grain more energy than that of the highest-enthalpy bin are treated as if their final state was the highest bin. The matrix elements corresponding to transitions into the Nth. bin are therefore given by

A^V.i = Qabs(A)7Ta^WAAf/;V^2^ + ^ A'Qabs(A')uA'dA' (5.16) where the first term on the right-hand side of the expression is for transitions into the

Nth bin, and the second term is for transitions which would go beyond the Nth bin.

The wavelength A = he/{Un — U{), as before (since f= N ), while A,- = hcjUi^trunc • The

‘truncation energy’, f7,-,tnmc, is the minimum amount of energy to heat a grain from the initial state i to an enthalpy beyond that of the highest enthalpy bin Un ', and is given by

f^t'.tnmc = Un -h \ ^ U n - Ui (5.17)

151 Similarly, a state can be de populated by cooling into the state immediately below it, and by discrete heating into any of the higher states. Depopulation terms are included only in the diagonal terms of the matrix which, as can be seen from Equation 5.7, is the sum of all terms corresponding to a grain being taken out of a state i, multiplied by (- 1 ).

Therefore

~ ~K U - ^~dt) ~ ^ Qabs('^)wA d\ (5.18) where \ki = hcj{Uk — Ui). For the lowest enthalpy bin, dU\fdt = 0, so cooling is not possible out of this bin, while for the highest enthalpy bin, discrete heating out of the bin is ignored, so

The calculation of the matrix elements described above was modified slightly to lessen any possible inaccuracies due to having widely-spaced bins. The discrete heating terms (Equation 5.14) were modified in the cases where Af// > 0.1{Uf — Ui), i.e. where the final bin width was a significant fraction of the enthalpy change of the grain, since the expression for A/^i assumes that the transition wavelength A is constant over the width AUf of the final enthalpy bin. This also implies that the radiation field energy density, u\, is assumed to be constant over the bin. For a bin of infinitesimal width dU, this would be correct. For a bin of finite width, however, the energy required to promote a grain to the lower-enthalpy limit of the bin would be less than that required to promote the grain to the higher-enthalpy limit of the same bin. There would thus be a range of possible transition wavelengths which could allow a grain to be promoted from a given initial bin to a particular final bin, and the discrete-heating term should be an integral over this wavelength range.

As a first-order correction, the wavelengths Along and Aghort corresponding to transitions from a given initial state, i, to the two limits {U—\AU ) and ((/-|-^A(7) of the final enthalpy bin were calculated, where

Along = hc/[Uf — ^AUf — Ui) (5.20) and

-^short = hc/[Uf + \A U j — Ui) (5.21)

152 Values of the product Qabs(-^)wAA^ which appears in Equation 5.14 were then calculated for

Aghort and Along, as well as the usual value of A, as defined in Equation 5.15. This allowed an approximate integration over the bin width to be performed using the trapezium rule, rather than simply multiplying a single value of (Qabs(A)nAA^) by 6U^ as in Equation 5.15.

A second correction for the effects of large bins was made to the cooling terms. In the

standard GD89 treatment, the effects of any photons of wavelength less than the cutoff

wavelength Ac, but which are insufficiently energetic to raise the grain from one bin to the

next, are ignored. For narrow bins, ACT wiU be small enough that any photon with A < Ac

will have sufficient energy to raise a grain to a higher bin. For wide bins, this need not

be true, and so an extra continuous heating term was added to the A/,y+i terms, which

accounts for photons with wavelength in the range hc/(^AÏ7/^.i) < A < Ac.

5.4 Solving for the Steady State

In the steady state, the probabilities are independent of time, and so Equations 5.8

and 5.9 imply that N = 0 for/= (5.22) 1 = 1 Defining as the vector whose N elements are the probabilities • • •, we can write

= 0 (5.23)

This implies that the set of equations (5.22) are not linearly independent, and so a further

equation is needed to solve for the P^^. This is provided by the fact that the grain must

be in one or other of the bins, so

' £ P f ^ = l (5.24) 1 = 1 can serve as the iVth independent equation.

As mentioned above, the Guhathakurta & Draine scheme does not allow discrete cool­

ing transitions. This means that all the matrix elements for which / < (* — 1) will have

Af^i = 0 (see Figure 5.2). Thus in the absence of discrete cooling, the subset S of states

j = 1 , 2 , . . . , / — 1 can only be entered by a grain cooling from bin /, as there are no levels

lower than S from which a grain could be promoted into S.

153 A grain can only leave S by discrete heating to a state k > f. The net rate of grains entering 5 is then

i ( g - g ( f , g (5.25) where the first term on the right-hand side is for cooling into 5, and the second term represents heating out of S. In the steady state, there is no net change in the probability of a grain being in 5, and so the probability per unit time of a grain leaving 5 must equal the probability per unit time of a grain entering 5, i.e.

f - i / N \ = X) ( Z) 1 (^ 26) j=i \ k=f J

If the quantities X{ are defined such that

X i = (5.27) with Ai = l, and if B fj is the probability of a grain being heated from a state j to, or beyond, a higher state /, then

N B/J = E ( / > i) (5.28) k=f and so Equation 5.26 becomes, after dividing by Pi

/ —I = (5.29) i=i and therefore 1 X , = Y . B p iX i (5.30)

The overall form of the transition matrix is represented in Figure 5.2. Above the main diagonal, / is greater than i, and so the elements in this region of the matrix are the discrete heating terms. On the diagonal are the terms, defined in Equation 5.7. Below the diagonal, / is less than t, corresponding to cooling of the grains. The region below the diagonal thus contains two types of elements: the diagonal immediately below the main diagonal represents transitions with / = i — 1 , and so is populated by the (continuous) cooling terms, while all the other matrix elements below the main diagonal, which would correspond to discrete cooling, are zero.

154 N h h h h h D

{ N -l) h h h h D c

: Final state, / h h h D c 0

3 h h D c 0 0

2 h D c 0 0 0

1 D c 0 0 0 0

1 2 3 (AT-1) N

Initial state, i

Figure 5.2: Location of the different types of element in the transition matrix. Symbols are: h = heating term; c = cooling term, D = diagonal element (Equation 5.7); 0 = term has the value zero

Having previously obtained all the A fj terms, the calculation could proceed by ob­ taining the values of the B fj terms by downward recursion, since from Equation 5.28

- f Af^i (5.31)

The values of X 2 ...X 7V could then be determined by upwards recursion from Equa­ tion 5.30, using the fact that Xi = l. The final step in the computation of the P f^ is to recover the actual probabilities from the ratios A",-, which is done by making use of the sum of the probabilities being unity (Equation 5.24), therefore

p S S ^ (5.32)

5.5 Results

The results from the model were output in two forms— a probability distribution function and a spectral energy distribution. The probability distribution function was found by converting the discrete steady-state probabilities into values of the continuous probability distribution function P{T). This was achieved by dividing the probability of a grain being in a bin by the temperature interval covered by the bin, AT,-. The definition of AT,- is analogous to that of the bin width AUi in Equation 5.3. The quotient obtained is a good

155 approximation to the value of the probability distribution function at the temperature T,-.

Since a grain is required to be in one or other of the bins, the value of the probability distribution function is zero for TTmax* In order to make comparisons with the figures plotted in Guhathakurta & Draine, the probability distribution function could also be calculated in terms of the probability per unit logarithmic temperature interval d(lnT). For this, the probability associated with a bin was divided by the interval of In T covered by the bin. Tests using a model of a B3V star gave good agreement with the results of Guhathakurta & Draine.

The spectral energy distribution was determined by calculating the spectrum expected from a grain at the temperature of each bin, and then adding all N such contributions together, weighted by their respective probabilities:

N 5a,out « g.b.(A) 53 Pf^BxiTi) (5.33) 1 = 1 where B\{T) is the Planck function, and T,- is the temperature of the tth bin. Since the flux emitted by a single small grain is likely to be a very small number in conventional units (W m“^/im“' or Jy etc.), which could lie beyond the floating-point range of a computer, all the contributions were multiplied by an arbitrary factor of 10^^. In effect, the output spectral energy distribution was therefore the SED due to emission from an ensemble of

1 0 ^® identical small grains.

5.5.1 Effects of Grain Size

It is instructive to consider the probability distribution functions of different-sized grains exposed to the same radiation field. Figure 5.3 shows how the probability distribution function varies with grain size for amorphous carbon grains of radii from 5 to 50 Â situated

1 0 ^® cm (670 AU) from a B9V star (modelled with a Teff = 10500 K, log g = 4.0 Kurucz

(1991) model atmosphere). The progression with grain size from a predominantly cold distribution to near thermal equilibrium is evident. The area under each curve in Figure 5.3 is the same, corresponding to a total probability of unity for each distribution.

The smallest grains (a= 5Â) have the smallest cross-section for photon absorption, so they absorb fewer photons in a given time interval than would a larger grain. They also have the largest ratio of surface area to volume, and therefore will cool more rapidly than larger grains, since for radiative cooling dUjdT is proportional to the grain surface area,

156 .055

.050

.045

.040

.030

.025

•S .0 2 0

.015

.010 /\ .005

0 20 60 8040 100 120 140 160 160 200 Temperature (K)

Figure 5.3: The probability distribution functions of different-sized grains exposed to the radiation field of a B9V star. Leftmost solid curve: grain radius =5 Â; dashed curves (in order of increasing peak temperature) 7, 10, 15, 20, 35 Â; rightmost solid curve: 50 Â.

157 while the total enthalpy of a grain at a given temperature, U{T) varies as the volume (for a given composition).

Conversely, larger grains have larger absorption cross-sections, implying a high rate of absorption events. They also have small surface-to-volume ratios, and therefore long cooling times, as mentioned above, this combination of frequent absorption events and slow cooling lead to the grain spending significant amounts of time at elevated temper­ atures — hence the peak of the probability distribution (i.e. the maximum-probability temperature) is at a higher temperature than that of a smaller grain; while the increase of grain heat capacity with size means that photon absorption events wiU cause only small fluctuations in temperature. In the limit of large grain size, the peak temperature is the thermal equilibrium temperature, and the fluctuations are negligibly small — the probability distribution narrows to become a delta function. For the example presented in Figure 5.3, the 50-Â grain is close to being in thermal equilibrium: its most probable temperature is 124 K, compared with the equilibrium tem­ perature of 125 K calculated using the radiative balance method described in Chapter 4. The good agreement between the thermal equilibrium temperature and the most proba­ ble temperature for a relatively large grain provides confirmation of the accuracy of the transient-heating calculations.

The probability distribution function for the 50-À grain is still quite broad, there being approximately a 50% probability that the grain will be within ±5 K of the peak temperature. A good fit to the probability distribution function can be obtained with a

Gaussian of fuU width at half-maximum of 17 K. The distribution for a 200-Â grain is considerably narrower, with a 50% probability of the grain being within ±0.5 K of the peak temperature.

At high temperatures, other effects of grain size on transient heating can be observed (Figure 5.4). Despite having probability distributions that peak at the coolest tempera­ tures, the smaller grains have a greater probability of being found at high temperatures

(greater than, say, 350 K in the present example) than do the larger grains. This is because the lower specific heat of the smaller grains means that they will reach higher tempera­

tures on absorption of a single photon of a given energy than will the larger grains; hence

for these larger grains there are very few photons energetic enough to excite them to high

temperatures, and so the probability distribution function falls off very rapidly at high

158 temperatures.

The probability distribution functions for the 5- and 50-Â grains are an alternative way of expressing graphically the behaviour described by Figures 5.1(a) and (b).

Figure 5.5 shows the model spectral energy distributions for the 5- and 50-Â grains, along with normalised blackbody functions chosen to peak at approximately the same wavelengths as the models. The SED for the 50-Â grain has a higher total dux than the smaller grain. This is because the larger grain absorbs more energy per unit time.

Integrating under the two spectral energy distributions (which were calculated for 10®° grains in each case) gives a ratio of total dux of approximately 1 0 0 , the ratio of the cross- sectional areas of the two grains. The same optical constants were used for both grains, so any effects due to variation in the absorption efficiency with size were neglected.

The spectral energy distribution for the 5-Â grains peaks at a shorter wavelength than that for the 50-Â grains. This is due to the higher temperatures attained by the 5-Â grains. Although the 5-Â grains are more likely to be at low temperatures than high

(Figure 5.3), the fact that they radiate more strongly at high temperatures means that their SED is dominated by emission from hot grains.

For blackbodies, the total dux varies as T^, so the spectral energy distribution of a

(hypothetical) collection of thermally-spiking grains with blackbody emissivity would be

dominated by the spectra of grains at the temperature where the product T^P{T) reaches its maximum value.

To compare the model SEDs with those of single-temperature blackbodies, Planck

functions chosen to peak at the same wavelengths as the models were normalised to the

peak duxes of the models, and are presented in Figure 5.5. Temperatures of 720 and 155 K

were found to give good fits to the 5- and 50-Â grain models respectively.

The spectral energy distribution of the 50-Â grain is narrower than that of the 155-K

blackbody. This is due to there being a narrow range of grain temperatures with high

enough probabilities to contribute significantly to the SED, together with the fact that

the grain emissivity falls off with increasing wavelength over the entire wavelength range of Figure 5.5. The SED of the 5-Â grain is broader than that of the 720-K blackbody, due

to the wide range of temperatures which contribute significantly to the model emission.

159 1.8

1.6

1 .4 T o 1.2

& 1.0

! . 6 Q I •S . 6 I .4

.2

0 150 200 250 300 350 400 450 500 Temperature (K)

Figure 5.4: High-temperature portions of the curves shown in Figure 5.3. Leftmost solid curve: 50 Â; dashed curves (in order of increasing temperature at the abscissa) 35, 20, 15, 10, 7 Â; rightmost solid curve: 5 Â.

160 -9

-1 0

1-11

-12

-13

-1 4 I I -15 T B -16

s -17

—18 \ - -19

-20

-2 1

Wavelength (/xm)

Figure 5.5: Model spectral energy distributions of small grains situated 10^® cm from a

B9V star. Solid line: 50 Â grain; dashed line: 5 Â grain; dotted line: 720 K blackbody fit to the 5-Â SED; dash-dotted line: 155 K blackbody fit to the SED of the 50-Â grain.

161 5.6 Effects of the Radiation Field

It is clear that the thermal behaviour of a small grain must be strongly dependent on the radiation held in which it is immersed. For the present discussion, the radiation held can be described simplisticaUy in terms of two properties, its ‘hardness’ and its total intensity.

Hardness is the proportion of short-wavelength (UV, X-ray etc.) photons compared with less- energetic photons, such as visible or near-infrared. In a circumsteUar environment, the hardness of the radiation held is determined by the effective temperature of the star, while the intensity of the radiation held varies with distance from the star, due to dilution of the stellar radiation.

5.6.1 Hardness

A small grain in a hard radiation held is likely to undergo temperature huctuations of greater amplitude than an identical grain in a ‘softer’ radiation held, due to the larger proportion of energetic photons in the harder held. If the frequency averaged intensities,/, of the radiation helds are the same, a large grain (with approximately grey absorptivity over the wavelength range of the radiation held) wiU have the same temperature when exposed to either held, since it wiU absorb energy at the same rate from each.

For a small grain, however, individual photon events are important, so the way in which the energy of the radiation held is distributed with wavelength wiU affect the behaviour of the grain. In a hard radiation held, the average energy per photon is greater than for a softer radiation held. For a given intensity, the total rate of photons impinging on some surface exposed to the radiation held will therefore be lower, and so the interval between successive photon absorption events for a small grain wiU be greater. This longer interval between heating events, combined with the larger amount of energy transferred to the grain in a single event, lead to the behaviour of a smaU grain in a hard radiation held being more extreme and further removed from thermal equilibrium than in a softer radiation held.

Increasing the hardness of the radiation held therefore gives similar effects (longer time between heating events, larger ratio of photon energy to grain enthalpy) as reducing the grain size for a given radiation held.

The effects of the hardness of the radiation held for smaU circumsteUar grains, reaUsed

162 in terms of the effective temperature of the star, are illustrated in Figure 5.6. The three curves are for 1 0 -A grains in the radiation fields expected for stars of spectral types

BOV, B9V and G5V, represented by Kurucz (1991) model atmospheres with effective temperatures of 30000 K, 10500 K, and 5750 K respectively. The distances from the star to the grain were set so that in each case, the equilibrium temperature of a grain would be approximately 130 K.

The probability distribution function varies with stellar temperature in accordance with the arguments presented above. A grain in the hardest radiation field — that of the

BOV star - has the highest probability of being at low temperatures (due to the relatively long time interval between heating events), but also has the greatest probability of being at high (<300 K) temperatures, due to the abundance of energetic photons in the radiation field.

A grain exposed to the ‘softest’ radiation field — that of the G5V star — has a narrower probability distribution, and so is nearer to being in thermal equilibrium than are the other cases displayed in Figure 5.6. The steep fall-off at high temperatures is due to the relative paucity of UV photons emitted by a G-type star.

The UV-visible spectra of the three radiation fields, normalised to give the same integrated intensity, are presented in Figure 5.7. The large increase in short-wavelength flux with increasing stellar effective temperature is clearly visible. Multiplying the flux density by the wavelength would give a measure of the number of photons emitted per

second as a function of wavelength.

5.6.2 Intensity

Varying the intensity of the radiation field wiU alter the rate at which photons are absorbed

by a grain, but not the average energy per photon. For large grains, an increase in the

intensity of the radiation field, and therefore of the rate of absorption of energy by the

grain, wiU cause an increase in the equilibrium temperature.

For thermaUy-spiking smaU grains, the situation is somewhat different: an increase

in the intensity wiU reduce the typical interval between absorption events, and so reduce

the probability that a grain wiU be at low temperature. This wiU cause a decrease in the

peak value of the probability density, which occurs at low temperatures. Since a grain

wiU typicaUy have less time to cool, it wiU not reach as low a temperature as in a less-

163 -1

-2

-3

k t —6 Qs - 6 a i Xi O -7 £

10 “ ®

-9

50 100 150 200 250 300 350 400 Temperature (K)

Figure 5.6: The probability distributions of 10-Â grains exposed to different radiation fields. Solid Une: B9V star (Teff= 10500 K); dashed line: BOV star (Teff= 30,000 K); dotted line: G5V star (Tcf[= 5750 K).

164 5.0

4.5

4.0

3.5

3.0

2.5 I 2.0

1.5

1.0

.5

0 1000 1500 2000 2500 3000 3500 4000 4500 5000 Wavelength (A)

Figure 5.7: UV-visible spectra of stellar radiation fields. Solid fine: B9V star

(Tefr=10500K); dashed fine: BOV star (Teff=30000K); dotted fine: G5V star (Teff=5750K).

165 intense radiation field, and so the temperature corresponding to the peak of the probability distribution function will be higher. With an increase in intensity, multiple absorption events become more common, so the probability of a grain being at high temperatures increases.

The low-temperature effects of an increase in the intensity of the radiation field are similar to the effects of an increase in grain size, where the rate of absorption events increases, reducing the peak value of the probability distribution function, and causing a shift of the peak towards higher temperatures. However, the high temperature behaviour is different, since the greater heat capacity of a larger grain reduces the amplitude of the temperature fluctuations, thereby reducing the probability density for high temperatures.

The effects of varying the intensity of the radiation field are illustrated in Figure 5.8, which shows the probability distribution functions for 1 0 -Â grains situated lO'®, 1 0 ^®, and 10^^ cm from a B9V star. As expected, the probability distribution function for the grains closest to the star peaks at higher temperatures, but with a lower peak probability density, than the lower temperature peak for the more distant grains, and has a higher probability density at high temperatures. Figure 5.9 shows the spectral energy distributions of the emission from the 10 Â grains at the three distances from the star. As could be predicted from the conservation of energy, the grains closest to the star (i.e. exposed to the most intense radiation field) emit most strongly. The peak wavelength of the emission is displaced towards shorter wavelengths with increasing intensity, although the difference (approximately 15% for a factor of 100 change in distance) is much less than the shift in peak wavelength that would be expected for grains in thermal equilibrium (approximately a factor of 1 0 increase in wavelength for a hundredfold increase in distance).

Shortward of roughly 50 /im, the SEDs of the grains at lO'® and 10*^ cm from the star have the same shape, as can be seen when the spectrum of the grains at 1 0 ^® cm is normalised to the spectrum of the grains at 10^^ cm (this normalised SED is the dotted curve on Figure 5.9). This is because multi-photon absorption events are rare for 10-Â grains at 1 0 ^® and 1 0 ^^ cm, so the high-temperature parts of the probability distribution functions for both distances are due only to single-photon events, and therefore have

the same shape. The absolute values of the probability density at high temperature are greater for the grains closer to the star; hence they emit more flux, especially at shorter

166 10

10

10

10 \ o 10

1 0

1 0 50 100 150 200 250 300 350 400 450 500 55 0 600 T em p eratu re (K)

Figure 5.8: Effects of radiation field intensity on small grains. Solid line: 10-Â grain at 10^® cm from a B9V star; dotted line: distance = 10^^ cm; dashed line: distance =

10^^ cm.

167 10“ ®

s G

10 ® W avelength (/xm)

Figure 5.9: SEDs for the probability distributions in Figure 5.8. Sobd line: grain at

10^® cm; dashed Une: 10^^ cm; dash-dotted line: 10^^ cm; dotted line: SED of grain at

1 0 ^^ cm normalised to that of the grain at 1 0 ^^ cm.

168 wavelengths.

The more distant grains spend longer at low temperatures; during these intervals between heating events they will emit primarily long-wavelength radiation. This explains the higher millimetre-wave flux of the grains at 1 0 '^ cm compared with the normalised spectrum of the grains at 1 0 ^® cm.

The similarity in the shapes of the SEDs, and the rapid fall-off in the total model flux with increasing distance from the star mean that in practice a spatial distribution of small grains can be modelled by considering grains at a single distance from the star, since more distant grains will make a negligible difference to the shape of the near- and mid-infrared portions of the small-grain SED, and any contribution they make to the mm-wave flux will be negligible compared with the flux from large grains in thermal equilibrium.

The results of using small grains to model the emission from Vega-excess stars are presented in Chapter 6 .

169 C hapter 6

Results of Modelling

This chapter presents the results of modelling Vega-excess systems using the techniques described in Chapters 4 and 5. New models are presented for sixteen stars; the results of the Skinner et al. (1995) modelling of SAO 26804, which used the observations and modelling techniques presented in this thesis, are also reported. The seventeen stars cover a wide range of spectral types (A0-K5) and fractional luminosities. As noted in Chapter 4, the modelling technique treats the discs as being optically thin: for the stars with the largest fractional luminosities, this is not likely to be true. OpticaUy-thin models do however provide a useful approximation to the circumsteUar environments of Vega-excess stars, in the absence of more elaborate techniques.

The procedure for combining equiUbrium and smaU-grain models for stars with near-IR

excess emission was to use the equiUbrium disc model first, and fit the mid-IR to mm-

wave data. AU models which gave good agreement with the mid- and far-IR observations

were found to make negUgible contributions to the near-IR flux, which aUowed the two

modeUing techniques to be used nearly independently.

A check on the internal consistency of the photosphere models could be made by

determining the best-fitting distances to the stars without reference to the values expUcitly

calculated in Chapter 3. Having adopted a model atmosphere and steUar radius based on

the spectral type of the star (see Chapter 4), models were run, varying the distance to the

star until the model predicted fluxes in the optical region which were in agreement with

the dereddened spectral energy distribution. The distances obtained in this fashion were

found to be in close agreement with those calculated in Chapter 3 from the absolute and

apparent visual magnitudes. Any errors in the original distance calculations, the choice

170 of model atmosphere, or in the adopted stellar radii would have shown up at this stage in the form of discrepancies between the two distance estimates.

Having obtained a well-fitting disc model, small-grain models were computed, with the grains situated at the inner radius found for the disc models, and the mass of smaU grains was determined by fitting the near-IR excess fluxes. The emission from the small grains was then simply added to the fluxes from the disc model, which included the photospheric contribution. Sometimes the non-zero flux from the small grains in the mid-IR caused the fit to the CGS3 spectrum to deteriorate; a slight increase in the inner radius of the disc model generally sufficed to decrease the disc model’s contribution at 1 0 ^m, and allowed the fit to be recovered.

For several stars with near-IR excesses, it was found that thermally-spiking small grains gave unsatisfactory fits to the observations, and so the distance between the small grains and the star was reduced until the emission from the grains (now approximately in thermal equilibrium) matched the near-IR excess spectral energy distribution. This was not merely a cosmetic exercise in fitting the data points, but provided useful measures of the grain temperature characterising the near-IR excess, and lower limits on the amount of mass required to produce such an excess. The mass lower limits and dust temperatures are valid irrespective of the mechanism which is actually heating the grains - thermal spiking by excess UV photons, equilibrium heating of grains close to the star, or even some process intrinsic to the disc, such as coUisional heating.

Detailed descriptions of the models for each star are presented below. For ease of

comparison of similar sources, the stars with significant near-IR excess are treated before

those with no near-IR excess, and the stars with little or no excess at 10 //m are dealt

with last. Within each group, the stars are presented in order of SAO number.

The disc outer radii were usually set to 10 arcseconds, corresponding to the approxi­

mate size of the JCMT beam. If it was suspected that emission originating further from

the star is contributing to the IRAS fluxes, the disc outer radius was increased, typically

to 30 arcsec. However, only the flux arising in the inner 20 arcseconds (diameter) was included for the tabulated values of the predicted mm-wave fluxes, to allow comparison

with the JCMT measurements.

The minimum and maximum grain radii for the disc models were usually set to 50 Â and

1 mm respectively, which were the values found by Skinner et al. (1992) for SAO 179815.

171 Using a value of Omax greater than 1 mm gave model spectral energy distributions indis­ tinguishable at mm and shorter wavelengths from those of models with Omax = 1 mm.

The equilibrium models for each star are assigned a reference number which takes the form of a letter followed by two numbers. The letter refers to the type of dust material used: M refers to ‘pure’ astronomical silicate, C to amorphous carbon, and B to a blend of silicate and carbon. The two numbers refer to 7 , the grain size distribution parameter, and the density distribution parameter, (i. Decimal points and minus signs are symbolised with the letters p and m respectively. Thus model M22 for a particular star would be a pure silicate model with 7 and (i set to 2, while B2p52 would be a ‘blend’ model with

7 = 2.5 and /) = 2 .

6.1 Stars with a Near-infrared Excess

6.1.1 SAO 77144 (HD 35187)

SAO 77144 was first identified ats a Vega-excess star by Walker & Wolstencroft (1988); it also appears in the list of Gudmaijer et al. (1992). On the basis of its IRAS colours, it was listed a a possible OH/IR star by Lewis et al. (1990), who observed it at 1612 MHz with the Arecibo telescope, but did not detect any OH maser emission. Zuckerman et al.

(1995) detected mm-wave emission from ^^CO and ^^CO transitions.

There is no MK spectral type in the sim bad database for this star, so the HD classi­ fication (A2) was used, and luminosity clziss V assumed. Zuckerman et al. (1995) give a spectral type of A2/3IV/V, consistent with the type adopted for the modelling.

SAO 77144 is listed in the Hipparcos Input Catalogue (Turon et al. 1992) as a double star. The two components are separated by 1.2 arcsec, and have equal V magnitudes. The

JKT observations described in Chapter 3 were made with the telescope de-focussed, and so the two components of the star were not resolved on the CCD image. It was therefore not possible to compare the optical colours of the two components and determine if they were of different spectral types.

For the purposes of modelling this system, it was assumed that the two component stars were identical, but that the grains were heated by only one of them. The results of modelling SAO 77144 are summarised in Table 6.1.

Unless otherwise stated, aU the models listed in Table 6.1 had a maximum grain size of

172 Table 6.1: Models for SAO 77144 (HD 35187)

Model 7 a R'm ■Mdigc F u ^25 J^60 J^ioo Fq.% f i.i cm M© Jy m Jy

Observations 5.4 11.5 8 . 0 5.0 115 80 (± error) 0.3 0.7 0 . 8 0.5 2 2 1 0

M22 2 2 1.3x10^'* 9.2x10-* 3.6 11.5 8 . 0 3.8 94 41 6.0x10^3 M21 2 1 1X1x10-4 5.7 11.4 8 . 0 4.9 277 127

M12 1 2 1 . 1 x 1 0 ^^ 2 .8 x 1 0 -* 3.7 11.4 8 . 0 4.0 149 74

M il 1 1 3.8x10'^ 2.6x10-4 7.0 11.4 8 . 0 5.1 452 239

M31 3 1 6 . 2 xlO^^ 4.0x10-* 1.4 11.5 8 . 0 3.9 39 14

M2p51 2.5 1 2.4 xlO''* 2 .2 x 1 0 -* 3.5 11.4 8 . 0 4.4 119 48

M30p5 3 0.5 2.5 xlO^'* 6 . 2 xlOr* 2.9 11.4 8 . 1 4.4 53 19 5.0x10^2 M20p5 2 0.5 3 .2 x 1 0 -4 10.3 10.4 8.3 6.7 724 344

M2p50p5 2.5 0.5 6x1013 5.4x10-* 6.5 11.5 8 . 1 5.3 2 2 1 91

M2p50p7 2.5 0.7 1.3x101^ 3.8x10-* 4.4 1.5 8 . 0 4.9 173 71

M22a 2 2 1 .8 x 1 0 1 ^ 1 .6 x 1 0 -* 2 . 6 11.5 1 0 . 2 5.3 145 63

B22 2 2 l.OxlOi'i 6.4x10-* 3.7 11.4 8 . 0 3.8 92 40

B21 2 1 7.0x1013 4 .8 x 1 0 -* 5.8 11.5 8 . 0 4.7 246 1 1 2

B31 3 1 7.7x101^ 1.7x 1 0 -* 3.1 11.4 8 . 0 3.7 33 1 2

B22a 2 2 2.4x101^ 1.3x10-* 2 . 6 11.5 1 0 . 6 5.6 155 67

173 1 mm, a minimum grain size of 50 Â, and a dise outer radius of 1430 AU (corresponding to an angular diameter of 2 0 arcsec).

After running a few preliminary models to check the distance (202 pc, the value derived from the photometry in Chapter 3 was found to give a good fit and so was adopted), a grid of pure silicate models was defined (models M22-M11). Values of inner radius and disc mass were chosen to obtain a good fit at 25 and 60 /xm. Models M22, M21, M12 and M il all overestimated the flux in the CGS3 spectrum, even though M12 and M22 actually underestimated the IRAS 12-fim flux. The effects of beam size were tested by re-running

M22 with a 5.5 arcsec diameter beam; this was found to make no significant difference to

the flux in the 1 0 -/xm region.

Model M31, with 7 (the grain radius parameter) set to 3 and /?, the density distribution parameter set to 1, was the first not to overestimate the 7-13/xm flux, but it severely underestimated the flux at 0.8 and 1.1 mm. A further set of models was produced to

explore parameter space near 7 = 3, /? = 1 (models M2p51-M2p50p7). Model M2p50p7

gives a good fit to the IRAS 25-100/im data, and to the flux at 1 . 1 mm, although the fit

is not so good at 0 .8 /xm. If the CGS3 spectrum is normalised to the IRAS 12-fj.m datum ,

model M2p50p7 was found to give a good fit to the 10-13/xm portion of the spectrum (but

falling off too fast towards shorter wavelengths). If, therefore, the absolute flux calibration

of the CGS3 spectrum is incorrect, this model gives a good fit to the data from about

1 0 fim to 1 mm.

A number of models were run using a blend of 75% silicate grains and 25% amorphous

carbon grains (models B22-B31). These also gave too much 8-13/xm flux compared with

the un-normalised CGS3 spectrum. Finally, a pair of models were run with the inner

radius set to give a good fit to the CGS3 flux at approximately 1 2 /xm, and the disc mass

normalised to give a fit to the 25-^m point. Model B22a used the silicate/amorphous

carbon blend, while M22a used only silicate grains. Both had 7 = /? = 2, and gave

reasonable fits to the data, with the exception of the 60-/xm point (and of course the IRAS

1 2 -/xm point).

Given that beam-size effects are not predicted to remove the inconsistency between the

IRAS and CGS3 fluxes, further spectrophotometry is required to determine the true flux

in the 10-/xm region, and so determine which of the two ‘best-fitting’ models M2p50p7

and M22a gives the most accurate representation of the circumsteUar environment of

174 SAO 77144. For the present, it is assumed that the flux calibration of the CGS3 spectrum is in error, and so model M2p50p7 is plotted in Figure 6 .1 . The CGS3 spectrum plotted on the Figure has been scaled up by a factor of 1.45 to make it consistent with the IRAS

1 2 -/xm point.

The near-IR excess emission of SAO 77144 was modelled using the smaU-grain code.

Small (3Â radius) silicate grains at 5 X 10^^ cm (3 AU) from the star were found to be out of thermal equilibrium, and gave a good fit to the near-IR excess photometry.

However, they produced a strong silicate emission feature, far in excess of the observed silicate feature in the CGS3 spectrum. 3-Â radius grains of amorphous carbon also gave a good fit to the near-IR photometry without giving rise to any spectral features in the 10-;^m region. Combining the two materials, it was found that silicates could form up to approximately 1 0 % of the small­ grain population before giving rise to too strong a silicate feature. A mass of 1.2 x 10~®

AfEarth of Small AC grains was needed to provide the observed amount of near-IR flux. Grains of radius 3 Â (the largest that were show significant departures from thermal equilibrium) contain approximately 30 atoms, which is rather few for a realistic grain. For larger grains to be excited sufficiently to give rise to the observed near-IR excess emission, the stellar radiation field would need to be ‘harder’, i.e. have a greater UV component.

Figure 6.1 includes the emission from small grains. The details of the models in the 10-/xm region are presented in Figure 6.2.

Even after including the smaU-grain contribution, there is noticeable residual emission in the 8-9 fim part of the normalised CGS3 spectrum. This could weU be due to the

7.7-/zm UIR band, seen in a number of Vega-excess stars.

6.1.2 SAO 131926 (HD 43282)

SAO 131926 has received little attention in the literature, although it is included in the lists of SAO stars with infrared excess of Stencel & Backman (1991) and Oudmaljer et al

(1992). It has no MK spectral type, so (as usual in such cases) the HD classification of

AO has been adopted, with luminosity class V assumed. There is no previously published optical photoelectric photometry; the new JKT optical photometry presented in Chapter 3 is consistent with the AO spectral classification, and yields a distance of 547 pc. Near- infrared photometry (Chapter 3) and the IRAS 12-/im point both show excess emission.

175 -10

-1 1

-1 2

-1 3

-1 5

-1 6

-1 7

—10

-1 9 10° Wavelength (/xm)

Figure 6.1: Results of modelling SAO 77144. Large squares: photometric data, small squares: CGS3 spectrum normalised to IRAS 1 2 -^m flux. Solid line: model M2p50p7, dashed line: effect of adding small AC grains to M2p50p7.

176 2x10,-13

B 1.5x10"“

,-1 3 1 0

7 8 0 10 11 12 13 14 Wavelength ( j à u i )

Figure 6 .2 : Detail of the SAO 77144 models in the mid-IR. Error bars: CGS3 spectrum scaled up by a factor 1.45, large square: IRAS point, solid line Model M2p50p7, dashed line: effect of adding small grains.

However, no CGS3 spectrum is available for this source. The star was modelled using a TeflF=9500 K, log flr=4.0 model atmosphere. A luminosity of 54L© (Schmidt-Kaler 1982), implies a stellar radius of 2.7R©. Since the near-IR photometry of this source shows strong excess emission (Table 3.8), so there is probably a contribution to the flux in the IRAS 1 2 -/zm band from the m aterial responsible for the short-wave excess. For this reason, no attempt was made to fit the 12-//m point; the inner radius and disc mass were adjusted to give a fit to the 25- and

60-/xm points. The maximum and minimum grain sizes used were 1 mm and 50 Â, and an outer radius of 5470 AU was used, corresponding to a projected disc diameter of 20 arcsec.

Results of the modelling are presented in Table 6.2.

An initial grid of models (M22-M24) showed that the 7 = 2 models all gave significantly too much millimetre-wave emission, even with a very steep (/)=4) density distribution.

Conversely, the 7 = 3 models (M32, M31) both gave too little mm-wave flux.

A set of models with intermediate values of the grain radius parameter 7 was therefore constructed (models M2p52-M2p63), which tended to give better agreement with the observations. The best-fitting of these models was model M2p72.

Three models were calculated using a blend of silicate and amorphous carbon grains, in a 3:1 proportion (Models B22-B2p72). Again, the maximum and minimum grain sizes

177 Table 6.2: Models for SAO 131926 (HD 43282)

Model 7 P R'm Fu F25 Feo ^ 1 0 0 Fq.8 Fi.i cm M© Jy m Jy

Observations 0.70 1.63 1 0 . 8 10.7 409 183 {± error) 0.07 0 . 1 0 0 . 1 0 . 1 27 17 3.0x10^5 M22 2 2 6 .1 x 1 0 "^ 0.04 1.79 1 0 . 8 16.7 > lJ y > lJ y

M32 3 2 1 .0 x 1 0 ^® 1 .8 x 1 0 -'' 0 . 0 1 1.83 10.9 9.2 155 56 9.0x10^5 M31 3 1 3 .2 x 1 0 -'' 0 . 0 1 1.65 1 1 . 0 10.7 230 84

M23 2 3 4.0x10^5 4.8x10-^ 0 . 0 2 1.59 10.7 18.0 > lJ y > lJ y 4.0x10^5 M24 2 4 3.3x10-^ 0.03 1.67 1 0 . 8 17.6 > lJ y 828 8.0x10^5 M2p52 2.5 2 2 .3 x 1 0 -3 0 . 0 1 1.76 1 0 . 8 1 1 . 6 897 383

M2p82 2 . 8 2 1 .0 x 1 0 '® 4.9x10-'' 0 . 0 1 1.64 10.7 1 0 . 0 284 109

M2p72 2.7 2 9 .5 x 10'5 8 .4 x 1 0 -'' 0 . 0 1 1.67 1 0 . 8 10.5 413 165

M2p53 2.5 3 9 .4 x 10'5 1.8x 1 0 -3 0 . 0 1 1.65 1 1 . 1 11.7 827 348

M2p73 2.7 3 1 .0 x 1 0 '® 5 .6 x 1 0 -'' 0 . 0 1 1.79 10.9 9.8 330 131

M2p63 2 . 6 3 1 .0 x 1 0 '® 1.0x10-3 0 . 0 1 1.62 1 0 . 8 1 0 . 6 529 215

B22 2 2 4.0x10'® 9 .4 x 1 0 -3 0.08 1 . 6 8 1 0 . 8 15.7 > lJ y > lJ y

B32 3 2 1 .8 x 1 0 '® 2 .8 x 1 0 -'' 0.03 1.70 10.8 10.8 200 73

B2p72 2.7 2 1.5x10'® 1.3x10-3 0.03 1.82 10.7 11.5 464 185

C22 2 2 4.6x10'® 8 .4 x 1 0 -3 0.14 1.80 1 0 . 8 1 0 . 1 144 51

C 2 1 2 1 4.3x10'® 2 .5 x 1 0 -2 0 . 1 2 1.58 1 0 . 6 1 2 . 1 303 1 1 1

C20p5 2 0.5 3.3x10^® 4 .3 x 1 0 -2 0.14 1.762 1 0 . 8 13.4 458 170

C 1 2 1 2 3.1 xlO'® 2 . 1 xlO - 2 0 . 0 2 1.60 10.7 8.3 93 33

C ll 1 1 2.5x10'® 7.4x 1 0 -2 0 . 0 2 1.65 10.9 1 0 . 2 215 78

C0p50p5 0.5 0.5 2.0x10^^ 1.9x10-' 0.03 1.67 1 0 . 8 1 2 . 2 394 146

C10p5 1 0.5 2.0x10^5 1 .6 x 1 0 -' 0.03 1.67 1 0 . 8 1 2 . 2 395 146

M2p71 2.7 1 8 .0 x 1 0 '® 1.4x10-3 0 . 0 1 1.63 1 0 . 8 11.5 565 230

M2p81 2 . 8 1 8 .0 x 1 0 '® 7.8x10-'' 0 . 0 1 1.74 10.7 1 0 . 8 375 146

M2p71a 2.7 1 8 .0 x 1 0 '® 4 .5 x 1 0 -3 0 . 0 1 1.61 1 0 . 8 12.5 556 227

178 -10

-11

-1 2

-1 3

-1 4

-1 5 I -1 6

-1 7

-1 8

10° Wavelength (/xm)

Figure 6.3: Results of modelling SAO 131926. Solid line: model M2p72, dashed line: effect of adding small AC grains to model M2p72

179 were 1 mm and 50 Â, and the outer radius was 5470 AU. The best fitting of the blended models was B2p72, which had the same values of 7 and as the best-fitting pure silicate model. A final grid of models using only amorphous carbon grains (models C22-C20p5) was calculated, with the same outer radius and range of grain sizes as the previous models.

The AC models required lower values of 7 and than did the silicate and blended models.

The best-fitting amorphous carbon model was C20p5, which nevertheless gave a 1 0 0 -/xm flux which was somewhat high. The best-fitting of all the models in Table 6.2 was therefore

M2p72, the SED of which is presented in Figure 6.3. The near-IR excess of SAO 131926 was modelled using the small-grain technique. 3-Â grains (silicate or amorphous carbon) were found to be thermally spiking, and emitting in the near-IR. The fit is not ideal, with a A /L flux ratio that is too low. Using larger grains caused the fit to deteriorate. In the absence of a CGS3 spectrum, it cannot be determined whether the material is silicaceous or carbonaceous. Using AC grains situated 8 x 10*® cm (530 AU) from the star, comparable to the inner radii of the disc models, it was found that approximately 1 Earth mass of small grains was required to produce sufficient near-IR flux. This mass is roughly one percent of the mass of grains in the disc model M2p72. The effect of combining this small-grain model with model M2p72 is illustrated in Figure 6.3.

6.1.3 SAO 183956 (HD 142666)

SAO 183956 was first noted to be a Vega-excess star by Walker h Wolstencroft (1988).

Te Lintel Hekkert et al. (1991) observed it as part of their 1612 MHz survey of IRAS point sources, but did not detect any OH emission. It was also one of the sources in the Likkel et al. (1991) IRAM carbon monoxide survey of candidate AGB and post-AGB

IRAS sources, but no CO emission was detected. Van der Veen et al. (1993) also obtained only upper limits in CO observations of SAO 183956. Van der Veen et al. (1994) detected continuum emission from SAO 183956 at 0.45, 0.8 and 1 .1 mm, and found that the near-IR to mm-wave excess energy distribution could not be successfully modelled with a single dust shell.

The SIMBAD database lists SAO 183956 as a suspected variable star, but there is no previously published UBV photoelectric photometry to confirm this. SAO 183956 has a large infrared excess (L ir /L* = 0.34), due in part to the substantial amounts of near-IR

180 excess emission. Its CGS3 1 0 -/xm spectrum shows silicate emission (Figure 3.3).

Models of SAO 183956 are presented in Table 6.3. The star was modelled using a

Kurucz (1991) model atmosphere with an effective temperature of 7500 K and a surface gravity log ^=4.0. Adopting a luminosity for an A 8 V star (spectral type from Houk

1988) of 8 . 6 L© (Schmidt-Kaler 1982), gives a stellar radius of 1.7 R@. The distance to

SAO 183956 derived from the optical photometry is 116 pc; preliminary modelling showed that this distance gave good agreement between the models and observations.

The IRAS 1 2 -/zm point and the CGS3 10-/im spectra were treated as upper limits for flux from the thermal equilibrium models, because the material responsible for the near-IR excess could make some contribution to the flux in the 1 0 -/im region.

A grid of silicate models (models M33-M11) was produced, with minimum and maxi­ mum grain sizes of 50 Â and 1 mm. The disc outer radius was 1160 AU. The inner radius and disc mass were adjusted for each model to obtain a fit to the IRAS data at 25 and

60 fim .

The models with grain radius parameter 7 = 3 (M33-M31) gave far too little 100-fim

and mm-wave flux. Of the models with 7 = 2, models M23 and M 2 2 both gave far too little

mm-wave flux, while model M21 gave markedly better results, giving approximately 80%

of the observed flux at 0.8 and 1.1 mm. Decreasing the density distribution parameter

stiU further (model M20p7) gave mm-wave fluxes higher than the observed values. Setting

(3 = 0.8 gave slightly too much mm-wave flux (model M20p8), while /? = 0.9 gave 0 .8 -mm

and 1.1-mm fluxes that agree well with the JCMT measurements (model M20p9).

Models M20p8 and M20p9 slightly overestimated the flux in the CGS3 10- and 20-

/im spectra (see Figure 6 .6 ). Increasing the inner radius (model M20p9a; see Figure6.5)

gave fluxes which did not exceed the CGS3 data, but were consequently somewhat low

compared with the IRAS 1 2 and 25 fim fluxes.

The contrast in the 10-//m silicate feature of models M20p8-M20p9a is slightly too

low; however if the material responsible for the near-IR excess emission contains silicates,

it could well augment the contrast of the 1 0 -/im silicate feature.

The 7 = 1 models (models M13-Mllp2) had a similar dependence on the density distri­

bution parameter (3 as the 7 = 2 models. The models with (3=3 and (3=2 (models M13, M12)

gave significantly too little long-wavelength flux, while (3=1 (model M il) gave roughly the

correct flux at 0.8 and 1 .1 mm. In fact, model M il slightly overestimated the mm-wave

181 Table 6.3: Models for SAO 183956 (HD 142666)

Model 7 R'm Afdisc Fi 2 f25 Feo ^ 1 0 0 Fo.g Fia cm M© Jy m Jy Observations 8.7 11.5 7.5 5.1 351 167 (± error) 0.5 0.7 0 . 8 0.3 23 17

M33 3 3 5.0 xlO^'* 3.5x10-'^ 0 . 8 11.4 7.5 2.9 19 7

M32 3 2 4 .0 x 1 0 '^ 6 .0 x 1 0 " 0.9 1 1 .6 7.5 3.0 24 8

M31 3 1 2 .1 xlO^^ 2 .0 x 1 0 -® 1.7 1 1 .6 7.5 3.8 74 17

M23 2 3 8.3x10^3 1.1 xlO"® 3.2 11.4 7.5 3.3 65 26

M22 2 2 6.5x10^3 2.7x10-® 3.8 11.4 7.4 3.5 82 36 2.7x10^3 M21 2 1 3.4x10-® 6.5 11.5 7.5 4.4 280 130

M20p7 2 0.7 1.8x10^3 9.0x10-® 6 . 0 9.5 7.3 5.3 560 270

M20p8 2 0 . 8 1.6x10^3 4.4x10-® 8.3 11.5 7.7 5.0 438 208

M20p9 2 0.9 2 .1 xl0^3 4.6x10-® 7.4 11.4 7.5 4.6 340 160

M20p9a 2 0.9 4.0x10'^ 5.4x10-® 3.6 9.0 7.6 5.0 395 186

M13 1 3 7.0x10^^ 3.5x10-® 3.4 11.5 7.5 3.4 104 51 5.5x10^3 M12 1 2 8.5x10-® 4.0 11.4 7.6 3.7 137 6 8

M il 1 1 1.7x10^3 1 .1 xlO -4 8 . 2 1 1 . 6 7.5 4.7 463 248

M llp 5 1 1.5 3 .8 x 1 0 " 2.5x10-® 5.3 11.7 7.5 4.0 2 0 0 103

M llp 3 1 1.3 4.0x10" 5.0x10-® 4.2 1 0 . 2 7.5 4.4 291 152

M llp 2 1 1 .2 4 .0 x 1 0 " 7.0x10-® 3.8 9.6 7.5 4.6 355 187

M lp51 1.5 1 1 .8 x 1 0 " 7.7x10-® 7.7 11.4 7.5 4.7 417 213

Mlp51p5 1.5 1.5 3.8x10" 2.5x10-® 5.2 11.5 7.5 4.0 180 87

B31 3 1 2 .7 x 1 0 " 1 .6 x 1 0 -® 3.9 11.4 7.4 3.6 38 14

B22 2 2 8 .0 x 1 0 " 3.9x10-® 3.8 11.4 7.5 3.5 83 36

B21 2 1 3.5x10" 4.2x10-® 6 . 0 11.4 7.6 4.4 260 1 2 0

B20p7 2 0.7 1 .5 x 1 0 " 1.0x10-4 8 .1 10.7 7.5 5.1 425 267

B20p9 2 0.9 2.5x10" 5.4x10-® 7.5 1 1 . 6 7.5 4.5 304 142

B20p8 2 0 . 8 3.0x10" 7.8x10-® 5.3 9.9 7.5 4.9 401 189

182 -1 0

-1 1

-12

-1 3

-1 5

-1 6

-1 7

-1 8

-1 9 10° Wavelength (/xm)

Figure 6.4: Results of modelling SAO 183956. Solid line: model M20p9a, dotted line: effect of adding small (5 Â radius) silicate and AC grains to model M20p9a.

183 Table 6.3 continued

Model 7 /? ■^in ■^diac F u F25 ■^60 J^ioo Fq.8 Fi.i

cm M© Jy m Jy

B ll 1 1 2 .5 x 1Q13 1.4x10-1 7.8 11.7 7.5 4.6 431 231

B llp 5 1 1.5 5.0x10^3 3.5x10"^ 4.7 11.3 7.5 4.0 2 0 0 103

B ll p l 1 1 .1 3.0x10^3 1 .1 xlO - 1 6.3 1 1 .2 7.5 4.4 360 191

C ll 1 1 9.0x1013 3.8x 1 0 -1 3.4 10.9 7.5 3.6 37 13

COl 0 1 9.0x1013 4 .8 x 1 0 -1 3.4 10.9 7.5 3.0 33 13

C00p5 0 0.5 3.0x1013 1.4x10-3 4.5 8.3 7.4 5.2 86 31

2.5x10

6 2x10

S 1.5x10 " -P

-1 3

5x10"'*

8 10 12 14 16 18 20 22 24 Wavelength(/im)

Figure 6.5: Detail of the SAO 183956 models in the mid-IR. Errorbars: CGS3 spectrum, large squares: IRAS points, solid line Model M20p9a, dashed line: effect of adding small grains.

184 2.5x10,-13

S 1.5x10""

,-13

8 10 12 14 16 18 20 22 24 Wavelength (A«n)

Figure 6 .6 : Detail of other SAO 183956 models in the mid-IR. Errorbars: CGS3 spectrum, large squares: IRAS points, solid line Model M20p8, dashed line: M20p9, dotted line:

Mlp51, dash-dotted line: M il

flux. Increasing (I to 1.5 (model M llp5) gave too little long-wavelength flux. Putting

0=13 (model M llp3) also gave mm-wave fluxes that were marginally too low, while

0=1.2 gives good agreement with the JCMT data (model M llp2). This model has the inner radius set to give a good fit to the CGS3 spectra, rather than to the IRAS 25-/xm

flux (quoted in Table 6.3).

Since models with 7 = 2 and 7 = 1 were able to give a fit to the observations (with

suitable values of 0), a pair of models with the grain radius parameter 7 = 1 .5 were run.

Model Mlp51, with 0=1, gave slightly too much mm-wave flux, while the model with

0=1.5 (Mlp51p5) gave too little. A well-fitting model would thus have some value of 0

between 1.0 and 1.5.

The grid of silicate models shows that for SAO 183956 there is a fairly well-defined

locus in (7 ,0 ) parameter space in which well-fitting models are found. The fact that a

contribution to the 1 0 -/im silicate feature may arise in the long-wavelength tail of the

near-IR excess means that it is not possible to use the contrast of the silicate feature

to determine the value of 7 , which would allow a unique model to be specified. Future

high-resolution imaging of the system might allow the spatial distribution of the dust, and

hence 0 , to be determined with sufficient precision to specify a unique model, even if 7

cannot be determined directly.

185 A second set of models was produced, this time using a 75% silicate: 25% amorphous carbon mixture of grains. Only one model with 7 = 3 was calculated (model B31); as with the pure silicate models, it gravely underestimated the millimetre-wave flux. Any

7=3 model with the density distribution parameter /? > 1 would therefore also give too little flux at mm wavelengths.

The 7=2 models B22 and B21 both gave too little mm-wave flux, while decreasing /? to 0.7 (model B20p7) gave too much. Setting (3 to 0.9 (model B20p9) or 0.8 (B20p8) gave mm-wave fluxes that were slightly too low and too high respectively. A model with 7 = 2 that gives a good fit should therefore have a value of j3 somewhere between 0.8 and 0.9.

As in the case of the silicate models, the 7 = 1 models with the density distribution pa­ rameter set to 1.0 and 1.5 gave too much and too little long-wavelength flux respectively.

Setting = 1.1 gave a reasonable fit to the mm-wave data.

Small-grain models were used to determine whether emission from thermally-spiking

grains could fit the near-IR excess of SAO 183956. The small-grain code was run for

silicate and amorphous carbon grains of radius 5 Â, situated 1.5 AU from the star (a distance comparable to the inner radius of the disc models). These grains were found

to be close to thermal equilibrium, with peak temperatures of approximately 400 K for silicate and 750 K for carbon grains.

Even smaller grains, of radius 3 Â, exhibited thermal spiking behaviour, but the result­

ing spectral energy distribution of the smaU-grain emission peaked at too long a wavelength

to give a good fit to the near-IR excess. A 3-Â radius grain contains roughly 30 atoms

(Chapter 5): any smaller ‘grain’ would be unlikely to emit the continuum near-IR radi­ ation that is observed. For small-grain emission to be the dominant mechanism causing

the near-IR excess, the radiation field of SAO 183956 must therefore be harder than that

of the model atmosphere, i.e. excess ultraviolet emission would be required.

Irrespective of the heating mechanism (thermal spiking, accretion heating, equilibrium

radiative heating), some information can be deduced about the temperature and minimum

mass of the material which is responsible for the near-IR excess. This can be achieved by

considering grains close enough to the star that they are hot enough to emit strongly in

the near-IR.

For SAO 183956, a fit to the observed near-IR excess could be obtained using 5-Â

grains of silicate situated 3 X 10^^ cm (0.2 AU) from the star. The peak temperature

186 of such grains was approximately 1300 K, and a mass of 5 X 10“^ Earth masses was required to produce sufficient near-IR flux. For amorphous carbon grains, a distance of

0.4 AU gave a good fit, with a temperature of 1300 K and a mass of 1 x 10“® A/Earth* These mass estimates are likely to be lower limits on the actual mass involved, since larger grains would have a lower surface area per unit mass, and not all the grains in whatever population is responsible for the near-IR excess need be hot at any given time.

Using only small silicate grains gave a 10-/im silicate feature with much higher contrast than that observed in the CGS3 spectrum, implying that the material radiating in the near-IR cannot be composed entirely of small silicate grains. Larger silicate grains, with weaker 10-/zm features, or grains of a different composition must also be present. Adding the spectrum of small grains of amorphous carbon to that of the silicate grains, in a 2:1 ratio, gives a silicate feature of similar strength to that observed in the CGS3 spectrum. Combining the emission from this small-grain mixture with model M20p9a gives a good fit to the observed SED of SAO 183956 (Figure 6.4). Details of the fit in the mid-IR are presented in Figure 6.5. No combination of models could provide enough flux to match the 8-9^m portion of the CGS3 spectrum without greatly overestimating the flux at M. This wavelength region includes the wing of the strong 7.7-/im UIR band seen in the spectra of a number of Vega- excess stars (Figure 3.3), and so it is possible that there is a UIR-band contribution to the 10-/xm spectrum of SAO 183956. The inflection at approximately 11 fim in the observed spectrum (Figure 6.5), not matched by the model spectrum, is also suggestive of a weak

UIR feature.

6.1.4 SAO 183986 (HD 143006)

The infrared excess of SAO 183986 was first noted by Odenwald (1986); it is also included in the Walker & Wolstencroft (1988) list of Vega-excess stars. SAO 183986 displays Ha emission (Stephenson 1986). Although Manchado et al. (1989) proposed that it is an object in transition between the asymptotic giant branch and planetary nebula stages, a proposal also made by van der Veen et al. (1993), Weintraub (1990) listed it as a pre-main sequence star. Zuckerman et al. (1995) detected CO emission from this source.

van der Veen et al. (1994) gave a spectral type for SAO 183986 of G5V, and made

JCMT continuum observations at 0.45, 0.8 and 1.1 mm. As in the case of SAO 183956,

187 they concluded that it was impossible to obtain a satisfactory model fit to the observed

excess energy distribution with a single dust shell. The Michigan spectral catalogue (Houk

1988) gives a classification of G 6 /G 8 .

The star was modelled using a Kurucz atmosphere with an effective temperature of

5750 K, and surface gravity log ^=4.5, appropriate for a G5V spectral type. A luminosity of 0.79 L© (Schmidt-Kaler 1982) implies a stellar radius of 0.89 R©. A distance of 85 pc was found to give a good fit with the dereddened optical fluxes, in good agreement with the distance of 82 pc calculated in Table 3.4.

A grid of models was run using astronomical silicate grains (models M22-M2p71, see Table 6.4). The disc outer radius was set to 850 AU, corresponding to a projected disc diameter of 20 arcsec. Minimum and maximum grain sizes were 50 Â and 1 mm.

The presence of UIR-band emission in the 1 0 -/^m spectrum of SAO 183986 meant that a good fit could not be obtained to the shape of the spectrum; it was therefore treated as an upper limit to the model flux in that wavelength region. The inner radius and mass of the disc were adjusted to fit the IRAS data at 25 and 60 /im.

The first model, M22, gave slightly too little flux at millimetre wavelengths. Decreasing the value of the density distribution parameter to unity (model M21) gave significantly

too much mm-wave flux. Setting ^ to 1.8 gives good agreement with the observations from 25 /xm to 2 mm.

Model M12, the first of the 7 = 1 models to be calculated, gave slightly too much long-

wavelength flux. Increasing j3 from 2 to 2.3 gave good agreement with the IRAS 100-/xm

and JCMT fluxes (model M12p3).

The only 7 = 3 model to be run (model M31) gave significantly too little long-wavelength flux. Any 7 = 3 models with higher values of would therefore also give too little mm-

wave flux. Since model M31 gave too little mm-wave flux and M21 gave too much, two

further models were run keeping /3 = 1, and values of 7 that lay between 2 and 3. Model

M2p51 ( 7 = 2 .5 ) gave too much long-wavelength flux, while model M2p71 ( 7 = 2 .7 ) gave good agreement at 0 . 8 /xm, but slightly too little flux at 1 .1 mm.

A second grid of models (B22-B31) was calculated, using a mixture of 75% silicate and

25% AC grains. Similar results were found as for the pure silicate models, with a good

fit to the data being found for 7 = 2 and /3=l.S (model B21p8), another well-fitting model

being found using 7 = 1 and j3 between 2 and 3 (model B12p5), and a grain size parameter

188 Table 6.4: Models for SAO 183986 (HD 143006)

Model 7 R'm Afidisc Fi2 F25 ■^60 J^ioo J^O.8 Fia cm M e Jy m Jy

Observations 0.86 3 . 2 6.6 4.8 233 114 (± error) 0.05 0 . 2 0.7 0.5 25 14

M22 2 2 7.7x10^3 6.9x10"® 0.23 3 . 2 6.5 4.7 193 86

M21 2 1 5.5x10^3 8.5x10"® 0.29 3 . 2 6.6 5.6 670 333

M21p8 2 1.8 7 .5 x 1 0 '^ 1.1 xlO"® 0.23 3 . 2 6.6 5.0 229 103

M12 1 2 5.9x10'^ 1.7x10"® 0.20 3 . 2 6.6 4.7 267 136

M12p3 1 2.3 6.2x10^3 1.1 xlO"® 0.19 3 . 2 6.6 4.6 229 115

M31 3 1 2.2 xlO'^* 4.6x10"® 0.08 3 . 2 6.54 4.93 119 44

M2p51 2.5 1 1.5x10^^ 2.8x10"® 0.13 3 . 2 6.6 5.6 361 157

M2p71 2.71 1 .9 x 1 0 '^ 1.3x10"® 0.10 3 . 2 6.6 5.3 222 90

B22 2 2 1.0x10'^ 1.1x10"® 0.28 3 . 2 6.6 4.9 209 93

B21 2 1 7.0x10^3 1.1 x l0 "4 0.34 3 . 2 6.6 5.6 630 312

B21p8 2 1.8 9.7x10^^ 1.6x10"® 0.28 3 . 2 6.7 5.0 242 110

B ll 1 1 5.2x10^3 3.4x10"^^ 0.32 3 . 2 6.6 5.8 > lJ y 580

B12 1 2 7.2x10^3 2.5x10"® 0.24 3 .1 6.4 4.6 269 138 8.5x10^3 B13 1 3 1.0x10"® 0.21 3 .1 6.6 4.5 205 102

B12p5 1 2.5 7.8x10^^ 1.3x10"® 0.23 3 . 2 6.6 4.6 224 113

B31 3 1 3.5 xlO^'^ 4.0x10"® 0.29 3 . 2 6.5 4.8 103 38

C22 2 2 2 .0 x 1 0 '^ 3.2x10"® 0.23 3 .1 6.6 3.6 30 11

C21 2 1 1.4x10^'* 1.8x10"'* 0.28 3 .1 6.6 4.6 87 32

C ll 1 1 1.2x10^^ 7.5x10"'* 0.17 3 . 2 6.6 4.5 84 31

C0p50p5 0.5 0.5 7.5x10^3 2 .8x10"^ 0.27 3 . 2 6.6 6.0 214 80

189 -1 1

-12

-1 3

-1 7

—IB

-1 9 10° Wavelength (/xm)

Figure 6.7: Results of modelling SAO 183986. Solid line: model B21p8, dashed line: effect of adding small silicate and AC grains to model B21p8

190 5x10^*

4 x l(T " '6 3. ? 3X1Q-" a ► 2 x l(T " g E 10-''

0 I I I I I I I I I I I I I I I I I I I I I I I _ J I L 9 10 11 12 13 14 Wavelength (/im)

Figure 6.8: Detail of the SAO 183986 models in the mid-IR. Errorbars: CGS3 spectrum,

large square: IRAS point, solid line Model B21p8, dashed line: effect of adding small

grains.

7 = 3 giving too little long-wavelength flux (model B31).

The presence of the UIR bands in the 10-/xm spectrum implies a carbonaceous compo­

nent in the circumstellar dust of SAO 183986, so these ‘blend’ models are more plausible than their pure silicate counterparts. Accordingly, one of the best-fitting blend models,

B21p8 is presented in Figure 6.7. Using the small grain code showed that 5-Â grains of silicate or AC located 6 x 10^^ cm (4 AU) from the star (similar to the inner radii of the disc models) exhibited thermal

spiking behaviour, but the resulting emission spectrum peaked at approximately 5 //m,

giving a poor fit to the observed near-IR excess. Similar results were obtained using 3-Â

grains. Good agreement with the observations could be obtained using 5-Â AC grains at

1.2 X 1 0 ^ 2 cm (0.08 AU) from the star. These grains were close to thermal equilibrium,

with a peak in the probability distribution function at approximately 1400 K. A mass of

4 X 10~® MEarth of these grains was required to provide sufficient near-IR flux. A similar fit could be obtained using 5-Â silicate grains at 6 x 10'^ from the star.

These had a peak temperature of approximately 1500 K, and a mass of 1 x 10“^ Msarth

was required. The small silicate grain gave a strong silicate feature, exceeding the flux

in the observed CGS3 spectrum. A superposition of these two smaU-grain models, with

weighting factors of 0.8 for AC and 0.2 for silicate gives a lower-contrast silicate feature.

191 which is in reasonable agreement with the 10-13/zm portion of the CGS3 spectrum. The effects of adding this model to model B21p8 are illustrated in Figures 6.7 and 6 .8 . The combined model gives a good fit to the general shape of the 9-13/im emission, and clearly shows the 7.7- and 11.3-/im UIR bands in the CGS3 spectrum of this star (see also Chap­ ter 3).

6.1.5 SAO 184124 (HD 144432)

This A9/F0V star (Houk 1982) shows Ha emission (Wackerling 1970), and was first listed as a Vega-excess stars by Walker & Wolstencroft (1988). Gregorio-Hetem et al. (1992) suggest it is a Herbig Ae star, while Pottasch & Parthasarathy (1988) proposed that it is an AGB or post-AGB star.

SAO 184124 was observed as part of the te Lintel Hekkert et al. (1991) 1612-MHz maser survey, but no OH emission was detected. Zuckerman et al. (1995) obtained only an upper limit for CO emission from this star. SAO 184124 shows the strongest silicate feature of any of the stars in the present sample. A Kurucz(1991) model atmosphere with Teff=7250 K and log ^ = 4, appropriate for a star of spectral type FOV was used to model SAO 184124. The luminosity of an FOV star (6.5 L@) was adopted from Schmidt-Kaler (1982), giving a radius of 1.6 R©. A distance of 1 1 0 pc was found to give good agreement with the dereddened optical fluxes, consistent with the distance of 119 pc calculated from the UBV photometry (Table 3.4). The usual maximum and minimum grain sizes (1 mm and 50 Â) were used, and the disc outer radius was set to 1100 AU, corresponding to a projected disc diameter of 20 arcsec.

In the modelling, the disc mass and inner radius was adjusted to fit the IRAS fluxes at 60 and 25 ^m, and/or the CGS3 2 0 -/zm spectrum .

A grid of pure silicate models was run (models M 32-M llp8), with different values of the grain size parameter 7 and the density distribution parameter (3. The first model with

7 = 3, model M32, predicted far too little 100-/im and millimetre-wave flux for /3 = 2.

Decreasing the value of (5 to unity (model M31) gave better agreement at 100 /xm, but the model fluxes at 0 . 8 and 1 .1 mm were still considerably too low.

Of the 7 = 2 models, model M22 (with a density distribution parameter /?= 2 ) gave too little long-wavelength flux, while model M21 (with 0=1) gave too much. Three models were therefore run with intermediate values of 0 (models M21p5-M21p2). Model M21p5

192 Table 6.5: Models for SAO 184124 (HD 144432)

Model 7 R'm ^diBC F u F25 ^60 J^ioo J^O.8 f l.l

cm M q Jy m Jy Observations 7.6 9.2 5.7 3.3 103 72 (± error) 0.5 0.6 0.6 0.3 34 12

M32 3 2 2.5 X 0i4 3 .8 x 1 0 "^ 1.5 11.5 5.7 2.1 15 5 Oi4 M31 3 1 1.6 X 9.6x10-® 1.6 9.9 5.7 2.9 36 13

M22 2 2 5.0 X 013 1.7x10-® 3.8 9.9 5.9 2.6 60 26

M21 2 1 3.2 X 013 2.7x10-® 3.5 7.7 5.7 3.5 230 110 013 M21p5 2 1.5 5.5 X 6.6x10-® 2.4 7.7 5.7 3.0 106 47 013 M21p3 2 1.3 3.5 X 9.6x10-® 4.1 8.9 5.6 2.9 121 55

M21p2 2 1.2 3.8 X 013 1.4x10-® 3.3 8.0 5.6 3.1 152 70

M13 1 3 7.0 X 013 2.7x10-® 2.1 8.2 5.7 2.7 90 42 013 M12 1 2 6.0 X 7.0x10-® 2.0 9.4 5.7 3.0 114 57

M llp S 1 1.8 5.0 X 013 9.5x10-® 2.6 7.9 5.7 3.0 124 62 Ol4 B31 3 1 2.5 X 1.2x10-® 2.7 8.2 5.6 2.7 31 11 013 B23 2 3 9.0 X 1.1x10-® 2.6 8.7 5.7 2.5 50 21

B22 2 1 8.0 X 013 3.0x10-® 2.4 7.9 5.7 2.7 67 29

B21 2 1 4.0 X 013 3.3x10-® 3.4 7.7 5.8 3.5 215 100 013 B21p5 2 1.5 6.0 X 8.0x10-® 2.9 8.1 5.6 2.9 96 43

B21p3 2 1.3 6.0 X 013 1.5x10-® 2.5 7.4 5.6 3.1 130 60

B13 1 3 8.0 X 013 3.7x10-® 2.3 8.4 5.8 2.7 83 41 013 B12 1 2 6.0 X 8.4x10-® 2.8 8.4 5.7 2.8 103 51

Bll 1 1 3.0 X 0^7 1.1 xlO -4 3.6 7.3 5.5 3.6 360 190

Blips 1 1.8 6.0 X 013 1.3x10-® 2.5 7.8 5.6 2.9 121 61

193 -1 0

-1 1

-1 2

-1 3

T

-1 7

—18

-1 9 10° Wavelength (/xm)

Figure 6.9: Results of modelling SAO 184124. Solid line: model B21p3, dashed line: effect of adding small silicate and AC grains to model B21p3.

194 ,-is 4x10

3x10,-is I 2x10,-13 &

10,-13

8 10 12 14 16 18 20 22 24 Wavelength (/im)

Figure 6.10: Detail of the SAO 184124 models in the mid-IR. Errorbars: CGS3 spectrum large squares: IRAS points, solid line: Model B21p3, dashed line: effect of adding small grains. gave slightly too little flux at 1.1 mm, while models M21p3 and M21p2 agreed with both

JC M T points to within 1.5

A second grid of models was calculated, using a mixture of silicate and AC grains, in a 3:1 ratio (models B31-Bllp8). Only one model was run with 7 = 3 (model B31) — as in the case of the pure silicate models, it gave far too little mm-wave flux, so no further

7=3 models were attempted.

Several models were run with 7 = 2; models B23 and B22 gave far too little long- wavelength flux, while model B21 gave somewhat too much. Two models were run with values of(3 between 1 and 2. Model B21p5 gave slightly too little 1.1-mm flux, while model

B21p3 gave good agreement with both JCMT points, and is presented in Figure 6.9.

Of the models with 7 = 1 (models B13-Bllp8), models B13 and B12 gave too little long-wavelength flux, while model B ll gave too much. Setting /?=1.8 (model Bllp8) gave good agreement with the observed fluxes.

Using the smaU-grain technique to attempt to fit the near-IR excess of SAO 184124, it

195 was found that 5-Â radius grains of silicate or amorphous carbon located at a distance of

5 X cm (3 AU) from the star (typical of the inner radii of the disc models) exhibited thermal spiking, but the peak of the resulting emission spectrum lay at approximately 4 /im, loo long to give a satisfactory fit to the observed near-IR excess. 3-Â radius grains also gave a spectrum that peaked at too long a wavelength.

Decreasing the distance from the grains to the star brings them closer to thermal equi­ librium, and increases the peak temperature of the probability distribution (Chapter 5). A good fit to the observed near-IR excess could be found for 5-Â silicate grains at 3.3 x 10'^ cm (0.2 AU), and for amorphous carbon grains at 7 x 10^^ cm (0.5 AU).The peak tem­ peratures of both grain species were approximately 1100 K. A mass of 6 x 10“^ MEarth of silicate grains, or 1 x 10~® MEarth of AC grains was needed to obtain sufficient near-IR flux. Using only small silicate grains gave a 10-/tm silicate feature with higher contrast than that observed in the CGS3 spectrum. Combining the two ‘hot’ small-grain models, with equal weightings, gave a reasonable fit to the CGS3 data. The effects of adding this combined model to disc model B21p3 are shown in Figures 6.9 and 6.10.

6.1.6 SAO 186777 (HD 169142)

SAO 186777 was first noted as a Vega-excess star by Walker & Wolstencroft (1988). It was classified as a B9V star by Houk (1982), and shows Ha in emission (Merrill & Bur well

1949). It has recently been reclassified as an A5e star on the basis of echeUe spectra

(Dunkin et al., in preparation).

van der Veen et al. (1989) proposed that SAO 186777 is an object in a transition phase between the asymptotic giant branch (AGB) star and planetary nebula stages. They obtained Walraven (UV-visual) and near-IR photometry of this star. As in the case of SAO 226057, the Walraven photometry shows some evidence for excess UV flux, which together with the presence of emission lines, could indicate that is a young star.

SAO 186777 was observed in the CO J= l-0 line (Likkel et al. 1991) and in the OH maser lines (Likkel 1989), but no emission was detected from either species.

SAO 186777 was the first Vega-excess star discovered to show the UIR bands in its mid-IR spectrum (Sylvester et al 1994b). Since the 20-/im spectrum of this source shows silicate emission, models were run using a mixture of silicate and amorphous carbon grains.

196 -1 0

-1 1

-1 2

-1 3

T -1 4 I -1 5

-1 7

-1 8

-1 9

-2 0 IqO 10 2 Wavelength (jim )

Figure 6.11: Results of modelling SAO 186777. Large squares: photometric data, small squares: CGS3 spectrum, with the fluxes multiplied by 1.3. Solid line: model B23, dashed line: effect of adding hot (TwllSG K) grains.

197 Table 6.6: Models for SAO 186777 (HD 169142)

Model 7 P R'm Afdjgc F u F25 Feo J^ioo Fq.8 Fi,i

cm M© Jy m Jy Observations 2.95 18.4 30 23.4 554 287 (± error) 0.17 1 .1 3 2 . 0 34 13

B33 3 3 3.2x10'® 1.3x10-® 1 .0 1 16.3 33 2 0 . 0 2 2 1 78

B31 3 1 1 .8 x 1 0 '® 1.9x10"® 1.58 17.0 30 19.7 266 95

B23 2 3 3.7x10''* 3.6x10"® 1.99 18.3 29 18.7 547 236

B22 2 2 3.5x10''* 9.0x10"® 1.85 17.4 30 2 1 .1 810 358

B13 1 3 2.7x10''* 8.5x10"® 1.63 19.1 30 18.6 753 374

B14 1 4 3.0x10''* 7.0x10"® 1.46 18.8 30 18.5 708 350

B2p52 2.5 2 1 .2 x 1 0 '® 6.7x10"® 1 .8 6 18.1 31 2 2 .1 635 253

B2p52a 2.5 2 1 .2 x 1 0 '® 1.7x10"'* 1.77 17.3 30 21.3 627 252

B2p51p5 2.5 1.5 9.0x10''* 7.8x10"® 2.27 19.1 30 2 0 . 8 638 256

with the carbon grains making up 2 0 % of the total dust mass. The new spectral type of A5Ve from Dunkin et al. (1995, in preparation) was adopted.

The star was modelled using a Kurucz (1991) model atmosphere with an effective tem­ perature of 8250 K and log gf=4.0. The adopted luminosity of an A5 star is 14 L©

(Schmidt-Kaler 1982), implying a radius of 1.88 R©. A distance of 145 pc, obtained from the optical photometry, was found to give a good fit to the dereddened fluxes.

The minimum and maximum grain sizes were 50 Â and 1 mm, and the disc outer radius was set to 1450 AU, giving a projected disc diameter of 20 arcsec. The inner radius and mass of the disc were adjusted to fit the IRAS fluxes at 25 and 60 /xm.

Two models were run with a grain size parameter of 7 = 3 (models B33, B31). Both gave significantly too little flux at millimetre wavelengths. Of the 7 = 2 models, model B23 gave reasonable agreement withthe JCMT data, while model B22 gave mm-wave fluxes that were somewhat too high.

Since model B22 predicted too much long-wavelength flux, any model with 7 = 1 and

/3 < 2 would also overestimate the long-wavelength fluxes. The first 7 = 1 model therefore had P=3 (model B13), but even this gave too much mm-wave flux. Increasing ^ to 4 made little difference (model B14).

198 1.2x10 -IS L ? i 7 8x10 B 6x10"

^ 4x10

2x10"

14 16 18 Wavelength Oxm)

Figure 6.12: Detail of the SAO 186777 models in the mid-IR. Errorbars: CGS3 spectrum scaled up by a factor 1.3, large squares: IRAS points, solid line Model B23, dashed line: effect of adding small grains.

Setting 7 to 2.5 and /3 to 2 (model B2p52) gave a better fit to the data than model

B22. Compared to model B23, B2p52 gives better agreement with the JCMT data at 1.1 mm, but does not fit as well at 0.8 mm. Increasing the maximum grain size to 10 mm (model B2p52a) made little difference to the long-wavelength fluxes. Decreasing f3 to 1.5

(with a maximum grain size of 1 mm) also had little effect at mm wavelengths.

Model B23 was taken as the best-fitting model. The inner radius of this model was set to provide a fit to the IRAS 25-/zm flux; compared with the 20-/im CGS3 spectrum, the model predicts the right amount of contrast in the silicate feature, but the flux level is somewhat too high. Essentially aU of the model flux in the mid-IR is predicted to emerge from the inner few arcseconds of the disc, so the difference between the CGS3 and IRAS fluxes does not appear to be a beam size effect. Scaling the CGS3 fluxes up by a factor of 1.3 gives good agreement between the IRAS and CGS3 fluxes at 12 /zm, and between the model and the

20-/zm spectrum (see Figure 6.12).

Using the small-grain model in order to fit the near-IR excess of SAO 186777, it was found that 5-Â and 3-Â radius grains of silicate or amorphous carbon located at the inner radius of the disc model B23 showed thermal spiking behaviour, but the resulting emission

spectra peaked at too long a wavelength to give good agreement with the observations.

199 Reducing the distance of the small grains from the star to 1.0 x 10'^ cm (0.7 AU) for

5-Â radius grains of amorphous carbon gave good agreement with the observed near-IR excess. The grains were found to be close to thermal equilibrium, with a most probable temperature of 1150 K. A mass of 1.2 X 10~® MEarth of such grains was required. Adding this model to model B23 gave good agreement to all the photometry, but slightly too much flux in the 10-/xm spectrum (Figure 6.12).

6.1.7 SAO 206462 (HD 135344)

SAO 206462 was included in a sample of post-main sequence sources with infrared excess emission which were surveyed for H 2 O maser emission (Zuckerman & Lo 1987). No maser emission was found from SAO 206462. It was detected in CO by Zuckerman et al. (1995) who list an F4Ve spectral classification. Walker & Wolstencroft (1988) listed SAO 206462 as a Vega-excess candidate; it also appears in the list of Oudmaijer et al (1992). Coulson & Walt her (1995) made extensive optical and infrared observations of this star. They found that its spectral type is misclassified in the SAO catalogue: it shares the same HD number as SAO 206463, and the A2 classification appropriate for SAO 206463 is repeated for SAO 206462. The Michigan catalogue gives a combined spectral type of

AOV. Coulson & Walther determined a spectral type for SAO 206462 of F8V, roughly consistent with observations made at Lick Observatory (Zuckerman et al. 1995) and at the AAT (Dunkin et al. 1995). Coulson h Walther detected near-IR excess continuum emission from SAO 206462, and found hydrogen emission lines and the 3.3-/xm UIR feature to be present in the near-IR spectrum of this source. They also obtained a CGS3 spectrum which shows UIR emission in the 7.7- and 11.3-/zm bands, in good agreement with the spectrum presented in Chapter 3, along with a mm-wave spectrum that possibly shows the CO 2-1 (230 GHz) line in emission.

Coulson & Walther (1995) modelled the infrared excess emission of SAO 206462 with two blackbodies — one of temperature 1500 K, which fitted the near-IR excess, and one of temperature 95 K, which fitted the long-wavelength data.

For the present modelling, the star was treated as F8V. A model atmosphere with

Teff = 6250 K and log g = 4.5 was used. Adopting a stellar luminosity of 21 L@, and an effective temperature of 6200 K (Schmidt-Kaler 1982) gave a radius R* = 8.7 X 10^° cm.

The distance derived from the UBV photometry was 84 pc; this distance was adopted

200 Table 6.7; Models for SAO 206462 (HD 135344)

Model 7 ^in ■A/djgc F u F25 ^60 ^ 1 0 0 fb.8 Fi.i cm M© Jy m Jy Observations 1.59 6.7 25.6 25.7 570 209 (± error) 0.01 0.9 3.6 2.6 21 14

B22 2 2 3.5x10^^ 1.2x10-'* 0.33 6.5 25.5 26.2 >1 Jy 809 B32 3 2 1.8x10'® 1.1 XlO-® 0.19 6.2 25.3 21.7 389 140

B23 2 3 4.0x10'^ 6.0x10-® 0.31 6.4 25.6 25.8 >1 Jy 617 B24 2 4 4.0x10'^ 4.0x10-® 0.33 6.5 24.8 23.9 >1 Jy 493 B31 3 1 1.4x10'® 1.7x10-® 0.25 6.5 25.5 23.0 483 176

B2p51 2.5 1 3.0 xlO''* 1.3x10-® 0.34 6.3 26.2 27.4 >1 Jy 716

B2p52 2.5 2 1.0x10'® 6.4x10-® 0.32 6.5 26.2 25.0 >1 Jy 469 B2p53 2.5 3 1.1 xlO'® 4.1 XlO-® 0.32 6.6 25.9 23.8 922 372 B2p54 2.5 4 1.1 xlO'® 3.0x10-® 0.32 7.1 25.9 22.8 788 314

B2p72 2.7 2 1.3x10'® 3.0x10-® 0.28 6.5 25.6 23.1 676 261

B2p73 2.7 3 1.4x10'® 2.0 XlO-® 0.26 6.7 25.3 21.6 543 207

C22 2 2 5.5 xlO''^ 2.0x10-'* 0.39 6.5 25.3 17.8 186 64

C21 2 1 4.3x10'^ 6.0x10-'* 0.43 6.5 25.7 21.6 373 135

C ll 1 1 3.5x10''* 2.4x10-3 0.15 6.4 25.6 20.7 344 124

M22 2 2 2.5 XlO''* 6.5x10-® 0.25 6.4 25.5 25.4 >1 Jy 690 M32 3 2 8.5x10''* 6.6x10-® 0.1 6.5 25.6 19.2 290 103

M2p72 2.7 2 2.5x10''* 1.9x10-® 0.1 7.1 25.8 21.1 597 230

M2p73 2.7 3 8.6x10''* 1.2x10-® 0.1 6.9 25.5 20.0 482 183

201 for the modelling and gave good agreement between models and observations. The CGS3 flux level agrees well with the IRAS fluxes (Figure 6.14).

Since the 10-/im spectrum of this source shows UIR-band emission (Chapter 3; Coulson

& Walther 1995), the first grid of models included some carbonaceous grains — a 25%: 75% amorphous carbon: silicate mixture was used. An outer radius of 840 AU was adopted, and as usual the grain sizes ranged from 50 Â to 1 mm. No attempt was made to fit the IRAS 1 2 -/xm flux, since the 1 2 -//m band contained UIR -band emission, which is not treated by the model. The first model, B22, gave too much mm-wave flux, while the second, B32, gave too little. Two models with 7 = 2 (as for model B22), but with steeper density power-laws

(models B23, B224) were run to determine whether decreasing the amount of distant, cool material could reduce the long-wavelength flux sufficiently to provide a good fit to the observations. In fact, the reduction in millimetre-wave flux was not enough to obtain a good fit to the JCMT data. Setting 7 = 3 (as for model B32) and decreasing /3 to I (model B31) gave an improvement over model B32, but the mm-wave fluxes were still slightly too low.

A grid of models with values of the grain size parameter 7 between 2 and 3 was therefore run, (models B2p51-B2p73). Of these, model B2p73 gave the best fit to the data. Three models using only amorphous carbon grains were run (models C23-C11); aU of these, even with 7 and /? both set to unity gave too little millimetre-wave flux. The spectral energy distribution of model B2p73 is presented in Figure 6.13, and the fit in the mid-IR is shown in Figure 6.14 For completeness, a set of models using only silicate dust was calculated (models M22-

M2p73). Of these, model M2p72 gave a reasonable fit to the observations.

The small grain code was used to try and fit the near-IR excess of SAO 206462. Initially,

5-Â radius grains of amorphous carbon were considered, at a distance of 1.4 x 10'® cm

(9 AU) from the star (the inner radius of disc model B2p73). These grains displayed

thermal spiking behaviour, but excursions to very high temperatures were too infrequent for the resulting SED to give good agreement with the observed near-IR excess emission.

The small-grain SED peaked at approximately 10 /xm, compared with approximately 2 /xm

for the observed excess spectrum. Grains of radius 3 Â behaved in a similar fashion; again

the resulting spectrum peaked at too long a wavelength.

202 -1 0

-1 1

-1 2

-1 3

-1 5

-1 6

-1 7

-1 8

-1 9

Wavelength (jim)

Figure 6.13: Results of modelling SAO 206462. Solid line: model B2p73, dashed line: effect of adding hot (T«1000 K) grains to model B2p73, dotted line: model M2p73.

203 1.5x10,- 1#

I 10 ’’a I 5x10,-14

0 8 10 12 14 16 18 20 22 24 Wavelength (/im)

Figure 6.14: Detail of the SAO 206462 models in the mid-IR. Errorbars: CGS3 spectrum, large squares: IRAS points, solid line Model B2p73, dashed line: effect of adding small grains.

To obtain some insight into the temperature and mass of the material emitting in the near-IR, the distance of the 5-Â grains from the star was decreased until a fit to the near- IR excess emission was obtained. A distance of 4 x 10*^ cm (0.26 AU) was found to give good agreement. The grains were close to thermal equilibrium, with a peak temperature of 1060 K. The mass of 5-Â amorphous carbon grains required to match the near-IR flux was 3 X 10“ ^ AfEarth» equivalent to the mass of a 100-km diameter asteroid. The effect of adding this amount of hot material is illustrated in Figure 6.13.

6.1.8 SAO 226057 (HD 139614)

SAO 226057 is an emission-line star (Wackerling 1970), which was first noted to have an infrared excess by Walker & Wolstencroft (1988). van der Veen et al. (1989) proposed that it is an object in a transition phase between the asymptotic giant branch (AGB) star and planetary nebula stages. They obtained Walraven (UV-visual), near-IR and narrow­ band 10-/im (Nl, N2, N3) photometry of this star. The Walraven photometry shows a possible UV excess, which together with the presence of emission lines, could indicate that

SAO 226057 is a young star. The spectral type given in the Michigan catalogue is A7V.

Silva et al. (1993) observed SAO 226057 at 1612 and 1667 MHz, but did not detect any OH emission.

204 The 0.8-mm flux («0.6 Jy) of SAO 226057 is the highest for any source in the present sample, and is more than an order of magnitude larger than the 0 .8 -mm fluxes of the (much

closer) prototypes Vega and (i Pic (e.g. Zuckerman & Becklin 1993). The fractional excess luminosity, LiR/Lfg^^r is 0.39 (Table 3.19). The star was modelled using a Kurucz (1991) model atmosphere, with an effective

temperature of 7750 K, and a surface gravity log g = 4.0. Adopting this T«ff and a luminosity of 10.5 L©, appropriate for an A7V star (Schmidt-Kaler 1982) gives a stellar

radius of 1.75 R©. The distance to SAO 226057 derived from the optical photometry is 151 pc; this was adopted for the modelling, and gave good agreement with the observations.

A grid of models (see Table 6 .8 ) was run, using only silicate dust for models M22-

Mlp51p5. The minimum and maximum grain sizes were 50 Â and 1 mm; the disc outer

radius was set to 1500 AU, corresponding to a projected disc diameter of 20 arcsec. The disc mass and outer radius were adjusted to fit the IRAS fluxes at 25 and 60 /xm. Given that the long-wavelength tail of the strong near-IR excess may contribute to the 12-/zm

flux, the IRAS 1 2 -/xm point was treated as an upper limit to the flux from the equilibrium models.

The first model, M22, gave too little flux longwards of 60 /xm. Decreasing the density

distribution parameter, /?, to unity (model M21) gave a 100-/xm flux that was consistent

with the IRAS value, but gave 0.8- and 1 . 1 -mm fluxes that were too high. Models keeping

7 = 2 , but with intermediate values of (3 were therefore run (models M21p5, M21p3). Model

M21p3 gives a good fit to the data from 25 /xm to 1 mm, and is presented in Figure 6.15.

Given that a rather low value of j3 was required for the 7 = 2 models, the first model

with 7 = 3 also had a low value of (3 (model M31). This model gave far too little mm-wave

flux, so the value of /3 was reduced to an even lower value (model M30p5). This model,

although consistent with the IRAS 1 0 0 -/xm point, still gave too little mm-wave flux. A

model with 7 = 2 . 5 (model M2p51) gave a better fit than the 7 = 3 models.

The first 7 = 1 model (model M12) gave slightly too little long-wavelength flux. De­

creasing (3 to 1.5 gave slightly too much mm-wave flux (model M llp5), while setting

/?=1.7 gave a better fit (model M llp7). Setting (3 once again to 1.5, but increasing 7 to

1.5, gave mm-wave fluxes that were less than those of model M llp5, but stiU somewhat

high compared with the observations.

A grid of models (B22-Bllp7) was produced, using a blend of 75% silicate and 25%

205 Table 6.8: Models for SAO 226057 (HD 139614

Model 7 R'm ^Ifdisc Fi2 F2S J^ioo J^O.8 Fi.i cm M© Jy m Jy Observations 4.1 18.1 19.3 13.9 608 272 (± error) 0.2 2.5 2.7 2.0 27 13 M22 2 2 1.4 xlO'^ 2.3x10“® 3.1 18.3 19.3 10.7 317 138

M21 2 1 8.0x10^3 2.4x10“^ 4.3 18.3 19.3 13.2 > lJ y 481 M21p3 2 1.3 1.0 xlO^'* 1.1 xlO “ 4 3.6 18.1 19.3 12.1 623 288

M21p5 2 1.5 1.1 xlO^^ 6 .4 x 1 0 “ ® 3.4 18.2 19.2 11.5 475 214

M31 3 1 4 .8 x 1 0 '^ 1 .3 x 1 0 “ ® 1.0 18.0 19.3 11.4 165 59

M30p5 3 0.5 2.4x10'^ 2 .5 x 1 0 “ ® 2.2 18.1 19.3 13.9 266 97 M2p51 2.5 1 2.5 xlO^^* 7 .5 x 1 0 “ ® 2.1 18.0 19.2 12.8 504 209 M12 1 2 1.1 xlO^^ 6 .7 x 1 0 “ ® 3.0 18.4 19.4 11.2 488 254

M llp 5 1 1.5 9 .0 x 1 0 '^ 1.9x10“^* 3.5 18.2 19.2 12.0 741 382

M llpT 1 1.7 9.8x10^3 1.2x10“^ 3.3 18.2 19.2 11.5 595 303

M lp51p5 1.5 1.5 8.8x10^3 1.3x10“^ 3.6 18.2 19.3 11.9 661 325

B22 2 2 1.7x10'^ 3.5x10“® 3.2 18.1 19.3 10.8 324 141 B21 2 1 9.9x10'^ 3.0x10“'* 4.4 18.2 19.3 13.1 939 442

B21p3 2 1.3 1.3 xlO^'^ 1 .4 x 1 0 “ ^* 3.9 18.2 19.3 12.0 596 273

B31 3 1 7.1 xlO '^ 1.1 xlO “ ® 3.5 18.1 19.2 10.9 139 50

B12 1 2 1.3 xlO^^ 9.7x10“® 3.0 18.2 19.3 11.2 492 248

B llp 5 1 1.5 1.1 xlO^^ 2 .7 x lO “ 4 7.5 18.2 19.4 10.0 739 383

BllpT 1 1.7 1.2x10^^ 1.7xlO“4 3.3 18.2 19.3 11.6 603 308

C ll 1 1 2.0x10^^ 2.4xlO“3 2.6 18.1 19.3 10.6 127 45

C0p50p5 0.5 0.5 6.8x10^^ 7 .6 x 1 0 “ ^ 6.1 18.1 19.3 14.4 274 99

206 -1 0

-1 1

-12

-1 3

T -14

I -1 5 -1 6

-1 7

-IB

-1 9

0 1 10 2 Wavelength (jim )

Figure 6.15: Results of modelling SAO 226057. Solid line: model M21p3, dashed line: effect of adding small AC grains to model M21p3.

207 amorphous carbon grains. Similar results were obtained as for the pure silicate models,

with the best-fitting model having 7 = 2 and /)=1.3. Again, models with 7 = 3 gave far

too little mm-wave flux, while for 7=1, the best fit could be obtained with a value of (3

between 1 and 2 .

Two models were run using only amorphous carbon grains (models C ll and C0p50p5).

Both gave significantly too little long-wavelength flux, even with rather low values of 7

and p.

The near-IR excess of SAO 226057 was modelled using the small-grain technique, grains of radius 5 Â located lO'^cm (70 AU) from the star (the inner radius of model M21p3) showed departures from thermal equilibrium, but the peak wavelength of the

resulting emission spectrum was too long.

3-Â radius grains gave better results, although the fit to the near-IR observations was not perfect, with too much flux in the M band, and too little at A harder UV- optical radiation field than that predicted by the Kurucz model atmosphere would increase

the probability of high-temperature excursions (Chapter 5), and so cause the small-grain emission to peak at shorter wavelengths.

The narrow band 1 0 -/im photometry of SAO 226057 does not suggest the presence of a

strong silicate feature, so only amorphous carbon grains were considered in the small-grain

modelling. The mass of thermally-spiking small grains at lO'^cm required to produce the

near-IR flux was 6 X 10^^ g (lO"'*MEarth)- The effects of adding thermally-spiking grains

to model M21p3 are shown in Figure 6.15.

6 . 2 Stars with mid-IR excess but no near-IR Excess

6 .2.1 SAO 26804 (HD 233517)

This star, classified K2 in the HD catalogue, was first noted to be a Vega-excess star by

Walker & Wolstencroft (1988); it also appears in the list compiled by Stencel & Backman

(1991). Likkel et al. (1991) observed SAO 26804 in the CO 1-0 line but did not detect any

emission. Zuckerman et al. (1995) obtained only an upper limit for CO emission from this

source. The JCMT observations obtained as part of the present programme (Chapter 3)

yielded an upper limit (of 36 mJy) at 1 .1 mm, while near-IR photometry shows only

photospheric emission.

208 CM I

100 1000 Wavelength (/^m)

Figure 6.16: Results of modelling SAO 26804 (taken from Skinner et al. 1995). Filled circles: photometric data, arrowed symbol: JCMT upper limit, error bars: CGS3 spectra.

Solid line: Disc model plus effects of small grains and synthetic UIR-band spectrum, dashed line: disc model onlv.

209 Skinner et al. (1995) obtained a 1 0 -/im image of SAO 26804 which showed extended emission, making this the first Vega-excess star other than /3 Pic for which the excess emission has been shown to be confined to a disc. The image of SAO 26804 appears elliptical with a FWHM of about 1.1 arcsec in right ascension and about 1.5 arcsec in

declination; the position axis of the semi-major axis is approximately 2 0 ° east of north.

The FWHM of the point-source calibrator, /? Gem, was symmetrically 1.1 arcsec, implying

that SAO 26804 was unresolved in the east-west direction, and consistent with a disc

inclined at less than 30° from edge-on.

Skinner et al. (1995) also modelled the SAO 26804 system in some detail, using methods almost identical to those described in Chapters 4 and 5. These authors found that small

silicate grains were required to fit the rather narrow silicate feature that they judged to

be present in the 1 0 -//m CGS3 spectrum. A disc model using a mixture of silicate and amorphous carbon grains in a 3:1 ratio

by mass was found to give the best fit to the observational data. The power-law indices 7

and 13 for this model were 2.3 and 2.5 respectively, while the inner and outer radii of the disc were 10.7 AU and 100 AU. The maximum and minimum grain sizes were 100 /xm and 50 Â. Any increase in the maximum grain size was found to cause the models to violate

the upper limit on the 1.1-mm flux. The mass of dust in the disc was 3 X 10"^ M©; a

m ass of 6 X 10”^® M© of small (5-Â radius) silicate grains was also required. The SED of this model, with the effects of small silicate grains and a synthetic UIR-

band spectrum, is shown in Figure 6.16. The composite model does not fit the 10-/xm

image too well, having too narrow a FWHM. The disc model without the small-grain

contribution gave better agreement, suggesting that the spatial distribution of the small

grains may be less concentrated towards the star than the distribution adopted by Skinner

et al.

6.2.2 SAO 112630 (HD 34700)

The infrared excess of this GOV (Zuckerman et al. 1995) star was first noted by Odenwald

(1986). SAO 112630 also appears in the lists of stars with IR excess compiled by Walker

& Wolstencroft (1988) and Oudmaijer et al. (1992). Odenwald (1986) was able to fit the

IRAS excess with the spectra of two blackbodies, with temperatures of 475 K and 96 K.

Zuckerman et al. (1995) detected CO emission from this source.

210 Cohen (1992) associated the IRAS source (IRAS 05170-1-0535) with an anonymous galaxy, rather than the star SAO 112630. Close examination of the relevant Palomar Observatory Sky Survey plates revealed no hint of a galaxy at the IRAS position, which is in good agreement with the position of SAO 112630. CGS3 observations have not yet

been attempted of this source; the small beamsize used with CGS3 would make it possible

to determine whether the source of the mid-infrared flux is coincident with the optical

position of SAO 112630. For the present, all the IRAS flux is assumed to be due to the

star and its circumstellar dust.

The star was modelled using a Kurucz (1991) model atmosphere with Teff= 6000 K and

log g = 4.5, adopted as the most appropriate parameters for a GOV star (Schmidt-Kaler

1982). Adopting an effective temperature of 6030 K and a luminosity of 1.5 L@(Schmidt- Kaler 1982), the radius of the star is 1.12 R@. The dereddened optical photometry (Chapter 3) gives a distance to SAO 112630 of

55 pc; this was adopted for the modelling. A grid of models (see Table 6.9) using astronomical silicate was calculated (models M32-M11). As usual, the projected disc diameter was set to 20 arcsec, giving an outer

radius of 550 AU in this case. The minimum and maximum adopted grain sizes were 50 Â

and 1 mm respectively. For each model, the dust mass and disc inner radius were adjusted

to fit the IRAS fluxes at 1 2 and 25 /xm. AU of the models in the set M32-M11 failed to give enough flux at 60 and 100 /xm,

although most of them gave too much flux at 1.1 mm. In an attempt to increase the

1 0 0 -/xm flux without giving too much mm-wave emission, the maximum grain size was

set to 50 /xm; grains of this size have a turnover in emissivity at approximately 100 /xm

(see Chapter 3). Since model M il gave the largest 100-/xm flux, a new 7 = 1, /3=l model (M ila) was calculated with the 50-/xm maximum grain size. This model did give more 60-

and 100-/xm flux than model M il, and less 1.1-mm flux, but the change was not sufficient

to obtain a good fit to the data.

The grain size distribution power-law index, 7 , was reduced to 0.7 with only a sUght

improvement in the fit. Decreasing the maximum grain size stiU further, to 10 /xm, with

7 = /) = 1 (model M l lb ) caused the 1.1-mm flux to faU, but also gave 60- and 100-/xm

fluxes that were too low due to the turnover wavelength being too short.

It therefore appears that the models are unable to match the high 12/xm/25/xm flux

211 Table 6.9: Models for SAO 112630 (HD 34700)

Model 7 /? R i A fd isc F i 2 F25 Reo Rioo F i.i cm M© Jy m Jy Observations 0.60 4.4 14.1 9.4 39 (± error) 0.04 0.3 1.4 0.9 13

M32 3 2 1 . 1 x 1 0 '^ 3.3x10"® 0.50 4.5 2.5 0.9 2

M22 2 2 7.0x10^3 1.5x10"® 0.57 4.6 6.4 4.0 58

M12 1 2 5.0x10^^ 3.1 XlO"® 0.63 4.4 5.5 3.3 78

M21 2 1 5 .0 x 1 0 '^ 1 .4 x 10"5 0.67 4.4 6 . 6 5.0 2 0 0

M il 1 1 4 .5 x 1 0 '^ 5 .4 x 10"5 0.61 4.4 7.3 6 . 1 447 4.0x10^3 M ila 1 1 2.4x10"® 0.57 4.5 8 . 1 6.7 83

MOpTl 0.7 1 4.0x10^^ 2.7x10"® 0.56 4.4 8 . 1 6.9 72

M llb 1 1 4.0x10^^ 4.1 XlO"? 0.59 4.4 6.9 3.8 1 0

M22a 2 2 1.7 xlO'^* 1 . 1 x l0 "5 0.25 4.4 14.5 13.1 307

M2p52 2.5 2 5.0x10^^ 8.7x10"® 0.13 4.3 14.4 13.0 226

M32a 3 2 6 .0 x 1 0 ^^ 1.3x10"® 0 . 1 1 4.4 14.1 9.9 48

M23 2 3 1 .8 x 1 0 ^^ 4.7x10"® 0.26 4.5 14.2 11.9 203

M33 3 3 6 . 8 xlO^'* 8 .3 x 1 0 "? 0 . 1 1 4.3 14.0 9.3 38

B22 2 2 2.3x10^^ 1 .9 x 10"5 0.31 4.3 14.2 13.1 337

B32 3 2 1.2x10^5 2 .0 x 1 0 "® 0 . 2 2 4.3 14.4 11.4 64

B33 3 3 1.3x1015 1.5x10"® 0 . 2 1 4.4 14.1 1 0 . 6 52

C22 2 2 3.8x101'* 3 .6 x 10"5 0.33 4.4 13.9 8.9 28

C 2 1 2 1 2.9x10*'* 1 .0 x l 0 " i 0.36 4.4 14.1 10.9 57

C31 3 1 1.3x10*5 4.4 XlO"® 0 . 2 1 4.4 14.1 11.4 83

C31a 3 1 1.4x10*5 1 .6 x 1 0 "® 0 . 2 0 4.6 14.2 1 0 . 0 45

C21p5 2 1.5 3.5x10*1 5 .9 x 10"5 0.33 4.4 14.1 9.8 39

212 -1 0

-1 1

-1 2

-1 3

-1 5

-1 7

—18

-1 9

0 Wavelength (/im)

Figure 6.17: Results of modelling SAO 112630. Solid line: model M33, dashed line: model

C21p5.

213 ratio and still give sufficient flux at 60 and 1 0 0 /xm.

Further models (M22a-M33) were calculated, adjusting the inner radius and disc mass to fit the IRAS data at 25 and 60 /xm, and making no attempt to fit the 1 2 -/xm point.

The disc outer radius was kept at 550 AU, and the largest grain size was 1 mm. Models

M22a, M2p52, and M23 all gave too much flux at 100 /xm and 1.1 mm. Models M32a and

M33 gave good agreement with all the data except the 12-/xm point.

Many of the Vega-excess stars which exhibit UIR-band emission (e.g. SAO 186777,

SAO 183986) have 12-/xm fluxes which are too large to large to be fitted with an equi­ librium dust model that is simultaneously consistent with the longer-wavelength data. It may therefore be the case that SAO 112630 has UIR-band emission in the IRAS 12-/xm bandpass, or a strong silicate emission feature, such as that of SAO 184124, which is probably due to emission from small grains.

A grid of models comprising a blend of 75% silicate and 25% amorphous carbon dust, by mass, was calculated (models B22-B33). The outer radius was again 550 AU, and the largest grains had a 1 mm radius. Models B22 and B32 gave too much flux at 1.1-mm, while B33 gave a reasonable fit to the data (other than the 1 2 -/xm flux).

A further grid of models was calculated using only amorphous carbon grains (models

C22-C21p5). The maximum and minimum grain sizes were as for the previous models, and the outer radius of the disc was 1650 AU for model C31, and 550 AU for the other models.

Models C 2 1 and C31 gave slightly too much 1 0 0 -/xm and 1 .1 -mm flux; the others fitted the data within the uncertainties.

The best-fitting models are M33 and C21p5; these are plotted in Figure 6.17.

6.2.3 SAO 140789 (HD 141569)

SAO 140789 is a visual double star with components separated by 1.5 arcsec (Lindroos

1983). No magnitude estimate is given by Lindroos for the B component, so it was assumed to be much fainter than the primary at all wavelengths, and was neglected for the purposes of modelling.

SAO 140789 is included in the Walker & Wolstencroft (1988) and Stencel & Backman (1991) catalogues of main sequence stars with IRAS excess emission, but was first noted to have an infrared excess in the IRAS bands by Jaschek et al. (1986). Spectroscopy by

214 Andrillat et al. (1990) showed an AOVe spectral type with double-peaked emission in Hot and in the neutral-oxygen line at 8846 Â. For both these lines, the separation between the peaks was approximately 275 km/s. The spectra obtained by Andrillat et al. (1990) in the photographic (i.e. blue) region show rotationaUy-broadened photospheric absorption lines.

Dunkin et al. (1995) obtained a rotational velocity u sin * = 24 km/s for the photospheric lines. Rotational broadening and the presence of emission lines are strong indications of the youth of SAO 140789: Andrillat et al. suggested that it is a Herbig Ae star in a quiescent phase. Zuckerman et al. (1995) detected CO emission from SAO 140789. SAO 140789 does not have a strong near-IR excess, but there is possibly weak excess emission at L and

M; more observations are needed to confirm this.

Models for SAO 140789 are presented in Table 6.10. The star was modelled using a

Teff=9500 K, log flf=4.0 model atmosphere, appropriate for an AOV star. A luminosity of

54 L@ (Schmidt-Kaler 1982) was adopted, giving a stellar radius of 2.7 R©. Prelim inary models showed that a distance of 190 pc gave good agreement with the observations.

The CGS3 1 0 -/im spectrum of SAO 140789 shows strong UIR-band emission, while the 20-/xm spectrum shows some curvature which may be the 18-/xm silicate feature (Fig­ ure 3.3). Most of the models therefore included both carbonaceous and silicaceous grains, with the proportions 75% : 25% by mass for silicate: amorphous carbon. The modelling codes do not treat UIR-band emission, so the models were not required to fit the details of the 1 0 -/im spectrum; rather the lO-fim spectrum was considered as providing an upper limit to the model flux in the 7-14 /im region.

A grid of ‘blend’ models was run (models B22-B42), with minimum and maximum grain sizes of 50 Â and 100 //m (the non-detection at 1.1 mm implies that there is little or no emission from mm-sized grains). The disc outer radius was set at 1900 AU (corresponding to the usual projected disc diameter of 20 arcsec). The dust mass and the inner radius were adjusted to fit the IRAS fluxes at 25 and 60 /xm. The two models with a grain size distribution parameter 7 = 3 (models B22, B23) both gave too much flux at 100 /xm, and exceeded the JCMT upper limit at 1.1 mm.

The first model with 7 = 3 , model B32, gave a good fit to the long-wavelength data and to the flux level of the 2 0 -/xm CGS3 spectrum, although it failed to reproduce the curvature of the spectrum. Altering the value of the density distribution parameter

(models B33, B31) made little difference to the overall fit. Increasing 7 to 4 (model B42)

215 Table 6.10: Models for SAO 140789 (HD 141569)

Model 7 Rin ■Mdjgc F n f25 Feo J^ioo Fi.i

cm M© Jy m Jy Observations 0.53 1.82 5.3 3.6 <36 (± error) 0.03 0 . 1 1 0.5 0.4

B22 2 2 1.9x10'® 1.5x10-® 0.19 1.79 5.3 5.1 65

B23 2 3 2 .2 x 1 0 '® 1 .0 x 1 0 -® 0.18 1.78 5.4 5.1 55

B32 3 2 1.1 XlO'® 4.0x10-® 0 . 1 1 1.82 5.4 3.6 15

B33 3 3 1 .2 x 1 0 '® 4.0x10-® 0 . 1 1 1.80 5.4 3.7 15

B31 3 1 1 .0 x 1 0 '® 4.2x10-® 0 . 1 2 1.81 5.3 3.7 15

B42 4 2 1 .2 x 1 0 '® 2 .0 x 1 0 -® 0 . 1 1 1.83 5.4 3.3 9

B32a 3 2 1.1 XlO'® 6 .0 x 1 0 -® 0 . 1 1 1.82 5.4 3.6 16

B32b 3 2 1.1 XlO'® 2.7x10-® 0 . 1 1 1.84 5.4 3.6 1 2

B32c 3 2 1 .2 x 1 0 '® 2 .0 x 1 0 -® 0 . 1 1 1.81 5.3 3.3 9

C32 3 2 2 .0 x 1 0 '® 3.8x10-® 0.09 1.82 5.4 3.3 13

C31 3 1 2 .0 x 1 0 '® 3.9x10-® 0.09 1.80 5.4 3.3 13

M22 2 2 1.5x10'® 1 .1 x 1 0 -® 0.14 1.78 5.4 5.3 6 6

M32 3 2 6.7x10'® 3.1x10-® 0.08 1.79 5.3 3.4 13

B32d 3 2 1 .0 x 1 0 '® 6.5x10-® 0 . 1 2 1.81 5.4 3.7 1 2

C32a 3 2 1.5x10'® 5.8x10-® 0 . 1 0 1.81 5.4 3.5 7

C31a 3 1 1 .2 x 1 0 '® 7.4x10-® 0 . 1 1 1.81 5.4 3.7 6

C23 2 3 2.9x10'® 1.5x10-® 0.28 1.83 5.3 3.3 9

C22 2 2 2 .6 x 1 0 '® 2.9x10-® 0.28 1.81 5.3 3.6 13

C42 3 2 1.5x10'® 2.3x10-® 0 . 1 0 1.81 5.3 2.9 7

M32a 3 2 6.5x10'® 5.0x10-® 0 . 1 2 1.79 5.4 3.7 1 2

M32b 3 2 6 .0 x 1 0 '® 4.5x10-® 0.08 1.98 5.3 3.5 1 1

M42 4 2 6 .6 x 1 0 '® 2.5x10-® 0.08 1.82 5.4 3.4 1 1

M23 2 3 1 .6 x 1 0 '® 5.8x10-® 0.15 1 . 8 8 5.3 5.0 50

216 -9

-10

-11

-12

-1 3 I -1 5

k-1 6 I -1 7

-1 8

-1 9

-2 0

10° Wavelength (/zm)

Figure 6.18: Results of modelling SAO 140789. Filled squares: observed fluxes, open squares: upper limits, solid line: model B32d, dashed line: model M32b.

217 caused a reduction in the 1 0 0 -/xm model flux, but it was still consistent with the IRAS flux, within the quoted uncertainties.

Three further models were run with 7 = 3 and ^ = 2, but with different maximum grain radii: 50 mm (model B32a), 5 fim (B32b), and 0.5 fim (B32c). The three models gave quite similar fluxes, and were all consistent with the observations.

Two models were run using only amorphous carbon grains (models C32, C31). Both were consistent with the IRAS 25-100/xm data and the JCMT upper limit, but did not match the curvature of the CGS3 2 0 -/zm spectrum .

Two models were run with only silicate grains (models M22, M32) and a maximum grain size of 100 fim . Model M22 gave too much 100-/xm and mm-wave flux, while model

M32 gave a good fit to the observations, including the curvature in the 25-/xm spectrum.

The rather large inner disc radii required to fit the 20/60 /xm flux ratio, particularly for the amorphous carbon models, gave rise to rather narrow, ring-like discs, with the outer radius only slightly larger than the inner radius. In an extreme case, such as model

C32, the inner radius is 1300 AU, compared with an outer radius of 1900 AU. To test the effects of the outer radius on models of SAO 140789, a further set of models was run, with an outer radius of 5700 AU, equivalent to a projected disc diameter of 60 arcsec (models

B32d-M23). Maximum and minimum grain sizes were again set to 100 /xm and 50 Â. To enable comparison with the JCMT observation, only that part of the 1.1-mm flux which arose in the central 20 arcsec of the disc is included in Table 6.10.

The increase in outer radius, which gave a 16-fold increase in the area of the disc, made very little difference to the fit that was obtained. Larger values of the dust mass were required to give enough flux, while the inner radius had to be decreased slightly to maintain the fit to the 25/60 /xm flux ratio.

Model M32a gives a good fit to the observations, including the apparent curvature in the CGS3 20-/xm spectrum. Decreasing the inner radius slightly (model M32b) improves the fit to the flux level of the 20-/xm spectrum. This model is presented in Figure 6.18, along with model B32d, a ‘blend’ model which also gives a good fit to the data. As noted above, the presence of UIR-band emission leads one to expect a priori a carbonaceous component to be present in the dust around SAO 140789.

218 6.2.4 SAO 158350 (HD 123160)

SAO 158350 was first noted to have an infrared excess by Stencel & Backman (1991).

It has no MK spectral classification; its HD classification of K5 was therefore adopted, with an assumed luminosity class V. Such a spectral type implies that SAO 158350 may be similar to SAO 179815, the star which was found by Skinner et al. (1992) to show

10-/zm silicate emission. SAO 158350 has a much weaker IR excess than SAO 179815, with a fractional luminosity, of 4 xlO“^ , over an order of magnitude less than that of SAO 179815. The CGS3 1 0 -;/m spectrum of SAO 140845 shows only photospheric emission (Figure 3.3). SAO 158350 was observed with the JCMT (see table 3.12), but only upper limits were obtained at 0 . 8 and 1 . 1 mm.

A model atmosphere with an effective temperature of 4250 K and surface gravity log ^=4.5 was adopted for this star, along with a distance of 11.3 pc and a stellar radius of 0.68R©. A grid of models (M33-M21) was run using only astronomical silicate grains. Minimum and maximum grain sizes were 50 Â and 1 mm. The outer radius of the disc was set to 110 AU, consistent with a projected disc diameter of 20 arcsec. The results of the modelling

are presented in Table 6.11.

AU of the models gave a 1 2 -//m flux which is sUghtly below the IRAS point, but

consistent with the CGS3 spectrum. The models with 7 = 3 gave too Uttle 1 0 0 -//m flux, while the 7 = 2 models gave too much. AU six models gave 0.8- and 1 . 1 -mm fluxes that were in excess of the JCMT upper Umits.

A similar grid of amorphous carbon models was calculated (models C33-C21) with the same outer radius and range of grain sizes as for the siUcate models. AU of these models gave too Uttle 1 0 0 -/xm flux, and gave mm-wave fluxes that were close to, or sUghtly above, the JCMT upper Umits.

The maximum grain size was decreased to 100 //m, and a further grid of models (models

C33-C21) was produced. This reduction in the maximum grain radius did not improve

the fit of the models to the JCMT data.

Two more siUcate models (M23a, M33a) were run with a maximum grain size of

100 /xm; they both predicted mm-wave fluxes that exceeded the JCMT upper Umits.

Decreasing the largest grain size stiU further (models M23b-M33c) gave models which

did not exceed the mm-wave flux upper Umits. Models M23b and M33b had a maximum

219 Table 6.11: Models for SAO 158350 (HD123160)

Model 7 ■^in -Mdigc f l 2 J^60 J^ioo F i.i

cm M © Jy m Jy Observations 0.62 0.37 3.1 4.4 <41 <16 (± error) 0.05 0.06 0 . 2 0.5

M33 3 3 3.7 x l O ^ ^ 2.3 X 10"® 0.52 0.37 3.1 3.1 56 2 0

M32 3 2 3.5 x l O ^ ' ^ 2.9x10"® 0.52 0.36 3.1 3.3 65 23

M31 3 1 3.0 x l O ^ ^ * 3.8 X l O " ® 0.52 0.38 3.1 3.5 79 29

M22 2 2 2 . 0 x l O ^ ^ 1 .0 x 1 0 "® 0.52 0.36 3.1 5.8 900 420

M21 2 1 1.5x10^^ 1.5x10"® 0.52 0.38 3.1 5.6 > lJ y 520 C33 3 3 9.0x10^^ 2.4x10"® 0.52 0.37 3.1 3.1 46 16

C32 3 2 9.0x10'^ 2.6 X l O " ® 0.52 0.36 3.1 3.2 50 18

C31 3 1 8.5 x l O ' ^ 2.6 X l O " ® 0.52 0.37 3.1 3.1 50 18

C23 2 3 3.0x10^^ 7 .2 x 1 0 "? 0.52 0.37 3.1 3.1 37 13

C22 2 2 2.7 X l O ' ' * 9 .0 x 1 0 "? 0.52 0.28 3.1 3.2 43 15

C21 2 1 2.3x10^'* 1.3x10"® 0.52 0.38 3.1 3.4 55 2 0

C33a 3 3 9.1 x l O ' ^ 2 .0 x 1 0 "® 0.52 0.38 3.2 3.2 48 17

C32a 3 2 9.1 x l O ^ ^ 2.1 X l O " ® 0.52 0.36 3.1 3.2 50 18

C31a 3 1 8.6x1014 2.1 X l O " ® 0.52 0.36 3.1 3.1 50 18

C23a 3 2 3.3x1014 1.1 X l O " ? 0.52 0.36 3.1 3.2 41 15

C 2 2 a 2 2 3.0x1014 1 .4x10"? 0.52 0.37 3.1 3.3 47 17

C 2 1 a 2 1 2.6x1014 1 .9x10"? 0.52 0.37 3.1 3.5 60 2 1

M 33a 3 3 3 . 7 x 1 Q 1 4 1.9x10"® 0.52 0.37 3.1 3.1 53 18

M23a 2 3 2.5x1014 1.7x10"? 0.52 0.38 3.2 5.3 480 151

M23b 2 3 3.2x1014 1.3x10"® 0.52 0.38 3.1 2.9 37 13

M23c 2 3 3.0x1014 2 .0 x 1 0 "® 0.52 0.36 3.1 3.7 47 16

M33b 3 3 3.7x1014 1.3x10"® 0.52 0.37 3.1 2.9 38 13

M33c 3 3 3.8x1014 1 .2 x 1 0 "® 0.52 0.37 3.1 2.9 38 13

C33b 3 3 9.1 X l 0 i 4 1 .2 x 1 0 "® 0.52 0.38 3.1 3.0 45 16

B33 3 3 7.2x1014 2 .0 x 1 0 "® 0.52 0.36 3.1 3.5 58 2 1

220 -1 0

-1 1

-1 2

-1 3

-1 4

-1 5

3 10-16

-1 7

-1 8

-1 9

-20

Wavelength (/xm)

Figure 6.19: Results of modelling SAO 158350. Filled squares: observed fluxes, open squares: JCMT upper limits, solid line: model M33b.

221 Table 6.11 continued

Model 7 R'm A/diac F u F25 ■^60 -fioo ^ 0 .8 Fi.i cm M© Jy m Jy

M33d 3 3 4.0 XlO''* 2 .1 x 1 0 *® 0.52 0.34 3.1 3.3 41 16

M33e 3 3 4 .0 x 1 0 '^ 1 .6 x 1 0 *® 0.52 0.36 3.1 3.1 41 14

M31a 3 1 3 .0 x 1 0 '^ 6.2 xlO*® 0.52 0.38 3.2 3.8 49 17

M32a 3 2 3.6x10*'* 2.6 XlO*® 0.52 0.36 3.1 3.3 44 15

M31b 3 1 3.0x10*'* 7.4x10*® 0.52 0.37 3.1 3.9 54 19

M22a 2 2 3.2x10*'* 3.1 XlO*® 0.52 0.35 3.2 3.3 47 16

C22b 2 2 3.9x10*'* 2 .6 x 1 0 *® 0.52 0.35 3.1 3.7 55 2 0

C23b 2 3 3.9x10*'* 1.4 XlO*® 0.52 0.39 3.1 3.4 45 16

C23c 2 3 4.7x10*'* 1 .0 x 1 0 *® 0.52 0.36 3.1 3.6 53 19

grain size of 5 //m, while model M33c had an even smaller maximum size of 2 /xm. Model M23c with a maximum grain size of 10 /xm gave slightly too much mm-wave flux.

An amorphous carbon model (C33b) and a model with a 25%:75% ACrsilicate blend of grains (model B33), both with amax= 2 /xm, were run; both gave too much mm-wave flux.

A final grid of models was calculated, with the disc outer radius increased to 660 AU, giving a projected disc diameter of 60 arcsec. The 0.8-mm and 1.1-mm fluxes were cal­ culated for a 20-arcsec beam centred on the star. A variety of maximum grain radii were used: model M32d had Umax=20 /xm, models M 31e-M 32a had Umax=2 /xm, model M31b had Umax=10 /xm, and model M22a had Umax=5 /xm. None of these models were a sig­ nificant improvement on models M23b, M33b, and M33c, so the steep fall-off in observed flux from 100 /xm to 0.8 mm is not due to the disc being resolved by the JCMT beam.

Since no model could give enough 100-/xm flux without giving too much mm-wave flux, it may be that roughly one-quarter of the 1 0 0 -/xm flux is due to emission by infrared cirrus.

Examination of the IRAS Sky Survey Atlas image of the region around SAO 158350 shows that some cirrus emission is present close to the star. The best fit to the observations was obtained with models M33b and M33c; M33b (which has the less restricted range of grain sizes) is presented in Figure 6.19.

222 Table 6.12: Models for SAO 158350 (HD123160) as a G5V star

Model 7 Rin ■A/djac Fi 2 F25 Feo J^ioo J^O.8 Fi.i

cm M© Jy m Jy Observations 0.62 0.37 3.1 4.4 <41 <16 (± error) 0.05 0.06 0 . 2 0.5

B33 3 3 2.9x10^® 1.7x10"^ 0.63 0.34 3.2 4.3 0 . 1 0 . 1

B32 3 2 2.7x10'® 1.7x10"^ 0.63 0.34 3.1 4.1 0 . 1 0 . 1

B31 3 1 2.3x10'® 1.7x10-^ 0.63 0.37 3.1 4.1 2 . 1 0 . 8

B22 2 2 7.5x10'^ 4.5x10-® 0.64 0.36 3.1 5.4 809 378

B23 2 3 7.5 X l O ' ' * 2 .6 x 1 0 "® 0.64 0.36 3.1 5.2 740 340

B23a 2 3 9.0 X l O ' ' * 2.3x10"® 0.64 0.37 3.1 4.7 167 51

SAO 158350 has recently been re-classified as a G5V star by Dunkin et al. (1995, in preparation). Accordingly, a set of models was run with the appropriate stellar parameters for the new classification. A Kurucz model atmosphere with Tcff = 5750 K and log^r = 4.5, the stellar radius was set to 6.19 xlO^® cm, and a distance of 15.7 pc was adopted. The models were run with the minimum and maximum grain radii set to 50 Â and 1 mm, as usual, and an outer radius for the disc of 470 AU, corresponding to a projected disc diameter of 1 arcminute. A silicate: amorphous carbon blend was used, in the usual 75:25 proportions. Table 6 . 1 2 presents the results of this modelling. Only the emission from the innerm ost 2 0 arcsec was included for the predicted mm-wave fluxes.

Three models were run with the grain-size distribution parameter 7 = 3 (models B33,

B32 and B31). All three models gave good agreement with the IRAS data. The predicted mm-wave fluxes were consistent with the JCMT upper limit, because the disc inner radii were so large that very little of the disc emission lay within the 2 0 arcsec diameter beam.

The total predicted mm-wave flux for the entire disc was greater than the JCMT upper limit for all three models (predicted values ~ 50 mJy at 1 . 1 m m ).

Three models were run with 7 = 2 (models B23, B22, and B23a). Models B23 and

B22 predicted too much flux at 100 ixm and at mm wavelengths. For model B23a, the maximum grain size was decreased to 50 fim . This model is consistent with the IRAS data, but stiU predicts too much mm-wave flux. The best-fitting model, B33, is presented in Figure 6.20, along with model B23a.

223 -4

-10

-1 1

-1 3 I

-1 4

-1 5

-1 6 10° Wavelength (/xm)

Figure 6,20: Models of SAO 158350 as a G5V star. Filled squares: observed fluxes, solid line: model B33, dotted line model B23a.

224 Table 6.13: New models for SAO 179815 (HD 98800)

Model 7 R ’m -Afhigc Fi 2 ^25 ^60 f^ioo ^0.8 Fi.i cm M© Jy m Jy

Observations 2 . 0 9.4 7.9 4.6 1 1 1 63 (± error) 0 . 1 0.9 1 . 1 0.5 1 2 6 1.5x10^3 M23 2 3 5.7x10"® 2 . 0 9.4 7.5 3.5 74 31

M22 2 2 1.3x10^^ 1.7x10"^ 2 . 0 9.5 8 . 2 4.2 1 1 1 48

B22 2 2 1.3x10^3 1 .7 x 1 0 -^ 2 . 6 9.3 6.9 3.3 83 36

B32 3 2 5.0x10^3 2 .0 x 1 0 -^ 2 . 0 9.5 6.4 2 . 6 19 7

B32a 3 2 3 .3 x 1 0 '^ 1 . 2 X 1 0 "® 2 . 0 9.4 5.0 1 . 8 13 4

B31 3 1 2.5x10^3 1 . 1 xlO -7 2 . 1 9.4 6.7 3.6 53 19

B22a 2 2 1.5x10'^ 2 .2 x 1 0 -^ 1.9 9.3 8.5 4.4 1 2 0 52

B2p32 2.3 2 2 .0 x 1 0 ^^ 1 .2 x 1 0 "® 1.9 9.3 7.7 3.8 76 31

B2p22 2 . 2 2 1.8x10^3 1.5x10"^ 2 . 0 9.5 8 . 2 4.2 93 39 1.7x10^3 B2p21p6 2 . 2 1.6 3.8x10"^ 1.9 9.4 8.7 4.7 140 60

6.2.5 SAO 179815 (HD 98800)

SAO 179815 consists of a single-lined spectroscopic binary with a period of 262 days and

an orbital separation of ~1 AU (Torres et al. 1995) plus a visual companion, which is

a double-lined spectroscopic binary and which in 1989 was 0.4 magnitudes fainter and

0.73 arcsec to the north of the brighter component (Heintz 1990). Torres et al. (1995) found little evidence for acceleration in the path of the visual companion during the 84

years since its discovery and conclude that it either has a very wide orbit or is physically

unconnected with the primary.

Optical spectroscopy of SAO 179815 by Fekel & Bopp (1993) revealed Ha emission,

strong Li I A6708 absorption and rotationaUy-broadened photospheric lines, aU of which

could be attributed to youthfulness. Fekel & Bopp suggested that SAO 179815 is a BY Dra

star with an active chromosphere, and predicted photometric variability for SAO 179815, which was confirmed by Henry & HaU (1994), who found an amplitude of AU = 0.07 mag

and a period of 14.7 days, which they attributed to the rotational period of star-spots.

225 -1 0

-11

-12

-1 3

-1 4

-1 5 I -1 6

-1 7

—10

10° Wavelength (/zm)

Figure 6.21: Models for SAO 179815. Large filled squares: photometric data, small filled squares: CGS3 spectra. Dashed line: disc model B 2 p 2 1 p 6 including one stellar component, solid line: same model, but including the visual companion (see text).

226 8x10 - 1 4

2x10,-14

8 10 12 14 16 18 20 22 24 W avelength (/xm)

Figure 6.22: Detail of the SAO 179815 models in the mid-IR. Errorbars: CGS3 spectrum, large squares: IRAS points, solid line: Model B2pl2p6, dashed line: effect of including visual companion.

Skinner, Barlow, & Justtanont (1992; SBJ) obtained a 10 /xm spectrum of SAO 179185, which revealed a broad 9.7 /xm silicate emission feature. They presented models of the system, showing that silicate particles with a wide range of sizes ( 0 . 0 1 /xm to at least 100 fim ) were needed in order to reproduce aU the infrared properties of its disk. Narrow­

band photometric observations of SAO 179815 made by Zuckerman & Becklin (1993)

confirmed the silicate identification. Zuckerman et al. (1995) obtained only an upper limit

for CO emission from SAO 179815. SBJ modelled SAO 179815, using the modelling technique upon which the method

described in Chapter 4 was based. The SBJ models, although they were calculated without

the benefit of a 20-/xm spectrum or the JCMT photometry, formed a useful starting point

for the present modelling of SAO 179815, since they rule out large areas of parameter

space, corresponding to models which are inconsistent with the IRAS data or the 1 0 -/xm

spectrum . A number of new models for SAO 179815 were run (see Table 6.13). Following SBJ,

the minimum and maximum grain radii were taken to be 50 Â and 1 mm. The disc

outer radius was 230 AU, corresponding to a projected disc diameter of 20 arcsec. For

the new models, it was assumed that the visual companion star plays no role in heating

the dust and that the secondary component in the single-lined spectroscopic binary does

227 not perturb the adopted spectral type and V magnitude, and so a single Kurucz model atmosphere with an effective temperature of 4250 K and surface gravity log ^=4.5 was used to represent the K5V primary. A distance of 23 pc, derived from the photometry of Gregorio-Hetem et al. (1992) and Heintz (1990), and a stellar radius of 0.74 R@, were adopted.

Model M23 is essentially SBJ’s best-fitting model M5A, calculated to longer wave­ lengths and using the new stellar parameters. This model was found to underestimate the

JCMT fluxes by approximately a factor of 2. The 1.1-mm flux of model M23 (31 mJy) is consistent with the flux of 30 mJy at 1 mm quoted by SBJ for their model M5A.

Decreasing the density distribution parameter (3 from 3 to 2 (model M22) gave better agreement with the JCMT data. Neither of these models gave sufficient flux in the 7-Sfim portion of the CGS3 spectrum, although the overall contrast in the silicate features is in good agreement with the observations.

Since there is a carbonaceous component in the dust of many other Vega-excess stars, a grid of models was calculated using a mixture of silicate and amorphous carbon grains

(models B22-B2p21p6). Models B22 and B32 both had 25% of the dust mass in AC grains.

Neither model gave sufficient contrast in the silicate feature, and model B32 significantly underestimated the mm-wave flux, making infeasible any further increase in 7 to boost the contrast in the 10-/xm silicate feature.

To recover the silicate contrast, the proportion of AC grains was decreased to 10% for models B32a-B2p21p6. Retaining 7 = 3 gave sufficient silicate feature contrast, but underestimated the mm-wave flux (models B32a, B31). Setting 7 = 2 gave too little silicate contrast. Values of 7 slightly larger than 2 gave acceptable contrast in the silicate feature and more mm-wave flux than for 7 = 3 (models B2p32- B2p21p6). The best-fitting of the models including carbonaceous grains is model B2p21p6, which gives good agreement with the JCMT 1.1-mm flux, but slightly too much flux at 0.8 mm. As for the pure-silicate models, this model underestimates the flux in the 7-Sfim part of the CGS3 spectrum.

Model B2p21p6 is presented in Figure 6.21.

Naturally, the optical and near-IR fluxes of the model underestimate the observed fluxes, which are due to both components of SAO 179815, not just the brighter component which is assumed to be heating the dust. Including a second photospheric contribution to model the observed flux from the visual companion gives better agreement with the

228 integrated photometric data. It also increases the flux in the 10-/xm region, improving the fit to the CGS3 spectrum. The effects of including the visual companion are shown in

Figure 6 .2 1 , while details of the fit to the CGS3 spectrum are shown in Figure 6 .2 2 .

6.3 Stars with no mid-IR excess

6.3.1 SAO 91022 (HD 218396)

SAO 91022 was first recognised as a Vega-excess star by Sadakane & Nishida (1986), and is also listed by Walker & Wolstencroft (1988) and Stencel & Backman (1991).

Welty et al. (1989) gave a spectral type of A5V for SAO 91022, and found that its pro­ jected position lies between those of two nearby molecular clouds, MBM 53 and MBM 54.

However, at an estimated distance of 56 pc (based on the spectral type and photometry; see Chapter 3), the star lies considerably closer than the molecular clouds, which are both more than 110 pc away. The spectrum of SAO 91022 obtained by Welty et al. showed no interstellar Nal absorption, unlike the spectra of stars which lay within or behind the clouds.

Smith et al. (1992) imaged SAO 91022 with the same coronagraph used to resolve the (3 Pic disc, but did not detect any extension of this source. The star was modelled using a model atmosphere with Tef[= 8200 K and log g = 4.0.

Adopting the luminosity of an A5V star as 14 L© (Schmidt-Kaler 1982), the stellar radius is 1.88 R©. The distance derived from the optical photometry of 56 pc (Table 3.5) was adopted for the modelling.

The IRAS 12-/im flux of SAO 91022 is slightly in excess of the expected photospheric flux, as can be seen in Figure 3.6. This is in accord with the modelling which pre­ dicts an IRAS 12-^m photospheric flux of 0.31 Jy, compared with the observed value of

0.40±0.04 Jy. The discrepancy is approximately 2 < 7 , so the observations are formally con­ sistent with there being no excess at 12 /xm. Models which are consistent with the 25 and

60-/xm IRAS fluxes give negligible excess flux at 1 2 /xm, so the excess, if real, may be due to warmer small grains or grain emission bands.

The IRAS PSC contains only an upper limit for the 100-/xm flux of this source, and the Faint Source Survey flux is clearly contaminated by cirrus emission, while our JCMT

1 .1 -mm measurement has a signal to noise ratio of less than 3. If the JCMT observation

229 is treated as giving only an upper limit, the excess is defined by only two data points (at

25 and 60 /xm), and so models of this source are poorly constrained.

A grid of models (Table 6.14) was run using silicate grains (models M33-M11). The disc outer radius was 1680 AU, corresponding to a projected disc diameter of 60 arcsec, for models M33-M31; for models M31a-Mll it was 3360 AU, (projected diameter =

120 arcsec). The maximum and minimum grain radii adopted were 1 mm and 50 Â. As mentioned above, all of the models, while giving good agreement with the IRAS 25- and 60-/xm points, gave 1 2 -/xm fluxes slightly lower than the IRAS value. All the models were consistent with the IRAS 100-/im upper limit, and with a 3 -cr upper limit of 33 mJy at 1 . 1 mm. The models with a grain size parameter 7 = 1 (M33-M31) all gave 1 . 1 -mm fluxes of approximately 1 mJy, while the models with 7 = 2 (models M23-M21) and 7 =

1 (M13-M11) aU gave larger 1.1-mm fluxes. None of the models gave as much 1.1-mm flux as the nominal JCMT value of 28 mJy, and only model M il gives a flux that lies within la- ( 1 1 mJy) of this value. Increasing the grain size to 50 mm (models M13a, M12a), and reducing it to 0.2 mm (model M ila) made little difference to the 1 . 1 -mm model fluxes.

To determine whether it was possible to match the 28-mJy JCMT nominal flux, a set of models with rather low values of (3 and 7 were run (models M01-M20p5). The grain sizes ranged from 50 Â to 1 mm, and the outer radius was again set to 1660 AU. Using low values of 7 (models MOl and M M ll), so that emission from large grains dominated the excess energy distribution, had little effect on the millimetre-wave flux. Using low values of the density distribution parameter /3 (models M10-M20p5) in order to have large quantities of material in the outer, cooler, parts of the disc, did produce an increase in the flux at 1 .1 mm. Model MIO actually exceeded the 3-a^ upper limit, while models

M20 and M10p5 gave 1 . 1 -mm fluxes that were comparable with the JCMT nominal value.

As usual, the predicted 1.1-mm fluxes given in Table 6.14 are for a beam of 20 arcsec diam eter.

Three models using amorphous carbon grains were run (models C33-C31), with grain radii ranging from 50 Â to 1 mm, and outer radii of 1680 AU. They all had similar 1 2 -/xm fluxes to the silicate models, gave good agreement with the IRAS data at 25 and 60 //m, and were consistent with the IRAS upper limit at 100 fim . All three models predicted very little mm-wave flux, with l.l-mm fluxes of approximately 1 mJy.

230 Table 6.14: Models for SAO 91022 (HD 218396)

Model 7 R'ui ■A(/

Observations 0.40 0.24 0.41 < 2 . 6 <33 (± error) 0.04 0.08 0.06

M33 3 3 2 .2 x 1 0 ^® 1 .8 x 1 0 -® 0.31 0.25 0.42 0.24 1

M32 3 2 2 .0 x 1 0 ^® 2.7x10"® 0.31 0.24 0.41 0.26 1

M31 3 1 1.5x10'® 5.0x10"® 0.32 0.24 0.41 0.29 1

M31a 3 1 1.5x10'® 1 .0 x 1 0 ""^ 0.32 0.23 0.41 0.31 1

M23 2 3 4 .4 x 1 0 '^ 9.0x10"® 0.32 0.24 0.41 0.30 4

M22 2 2 4.2 xlO''* 2.5x10"^ 0.32 0.23 0.41 0.32 6

M21 2 1 3.0 xlO''* 2.4x10"® 0.32 0.24 0.41 0.37 1 0

M13 1 3 3.3 xlO'^* 2 .0 x 1 0 "^ 0.32 0.24 0.42 0.29 7

M12 1 2 3.0 xlO''* 5 .6x10"^ 0.32 0.23 0.42 0.31 9

M il 1 1 2 .2 x 1 0 '^ 7.2x10"® 0.32 0.23 0.41 0.37 17

M13a 1 3 3 .5 x 1 0 '^ 1.3x10"® 0.32 0.24 0.42 0.28 5

M12a 1 2 3 .0 x 1 0 '^ 3.2x10"® 0.32 0.24 0.40 0.28 6

M ila 1 1 1 . 8 x lO ''' 1 .2 x 1 0 "® 0.32 0.24 0.41 0.37 15

MOl 0 1 2 .2 x 1 0 '^ 4.8x10"® 0.32 0.24 0.42 0.38 17

M M ll - 1 1 2 .2 x 1 0 '^ 4.8x10"® 0.32 0.24 0.42 0.38 18

MIO 1 0 3 .0 x 1 0 '^ 4.9x10"® 0.36 0.23 0.41 0.56 57

M20 2 0 7 .0 x 1 0 '^ 1 .2 x 1 0 "® 0.34 0.24 0.40 0.45 24

M30 3 0 1.3x10'® 2X3x10"? 0.32 0.24 0.43 0.26 1

M10p5 1 0.5 1.5x10'^ 1.3x10"® 0.33 0.23 0.40 0.43 30

M20p5 2 0.5 2 .2 x 1 0 '^ 3.9x10"® 0.33 0.24 0.41 0.40 15

C33 3 3 6 .0 x 1 0 '® 2.5x10"® 0.32 0.25 0.42 0.24 1

C22 2 2 9 .0 x 1 0 '^ 7.1x10"? 0.33 0.25 0.41 0 . 2 2 1

C ll 1 1 6 .0 x 1 0 '^ 9.4x10"® 0.32 0.23 0.40 0.27 1

231 -9

-1 0

-1 1

-12

-1 3

-1 4

-1 6

-1 7

—18

-1 9

0 1 2

Wavelength (jim )

Figure 6.23: Results of modelling SAO 91022. Filled squares: observed fluxes, open squares: upper limits, solid line: model M33, dashed line: model M20p5.

232 Given the rather extreme values of (3 that were required to obtain a 1.1-mm flux that was close to 28 mJy, it is probable that only the JCMT upper limit of 33 mJy to the

1 . 1 -mm flux of SAO 91022 can be trusted. Higher signal-to-noise JCMT observations are required to determine the flux, and so discriminate between the models presented in

Table 6.14.

With such a variety of models which fit the (rather sparse) data, it is not surprising that there is a wide range of values of the inner radius and disc mass which could fit the observations. The smallest inner radius obtained (model M20) is approximately 5 AU, while the largest (for model C33) is approximately 400 AU. It can therefore be deduced that there is a relatively dust-free region extending out to at least 5 AU, and possibly considerably further, from the star.

The smallest dust mass required by any of these models is 1.8 x 10“® M© (for model M33), equivalent to roughly 0.5 Lunar masses. This can be taken as an approximate lower limit on the mass of circumsteUar dust around SAO 91022.

To illustrate the range of SEDs produced by the models which are consistent with the observations, models M22 and M20p5 are presented in Figure 6.23.

6.3.2 SAO 93601 (HD 23680)

The infrared excess of SAO 93601 was first noted by Stencel & Backman (1991). Little else has been published about this star; there is no published MK spectral type, so the HD classification of 05 has been adopted, and luminosity class V assumed. No photoelectric photometry at visual wavelengths is available, so the photographic magnitudes listed by the SIMBAD database were used. Near-IR photometry with UKT9 (Chapter 3) shows that there is no near-IR excess emission, and so allows the photospheric flux level to be defined. The fractional luminosity of the excess emission from this star is 3 xlO“® , similar to that of (3 Pic. Inspection of the spectral energy distribution (Figures 3.6 and 6.24) of this source shows that there is negligible excess emission at 1 2 /xm.

Before applying any dereddening correction, the near-IR and optical photometry of this star strongly resembles the energy distribution of a late K star rather than that of a

05 star. Accordingly, SAO 93601 was modelled at first by treating it as a K5V star (the same spectral type as SAO 179815). A model atmosphere with an effective temperature of 4250 K and surface gravity log g = 4,5 was used, and the stellar radius was taken as

233 Table 6.15: Models for SAO 93601 (HD 23680)

Model 7 ■ R in -A/djgc Fi 2 ^ 2 5 Fso J’lOO Fi.i cm M© Jy m Jy

Observations 0.43 0.19 2 . 1 6 . 0 <45 (± error) 0.04 0.04 0 . 1 0 . 8

4 M33 3 3 5 .6 x 1 0 6.4xl0~® 0.34 0.19 2 . 1 2.4 18 4 M32 3 2 5 .6 x 1 0 1 .3 x 1 0 -^ 0.34 0.17 2 . 0 2.7 2 2 4 M31 3 1 4.5 xlO 3 .2 x 1 0 " ’’ 0.34 0 . 2 0 2 . 1 3.0 25 4 M23 2 3 3 .8 x 1 0 2.9x10"® 0.35 0.19 2 . 1 4.7 435 4 M22 2 2 3 .9 x 1 0 7.0x10"® 0.35 0.18 2 . 1 4.9 620 4 M21 2 1 2 .8 x 1 0 1 .6 x 1 0 "® 0.35 0 . 2 0 2 . 1 4.6 600 4 M13 1 3 1.1 xlO 6 .4 x 1 0 " ’’ 0.34 0 . 2 0 2 . 1 2.7 1 2 0 4 M12 1 2 1.1 XlO 1.9x10"® 0.34 0.18 2 . 1 3.0 190 4 M32a 3 2 5 .3 x 1 0 8 .6 x 1 0 "® 0.34 0.18 2 . 1 2 . 6 16 4 M31a 3 1 4 .5 x 1 0 2.2 XlO"® 0.34 0 . 2 0 2 . 1 3.0 2 0 4 M23a 2 3 4 .5 x 1 0 2 .4 x 1 0 " ’’ 0.34 0.19 2 . 1 3.7 58 4 M13a 1 3 1.1 XlO 3.2 XlO"® 0.35 0.19 2 . 2 3.0 18 4 M12a 1 2 1.1 XlO 9.5x10"® 0.35 0.18 2 . 1 3.3 30 4 M31b 3 1 4 .5 x 1 0 3.2x10"® 0.34 0 . 2 2 2 . 1 2.3 1 2 4 M31c 3 1 4 .5 x 1 0 1.1 X lO"’’ 0.34 0 . 2 0 2 . 1 2 . 8 19 4 M23b 2 3 4 .5 x 1 0 1 .7 x 1 0 "’’ 0.34 0.19 2 . 1 3.6 52 4 M23c 2 3 4 .5 x 1 0 2.2 XlO"’’ 0.34 0.19 2 . 1 3.7 60 5 C33 3 3 1.4x10 7.0 xlO"® 0.34 0.18 2 . 1 2 . 6 13 5 C33a 3 3 1.4x10 9.5x10"® 0.34 0.18 2 . 1 2 . 6 13 5 C32 3 2 1.4x10 1 .4 x 1 0 "’’ 0.34 0.17 2 . 1 2 . 8 1 2 5 C31 3 1 1.1 XlO 1 .8 x 1 0 " ’’ 0.34 0.18 2 . 1 2.9 1 0 4 C23 2 3 4 .5 x 1 0 1.9x10"® 0.34 0 . 2 0 2 . 1 2.3 1 2 4 C22 2 2 4 .5 x 1 0 4.1 XlO"® 0.34 0.19 2 . 1 2.7 16 4 C 2 1 2 1 3 .9 x 1 0 1 .2 x 1 0 "® 0.34 0.19 2 . 1 2 . 1 19 4 C13 1 3 3 .7 x 1 0 6 .0 x 1 0 "® 0.34 0.18 2 . 1 2 . 1 1 0 4 C 1 2 1 2 3 .4 x 1 0 1 .2 x 1 0 "® 0.34 0.18 2 . 1 2.3 1 2 4 C ll 1 1 2 .8 x 1 0 4.1 XlO"® 0.34 0.19 2 . 1 2.7 16

234 -1 0

1 -1 1 -

-12

1—13 7

s -1 5

-1 7

—18

-1 9

-20 10° Wavelength (/xm)

Figure 6.24: Results of modelling SAO 93601. Filled squares: observed fluxes dereddened to fit G-type star, filled triangles: observed fluxes without dereddening, open square:

1.1-mm upper limit, solid line: model GM32, dashed line: model M32.

235 Table 6.16: Models for SAO 93601 adopting a G5V spectral type

Model 7 R ’m Afdisc Fi2 F 25 -^60 Fioo Fi.i

cm M© Jy m Jy

Observations 0.43 0.19 2 . 1 6 . 0 <45 (± error) 0.040.04 0 . 1 0 . 8

GM33 3 3 1.3x10^® 8.7x10-* 0.39 0.19 2 . 1 2.5 15

GM32 3 2 1 .3 x 1 0 '^ 1/1x10-7 0.39 0.18 2 . 1 2.7 16

GM31 3 1 1 . 1 xlO^® 2 .2 x 1 0 -7 0.39 0.19 2 . 1 3.0 14

GM23 2 3 8.5x10^'* 4.8x10-* 0.39 0 . 2 0 2 . 1 4.6 490

GM13 1 2 2.5x10^'^ 1 .2 x 1 0 -* 0.39 0.18 2 . 1 3.1 153

GC33 3 3 4.0x10^^ 1.2x10-7 0.39 0.19 2 . 1 2.4 0 . 1

GC23 2 3 1.5x10^5 7.7x10-* 0.39 0.17 2 . 1 3.5 2 1

GC13 1 3 7 .5 x 1 0 '^ 8 .8 x 1 0 -* 0.39 0.18 2 . 2 2.3 1 0

G C ll 1 1 6 .0 x 1 0 '^ 3 .4 x 1 0 -* 0.39 0.18 2 . 1 2 . 8 1 1

5.9 X 10^® cm (0.85 R©). With these values, a distance of 31 pc was found to give a good fit to the photometry.

A grid of models using silicate grains was calculated (models M31-M12). A projected disc diameter of 60 arcsec, corresponding to an outer radius of 465 AU, was used for all of these models. The maximum and minimum grain sizes were set to 50 Â and 1 mm respectively. Results of the modelling are presented in Table 6.15. The model fluxes at

1 . 1 mm include only the flux observable in a 2 0 arcsec beam centred on the star, to match

the JCMT beam size.

The models with a grain size distribution parameter of 7 = 3 (M33-M31) were all

consistent with the JCMT measurement at 1.1 mm 33±15 mJy, or a 3 (7 upper limit of 45 mJy), but gave too little flux at 100 /xm compared with the IRAS photometry. The models with 7 = 3 and those with 7 = 2 (M23-M12) all gave too much 1.1-mm flux, but still

underestimated the 1 0 0 -/xm flux.

In order to obtain a steep fall-off in the spectral energy distribution between 100 /xm

and 1.1 mm, the maximum grain radius was set to 50 /xm: the emissivity of silicate grains

of this size turns over at approximately 100 /xm (Figure 4.2). Five models were run with

236 this maximum grain size, a disc outer radius of 465 AU and different values of 7 and /?

(models M32a-M12a). None gave sufficient flux at 100 /xm, although all except M23a were consistent with the 1.1-mm observation. It therefore appears that the IRAS 100-fim measurement may be contaminated with infrared cirrus emission. The 1 0 0 -/xm IRAS Sky

Survey Atlas image shows substantial amounts of cirrus near SAO 93601.

Four more models (M31b-M23c) were run with maximum grain sizes of 50 /xm, but

different outer radii of the disc. Models M31b and M23b had projected disc diameters

of 10 arcsec, corresponding to outer radii of 155 AU, while models M31c and M23c had

outer radii of 465 AU (projected diameter 30 arcsec). Again, all of these models underes­

timated the 100-/xm IRAS flux. Models M3 lb and M31c were consistent with the JCMT

observation at 1.1 mm, while models M23b and M23c gave too much millimetre-wave flux.

A grid of models using only amorphous carbon grains was also calculated (models

C33-C11). As in the case of the silicate models, all the models slightly underestimated

the 12-fim flux, and only gave about 50% of the 1 0 0 -/xm flux measured by IRAS. AU of

the amorphous carbon models were consistent with the JCMT 1.1-mm observation. For

amorphous carbon grains, therefore, the parameters 7 and (3 are unconstrained within the

range of values used in the modelling.

A separate grid of models was calculated, adopting the HD spectral type (05), with

luminosity class V. The central star was modeUed using a Kurucz (1991) atmosphere with

Teff=5750 K and log g = 4.5. Dereddening the photometry by E(H —F) = 0.65 gave optical

and near-IR colours similar to those of the Kurucz atmosphere. A distance of 20 pc was

found to give good agreement between the model SED and the dereddened photometry.

This amount of reddening is remarkably large, given the low values of distance to the star

(20 pc) and fractional excess luminosity {L m /L ^ =3 xlO“^ ).

A set of siUcate models (GM33-GM12) and another of AC models (GC33-GC31) were

run. The results of this modelling (presented in Table 6.16) were very similar to those

obtained assuming a K5 spectral type. For the siUcate models, a grain size parameter of

7 = 3 gave 1.1-mm fluxes consistent with the JCMT observations, while 7 = 2 and 7 = 1

both gave too much millimetre-wave flux. The 12-/xm flux of aU the models was less than

the IRAS value, but unUke the K-star models, the discrepancy was within the uncertainty

of the measurement. Like the K-star models, the G-star models for the SAO 93601 system

aU underestimated the IRAS 100-/xm fluxes by roughly a factor of 2 .

237 Models with equivalent values of 7 and /?, but calculated for the two different spectral types (e.g. M23 and GM23) predict similar fluxes in the IRAS and JCMT wavebands (cf.

Tables 6.15 and 6.16). The inner radii required by the G-star models are larger than those needed when a K-type central star is assumed, as would be expected, given the greater luminosity of a G5V star.

Based on these models, an approximate range of possible values of the disc mass and inner radius can be defined. For the G-star models, the inner radius is found to lie in the range 40-270 AU, and the disc mass in the range 0.03-11 Earth masses.

Figure 6.24 shows a typical model fit to the dereddened photometry, using a G-star model, GM23, and the equivalent model calculated adopting a K5V spectral type (model

M23).

6.3.3 SAO 111388 (HD 23362)

This K2 star was noted as a Vega-excess candidate by Stencel & Backman (1991). It had been included in a list of possible active galactic nuclei by de Grijp et al. (1987), on the basis of its IRAS colours. The de Grijp et al. list also includes the bright Vega-excess stars

(3 Pic and a PsA, so the inclusion of SAO 111388 is not sufficient evidence to consider it to be an extragalactic source. There is no published MK spectral type for this star, so the HD classification was adopted assuming it to be a dwarf. Combining this with the optical photometry obtained in the course of the present work (Chapter 3), gives a distance of 6.5 pc (see discussion in

Chapter 3).

The star was modelled with a Kurucz (1991) atmosphere with an effective temperature of 5000 K, and a surface gravity of log ^ = 4.5, appropriate for a K2 main-sequence star.

Using this model atmosphere, and adopting a stellar radius of 0.75 R©, a distance of 8 pc was found to give a good fit to the dereddened optical and near-IR photometry.

When running preliminary models to determine the distance to the star, it was clear that there was no appreciable excess at 12 /im (see also Figure 3.6). A set of three models

(M23-M33) was run, using only astronomical silicate grains, with the disc mass and inner radius selected to fit the IRAS fluxes at 25 and 60 //m. AU three had an apparent disc diameter of 1 arcminute, corresponding to an outer radius of 240 AU. Model M23 had a maximum grain radius of 2 0 /xm, while the others had a maximum grain size of 1 mm.

238 -9

-1 0

-1 1

-12

-1 3

—14

-1 6

-1 7

—18

-1 9

-2 0 10° Wavelength (/xm)

Figure 6.25: Results of modelling SAO 111388. Solid line: model M il, dashed line: model M33.

239 Table 6.17: Models for SAO 111388 (HD 23362)

Model 7 Rin Iodise Fi2 F25 Feo J^ioo Fi.i

cm M© Jy m Jy Observations 1.38 0.44 0.72 2.9 - (± error) 0.08 0.04 0.07 0.3

M23 2 3 2.5 xlO^'* 1.4x10-® 1.45 0.44 0.73 0 . 8 3

M il 1 1 6.0x10^3 2 .0 x 1 0 -'^ 1.45 0.44 0.72 0 . 8 70

M33 3 3 4.0 xlO'^^ 1.4x10-® 1.45 0.44 0.72 0 . 8 3

C ll 1 1 1.7x10'^ 5.3x10-’' 1.45 0.44 0.72 0 . 6 4

C33 3 3 1 .0 x 1 0 '^ 8 .6 x 1 0 - 1 ® 1.45 0.44 0.71 0.5 3

B ll 1 1 8 .0 x 1 0 '^ 2 .8 x 1 0 -"^ 1.45 0.44 0.73 0 . 8 80

B33 3 3 8 .0 x 1 0 ^^ 1.4x10-® 1.45 0.43 0.71 0 . 6 3

The minimum grain size for all three models was 50 Â. The results of these models are presented in Table 6.17. All of these models underestimated the IRAS 100-fim flux by roughly an order of magnitude. The large increase in flux density from 60 to 100 iim (Figures 3.6 and 6.25) indicates that the 1 0 0 -/xm point may be contaminated by infrared cirrus; this is confirmed by inspection of the IRAS Sky Survey Atlas image of the region. There are no sub­ millimetre observations of this source, so if the lOO-fim point is ignored because of this possible contamination, there are only two remaining data points which define the excess emission. A wide range of models with different input parameters could therefore fit the observations.

In order to gain some measure of this range of parameters, two more models were run using amorphous carbon grains (C ll, C33) and two with a blend of 75% silicate and 25% amorphous carbon grains (B ll, B33). AU of the models in Table 6.17 give satisfactory fits to the observations short wards of 1 0 0 //m.

Using these models, it was possible to determine an approximate range of values for the for the inner radius and dust mass of the disc, for reasonable values of 7 and j3. The

240 inner radii of the seven models lie in the range (0 .6 -1 0 )cm (4-67 AU), and the dust masses occupy the range (0.9-500)X10“^ M@, equivalent to 3 xlO"* - 0.17 Earth masses.

Submillimetre observations would help distinguish between some of the models of this source. For example, model M il predicts relatively strong sub-mm emission (140 mJy) at 0.8 mm), whereas M33 is much weaker (7 mJy) at this wavelength. UKT14 would certainly be sensitive enough to detect emission at al level corresponding to model M il, but would probably obtain only an upper limit for emission from model M33. These two models are presented in Figure 6.25.

6.3.4 SAO 147886 (49 Cet)

SAO 147886 (= 49 Cet = HR 451 = HD 9672) was first noted as a Vega-excess star by

Sadakane & Nishida (1986), who compared the Bright Star Catalog (Hoffleit, 1982) with the IRAS PSC, and found twelve new Vega-excess candidates. It was also included in the lists of Walker & Wolstencroft (1988) and Stencel & Backman (1990). The fractional excess luminosity, L/fl/L*, of SAO 147886 is roughly 10“^, similar to that of j3 Pic (see

C hapter 2 ).

Smith et al. (1992) observed this star with the coronagraph used to image (3 Pic by

Smith & Terrile (1984), but found no evidence for any extended disc or envelope visible in scattered light. Zuckerman & Becklin (1993) observed SAO 147886 at 0.8 mm with the JCMT, and obtained an upper limit on the flux density of 36 mJy. Zuckerman et al.

(1995) detected CO emission from this star.

The spectral type of SAO 147886 is AIV (Houk 1988), implying an effective temper­ ature of 9230 K (Schmidt-Kaler 1982), and a surface gravity given by log^r = 4.1 (Allen

1973). The Kurucz (1991) model which was closest to these parameters was adopted; it had Teff = 9250 K and log g = 4.0. An effective temperature of 9230 K and a stellar lumi­ nosity of 35 Lq imply a stellar radius Æ* = 2.3 R© (1.6 x 10^^ cm). Using these values, a distance of 80 pc was found to give a good fit to the dereddened optical photometry.

Adopting this distance, a grid of models using only astronomical silicate grains was produced (Models M33-M22; see Table 6.18), aU with grain radii ranging from 5 À to

1 mm, and an apparent disc diameter of 40 arcsec, corresponding to an outer radius of the disc of 1600 AU. The 0 .8 -mm fluxes listed in Table 6.18 include only the flux originating in an 18-arcsec diameter beam centred on the star to match the JCMT beam size.

241 Table 6.18: Models for SAO 147886 (49 Cet)

Model 7 R 't n -Afidjgc Fi2 f 2 5 Fqo J^ioo Fo.s cm M© Jy m Jy

Observations 0.34 0.38 2 . 0 1.9 <36 (± error) 0.03 0.04 0 . 1 0 . 2

M33 3 3 8.4x10^® 3.9x10"'^ 0.26 0.38 1.9 1.5 8

M32 3 2 8 .0 x 1 0 ^® 4.4x10"’^ 0.26 0.38 1.9 1 . 6 8

M31 3 1 7.0x10'® 4.8x10-"^ 0.26 0.39 2 . 0 1.7 8

M23 2 3 2.5x10'® 1 .0 x 1 0 "® 0.26 0.39 2 . 0 2.9 250

M22 2 2 2.5x10'® 1 .0 x 1 0 "^ 0.26 0.37 2 . 0 3.2 300

M 22a 2 2 2.5x10'® 1 .8 x 1 0 "® 0.26 0.39 2 . 0 3.0 250

M 23a 2 3 2.5x10'® 6 .0 x 1 0 "® 0.26 0.40 2 . 0 2.9 2 0 0

M 31a 3 1 6.5x10'® 1.1 XlO"® 0.26 0.37 2 . 0 1.9 6

M32a 3 2 8 .0 x 1 0 '® 7.4x10"^ 0.26 0.36 2 . 0 1.7 7

M32b 3 2 8 .0 x 1 0 '® 1 .0 x 1 0 "® 0.26 0.36 2 . 0 1 . 8 7

M23b 2 3 4.0x10'® 1.7x10"® 0.26 0.37 2 . 0 2 . 8 80

M23c 2 3 6 .0 x 1 0 '® 2.5x10"? 0.26 0.38 2 . 0 1 . 6 4

M23d 2 3 4.5x10'® 4.9x10"? 0.26 0.36 2 . 0 2 . 1 7

M23e 2 3 5.0x10'® 2.3x10"? 0.26 0.37 2 . 0 1 . 6 4

C33 3 3 2.5x10'® 6.7x10"? 0.26 0.36 2 . 0 1.5 0 . 1

C32 3 2 2.5x10'® 6.7x10"? 0.26 0.35 2 . 0 1.5 0 . 1

C32a 3 2 2 .0 x 1 0 '® 8 .8 x 1 0 "? 0.26 0.37 2 . 0 1 . 6 0 . 1

C31 3 1 1.7x10'® 9.8x10"? 0.26 0.38 2 . 0 1 . 6 0 . 1

C23 2 3 4.0x10'® 1.9x10"® 0.28 0.39 2 . 0 1.7 15

C 2 2 2 2 3.7x10'® 3.5x10"® 0.28 0.39 2 0 1.9 15

C 2 1 2 1 3.0x10'® 9.6x10"® 0.28 0.39 2 . 0 2 . 2 13

€13 1 3 2.7x10'® 4.2x10"® 0.26 0.37 2 . 0 1.4 1 1

€ 1 2 1 2 2.5x10'® 8 . 1 x 1 0 "® 0.26 0.37 2 . 0 1.5 1 1

€ 1 1 1 1 2 .0 x 1 0 '® 3.1x10"^ 0.26 0.36 2 . 0 1.9 1 2

€2 1 a 2 1 3.0x10'® 4.7x10"® 0.28 0.39 2 . 0 2 . 1 13

€2 1 b 2 1 3.4x10'® 2 .1 x 1 0 "® 0.28 0.38 2 . 0 1.9 13

242 -9

-10

-11

-1 3 I

-1 4

-1 5

-1 6 10° Wavelength (/xm)

Figure 6.26: Results of modelling SAO 147886. Solid line: model M31a, dashed line: model C21a, dotted line: model C22.

243 The models with a grain size parameter of 7 = 3 (M33, M32, M31) gave 100-/zm fluxes that were slightly lower than the observed IRAS value, while the 7 = 2 models (M23,

M22) gave 100-/xm fluxes that were too high, and also exceeded the upper limit on the

0.8 mm flux. No 7 = 1 models were run, as it was clear that they would produce too much flux at long wavelengths.

As can be seen in Figure 6.26, models which fit the 25-100 ^m data predict very little excess flux at 12 /xm. If the small (0.08 Jy) 12-fim excess seen in the IRAS d a ta is real, it is probably due to emission from UIR features, rather than dust continuum emission.

In an attempt to reduce the long-wavelength emission from the 7 = 2 models by decreasing the number of cool grains, the outer radius was set to 400 AU (5 arcsec; models

M22a, M23a). However, the flux at 100 and 800 /zm from these models was still too high.

Conversely, increasing the outer radius increases the amount of cool dust, and therefore the long-wavelength flux. This was done for models with 7 = 3 (models M31a, M32a,

M32b). These models have sufficient 100 /xm flux to be be consistent with the IRAS

1 0 0 -/xm point, without exceeding the 36-mJy upper limit at 800 /xm. A second way to decrease long-wavelength flux is to reduce the maximum grain size

(see Chapter 4). A set of 7 = 2 , /)=3 models were run, each with max smaller than the value used for model M23 (1 mm). The same disc outer radius as for M23 (1600 AU) was used in each case. Model M23c had a much smaller maximum grain radius (omax = 2 /xm), and gave a 1 0 0 -/xm flux th a t was lower than the IRAS value. Models M23d and M23e had larger values of «max (10 /xm and 5 /xm respectively). M23e stiU gave too little 100-/xm flux, while M23d gave a flux that was slightly higher than the IRAS nominal value, but which was consistent with it within the uncertainties.

Having explored the parameter space of silicate models, a grid of models using only amorphous carbon grains was set up. Maximum and minimum grain sizes were again set to 50 Â and 1 mm. Models C33 and C32 were produced with a projected disc size of

2400 AU.

It was found that for the 7 = 3 amorphous carbon models, a large inner radius

(2.5 X 1 0 '® cm) was required in order to yield a sufficiently low 25/60 /xm flux ratio.

This radius is equivalent to 1670 AU, giving a rather small dynamic range of dust dis­ tances. Also, the 100-/xm flux from the 7 = 3 models was too low. For models C32a -

C ll, a larger outer disc radius (4800 AU) was adopted. This corresponds to a projected

244 disc diameter of 2 arcminutes; slightly smaller than the IRAS beam size ('>^3-4 arcm in).

Models C32a and C31 both gave too little flux at 100 /im. The 7 = 2 models (C 23-

C21) gave more flux at 100 /xm than the 7 = 3 models; they also had inner radii that were roughly a factor of 10 smaller than those of the 7 = 3 model discs.

Models C23 and C22 agree with the IRAS 100-/xm flux within the errors on the mea­ surement; model C21 gave slightly too much 100-/xm flux. Decreasing the outer radius to

2400 AU (30 arcsec; model C21a) and 1000 AU (13 arcsec; model C21b) improved the fit to the IRAS data.

The 7 = 1 models actually gave less 100-/xm flux than the 7 = 2 models. This is because the 60-/xm point, used for normalisation of the models is affected by emission from the hottest dust, which is not the case for stars with a strong 12-/xm excess. Given that the excess is defined by only three data points and one upper limit (neglect­ ing the 12-/xm point), it is not surprising that more than one model provides an adequate fit to the observations. It is nevertheless possible to put some limits on the disc parameters.

The inner radius lies in the range (4.5-8.0)xl0^^ cm (roughly 300-500 AU) for the silicate models which provide a reasonable fit, and (2.0-3.7)xl0^^ cm (150-250 AU) for the car­ bon models. The dust mass required for silicate models is roughly 0.2-0.3 Earth masses, and 2-3 Earth masses for carbon grains. For ‘blend’ models comprising both silicate and carbonaceous grains, the results would be intermediate between the single-material cases. There is therefore a ‘cleared’ region, substantially free of dust around SAO 147886,

which extends to a few hundred AU from the star, a distance several times larger than the orbit of Neptune around the Sun. This raises the possibility that the dust disc is similar to

the Kuiper belt in the Solar System, which has a cleared zone extending to 40 AU from the

Sun (Luu 1994), due to perturbations from the giant planets. However, the SAO 147886

disc must be larger than the Kuiper belt, since the latter extend outwards to only 100 AU

(Luu 1994). The two best-fitting models, M31a and C22 are presented in Figure 6.26.

6.4 Summary of Modelling Results

The primary result of the modelling effort is that the observations of Vega-excess stars are consistent with the presence of circumsteUar dust discs with reasonable values of the

model parameters. The adjective ‘reasonable’ is used here to imply such things as:

245 • A grain-size distribution that favours smaller grains, as is found for interstellar grains

(Mathis, Rumpl & Nordsieck 1977), for asteroids in the Solar System (e.g Safronov

& Ruskol 1994), and for the particles in Saturn’s rings (e.g. Showalter & Nicholson

1990)

• A density distribution which decreases with increasing distance from the star, as one

might expect for a stable disc structure around a star

• Dust masses that are significantly less than the stellar mass and the observed masses

of many pre-main sequence discs (see e.g. HiUenbrand et al. 1992), consistent with

standard evolutionary models involving disc clearing (e.g. Shu et al. 1987)

• Spatial dimensions comparable to the size of the Solar System

For the stars with a near-infrared excess, however, it was found that no single set of model parameters could simultaneously give a fit to the near-IR photometry and the longer-wavelength data. This implies that either there are two (or more) spatially distinct dust populations present in the disc, or there are two types of grain behaviour taking place.

As discussed in Chapter 5, the high temperatures inferred from the near-IR colours (Chapter 3) are comparable with grain evaporation temperatures, suggesting that dust in thermal equilibrium cannot be responsible for the near-IR excess, and so thermally-spiking small grains were used to model the near-IR observations. However, for only three of the hottest stars with near-IR excesses, SAO 131926 (spectral type AO), SAO 77144 (A 2 ) and SAO 226057 (A7V), could thermally-spiking 3-Â radius grains provide a fit to the observations. The masses of small grains required were roughly 1, 10“® and 10“^ Earth masses for SAO 131926, 77144 and 226057 respectively. This indicates that only a very small fraction of the disc mass need be in the form of small grains for a near-IR excess to be observed. The masses were calculated assuming that all the small grains were located at the inner radius of the disc: if they are distributed throughout the disc, then a greater mass would be needed to absorb the same flux of exciting photons. Conversely, if some of the small grains were to be located inwards of the disc inner radius, fewer would be required.

For the cooler stars, thermally spiking grains were not hot enough on average to fit the observations. This implies that the assumed UV flux from these stars was insufficient

246 Table 6.19: Presence of silicate and UIR-band emission

HD SAO Silicate UIR-band 35187 77144 VV 98800 179815 V 135344 206462 y 141569 140789 y 142666 183956 V y 143006 183986 V y 144432 184124 V 158643 185470 V 169142 186777 V y 233517 26804 V y

to excite the grains. However, UIR-band emission was clearly detected in the spectra of three of the seven stars which were observed with CGS3 and have near-IR excesses

(Chapter 3), and the presence of UIR-bands in the spectra of a further two of these stars

(SAO 77144 and SAO 183956) was inferred from modelling the observed silicate feature

(this Chapter). Emission from the UIR bands is believed to be stimulated by UV photons

(e.g. AUamandola et al. 1989), so these stars may have greater UV fluxes than are predicted by the Kurucz model atmospheres. Table 6.19 shows which stars display silicate emission

(in either the 10- or 20-/im feature), and which display UIR-band emission, as determined from inspection of the 10-/im spectra and by the presence of excess 8-9 fim emission.

For the stars where out-of-equilibrium small grains did not provide a good fit to the observations, small grains closer to the star were used to obtain a fit. These grains were approximately in thermal equilibrium, with temperatures in the range 1100-1400 K. The masses of hot grains required were aU in the range 10~®-10“® Earth masses. These mass values should be taken as lower limits, since the presence of larger hot grains, with a lower ratio of surface area to volume, would require more mass. Similarly if the grains are heated by a stochastic process, e.g. if there was more UV flux, some proportion of the grains would be cold and not radiating. This is taken into account for the three stars where thermally-spiking grains can fit the observations, but for the others, virtually aU

247 the small grains are hot, since they are near thermal equilibrium. If the observed near-IR excesses are indeed due to grains which are hot enough to be evaporating, there would need to be some mechanism to replace the material which is lost. This could conceivably be the Poynting-Robertson effect, causing grains to spiral in towards the star from further out in the disc, or even infalling comets, as have been postulated to exist around (3 Pic (Chapter 1). Table 6.20 lists some of the parameters of the best-fitting models found for each star.

Where the models were poorly constrained (usually because of insufficient data to define the SED of the excess emission), the columns listing the grain size parameter 7 and the density distribution parameter (3 are marked with a colon. For these stars, lower limits are given for the inner radius and dust mass, as derived from the range of well-fitting models.

The entries in Table 6.20 are ordered by spectral type: inspection of the table shows that there are no strong correlations of any of the model parameters with spectral class.

The two earliest-type stars, SAO 140789 and SAO 131926, have the largest inner radii, but there is no systematic decrease in inner radius with later spectral type; for instance SAO 186777 (A5V) and SAO 158350 (K5V) have discs with the same inner radius. AU of the modeUed discs have inner radii of at least 1 AU, implying that large dust-

free inner zones are ubiquitous among this sample of Vega-excess stars, just as they were

deduced to be among the prototype Vega-excess stars (GiUett 1986). GiUett lists inner radii for the four prototypes, which are in the range 0.75-36 AU, similar to the range of

inner radii determined in this Chapter. In contrast, models of the discs around pre-main

sequence objects suggest that the disc extends inwards as far as the steUar photosphere

(Kenyon 1995). The infrared image of /3 Pic obtained by Lagage & Pantin (1994a) indicates

significant dust depletion in the inner 30 AU of the disc. The projected inner radii of most

of the discs in Table 6.20 are too smaU to be resolved with present infrared cameras, but

some, especiaUy that of SAO 140789, are comparable to the size of the cleared region

detected by Lagage Sz Pantin.

The average of the values of 7 in Table 6.20 is 2.4, which converts to a continuous-

distribution index (See Chapter 4) of 3.4, identical to that observed for asteroids (Dohnanyi

1969) and similar to the Mathis et al. (1977, MRN) index of 3.5 for intersteUar grains.

For a number of the stars there is a range of possible values of 7 which, combined with

suitable values of /), wiU give a fit to the observations, so the models may be consistent

248 Table 6.20: Best-fitting model parameters

SAO HD Spectral 7 ^ i n - ^ i n . p r o j -A ^ d is c Type (AU) (arcsec) {MEarth)

140789 141569 AOVe 3 2 670 3.5 2 . 2

131926 43282 AO 2.7 2 635 1 . 2 279

147886 9672 A IV :: > 150 ^ 2 > 0 . 2

77144 35187 A2e 2.5 0.7 8.7 0.06 1 2 . 6

91022 218396 A5V : : ^ 5 ^ 0 . 1 2:10-3

186777 169142 A5Ve 2 3 24.7 0 . 1 1 2 . 0

226057 139614 A7Ve 2 1.3 7.4 0.05 2 1 . 2

183956 142666 A 8 Ve 2 0.9 2.7 0 . 0 2 17.9

184124 144432 A9/F0Ve 2 1.3 4.0 0.03 5.0

206462 135344 F 8 Ve 2.7 3 93.6 1 .1 6 . 6

112630 34700 GO 3 3 45 0 . 8 0.28

183986 143006 G5Ve 2 1 . 8 6.5 0.08 5.3

93601 23680 G5 :: > 4 0 ^ 2 > 0 .0 3

111388 23362 K2 : > 4 ^ 0 . 6 2:10-4

26804 233517 K2 2.3 2.5 10.7 0.4 0 . 1 0

179815 98800 K5Ve 2 . 2 1 . 6 1 . 1 0.05 0.13

158350 123160 K5 3 3 24.7 2.3 4 x 1 0 -3 A colon in the 7 and (3 columns indicates that the models were poorly constrained.

An ‘e’ in the spectral type column indicates the presence of Ha emission (Dunkin et al. 1995).

249 with an MRN grain size distribution for most of the systems modelled in this chapter. All the derived values of 7 lie within 0.5 of the MRN value.

The maximum grain sizes were not fully constrained by the modelling. For the stars with strong mm-wave emission, grains of radius 1 mm gave sufficient mm-wave flux. In­ creasing the maximum grain size beyond 1 mm generally made no difference to the model fit. Longer-wavelength observations are required to determine whether grains larger than this are required. Decreasing the maximum grain size to 0.1 mm tended to give insufficient millimetre-wave flux for any reasonable value of 7 . When the sources which required a

1 -mm maximum grain size were modelled with 7 = 3 , the predicted mm-wave flux was always far too small. This underlines the need for a substantial contribution from large grains in these systems.

An approximate lower limit on the maximum grain radius in many Vega-excess systems can therefore be taken to be a = 1 mm. The presence of such large grains indicates that the observed dust is not composed of ‘primordial’ ISM grains, but has undergone some processing in the circumsteUar environment, involving grain growth and possibly fragmentation of larger bodies (see Chapter 1).

Three stars which have rather low upper limits on the 1 .1 -mm flux, SAG 158350,140789 and 26804, are all required to have maximum grain sizes smaller than 1 mm. SAG 158350 was required to have a maximum grain size of 5 /zm, while SAG 140789 was modelled with Umax = 100/xm, although models with Umax SLS low as 0.5/im were also consistent with the observations. SAG 26804 was also found to have a maximum grain size of 1 0 0 //m

(Skinner et al. 1995).

Models with different grain types showed that dust composed entirely of silicates was able to give good fits to the mid-IR to mm-wave data (apart from the UIR bands). It was usually possible to add a fraction (typically 25%) of amorphous carbon, and stifl obtain good agreement between models and observations. The presence of a carbonaceous component to the dust is implied by the detection of UIR bands in the CGS3 spectra of many of the sources, and is consistent with the composition of interstellar dust.

Some sources, e.g. SAG 206462 and SAG 140789, show UIR bands but no silicate feature in their 10-/zm spectra. Even for these stars, it was found that a substantial fraction of the dust must be silicates, since models using only amorphous carbon grains failed to give enough mm-wave flux.

250 The spread of the derived values of the density distribution parameter ^ is larger than that of the grain size parameter 7 , ranging from 0.7 to 3, leading to very different rates of change of dust density with radius in the disc. The grain surface mass density in the disc of SAO 77144 (/? = 0.7), drops by a factor of approximately 35 from the inner to the outer extreme of the disc (assuming constant thickness), while in the disc of SAO 186777

(0 = 3 ) the density drops by a factor of more than 10®. Both discs have similar dimensions.

Models of 0 Pic by Backman et al. (1992) had two spatial components, with the boundary between them at 80 AU. The outer component, corresponding to the region visible in coronagraph images, had a density power law corresponding to 0 = 1.7, while the inner component was not as well constrained, with possible values of 0 ranging from 0.4 to 1.7, consistent with the range of values determined for the stars in the present sample. The observations by Golimowski et al. (1993), using an adaptive-optics coronagraph, showed that the surface brightness gradient does indeed change abruptly at approximately 100 AU from the star, with a shallower gradient for the inner part of the disc. Golimowski et al. suggested that the surface brightness gradient in the inner (<^^40-90 AU) part of the 0 Pic disc is compatible with a density distribution parameter 0 ~ 0.5.

The total dust masses in Table 6.20 are all less than the mass of Jupiter (318 MEarth), and in all but one case are less than the mass of elements heavier than He in the outer planets (38 MEarthj Harper et al. 1984). They are therefore not unreasonably large masses of material to find in orbit around main-sequence stars.

Zuckerman et al. (1993) estimated dust masses for SAO 77144,112630,140789,179815,

183986 and 184124. For all of these stars, the Zuckerman et al. estimates and the masses derived in this Chapter agree within a factor of six. The method used by Zuckerman et al. involved adopting a mass absorption coefficient for circumsteUar dust at mm wave­ lengths and deriving a single dust temperature from the IRAS data. The mass of dust at this temperature required to produce the observed mm-wave flux can then be calculated.

Considering the relative crudeness of the Zuckerman et al. method, it is not surprising that the masses derived in this Chapter and those estimated by Zuckerman et al. do not agree exactly. There does not appear to be a systematic difference between the two sets of results.

Chini et al. (1991) estimated the mass of dust around 0 Pic to be 0.44 MEarth, toward the lower end of the range of masses in Table 6.20. This is reasonable, given that the

251 fractional luminosity of the /3 Pic dust disc (3 xlO~^ ) is less than that of most of the present sample of stars. On the other hand, the dust masses of Herbig Ae/Be stars with discs, calculated by Mannings (1994), lie in the range 30-1000 AfEarth- Only SAO 131926 amongst our sample has a dust mass in this range; the others in the present sample all have lower masses, consistent with the discs around the pre-main sequence Ae/Be stars clearing with time (e.g. Shu et al. 1987). By way of a comparison with the results presented here, one can consider the properties of the population of dust and small bodies in our Solar System. Interplanetary dust is the only form of cosmic dust which has been studied in the laboratory, since interplanetary dust particles (IDPs) impinge on the Earth’s upper atmosphere, and can be collected by high-altitude aircraft, such particles have diameters typically 5-30 /im (e.g. Bradley 1994).

Larger particles (~100 fim ) reach the Earth’s surface as micrometeoroids (e.g. Klock & Stadermann 1994) without undergoing severe atmospheric heating, and so can also be studied as examples of interplanetary dust. IDPs are found to be aggregates of individual mineral grains of size 0.1-1 ^m (Bradley 1994). Both silicaceous and carbonaceous grains are found (e.g. Klock & Stadermann 1984). A small number of IDPs have been shown to contain PAH-like structures (Clemmett at al. 1993). Interplanetary dust can be seen in scattered light as the zodiacal light, and can also be detected in emission in the IR. The 25-/xm zodiacal emission is due mainly to particles of radius approxim ately 10 fim (Dermott & Liou 1994). The bolometric luminosity of the zodiacal dust is 10~® L© with typical temperatures of roughly 200 K (Griin et al.

1985, Good et al. 1986). Spacecraft have directly sampled the zodiacal dust from 0.3 AU to 18 AU (Griin 1994). From 0.3-3 AU, the particles are in orbits of low inclination

(i < 30°) with (spatial) number density falling off as n(r)

the number density is constant, and the distribution of orbital inclinations is essentially random. The sources of interplanetary dust are short-period comets and asteroids, from

which the particles move inwards due to Poynting-Robertson drag. The zodiacal dust has

a mass estimated to be less than 10"^ MEarth (Backman & Paresce 1993). Other populations of orbiting solid material in the Solar System are the Oort Cloud

and the Kuiper Belt, believed to be the sources of the long-period and short-period comets

respectively. The inner Oort cloud is postulated to extend from 1000 AU to 2 xlO^ AU from the Sun, and the outer Oort cloud from 2 xlO'* AU to 1.5 X10^ AU (Weissman 1991,

252 Heisler & Tremaine 1986). In total, the Oort cloud is thought to contain or the order of

10^^ comets, with a total mass of roughly 50 Earth masses, and a number density which varies with distance as r~^ (Weissman 1991).

The Kuiper Belt extends from 40-100 AU, with the inner edge due to perturbation by the giant planets, particularly Neptune. Its total mass lies in the range 0.03-1 Earth mass, determined from the lack of perturbation of Comet Hailey by the belt (Luu 1994). Backman & Paresce (1993) show that if one Earth mass of material is distributed in the Kuiper belt with an size distribution between 10 fim and 10 km, it would have a luminosity Lir ^ lO'^L©, only slightly less than the luminosity of the dust around Vega, but would not have been detected by IRAS due to the foreground emission from the zodiacal dust.

253 C hapter 7

Conclusions and Future Work

This Chapter attempts to summarise the conclusions that can be drawn from this work, and to indicate possible lines for further work, some of which are already in progress.

7.1 M Supergiants

The unambiguous detection of UlR-band emission in the spectra of a number of M super­ giants shows that carbonaceous material is present in the outflows of these sources, and therefore that standard equilibrium condensation models do not adequately describe the processes which are at work.

The fact that MZ Cas does not lie in the same OB association as the h and % Per supergiants demonstrates that the phenomenon is not restricted to a single spatial grouping of stars.

The interpretation proposed in Chapter 2, which is based on non-equilibrium chemistry

(Beck et al. 1992), requires more UV flux from the star than is expected from photospheric

emission alone. As a consequence, it is predicted that all the M supergiants displaying UIR

bands have warm chromospheres. These stars should therefore have excess radio flux due

to chromospheric free-free emission, and should exhibit UV lines from ionised material in

the chromosphere. Observations at these wavelengths could provide a useful test of the

chromosphere model. However, due to their distances, the present sample of M supergiants

are likely to be faint at both UV and radio wavelengths. The radio observations may not be feasible with present-day instruments, whereas the UV observations may require use of

the HST for the fainter stars.

254 Preliminary observations with the VLA failed to detect emission from any of a subset of the M supergiants, but the flux upper limits obtained were not sufficiently low to rule out the presence of chromospheres. Observations of KK Per with the lUE (Stencel et al. 1986) show the presence of emission lines from singly-ionised calcium, aluminium and iron, confirming the presence of chromospheric activity.

Further insight into the circumsteUar environments of M supergiants should be gained from observations with ISO, the Infrared Space Observatory. Complete 2.5-45 /zm spectra wiU be obtained of a sample of approximately a dozen M supergiants, including several of the sources from Chapter 2, during Open Time observing. Observations with CGS3 of a larger sample of M supergiants whose IRAS LRS spectra resemble those of the h and \ Per sources with UIR bands would help determine what frac­ tion of M supergiants have carbon-rich condensates, and whether the apparent correlation with mass-loss rate noted in Chapter 2 appUes to the larger sample.

7.2 Vega-excess stars

The detection of most of the Vega-excess stars in the present sample with CGS3 (Chap­ ter 3), and the good agreement between the IRAS and CGS3 1 2 -/zm fluxes lead to the simple, but important, conclusions that the infrared emission is indeed associated with the stars, rather than being due to some other other source in the large IRAS beam, and that the 1 0 - and 2 0 -/xm emission is mainly confined to within a few arcseconds of the star rather than being some kind of extended nebulosity. The exception to this was SAO 208591, for which the CGS3 flux was substantiaUy lower than the IRAS flux, and was consistent with photospheric emission. It was concluded that SAO 208591 is not a real Vega-excess star, and that the flux detected by IRAS is mostly due to another source in the IRAS beam.

The CGS3 observations form the first infrared spectroscopic survey of a large sample of Vega-excess stars, and include the first 20-fim spectra, the first detection of UIR-band emission, and the first demonstration of the range of silicate profiles present in the spectra of Vega-excess stars.

The detection of silicate features in the CGS3 spectra demonstrates that the emission is due to orbiting dust grains, as is known to be the case for the prototypes Vega and

Pic. Silicate features were observed in the 1 0 -/im spectra of five sources: SAO 179815,

255 183956,184124, 77144 and 51 Oph. SAO 26804 and 183986 may also show weak sili­ cate features in the 1 0 -/im spectra; modelling of both stars suggests that silicates are indeed present in the CS dust. The 20-/im spectra of five sources, SAO 179815, 184124, 186777, 206462 and 51 Oph, show the IS-fim silicate feature. Since the 10-/zm spec­ tra of SAO 186777 and SAO 206462 do not show silicate emission, the total number of

Vega-excess stars in the sample with detected silicate features is 7-9. This demonstrates the utility of 20-fim spectra for detecting silicate emission when the 1 0 -/xm spectrum is dominated by the UIR bands. The presence of the UIR bands in the spectra of five Vega-excess stars (SAO 26804 shows the 7.7-fim band, while SAO 140789, 183986, 186777 and 206462 show the 7.7- and 11.3-^m bands), out of the sixteen which have an excess in the IRAS 12-fim band, indicates that the presence of carbonaceous material around Vega-excess stars is fairly common. The presence of carbonaceous dust around main sequence stars obviously has a bearing on the possible existence of extra-solar planets capable of supporting life. The observed combination of silicate and carbonaceous dust is consistent with an interstellar origin for the circumsteUar material. The best-fitting models obtained for SAO 77144 and SAO 183956, which gave good agreement with aU the photometry from optical to mm wavelengths, did not predict enough flux in the short-wavelength parts (A 9 /xm) of the CGS3 spectra, and failed to match the inflection at approximately 1 1 /xm in the spectrum of SAO 183956. This suggests that there is a UIR-band contribution to both spectra, with the strong 7.7-/xm band supplying the shorter-wavelength flux, and the 11.3-/xm band being seen as the inflection in the spectrum of SAO 183956. One can therefore predict that the spectra of these two stars should faU off rapidly shortwards of 7.7 ;xm, due to both the siUcate feature and the 7.7-fim band emission decreasing to shorter wavelengths. Both these are due to be observed using the ISO Short Wavelength Spectrometer in Guaranteed Time, so this prediction wiU soon be tested.

Near-IR observations revealed excess emission from nine out of the 23 Vega-excess systems studied, indicative of the presence of hot (~1000 K) material. The present study is the first to show that near-IR excess is common among Vega-excess stars. The stars which display near-IR excess emission are distributed over a wide range of spectral types

(A0-G5). Their positions in a near-IR colour-colour diagram (Figure 3.1) were found to be

256 intermediate between those of the Herbig Ae/Be stars and those of normal main-sequence stars.

IRCAM imaging showed that for SAO 131926 and SAO 186777, the excess emis­ sion is concentrated within approximately 0.6 arcsec of the central stars. Modelling of

SAO 131926 gives a projected inner radius of the mid-IR emitting material of 1.2 arcsec.

If this is correct, then the hot material must be located inside the ‘cleared’ zone revealed by the dust-disc modelling. The IRCAM instrument has recently been upgraded to use a 256x256 array, which, when used with a magnifier, allows an image scale of 0.06 arc- sec/pixel to be achieved. Use of this configuration would allow a more sensitive search for extension in the near-IR excess emission.

There appears to be some correlation between the presence of near-infrared excess emission and UIR-band emission in the mid-infrared spectra. Of the six stars which display near-IR excess (seven if one includes SAO 140789, which probably has a weak excess) which were observed with CGS3, only SAO 184124 does not show strong evidence for UIR-band emission. Modelling of SAO 77144 and SAO 183956 showed that the UIR bands are superposed on the silicate features of these stars, while simple inspection of the

CGS3 spectra is enough to confirm the presence of the UIR bands for the other stars.

Conversely, of all the stars with UIR-band emission, only SAO 26804 does not display any evidence of a near-IR excess. This supports the idea that the near-IR excess is due to thermally-spiking materials, since the UIR bands are thought to arise from non-equilibrium heating of small regions of a

HAC solid (Duley & Williams 1988), or of individual PAH molecules (e.g. AUamandola et al. 1989). The only star with a near-IR excess and no UIR emission apparent in the CGS3 spectrum, SAO 184124, has a very strong silicate feature. This may well be drowning out any UIR-band emission, and the high contrast of the silicate feature itself implies that it is due to small grains.

SAO 131926 has a strong near-IR excess, and a 12-//m flux in excess of that predicted by the best-fitting combination of equilibrium and smaU-grain models (which fits the data longwards of 12 fim ). These two factors suggest that this star has strong UIR-band emission in the mid-infrared, but a 10-//m spectrum has yet to be obtained.

The detection of strong mm-wave emission from a large number of Vega-excess stars indicates the presence of large grains (of order 1 mm radius), as confirmed by radiative-

257 transfer modelling. This is the largest sample to date of Vega-excess stars observed at millimetre wavelengths. For most of the stars detected with the JCMT, upper limits could not be placed on the maximum grain size. These objects could therefore possess a substantial population of grains larger than 1 mm. If this is the case, the dust masses derived from modelling will underestimate the true mass of solid material. Observations at longer wavelengths are needed to determine the turnover wavelength. VLA observations have already been scheduled to measure the flux from a number of Vega-excess stars at

7 mm. Such observations may allow us to determine whether grain growth has proceeded to sizes greater than 1 mm.

Modelling showed that the observed infrared excesses were consistent with emission from circumsteUar dust discs, heated by the star. Power-law grain size distributions were used; the indices derived for Vega-excess stars were similar to the value found for interstel­ lar dust and micrometeoroids. Grains larger than those in the intersteUar medium were required, indicating that substantial grain growth has taken place around Vega-excess stars. Disc masses varied significantly from star to star, with a range of approximately 10“^ - 10^ Earth masses. The disc models were found to have large dust-free regions with sizes ranging from a few AU to several hundred AU.

It was found that model parameters which gave a good fit to the mid-IR to millimetre data failed to predict the observed near-IR excesses, A model for these was developed which took into account the temperature fluctuations of very smaU grains. This was found to give satisfactory results for only the hottest stars in the sample; the cooler stars were found to have insufficient UV flux to excite the smaU grains.

If, however, the cooler Vega-excess stars possess hot chromospheres, the number of

UV photons available to excite smaU grains could be much higher. Observations using the

International Ultraviolet Explorer satellite are underway to search for excess UV emission due to chromospheric activity. Preliminary results seem to suggest that excess UV emission is indeed present in some Vega-excess stars.

The high values of the fractional excess luminosity Lir /L* obtained in Chapter 3 suggest that the dust discs of some Vega-excess stars may be optically thick. The next phase in the modelling effort wiU therefore be to use optically-thick radiative transfer methods to model the sources. Two stars in our sample, SAO 206462 and SAO 183986

(see table 3.19) have fractional luminosities that exceed the theoretical maximum of 0.5

258 for a flared, passively radiating disc. It may therefore be the case that ‘active’ heating of the discs, by dissipation of energy due to accretion or friction, need to be included in future disc models. The ISO mission will have a major impact on the study of Vega-excess stars. Ob­ servations of Vega-excess stars form part of the ISO Guaranteed Time programme; the target lists include many of the sources in the sample studied for this thesis. A number of them wiU be observed with aU four ISO instruments, giving complete spectral coverage over a wavelength range of approximately 2.5-200 /xm. A number of searches will also be made in order to increase the number of known Vega-excess stars, which should allow the evolutionary characteristics of Vega-excess discs to be studied in more detail.

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