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Wahlgren, Glenn Michael

A SPECTRAL ANALYSIS OF RV TAURI VARIABLES

The Ohio State University Ph.D. 1986

University Microfilms International 300 N. Zeeb Road, Ann Arbor, Ml 48106

Copyright 1986

by Wahlgren, Glenn Michael

All Rights Reserved A SPECTRAL ANALYSIS OF RV TAURI VARIABLES

DISSERTATION

Presented in Partial Fulfillment of the Requirements for

the Degree Doctor of Philosophy in the Graduate

School of The Ohio State University

By

Glenn Michael Wahlgren, B.S.,M.A.

*****

The Ohio State University

1986

Dissertation Committee: Approved by

Ronald Kaitchuck,Ph.D.

Arne Slettebak,Ph.D.

Robert F. Wing,Ph.D. Robert F. Wing, Adviser Department of As^onomy Copyright by Glenn Michael Wahlgren 1986 DEDICATION

To Sharon and Michael ACKNOWLEDGEMENTS

It is a pleasure to thank my adviser, Professor Robert F.

Wing, from whom I have learned much about being an astrono­ mer, for suggesting this topic and offering his insights.

Special thanks go to Brian Skiff and Dr. Nat White, of

Lowell Observatory, for making photometric observations, and Professors R. Kaitchuck and R.F. Wing for obtaining IDS spectra which were used in this dissertation. The staffs of both Lowell Observatory and Perkins Observatory have also been a great help, especially Peter Stoycheff, for the drafting of several figures presented in this dissertation.

The synthetic spectrum analysis was made possible by the generosity of Dr. C. Sneden, of the University of Texas, in allowing me to use his program, MOOG, as well as that of

Dr. R.E. Luck, of Case Western Reserve University, who kindly supplied the model stellar atmospheres.

Finally, I would like to thank my wife, Sharon, for being so understanding and providing incentive to finish. VITA

May 15, 1956... Born - Jersey City, New Jersey

1978 . B.S., Pennsylvania State University, University Park, PA.

1978 - 1981.... Scientist/Engineer, McDonnell Douglas Astronautics, Huntington Beach, CA.

1981 . M.A., California State University, Long Beach, CA.

1981 - 1984.... Teaching Associate (various times) Department of Astronomy, The Ohio State University, Columbus, Ohio

1982 - 1984.... Research Assistant (various times) Department of Astronomy, The Ohio State University, Columbus, Ohio

1984 - 1985.... Perkins Observatory Research Assistant, Department of Astronomy, The Ohio State University, Columbus, Ohio

1984 - 1985.... Consultant, Ohio Board of Regents, Columbus, Ohio

\ 1985 - 1986.... Graduate School Presidential Fellow, Department of Astronomy, The Ohio State University, Columbus, Ohio

PUBLICATIONS

"Remarkable Modification of Lightcurves for Shadowing Effects on Irregular Surfaces: The Case of 37 Fides", V. Zappala, DiMartino, F. Scaltriti, R. Burchi, L. Milano, G. Wahlgren, and K. Pavlovski, Astron. Astrophys. 123, 362, (1983). Atlas of Hiqh-Resolution IUE Spectra of Late-Type Stars, R.F. Wing, K.G. Carpenter, and G.M. Wahlgren, Perkins Observatory Special Publication No.l, (1983).

ABSTRACTS

"An Atlas of High-Resolution IUE Spectra of Late-Type Stars", R.F. Wing, K.G. Carpenter, and G.M. Wahlgren, BULL.A.A.S. JL4, 918, (1982).

"The Recent Deep Minimum of VX Sagittarii", R.F. Wing and G.M. Wahlgren, BULL.A.A.S. ^6, 897, (1984).

"Observations of TiO Absorption and Balmer-Line Emission in RV Tauri Variable Stars", G.M. Wahlgren, R.F. Wing, and N. White, BULL.A.A.S. 16, 897, (1984).

"The Peculiar Spectrum of HQ Mon", G.M. Wahlgren, R.F. Wing, R.H. Kaitchuck, S.R. Baird, D.J. MacConnell, and D.W, Dawson, BULL.A.A.S. 17, 599, (1985).

"Photometric and Spectroscopic Observations of R Set during a Strong-TiO Minimum and Subsequent Recovery", R.F. Wing, G.M. Wahlgren, G. Fontaine, and F. Wesemael, B U L L ^ A ^ J7, 875, (1985).

"Atmospheric Parameters of RV Tauri Variables", G.M. Wahlgren, BULL.A.A.S. 17. 875, (1985).

- v - TABLE OF CONTENTS

Page

DEDICATION ...... ii

ACKNOWLEDGEMENTS ...... i i i

VITA ...... iv

LIST OF FIGURES ...... viii

LIST OF TA B L E S ...... xii

CHAPTER

I. INTRODUCTION ...... 1

II. OBSERVATIONAL MATERIAL ...... 21

Introduction ...... 21 Spectroscopic Observations ...... 22 Instrumentation ...... 22 The Observations ...... 23 Data Reduction ...... 27 Photometric Observations ...... 30 The Photometric S y s t e m ...... ,. 30 Instrumentation and Observing P r o c e d u r e s ...... 32 Photometric Reductions ...... 34

III. OBSERVATIONAL PROPERTIES ...... 40

Spectral Classification ...... 40

- vi - Spectroscopic ...... 40 Photometric...... 47 Suspect Classifications ...... 56 Color Excesses ...... 59 Metallicity ...... 62

IV. SYNTHETIC SPECTRUM ANALYSIS ...... 76

Introduction ...... 76 The Synthetic Spectrum Program ...... 78 The Input D a t a ...... 89 Model Atmospheres ...... • . 90 Atomic Line D a t a ...... 91 Number Density ...... 94 Program Initialization ...... 102 Observational Considerations ...... 102 Spectrum Rectification ...... 103 Computational Resolution ...... 106 A n a l y s i s ...... 108 Application to RV Tauri Variables ...... 116

V. THE NATURE OF RV TAURI VARIABLES ...... 133

Introduction ...... 133 Metallicity ...... 134 Absolute Magnitudes ...... 138 Galactic Distribution and Population T y p e s ...... 146 Evolutionary Status ...... 150

APPENDICES

A. Spectra of the RV Tauri V a r i a b l e s ...... 153

BIBLIOGRAPHY 220 LIST OF FIGURES

FIGURE PAGE

1. Spectral features within photometric bandpasses...... 49

2. Eight-color bandpasses and warm stellar spectrum...... 50

3. Eight-color bandpasses and cool stellar spectrum...... 51

4. Eight-color photometry spectral classification...... 53

5. Photometry of R Set...... 55

6. R^ versus Spectral Type diagram...... 65

7. Rm versus Spectral Type diagram...... 66

8. Eight-color photometry luminosity discrimination...... 72

9. The 6cn - [Fe/H] diagram...... 73

10. Synthetic spectra for BD+1°2916...... 110

11. Synthetic spectra parameterization...... 115

12. The observed spectrum and derived continuum of TT Oph...... 122

13. TX Oph s observed and synthetic spectra. . . . 123

14. V564 Oph : observed and synthetic spectra. . . 124

15. The Mv - Period diagram...... 144

16. The spectrum of DY Aql on 23 May 1984...... 154

17. The spectrum of DY Aql on 24 May 1984...... 155

- viii - 18. The spectrum of DY Aql on 9 .Jun 1984. . .

19. The spectrum of DY Aql on 10 Jun 1984.

20. The spectrum of DY Aql on 23 Jun 1985. . . . 158

21. The spectrum of DS Aqr on 26 Jun 1985. .

22. The spectrum of IS Aur on 6 ,Jan 1985. . .

23. The spectrum of TW Cam on 11 Dec 1983. .

24. The spectrum of TW Cam on 13 Dec 1983. .

25. The spectrum of TW Cam on 6 ,Jan 1985. . .

26. The spectrum of TW Cam on 11 Jan 1985. .

27. The spectrum of RX Cap on 27 Jun 1985. .

28. The spectrum of EQ Cas on 6 ,Jan 1985...... 166

29. The spectrum of DF cyg on 21 Jun 1985. . . . . 167

30. The spectrum of V360 Cyg on 22 Jun 1985. . . . 168

31. The spectrum of SS Gem on 13 Dec 1983. .

32. The spectrum of ss Gem on 11 Jan 1985. .

33. The spectrum of su Gem on 12 Dec 1983. . . . . 171

34. The spectrum of su Gem on 13 Dec 1983. . . . . 172

35. The spectrum of su Gem on i :Dec 1984. . .

36. The spectrum of su Gem on 11 Jan 1985. . . . . 174

37. The spectrum of AC Her on 10 Jun 1984.

38. The spectrum of AC Her on 27 Jun 1985. .

39. The spectrum of BT Lac on 11 Jan 1985. . . . 177

40. The spectrum of EP Lyr on 26 May 1984. .

41. The spectrum of EP Lyr on 21 Jun 1985. .

42. The spectrum of U Mon on :L Dec 1984...... 180

43. The spectrum of U Mon on iLI Jan 1985. . .

- ix - 44. The spectrum of HQ Mon on 11 Jan 1985...... 182

45. The spectrum of HQ Mon on 23 Feb 1985...... 183

46. The spectrum of TT Oph on 26 May 1984...... 184

47. The spectrum of TT Oph on 8 Jun 1984...... 185

48. The spectrum of TT Oph on 9 Jun 1984...... 186

49. The spectrum of TT Oph on 10 Jun 1984...... 187

50. The spectrum of TT Oph on 21 Jun 1985...... 188

51. The spectrum of TT Oph on 27 Jun 1985...... 189

52. The spectrum of TX Oph on 23 May 1984...... 190

53. The spectrum of TX Oph on 24 May 1984...... 191

54. The spectrum of TX Oph on 8 Jun 1984...... 192

55. The spectrum of TX Oph on 9 Jun 1984...... 193

56. The spectrum of TX Oph on 10 Jun 1984...... 194

57. The spectrum of TX Oph on 21 Jun 1985...... 195

58. The spectrum of UZ Oph on 24 May 1984...... 196

59. The spectrum of UZ Oph on 8 Jun 1984...... 197

60. The spectrum of UZ Oph on 9 Jun 1984...... 198

61. The spectrum of UZ Oph on 10 Jun 1984...... 199

62. The spectrum of UZ Oph on 22 Jun 1985...... 200

63. The spectrum of V564 Oph on 26 May 1984. . . . 201

64. The spectrum of V564 Oph on 8 Jun 1984...... 202

65. The spectrum of V564 Oph on 9 Jun 1984...... 203

66. The spectrum of V564 Oph on 10 Jun 1984. . . . 204

67. The spectrum of V564 Oph on 22 Jun 1985. . . . 205

68. The spectrum of R Sge on 22 May 1984...... 206

69. The spectrum of R Sge on 24 May 1984...... 207

- x - 70. The spectrum of R Sge on 9 Jun 1984...... 208

71. The spectrum of R Sge on 10 Jun 1984...... 209

72. The spectrum of R Sge on 22 Jun 1985...... 210

73. The spectrum of R Sge on 27 Jun 1985...... 211

74. The spectrum of RV Tau on 11 Dec 1983...... 212

75. The spectrum of RV Tau on 13 Dec 1983...... 213

76. The spectrum of RV Tau on 6 Jan 1985...... 214

77. The spectrum of RV Tau on 11 Jan 1985...... 215

78. The spectrum of V Vul on 21 May 1984...... 216

79. The spectrum of V Vul on 10 Jun1984...... 217

80. The spectrum of V Vul on 21 Jun 1985...... 218

81. The spectrum of V Vul on 27 Jun 1985...... 219

- xi - LIST OF TABLES

TABLE PAGE

1. Grating Characteristics ...... 24

2. Spectroscopic Observation Log ...... 26

3. Characteristics of the Eight-Color Filters . . . 32

4. RV Tauri Photometric Observations ...... 37

5. Spectral Standards : Plate D a t a ...... 44

6. Spectral Standards : IDS D a t a ...... 45

7. Observed Properties Of the Variables ...... 46

8. Observations of R S e t ...... 54

9. Line Ratio Diagnostics for Non-Variables .... 67

10. Line Ratio Diagnostics for RV Tauri Variables . 68

11. Observations of Hydrogen Emission ...... 69

12. Non-Variable Star Data : [Fe/H] - 6cn D i a g r a m ...... 74

13. Saha Equation Coefficients...... 101

14. Parameters for Abundance Standards...... 103

15. Atomic Transitions in RVTa u ...... 125

16. Atomic transitions in RVTa u ...... 126

17. Atomic Transitions in TXOp h ...... 127

18. Atomic Transitions in TXOp h ...... 128

19. Synthetic Spectrum Parameters ...... 129

20. Variations in Spectral Line D e p t h ...... 132

- xii - Luminosity: P-L vs. Synthetic Fit

Distance from the Galactic Plane CHAPTER I

INTRODUCTION

The RV Tauri stars are a sparsely populated class of pulsa- tional variables of high luminosity found between the

Cepheids and the long-period variables on the H-R diagram.

Of the approximately 14,000 pulsating variables listed in the third edition of the General Catalogue of Variable

Stars (GCVS) (Kukarkin et al. 1969) only 104 are designated as confirmed or suspected RV Tauri stars, representing a scant 0.7%. In addition, only a handful of the 2000 vari­ ables in globular clusters are considered to be of this type (Hogg 1973). Investigation of these stars on an indi­ vidual basis is likely to decrease their numbers further as their classification criteria have not been unique among variable stars. However, their relative obscurity in terms of numbers and published studies should not be equated with unimportance. On the contrary they are important examples of post-asymptotic giant branch (AGB) evolution.

A broad working definition for an RV Tauri variable would include the following characteristics:

- 1 - • Light-curve period: 50 - 150 days measured between suc­

cessive primary (deep) minima

• - Light-curve shape: alternating deep and shallow minima

with a mean brightness that may be constant or variable

• Spectral type: mid F to K

• Luminosity class: I - II

Variations exist in each of these criteria and will be addressed individually. Interpretation of the class in terms of theoretical models or even a simple empirical mod­ el is hampered by the heterogeneity of its members.

Historically, van der Bilt (1916) appears to have been the first to suggest a separate class of variables based upon similarities in the light curves of RV Tau, R Sge, and

V Vul. Prior to this time these stars had been classified as either Irregular or 8 Lyrae eclipsing variables. After­ wards, the usual approach to classification was based sole­ ly upon the shape of the light curve, with its characteris­ tic alternation of deep and shallow minima. Naturally, incorrect classifications occurred, as conveyed by Campbell and Jacchia (1941);

"... it was almost a fashion, about ten years ago, to call any semi-regular variable with some­ what indefinite characteristics an 'RV Tauri Star'. ... the result was that all kinds of het­ erogeneous objects, many quite unlike typical RV Tauri stars, were classified as such" Even RV Tau itself was considered at one point not to belong to the class that bears its name (Payne-Gaposchkin and-Gaposchkin 1938). Confusion still exists when classi­

fying a star as either an RV Tauri or semi-regular of type

SRd. In general, the SRd variables are redder in color and

exhibit a more irregular light curve with a smaller ampli­

tude than the RV Tauri stars. Separation of these two

classes by DDO photometry has been attempted by Dawson

(1979) and a multivariate analysis of his data has been

conducted by Mantegazza (1984).

However, the various disturbances in the light curves of

the RV Tauri stars do make them somewhat irregular in

nature. These disturbances can take on a number of forms

(Tsesevich 1975):

1. Change in light-curve shape. The light curve becomes

Cepheid-like as the secondary minimum becomes deeper

while the primary minimum becomes shallower. When the

light curve resumes its normal appearance a shift in

phase equal to half the formal period may occur.

2. Periods of random oscillation. The semi-regular nature

is most evident in this case as the variations may

suddenly become random in their amplitude and/or peri­

odicity.

3. Double periodicity. A variation in the mean light lev­

el may occur with a period which is longer than the primary period by a factor of approximately 15. The

amplitude of the longer period can be as much as two

■ magnitudes, superimposed upon a primary amplitude of

generally one to two magnitudes. The star RV Tau is

an example of such a double periodicity.

Light curves with a constant mean light level are desig­ nated RVa, while those exhibiting the slow variation, or double period, are designated RVb (Kukarkin et al. 1958).

These light-curve anomalies are easily discernable in the work of Payne-Gaposchkin et al. (1943). Other sources of light-curve data include the photoelectric photometry for a large sample of variables by Preston et al. (1963), DuPuy

(1973), and Dawson (1979), and for smaller samples or sin­ gle stars by Kameny (1956), Wisse and Wisse (1973), Nakagi- ri and Yamashita (1979), Dawson and Patterson (1982), and

DuPuy et al. (1983). Visual brightness estimates for the brightest RV Tauri stars have been reported from time to time by members of the AAVSO. Erleksova (1971,1972) has studied the period instabilities and shapes for 21 vari­ ables, finding them to have periods less stable than the W

Vir stars but more so than the Mira variables.

The work of Preston et al. (1963) points out several observations regarding the colors of the RV Tauri stars.

Having spectroscopically categorized them into three groups (see below) where group A is of spectral type G - K while groups B and C are of spectral type F, Preston et al. found that group A stars had larger amplitudes in (B-V). On the assumption that the absolute visual magnitude for all RV

Tauri stars was M v = -3 and with reddening corrections to the UBV colors from either a color excess determined from nearby B-type stars or a slab model for galactic extinc­ tion, the variables were plotted in the (U-B) versus (B-V) plane at particular phases for most stars and all phases for a few stars. It was noted that groups A and (B+C) form a continuous sequence located along the locus of the lb supergiants of Kraft and Hiltner (1961). Both at primary minimum and maximum of the colors the groups remained sepa­ rated. For individual stars over their entire period the data formed elongated, inclined loops which did not repeat exactly from cycle to cycle although, as in the case of R

Set, they did remain along the lb locus. DuPuy (1973) has constructed similar color-color diagrams using UBVR data.

Dawson and DuPuy (1985) remarked upon how these loops, when plotted in the luminosity-effective temperature plane, either approach or cross the boundary for non-variable stars that separates coronal versus non-coronal structure.

Erleksova (1974) has also discussed the separation of groups A, B, and C in the period-color, H-R, and (dV/dB) versus (dU/dB) diagrams. The spectra of the RV Tauri variables display unique and interesting characteristics. Early attempts at classifica­ tion into subgroups from spectral data made use of both spectral features and radial velocities. The first compre­ hensive spectral analyses were those of Sanford

(1931,1933,1934) for the stars AC Her, U Mon, and R Sge and

V Vul, respectively. For each of these stars an extensive series of observations, in some cases spanning several years, was obtained at dispersions of 37 and 75 A/mm at H^.

Radial velocities were determined for all phases, although not necessarily within the same cycle, and spectral varia­ tions were noted. McLaughlin (1939) produced a similar study for R Set and reanalysed Sanford's data for R Sge and

V Vul (McLaughlin 1941).

Rosino (1951) observed 25 RV Tauri variables at a dis­ persion of 123 A/mm. His work summarized the spectral characteristics observable at classification dispersion:

• luminosity is generally high, corresponding to class la

or lb

• luminosity decreases on the descending branch of the

light curve before deep (primary) minimum is reached

• spectral types from atomic lines are of classes F, G,

or K

• earliest spectral type is reached at a point halfway

between the primary minimum and the ensuing maximum • hydrogen line emission primarily occurs during the rise

from primary minimum, but not in all stars

• • molecular absorption bands due to TiO appear around the

phase of primary minimum in some stars, even though all

other spectral indicators assign a type no later than

KO - K3

• the cooler variables are most likely to show hydrogen

line emission and TiO absorption

• the radial velocity curve appears to trail the light

curve by a small amount.

Rosino subdivided the RV Tauri variables into two groups: a "bright-line" or "U Mon" group consisting of stars which exhibit TiO absorption and hydrogen emission, and another group consisting of those which do not. He also noted that AC Her is a carbon star and classified it

Rp.

Joy (1952) observed 38 semi-regular and RV Tauri vari­ ables at low dispersion and formed two subgroups based upon residual velocity. The low-velocity group, v < 70 km/ Jl 6 o sec, contained nearly all of the RV Tauri stars, including all that were known to exhibit TiO absorption, as well as several semi-regulars, while the high-velocity group, v > dm C *3 70 km/sec, contained the majority of semi-regulars. In general, the low-velocity stars were more luminous, later in spectral type, and had weaker, less persistent hydrogen emission. Joy associated the high-velocity stars with

Baade's Population II and likened them to the RV Tauri variables found in globular clusters (Joy 1949), while the

low-velocity stars were tentatively denoted as anomalous

Population I. Therefore, in Joy's work we see the first

indication that the RV Tauri stars are not solely Popula­

tion II objects.

The current system of subclasses was devised by Preston

et al. (1963) on the basis of low dispersion spectra (430

A/mm). Three subgroups were formed having the following characteristics:

(A) G - K variables: All spectral features except TiO

indicate spectral type G or K. TiO bands may appear at

light minima. Irregualities in the strength of the CN

bands, X 4175 blend, or the G-band of CH may occur.

(B) Fp(R) variables: Spectral types based upon hydrogen

lines yield F5 - GO classifications with Ca II lines

giving earlier spectral types. Variations in CN and CH

strengths are conspicuous. AC Her, a carbon star, is a

member of this group.

(C) Fp variables: CN and CH bands are weak or absent at

all phases, although the spectra are otherwise similar

to group B. The globular cluster variables belong to

this group. 9

Dawson (1979) suggested a further subdivision of group A into A1 and A2, defined by the occurrence or absence of

TiO. From DDO photometry stars of group A2 appear underlu- - minous when compared against predictions from a period- luminosity relation and group A1 stars appear overluminous by a similar amount. Mantegazza (1984) also incorporates the A1,A2 subgroups into his factor analysis of the DDO colors of RV Tauri and SRd variables.

Progress towards understanding the atmospheric struc­ ture, and perhaps the pulsation mechanism, was not made until with the advent of high-resolution (^10 A/mm) spec­ troscopy, Abt (1953,1955) observed line doubling prior to primary maximum in the stars AC Her, U Mon, and R Set.

Sanford (1955) also observed doubling in metal lines near maximum in AC Her. Line doubling has been studied by Pre­ ston (1962,1964) for R Set and U Mon, respectively, at a dispersion of 2 A/mm. Howell et al. (1983) and Bopp (1984) reported on metallic emission lines in all three of these stars. Gehrz and Mozurkevich (1983) observed RV Tauri stars in the infrared with a fourier transform spectrome­ ter. Three systems of CO lines were observed: absorption lines with a constant velocity at +5 km/sec, a photospheric absorption component which varies between ±25 km/sec, and emission lines probably originating from a hot shocked region. From the high-dispersion work of Abt and Preston we can build an empirical picture of the stratification which must exist in RV Tauri atmospheres. Several velocity systems are evident. The nature of the line doubling is such that near luminosity minimum a metallic absorption line is shifted toward the red with a faint companion line violet- shifted from the rest position. As the stars's brightness increases the red component decreases in intensity while the violet component becomes stronger. Finally, the violet component moves redward, the redward component vanishes, and the former violet component assumes the position and strength of the original red component. This cycle is repeated twice during a single light period, suggesting that half the formal period is the more important period for pulsational considerations. Weak emission has been observed between the doubled components in some neutral metal lines. Other metal lines are not seen to double at any time. The occurrence of line doubling is correlated with the line's excitation potential, X . For Fe I lines, doubling occurs for subordinate lines with X > 0.9eV, while lines originating from lower levels with X < 0.2eV do not split and show a much lower amplitude of the radial veloci­ ty variation (Preston 1962). A curve-of-growth analysis on each component of the doubled system shows that the vio­

let (ascending) component originates in a hotter layer than 11 does the red (descending) component. Hydrogen emission observed during rising light appears to originate in a lay­ er that is rather deep in the atmosphere as evidenced by iron absorption lines observed in the violet wing of H emission. At very high resolution, Ha appears in emission throughout the light cycle and shows complex structure with

Ho absorption superimposed upon the emission feature.

Evidence for circumstellar gas surrounding RV Tauri stars was first obtained from high-resolution spectrograms showing sharp absorption components in the violet wings of the Ca II H and K lines in the spectrum of U Mon (Preston

1964). Two stationary components were found, which were interpreted in terms of two shells of gas moving outward from the star with velocities of -45 and -83 km/sec. Lat­ er, Preston (1972) observed that the two absorption lines had been replaced by a single absorption line of velocity

-71 km/sec, thereby ensuring that their origin was not interstellar. Prior to this the idea of circumstellar (CS) material had arisen in conjunction with the stars of group

A that show TiO absorption (Preston 1962). Good evidence for CS dust was not obtained until the early 1970’s, when infrared photometry was undertaken by Gehrz (1971,1972),

Gehrz and Woolf (1970), and Gehrz and Ney (1972). Ten- filter and four-filter photometry spanning the spectrum from 2.2 to 22 u m was used to construct continua for RV Tauri stars as well as other classes of variable and non­ variable stars. Generally, dwarfs and most luminous stars

(class I - III) as late as spectral type M2 do not exhibit an infrared excess as expressed by the color index

(3.6)-(11.3) urn. All of the RV Tauri stars observed showed

infrared excesses amounting to 1.2 to 4.9 mag, the majority of which were larger than 2.5 mag. The extremes were rep­ resented by R Set on the low end and AC Her on the high end. Although the infrared radiation varied by as much as a magnitude over a given star's period, the infrared colors remained essentially constant. Among the other classes of stars observed only the most luminous supergiants of later types (G8Ia,M2Ia), carbon stars and T Tauri stars had excesses as large as the RV Tauri's. Two types of continua were noted: one which is smooth and featureless and another which appears to be a composite of emission bumps in the

7-14 jjm and 18-22 um regions with a smooth underlying con­ tinuum. The excesses were interpreted as extended, cool

(hundreds of degrees) circumstellar shells which may have formed from matter ejected by atmospheric shock waves. The composition of the dust was considered most likely to be metallic silicates for the oxygen-rich stars, based upon the observed emission near 10 and 20 yin. For carbon-rich stars such as AC Her, with emission features at 7-14 ym and

18 pm, an unidentified substance was deemed responsible for 13 the grain condensations. This work suggested that the infrared continuum shape is correlated with the A, B, C spectroscopic subclasses. However, Lloyd Evans' (1974) optical spectra do not support this idea. Using wide-band

JHKL photometry, Lloyd Evans (1985) has estimated that the dust shells have a temperature of around 900 degrees.

Other studies with a bearing on circumstellar matter have to do with microwave OH emission, photopolarimetry, and ultraviolet spectra. Bowers and Cornett (1973) made measurements of the OH maser emission lines at 1612, 1665, and 1667 MHz for an extensive list of RV Tauri, SRd, and M stars. From the observed infrared excesses, similar in magnitude to those of the Mira variables, it was suspected that the RV Tauri stars may show evidence of masing. How­ ever, no OH emission was observed to the observational flux limit of 1 Jy. Later, Fix and Claussen (1984) observed semi-regular and RV Tauri variables at 1665 and 1667 MHz with a detection limit of 40 mJy. Of the few RV Tauri stars observed only RV Tau was even weakly detectable, at a level of 55 mJy. This suggested that the 35 ym radiation from CS dust believed necessary to pump OH masers (Elitzur et al. 1976) was apparently not sufficiently strong.

Unfortunately, the photometry of Gehrz only went as far as

22 ym and therefore cannot be used to test this conclusion. Polarization studies have been limited to two stars, R

Set and U Mon. Unfortunately, it is difficult to deter­ mine to what extent the polarization is coming from the stellar photoshere or CS material. Polarization measure­ ments of R Set have been made by Shchkovskoj (1963), Dom- brovkij et al. (1968), Serkowski (1970), Yakovleva (1973), and Landstreet and Angel (1977), and U Mon has been observed by Shchkovskoj (1963), Aliev (1965), and Serkowski

(1970). Both stars exhibit variable intrinsic polariza­ tion of up to two percent, with the polarization in the ultraviolet being stronger than at any longer wavelengths.

The strongest polarizations have for the most part been observed at the phase of primary minimum.

Ultraviolet spectra for three stars (AC Her, U Mon, R

Set) obtained with the IUE satellite have been used to study the X2200 A feature (Baird and Cardelli 1985). They find the CS reddening to be larger than the interstellar reddening for AC Her and R Set, while the opposite is true for U Mon. Possible interpretations of the data with regard to dust shells are given by Cardelli (1985).

Models involving shock fronts appear necessary to account for emission from the metallic and He I lines that are observed. Abt (1955) suggested a simple shock model for U Mon in a similar context as that suggested for W Vir 15

(Abt 1954). Preston (1964) listed several problems that the shock models had up to that time failed to answer.

Recently, Baird (1984) discussed various aspects of the observed spectra such as line splitting and applied the two-shock model of Willson and Hill (1979) to RV Tauri stars. Although the model does go much further towards explaining the occurrence of metallic-line emission, it also makes predictions which contradict the present data.

Modeling the characteristic alternation of deep and shallow minima of the light curve has proven to be a diffi­ cult theoretical problem. Most attempts have been cen­ tered about the idea of resonance effects between pulsa- tional modes. Christy (1966) proposed that coupling between the fundamental and first harmonic modes were responsible for alternating amplitudes in models intended for W Vir stars. Christy's simple pulsation models were criticized by Deupree and Hodson (1976) as being unrepro- duceable by their two-dimensional hydrodynamics code.

They found that time-dependent convective motion may be damped out on alternate periods when near-sonic convective velocities set up large horizontal pressure gradients, cre­ ating a shear flow that reduces the magnitude of convective instability during the following pulsation cycle. Takeuti and Peterson (1983) explored the possibility of resonance effects using linear, adiabatic, radial pulsation models 16 for Cepheid variables. Their stellar models could not produce the longer RV Tauri pulsational periods using the resonance between the fundamental mode and first overtone believed to be operating. However, Aikawa (1985) showed that non-adiabatic effects in low-surface-gravity models were important, and Fadeyev and Fokin (1985) invoking non- adiabat icity postulated that the fundamental-first overtone resonance will produce RV Tauri-like light curves. The aforementioned attempts at modeling the RV Tauri phenomenon must be considered first-order approximations since each deals with a specific aspect of the problem and none accounts for all reasonable possibilities. They assume that the light variations are due solely to pulsations of the star and ignore the peripheral phenomena such as shock fronts and dust shells.

The determination of basic physical parameters such as mass, radius, and luminosity for the RV Tauri variables depends upon secondary techniques due to their great dis­ tances. Several RV Tauri-like variables occur in globular clusters, and their distances are fairly well known. For these stars alone a period-luminosity (P-L) relation can be constructed (Stothers 1964; DuPuy 1973). The application of a globular cluster P-L relation to the RV Tauri stars found in the general field must be viewed with caution.

Field variables are likely to be of a different population type and may not obey the same P-L relation as the cluster variables. Luminosities have not as yet been determined

from the most direct methods of distance determination.

Only two stars, U Mon and R Set, are bright enough to have been included in the trigonometric parallax catalogue of

Jenkins (1952), and both of them have parallaxes smaller

than the quoted errors. No RV Tauri variables have been

found in open clusters, associations, or the Magellanic

Clouds. None are confirmed members of binary star systems.

U Mon was suspected of being a single-lined spectroscopic

binary by Preston (1964), but the data are inconclusive and

the interpretation of the slow variation in the light curve may be associated with the pulsational mechanism. DuPuy

(1973) determined statistical and secular parallaxes for a

sample of 23 variables. Values for mean visual absolute magnitudes ranged from -3.0 to -3.7 for several categories.

The most widely used methods of luminosity determinations,

other than P-L relations, are either spectral classifica­

tion or calibrations of photoelectric photometry. Both

require observing luminosity-dependent spectral features which may vary with pulsational phase or depend upon other

inexactly known quantities, such as effective temperature

and metallicity. Barnes and DuPuy (1975) argue that lumi­

nosities assigned from MK classification calibrations of

Population I stars are inappropriate for the luminous RV 18

Tauri variables, presumably of an older population and low­ er mass. Dawson (1979), using DDO photometry, determined

Mv for many RV Tauri and SRd variables but with major uncertainties in the photometric determinations of the sur­ face gravity. Photometric distances also must contend with another poorly known quantity, the interstellar absorption.

The radii of RV Tauri variables are found to be large.

Dawson's photoelectric mean radii range from 54 to 164 solar radii. Batyushkova (1984), using a modified Wessel-

ink method, found the radii of AC Her and V Vul to each be about 65 solar radii. DuPuy (1973) was unsuccessful in his application of Wesselink's method to AC Her and R Set due to unstable light and velocity curves.

The determination of stellar mass is also uncertain because direct methods of mass measurement cannot be applied. Without reliable direct measurements of quanti­ ties such as mass, radius, and luminosity, the position of an evolved star in the H-R diagram does not have a unique evolutionary interpretation. Early estimates based upon position in the H-R diagram placed RV Tauri masses at 20-50

M © (Kameny 1956). This obviously conflicts with masses of

< 1M q required for those variables found in globular clus­ ters. Dawson's (1979) photometrically computed masses fall between 1 and 10 times solar. Theoretical models used 19 to describe Population II Cepheids and RV Tauri stars assume asymptotic branch masses of 0.6-0.8 M 0 (Gingold

1974,1976; Mengel 1973; Sweigart 1973). Gingold (1974) interpreted the RV Tauri stars as low-mass stars undergoing the last of their relaxation cycles, brought on by helium shell flashes, in the post-AGB stage and/or the final blue- ward motion across the H-R diagram to the white dwarf stage. Possibilities for an interpretation by a more mas­ sive star, for the field variables, may be provided by the models of Iben and Truran (1978). Their work also predicts surface composition traits as a function of progenitor mass which may be of use in limiting the range over which RV

Tauri masses occur. Theoretical evolution models are to some extent hampered by an ignorance of mass loss.

Clearly, then, spectroscopic chemical analyses of the field RV Tauri star atmospheres are necessary to make fur­ ther conclusions regarding their mass and evolutionary his­ tory. Surprisingly, up to now very little such work has been done. Yoshioka (1979), in a differential curve-of- growth analysis, found AC Her to have a metallicity of one- tenth solar. Baird (1981), also analysing AC Her with the help of computed line strengths from stellar atmosphere models, found [Fe/H] = -1.22 with relatively enhanced C,

N, and 0, thereby quantifying its carbon star nature. Luck

(1981), also using a fine analysis technique, derived [Fe/H] = -0.87 for R Set, differing from the less accurate curve-of-growth analysis of Preston (1964) who estimated

[Fe/H] = -0.4 . Luck also found the s-process elements to be deficient by a factor of ten relative to the iron-peak elements. Aliev’s (1965) analysis of U Mon by the curve- of-growth method produced [Fe/H] = -2.93 with equally sur­ prising results for other elements. Photometrically derived [Fe/H] values by Dawson (1979) for 21 RV Tauri stars show that the metallicity has an extensive range:

-0.3 > [Fe/H] > -1.9 . But the DDO photometry determines

[Fe/H] from the strength of the CN molecule, a feature which is known to be variable and anomalous in its strength among the RV Tauri stars.

The approach taken in this dissertation is multi­ dimensional. Applying both spectroscopic and photometric techniques we address topics such as the heterogeneity of the class, atmospheric parameters, metallicity and its implications to Population type, and the occurrence of TiO absorption and hydrogen line emission. By far the bulk of the spectroscopic data has been obtained for the purpose of determining [Fe/H] by a synthetic spectrum fitting tech­ nique. The problems of the technique and its results are discussed in Chapters 4 and 5. CHAPTER II

OBSERVATIONAL MATERIAL

INTRODUCTION

Observations were made using both spectrophotometric and photometric techniques to address several topics in the study of the RV Tauri variables. Although originally con­ ceived to include the study of time-dependent phenomena, the realities and constraints of observing redirected the bulk of the spectroscopic observations toward the study of the atmospheric parameters, particularly the metallicity which one hopes to be independent of the time of observa­ tion.

The photoelectric photometry had the primary purpose of supporting the spectroscopic data for the metallicity anal­ ysis. Since the periods of these variables are fairly long it was felt that photometric observations made within a few days of the spectroscopic could be used for this purpose.

Photometry, in conjunction with the spectroscopy, is used to determine the total color excess, E(B-V). As a survey tool, photometry with the eight-color system is used here to detect the presence of TiO bands in the near-infrared

- 21 - 22 and to provide a measure of the near-infrared CN band strength at X8120 A.

SPECTROSCOPIC OBSERVATIONS

Instrumentation

Spectroscopic observations were made using the Ohio State

University Image Dissector Scanner (IDS) on the Perkins

72-inch telescope located at Lowell Observatory. The IDS

is a dual-channel device allowing for the simultaneous observation of sky and star+sky. It has been described by

Byard et al. (1981) and is similar in design to the image- tube scanner constructed by Robinson and Wampler (1972) at

Lick Observatory.

Simply explained, a spectrum from each channel is focused on the photocathode of the first of three consecu­ tive S-20 extended-red electrostatic image tubes, which altogether increase the gain by a factor of 10® . Thermal noise is reduced by circulating methanol, cooled to dry ice temperature, through tubing around the first stage of the

image-tube chain. The last image tube is fiber-optically coupled to an ITT image dissector which scans the output phosphor approximately once every 4 ms. Focus and scan coils around the image dissector act to image a part of the output phosphor onto a dissector aperture of 25 urn width. 23

Those electrons from the photocathode of the image dissec­ tor which pass through the aperture are amplified to produce output pulses of electrons which are directed to an amplifier-discriminator and transmitted to the counting circuits of the IDS. The image-tube chain and dissector scanner are encased in magnetic shielding to prevent the earth’s magnetic field from distorting the spectrum as the telescope is pointed to various positions throughout the night. Since the image dissector scan period is less than the decay time of the last image-tube phosphor, a single phosphor event may be counted several times. Therefore the

IDS is not a photon-counting device obeying Poisson statis­ tics.

The entire operation of the IDS is controlled from a warm room using a PDP-11/34 minicomputer, which also stores the data on diskette and displays the telescope position.

Each raw spectrum consists of 2048 channels with counts ranging from 0 to 32,767.

The Observations

All observations were made using a slit assembly with a pair of circular apertures of projected diameter 5", sepa­ rated by 35" from center to center along the direction of right ascention. Two different gratings were used; their characteristics are listed in Table 1. The resolution is approximate and applies to center of the observed spectrum.

The resolution deteriorates at the edges of the scan by more than 50% (Crenshaw 1985).

Table 1

Grating Characteristics

Grating(1/mm) 1800 600 Blaze position(A) 5000 5500 Order 1 1 Spectral range(A) 900 2500 Resolution (A) 2.5 7

During the course of observing, a star would be alter­ nated between apertures for exposures lasting no more than

300 seconds, depending upon its brightness. For the brightest stars ( V < 8 for the 1800 1/mm grating and V < 9 for the 600 1/mm grating) a neutral density filter was placed at the front of the spectrograph to reduce the light intensity by a factor of ten. By alternating between aper­ tures on short time intervals one acts to minimize the effects of image-tube afterglow, variable extinction, and changing sky conditions.

Choosing the RV Tauri stars to observe was constrained by three factors: brightness, accessibility from the Flag­ staff observing station, and the definitive nature of their classification in the third edition of the GCVS. Regarding the last point, 26 of the 104 RV Tauri variables in the GCVS are of uncertain classification and were not consid­ ered. The accessibility of an object involves the latitude of the observatory and limitations imposed by the physical structure of the telescope, IDS, and dome. Thus, stars were limited to those having declinations in the range -20

< 6 < +60. Of the approximately 40 variables considered those observed are listed in Table 2 along with pertinent information regarding the observations. At least 10 4 counts, in the channel of maximum counts, were obtained as an indication of the exposure time.

In addition to the program variables, the spectra of standard stars were obtained for several purposes. Since the 1800 1/mm grating produces spectra at a resolution sim­ ilar to that of MK spectral classification spectrograms, classification standard stars ranging in spectral type from

F5 to M and in luminosity from I to III were obtained in order to classify the variables spectroscopically. To aid in the calibration of the synthetic spectrum program, the spectra of stars with spectroscopically determined atmos­ pheric parameters (Teff/log g/vt/[Fe/H]) were obtained.

Finally, the spectra of stars with known flux distribu­ tions, from the list of Stone (1977), were observed nightly to correct the program stars for instrumental response and flux calibration. Flux standards were observed both with and without a neutral density filter to determine the transmission function of the filter. 26

Table 2

Spectroscopic Observation Log

Variable Date(UT) JD Range Res. Exp.Time 2440000.+ (A) (A) (sec)

DY Aql 23 May 84 5843.931 4240-5120 3 1800 24 May 84 5844.936 6100-8500 10 1200 9 Jun 84 5860.906 3900-6300 10 1200 10 Jun 84 5861.885 4240-5120 3 1200 23 Jun 85 6239.918 4000-4880 3 2400 DS Aqr 26 Jun 85 6242.943 4000-4880 3 1800 IS Aur 6 Jan 85 6071.755 4240-5100 3 1800 TW Cam 11 Dec 83 5679.774 6100-8500 10 2400 13 Dec 83 5681.844 3900-6300 10 2400 6 Jan 85 6071.645 4240-5100 3 1200 11 Jan 85 6077.805 4240-5100 3 800 RX Cap 27 Jun 85 6243.878 4000-4880 3 3600 EQ Cas 6 Jan 85 6071.645 4240-5100 3 3000 DF Cyg 21 Jun 85 6237.928 4000-4880 3 3000 V360 Cyg 22 Jun 85 6238.905 4000-4880 3 3600 SS Gem 13 Dec 83 5681.968 3900-6300 10 480 11 Jan 85 6077.881 4240-5100 3 800 su Gem 12 Dec 83 5680.984 6100-8500 10 1200 13 Dec 83 5681.993 3900-6300 10 1800 1 Dec 84 6035.991 4285-5120 3 2400 11 Jan 85 6077.847 4240-5100 3 2400 AC Her 10 Jun 84 5861.954 4240-5100 3 800 27 Jun 85 6243.819 4000-4880 3 1200 BT Lac 11 Jan 85 6077.613 4240-5100 3 1500 EP Lyr 26 May 84 5846.863 4240-5120 3 1800 21 Jun 85 6237.874 4160-4880 3 1800 U Mon 1 Dec 84 6035.948 4285-5155 3 1200 11 Jan 85 6077.944 4240-5100 3 1200 HQ Mon 11 Jan 85 6077.917 4240-5100 3 1800 23 Feb 85 6119.743 4240-5100 3 3600 TT Oph 26 May 84 5846.826 4240-5100 3 1800 8 Jun 84 5859.820 6100-8500 10 800 9 Jun 84 5860.769 3900-6300 10 1800 10 Jun 84 5861.782 4240-5100 3 1200 21 Jun 85 6237.816 4000-4880 3 1800 27 Jun 85 6243.760 4000-4880 3 1200 TX Oph 23 May 84 5843.803 4240-5100 3 2400 24 May 84 5844.811 6100-8500 10 1800 8 Jun 84 5859.838 6100-8500 10 800 9 Jun 84 5860.800 3900-6300 10 1800 10 Jun 84 5861.806 4240-5100 3 1800 21 Jun 85 6237.846 4000-4880 3 1800 UZ Oph 24 May 84 5844.841 6100-8500 10 1800 8 Jun 84 5859.858 6100-8500 10 800 9 Jun 84 5860.829 3900-6300 10 1800 27

Table 2 (continued)

10 Jun 84 5861.834 4240-5100 3 1200 22 Jun 85 6238.775 4000-4880 3 1800 V564 Oph 26 May 84 5846.902 4250-5130 3 1800 8 Jun 84 5859.875 6100-8500 10 600 9 Jun 84 5860.856 3900-6300 10 1800 10 Jun 84 5861.856 4240-5100 3 1800 22 Jun 85 6238.807 4000-4880 3 3000 R Sge 22 May 84 5842.912 4240-5100 3 840 24 May 84 5844.915 6100-8500 10 1200 9 Jun 84 5860.924 3900-6300 10 800 10 Jun 84 5861.925 4240-5100 3 600 22 Jun 85 6238.885 4000-4880 3 480 27 Jun 85 6243.862 4000-4880 3 360 RV Tau 11 Dec 83 5679.817 6100-8500 10 2400 13 Dec 83 5681.803 3900-6300 10 2400 6 Jan 85 6071.732 4240-5100 3 800 11 Jan 85 6077.830 4240-5100 3 800 V Vul 21 May 84 5841.958 4240-5120 3 360 10 Jun 84 5861.938 4240-5120 3 600 21 Jun 85 6237.967 4000-4880 3 600 27 Jun 85 6243.928 4000-4880 3 600

Data Reduction

Reduction and analysis of the IDS data was carried out at the Astronomy Department of The Ohio State University uti­ lizing a PDP-11/34 computer and the Interactive Reduction

System described by Jenkner (1980). The reduction software is similar to that used to operate the IDS. The purpose of the reduction procedure is to transform the observed spec- tum in units of counts per channel to one in units of flux

(ergs sec-1 cm-2 ) per unit wavelength (A). For a given star the data for each intergration is reduced separately by the following procedure: 28

1. Subtraction of sky spectrum from the star+sky spectrum

taken in the same aperture either immediately preced­

ing or following the star observation. For bright

stars, < 10, the sky spectrum was usually an insig­

nificant fraction of the star continuum level.

2. Division by the integration time, in seconds, to

arrive at the count rate, per second, per channel.

3. Division by the flat field scan. Flat fields, or

exposures of a guartz-halogen lamp, were made at the

beginning and sometimes at the end of the night and

are used to remove channel-to-channel sensitivity var­

iations of the image tubes.

4. Wavelength calibration of the spectrum. A dispersion

curve was determined for each aperture from a scan of

either a Fe-Ne or He hollow cathode lamp, depending

upon the wavelength region under observation. The

dispersion curve converts channel position into wavel­

ength .

5. Correction for atmospheric extinction. Effects of

atmospheric extinction at the airmass of the observa­

tion are removed using a standard extinction curve

determined for Lowell Observatory by Tug, White, and

Lockwood (1977).

At this point the reduced spectra for each aperture are averaged together. Next, the dispersion curve for each 29 aperture is linearized by resampling the data. All data were resampled to 2000 channels. Data from each aperture are then flux calibrated by multiplying by a calibration array. For each night the flux calibration arrays were determined by first reducing the flux standard star data as explained above and then comparing the intergrated flux

(count rate) in specific wavelength bins to the fluxes in the same bins of determined standard flux (Stone 1977).

Finally, the east and west aperture data are averaged together to obtain the final reduced spectrum.

In some instances the east and west data are markedly different in their overall sensitivity, possibly due to drift of the spectra on the phosphor scanned by the image dissector or bad initialization of the phosphor scanning positions, or 'sweeps'. A decision must then be made as to the usefulness of the data in either aperture.

For the purposes of this study the consistency of the absorption spectra between the two apertures is of extreme importance. Differences in line depth can normally be seen, but in most instances these variations are random in both wavelength and strength and not systematic with regard to aperture. However, a careful comparison of east versus west aperture data must be conducted in order to map the positions of extreme discrepancies which do occur due to instrumental glitches or cosmic ray events. 30

PHOTOMETRIC OBSERVATIONS

The Photometric System

Choosing an appropriate filter system for conducting pho­ toelectric photometry from the many that are available had to take into consideration several factors, such as desired photometric information, energy distributions of the pro­ gram stars, availability of instrumentation, and observa­ tion and reduction procedures. No single system is ideal, but the combination of B and V filters from the Johnson UBV system with the first four filters of the eight-color narrow-band near-infrared system (Wing 1971) did provide a very useful one. Inclusion of the UBV system has the advantage that comparisons can be made with previous obser­ vations by other researchers. Photometry is now available to some extent in the UBV, Stromgren four-color, DDO, and eight-color systems for these variables.

The filter set used was limited to six filters for prac­ tical reasons: the weak flux in the remaining filters of these two systems would have increased the observing time of each star so much as to limit the number of stars observable in a night without providing much additional information. Also, a reliable S-l photocell, necessary for observing in the 1 urn region, was not readily avail­ able. Observations were made for two classes of objects, 31

in addition to nightly standard stars: the RV Tauri vari­ ables, and giant stars with spectroscopically determined values for [Fe/H] from the list of Heifer and Wallerstein

(1968).

Much has been written on the UBV system and will not be repeated here. The eight-color system was designed to measure absorption from the molecules CN, TiO, and VO in stars of spectral types G, K, M, and C. It has been shown by White (1971) and White and Wing (1978) that the eight- color system provides an accurate determination of spectral type in stars exhibiting TiO absorption since both the MK and eight-color systems rely upon the strength of TiO for their classifications of M stars. Classification of lumi­ nosity in the eight-color system, however, is not on the MK system since the MK system relies upon ratios of atomic

lines whereas the eight-color system assigns a luminosity class based upon the strength of the infrared CN bands, which is positively correlated with luminosity.

The characteristics of the eight-color filters are pre­ sented in Table 3, taken from White and Wing (1978). The

filter transmission functions can be described as gaussians with full-width at half-power listed in the table. The system provides a long baseline between continuum points

for a more accurate color temperature. Advantages of the 32 eight-color system include its being defined solely by the filters and standard stars, and the fact that no color- dependent terms occur in determining the narrow-band instrumental magnitudes. The magnitude computed from the flux measured through filter number five, the 1(104) magni­ tude, can be considered a magnitude in the traditional sense since it is calibrated by the flux from the star

Vega.

Table 3

Characteristics of the Eight-Color Filters

No. Wavelength Bandwidth Primary Function Contaminants (A) (A)

1 7120 60 TiO y (0,0) CN &v=3 2 7540 50 Continuum, K4-M6 Weak CN 3 7810 40 Continuum, G,K,C TiO 4 8120 50 CN av=2 Weak TiO 5 10395 50 Continuum, 1(104) 6 10540 60 VO 7 10810 60 Continuum He I X10830 8 10975 70 CN (0,0)

Instrumentation and Observing Procedures

The photometric observations were made at two observatories using three telescopes and three photometers. The tele­ scopes were the 32-inch Schottland reflector of Perkins

Observatory in Delaware, Ohio, the 72-inch Perkins tele­ scope, and the 42-inch reflector, the latter two located at

Lowell Observatory in Flagstaff, Arizona. The 32-inch was equipped with a single-channel photometer using an EMI S-20 extended-red sensitive photomultiplier, thermoelectrically cooled and operating in a pulse-counting mode. Only 'six- filter' photometry was done at this site. At the Flagstaff station two single-channel pulse-counting systems were used. For observations on the 'six-filter' system, an RCA

31034-A photomultiplier with a high-sensitivity In-Ga-As photocathode was used, thermoelectrically cooled. This system was operated by a micro-computer, described by White and Wasserman (1984), with data stored on diskette. The B and V filters had the characteristics described by Fernie

(1974). On several occassions the entire eight-color fil­ ter set was used. This system, constructed by N. White, contained an ITT FW-118 photocell with an S-l cathode, cooled with dry ice.

The goal of the observations was to attain a total of at least 104 counts with each filter for star-sky so that by

Poisson statistics the internal accuracy of the measure­ ments would be about one percent. This goal was achieved for all photometric standard stars as well as for the pro­ gram stars in the B,V filters. For some of the fainter RV

Tauri stars observed, however, it was not always possible to achieve 104 counts in a reasonable amount of time when using the narrow eight-color filters. 34

Since two distinct photometric systems were being used on the same night, it was necessary to choose two sets of standard stars to compute the nightly extinction coeffi­ cients and color transformations. Fortunately, the eight- color system standards are bright, most with V < 6th magni­ tude. Therefore, the fainter eight-color standards could also be used as bright BV standards. Fainter BV standards were chosen from the list of equatorial standards of Lan- dolt (1973).

Photometric Reductions

All reductions were carried out at The Ohio State Universi­ ty using either the Amdahl 470 or IBM 3081 computer. Sepa­ rate reduction procedures were used for the BV and eight- color data sets. The BV data were reduced according to the method outlined by Hardie (1962). If the computed nightly extinction coefficients were found to be inade­ quate, then average extinction coefficients determined from good photometric nights at the same observing site were used. Seasonal UBV extinction data for the Flagstaff observing station were obtained from N. White (1985) and R.

Millis (1985) of Lowell Observatory.

The reduction of the eight-color data is divided into two parts and is simplified by the fact that the filter bandwidths are narrow. Color terms are removed from the 35 analysis by the fact that the observations are nearly monochromatic. In the first part of the analysis, Program

A computes the Julian Date, sec(z) or air mass, and instru­ mental magnitudes for each star observed. In addition, counts for individual integrations are compared against the mean value for the star to determine a scatter index for each filter. The output from Program A is written to a disk file and together with the standard star fluxes serves as the input to Program B. This program then computes the extinction and transformation coefficients for each filter using data from all observations of standard stars. Limits are placed on the range of values that can be assigned to the extinction coefficients, based on experience from pho­ tometrically good nights. The limits used were 0.035 and

0.085 for all filters at the Flagstaff site. For the Per­ kins Observatory site an inadequate amount of eight-color photometry has been done which can provide satisfactory limits on the extinction, and 0.030 and 0.100 were rather arbitrarily chosen as the extrema for all filters.

With the computed coefficients the program stars are placed on an absolute system where the fluxes, designated

F(l) through F(8), are expressed in units of magnitudes per unit wavelength. The system is zeroed to the stellar mag­ nitude at F(5), or the 1(104) magnitude, by the value

1(104) = 0.000 for aLyr, and the remaining filters have 36 been calibrated using the absolute energy distribution giv­ en for aLyr by Oke and Schild (1970). Table 4 presents the reduced photometry for the RV Tauri stars.

In order to estimate errors in the observations, BV and eight-color reduction programs both compute a residual between the observed and standard magnitude in each filter for the standard star data. All of the residuals are aver­ aged, irrespective of sign, to arrive at the mean deviation for each filter. The mean deviations for the eight-color data range from 0.005 to 0.02 mag. For the BV data the values are slightly higher, between 0.01 and 0.02 magni­ tude. Table 4

RV Tauri Photometric Observations

Variable Date (UT) JD V B-V F(l) F( 2) F(3) F {4) 2440000.+

DY Aql 9 Jun 84 5860.855 6.946 6.794 6.765 6.798 26 Jun 85 6242.846 9.80 1.62 7.342 7.050 7.075 7.073 V362 Aql 13 Oct 84 5986.648 13.03 1.49 10.745 10.661 10.647 10.840 IS Aur 9 Oct 84 5982.992 11.98 2.05 9.361 8.659 8.675 8.648 TW Cam 9 Oct 84 5982.934 10.18 1.61 7.708 7.588 7.552 7.656 17 Nov 84 6020.766 10.06 1.46 4 Jan 85 6069.672 9.67 1.52 7.497 7.453 7.438 7.484 RX Cap 26 Jun 85 6242.892 11.91 0.87 9.963 9.970 10.073 10.111 EQ Cas 11 Oct 84 5984.848 11.38 1.05 9.121 9.091 9.085 9.099 BI Cep 9 Oct 84 5982.801 11.95 1.74 8.742 6.355 7.117 5.871 9 Oct 84 5982.847 8.790 6.484 7.219 6.004 DF Cyg 11 Oct 84 5984.703 10.37 0.99 8.290 8.265 8.349 8.379 26 Jun 85 6242.862 12.41 1.40 9.992 9.807 9.665 10.005 V360 Cyg 11 Oct 84 5984.773 11.86 1.10 9.610 9.563 9.537 9.522 26 Jun 85 6242.924 11.08 0.84 9.097 9.238 9.214 9.184 V457 Cyg 13 Oct 84 5986.738 12.54. 1.52 10.109 9.998 9.984 10.113 CU Del 11 Oct 84 5984.723 11.97 1.83 9.574 8.144 8.513 8.039 SS Gem 6 Oct 84 5979.968 6.760 6.739 6.726 6.817 11 Oct 84 5984.977 9.14 1.28 6.897 6.744 6.749 6.780 17 Nov 84 6020.844 8.59 1.14 4 Jan 85 6069.691 8.73 1.30 6.695 6.725 6.656 6.786 SU Gem 5 Oct 84 5979.001 9.525 9.450 9.351 9.377 11 Oct 84 5984.992 11.29 0.52 9.559 9.588 9.654 9.732 3 Nov 84 6006.895 12.42 1.52 17 Nov 84 6020.875 12.11 1.60 4 Jan 85 6069.703 13.09 1.10 10.542 11.488 11.017 10.579 LO -~j Table 4 (continued)

Variable Date (UT) JD V B-V F(l) F(2) F(3) F(4) 2440000.*

AC Her 19 May 85 6204.811 7.77 1.03 5.853 5.876 5.867 5.976 26 Jun 85 6242.812 7.55 0.79 5.625 5.682 5.725 5.787 BT Lac 13 Oct 84 5986.828 14.12 1.71 11.580 11.382 11.298 11.326 EG Lyr 10 Oct 84 5983.724 9.307 7.185 7.830 6.967 EP Lyr 26 Jun 85 6242.824 10.61 0.97 8.604 8.553 8.710 8.776 HQ Mon 9 Oct 84 5983.015 11.640 11.667 11.512 11.591 U Mon 6 Oct 84 5979.997 5.339 5.301 5.316 5.403 13 Oct 84 5987.016 7.41 1.12 5.504 5.415 5.369 5.540 3 Nov 84 6006.914 7.90 0.98 17 Nov 84 6020.891 7.28 0.96 4 Jan 85 6069.715 7.18 1.03 5.305 5.333 5.320 5.409 31 Jan 85 6096.665 7.92 0.99 5.896 5.845 5.852 5.920 TT Oph 9 Jun 84 5860.824 8.136 8.217 8.237 8.296 26 Jun 85 6242.733 9.79 1.14 7.718 7.746 7.750 7.904 TX Oph 9 Jun 84 5860.773 8.159 8.209 8.200 8.272 19 May 85 6204.839 10.29 1.16 8.187 8.147 8.181 8.350 26 Jun 85 6242.742 9.99 0.98 7.937 7.981 7.983 8.032 UZ Oph 9 Jun 84 5860.762 7.987 8.070 8.087 8.146 26 Jun 85 6242.753 10.27 1.03 8.213 8.271 8.271 8.404 V564 Oph 9 Jun 84 5860.832 7.575 7.440 7.448 7.465 26 Jun 85 6242.796 10.22 1.69 7.745 7.540 7.542 7.558 CT Ori 4 Jan 85 6069.723 10.79 1.14 8.672 8.624 8.738 8.767 R Sge 9 Jun 84 5860.840 6.830 6.862 6.893 6.977 13 Oct 84 5986.707 9.86 1.30 8.042 7.908 7.875 8.151 26 Jun 85 6242.880 8.76 0.90 6.826 6.882 6.943 7.006

u> GO Table 4 (continued)

Variable Date (UT) JD V B-V F (1) F{ 2) F (3) F(4) 2440000.+

RV Tau 5 Oct 84 5978.969 7.170 6.986 6.882 7.089 9 Oct 84 5982.961 9.87 1.89 7.334 7.060 6.975 7.140 13 Oct 84 5987.004 10.06 1.67 7.666 7.492 7.365 7.593 3 Nov 84 6006.867 8.89 1.65 17 Nov 84 6020.793 9.35 1.68 4 Jan 85 6069.680 9.49 1.57 7.402 7.164 7.202 7.201 31 Jan 85 6096.672 9.32 1.68 6.838 6.748 6.691 6.858 V Vul 11 Oct 84 5984.738 8.51 1.18 6.365 6.468 6.422 6.557 3 Nov 84 6006.620 8.44 1.26 26 Jun 85 6242.914 8.86 1.41 6.666 6.670 6.658 6.844

u> VO CHAPTER III

OBSERVATIONAL PROPERTIES

Although the main thrust of the dissertation lies in the application of the synthetic spectrum program, the data are of a general enough nature to allow us to address several other topics in the study of RV Tauri variables. Both the spectroscopic and photometric data are essential for empir­ ically deriving the color excess and metallicity and each serves to complement the other in areas such as spectral classification. The topics covered in this chapter are quite diverse and reflect the heterogeneity of the constit­ uent members of this interesting class of pulsational vari­ able.

SPECTRAL CLASSIFICATION

S p eQjLrQJS-C-pp.i.Q

The classification of spectra is a vital part of the analy­ sis, in essence a cornerstone from which we can derive the atmospheric parameters. Yet this cornerstone sits precari­ ously upon the assumption that the spectrum of a variable star can be represented by that of a non-variable of simi­

- 40 - 41

lar color and luminosity. To some extent the correctness of such a substitution may depend upon the resolution of

the spectrum. One might expect that extremely fine detail

in the spectrum, indicative of subtle physical processes, would be lost at lower resolutions. For Population I

Cepheids, Kraft (1965) has recounted evidence of the close similarity of their spectra to those of non-variables simi­

larly placed in the H-R diagram. Obvious exceptions may

exist at certain phases due to the strength of hydrogen,

for example.

For Population II objects there exists no separate spec­

tral classification system. But for the RV Tauri vari­

ables, which up to now have appeared to be mostly moderate­

ly metal-deficient, the use of Population I classification

criteria are adequate for studying their gross properties.

Obviously in the past their spectra have been classified on

the MK system without regard to the effects of population

type. Even if the MK system is applicable, the subsequent

transformations to absolute magnitude may not be appropri­

ate (Barnes and DuPuy 1975), depending upon the assumed mass of the RV Tauri variables.

A unique resource at my disposal has been the invaluable

collection of photographic spectra obtained by P.O. Keenan

and his associates. From this collection useful plates of MK spectral standard stars were chosen to anchor the clas­ sification procedure. The spectra were intensity calibrat­ ed using plates exposed to a standard source taken usually on the same night as the star itself. The spectra were then traced by a densitometer at the Perkins Observatory to a resolution comparable to that of the 1800 line/mm grating of the IDS spectrograph. Typically, the wavelength cover­ age of the IIa-0 plates is XX3800-4900 A, obtained at a resolution of ^ 2 A, slightly higher than the 2.5 A resolu­ tion of the IDS spectra. The tracings serve two purposes.

First, by comparing the overall spectrum characteristics of the variables with those of standard stars, a spectral classification can be assigned to the variable at the observed epoch. With this classification an effective temperature and luminosity can be inferred from published calibrations. Secondly, the standard star tracings allow a quantification of line pair central-intensity ratios as a function of spectral type. Classification of stars in the

MK system is based upon line pairs, visually compared against plates of standards obtained under similar circum­ stances (emulsion, exposure, spectrograph, development pro­ cedure, ...).

Quantitative spectral classification schemes have been quite successful. Most recently, Rose (1984,1985) devised a scheme which employs to a large extent MK classification 43 criteria as diagnostic indices for various quantities such as luminosity and metallicity. One can get a good perspec­ tive on the current state of spectral classification from recent colloquia (McCarthy et al. 1979, Garrison 1984).

Table 5 lists the stars and their respective spectral types for which tracings were made.

The data for spectral standard stars from plates was supplemented by IDS spectra of stars classified on the MK system but which were not true MK standards. The IDS stan­ dard data acted to fill in some holes in the plate data as well as provide a calibration between the two systems using stars of identical spectral type. Table 6 lists the spec­ tral standards obtained with the IDS along with their spec­ tral types and reference.

The classification of the variable-star spectra followed as closely as possible the MK classification criteria as outlined by Keenan (1963) and Keenan and McNeil (1976).

Most of the necessary line pairs are found shortward of

X4300 A. For some variables no spectral data was recorded shortward of X4280 A, in which case greater importance was placed upon fitting the overall spectrum. Molecular fea­ tures were ignored in the classification process as the RV

Tauri variables are known to show anomalous molecular band strengths, particularly for CN, CH, and TiO. The assigned classifications are presented in Table 7 . Table 5

Spectral Standards : Plate Data

Star Classification

v Peg F8 III y Cyg F8 lb 31 Com GO III 0 Aqr GO lb 84 Her G2 Illb a Aqr G2 lb HD 32357 G5 III o UMa G5 Ilia a) Gem G5 Ila 9 Peg G5 lb e Vir G8 III HD 25877 G8 Ila e Gem G8 lb HD 12399 G8 lab BS 8952 G9 lb B Gem KO Illb 0 Cet KO II-IIIb k Oph K2 III e Peg K2 lb RW Cep K2 O-Ia HD 2665 K1 III

Spectral Standards : IDS Data

Star Classification Reference

HD 151070 F5 III 1 HD 155646 F6 III 2 HD 180028 F6 lb 3 HD 188328 F8 III 1 BD +1° 3907 F8 la 4 HD 144544 GO III 1 HD 190323 GO la 1 HD 150933 G2 V 1 HD 214714 G3 Ib-II (CN-1,Fe-1) 5 HD 178715 G5 III 1 HD 187299 G5 Iab-Ib 2 BD +29^ 3865 G7 la 5 HD 147025 G8 III 1 HD 168322 G8. 5IIIb(CN-l,Fe-.5) 5 HD 14500 K1 III 1 HD 232078 K4- 5 III-II 2 HD 213893 M0 + III—Illb (HV) 5 HD 144542 Ml III 5

References: (1) Harlan (1969) (2) Cayrel de Strobel (1985) (3) Bouw (1981) (4) Buscombe (1974) (5) Keenan (1983) 46

Table 7

Observed Properties Of the Variables

Variable Period Date (UT) Sp. Type (B-V) E (B-V (days)

DY Aql 131.42 23 May 84 K2 lb 23 Jun 85 K2 I 26 Jun 85 1.619 0.17 DS Aqr 78.21 26 Jun 85 K1 III TW Cam 85.6 4 Jan 85 1.515 6 Jan 85 G3 lb 0.62 RX Cap 67.92 26 Jun 85 0.874 27 Jun 85 GOe la 0.20 EQ Cas 58.31 6 Jan 85 F8e II/III DF Cyg 49.81 21 Jun 85 G6/7 Ib/IIa 26 Jun 85 1.403 0.42 V360 Cyg 70.45 21 Jun 85 F8e I 26 Jun 85 0.837 0.26 SS Gem 89.31 4 Jan 85 1.303 11 Jan 85 G2/5 I 0.46 SU Gem 50.12 4 Jan 85 1.102 11 Jan 85 F8/G0 lb 0.45 AC Her 75.46 26 Jun 85 0.794 27 Jun 85 F8/G0 I 0.14 EP Lyr 83.32 21 Jun 85 G2 II 26 Jun 85 0.966 0.17 U Mon 92.26 4 Jan 85 1.028 11 Jan 85 G8 II/IIIa 0.03 TT Oph 61.08 21 Jun 85 G5e lb 26 Jun 85 1.140 0.14 TX Oph 135. 23 May 84 GO lb 21 Jun 85 F8e la 26 Jun 85 0.978 0.40 UZ Oph 87.44 22 Jun 85 F8e la 26 Jun 85 1.025 0.45 V564 Oph 70.6 22 Jun 85 K3/4 lib 26 Jun 85 1.693 0.26 R Sge 70.59 22 May 84 G7/8 II 26 Jun 85 G2 lb 0.898 0.05 RV Tau 78.70 4 Jan 85 1.566 6 Jan 85 K3 lb 0.07 V Vul 75.72 26 Jun 85 1.409 27 Jun 85 G7 lab 0.31 47

Photometric

By their very nature photometric systems measure, categor­ ize , and discriminate among stars using only integrated light. Successful systems abound in which stars can be classified according to various criteria. The reader is referred to Golay (1974) and Philip (1979) in addition to the previously mentioned references on spectral classifica­ tion for background into many of these systems.

Greater insight into the interpretation of the photome­ tric measures is realized if the observer is knowledgeable of the spectral features which occur within the bounds of the filters. All too often the user of a photometric sys­ tem may not be aware of more than the basic feature(s) measured within a bandpass that applies to the calibrated astrophysical quantity. Figures 1 through 3 are presented to illustrate the relative importance of spectral features upon bandpasses from several systems. Of particular impor­ tance to this dissertation are the positions of the BV fil­ ters and the first four filters of the eight-color system.

Also represented are bandpasses from the Strdmgren four- color and DDO systems which are within the sensitivity range of the IDS. Shortward of 14000 A the IDS rapidly looses sensitivity with the image tubes employed. Figure 1 for TT Oph should be especially noted for the presence of hydrogen line emission. One sees that the '48' filter of 48 the DDO system would be particularly sensitive to varia­ tions in the emission flux of Hg. Similarly, the 'v' fil­ ter of the four-color system is affected by Hs emission.

Figures 2 and 3 show features measured by the filters of the eight-color system primarily used in this study. In the absense of TiO and strong CN the red spectrum is rather smooth for TT Oph, whereas in Figure 3 for DY Aql it is obvious that TiO affects the '71' and '78' filters.

Classification of M-stars in the eight-color system is based upon the strength of the TiO molecule for spectral type and CN for luminosity. The reductions for luminosity were ignored here since the position of CN formation in the atmosphere may not reflect the true photosphere and a less formal calibration would be required for lack of data from the latter four filters of the system. A TiO index, F(1) -

F(2), was formed using the first two filters and was cali­ brated from stars of known spectral type. Figure 4 is a pictorial representation of the classification scheme plot­ ting magnitude versus wavelength for the first four fil­ ters. From the comparison stars plotted it is evident that the slope of the computed color index becomes increasingly positive with later spectral type. The luminosity effect from CN is noticeable in a comparison between v Vir and BU

Gem as depressions of filters '71' and '81' at higher lumi­ nosity. FLRMBDR *10 Figure 1 : Spectral features within the photometric bandpasses. photometric the within features : Spectral 1 Figure 390 4

fT p ( Jn 84). (9 Jun Oph TT of h lctoso adass rmteUV StrOmgren UBV, the from bandpasses of locations The systems are shown here with the low-resolution spectrum low-resolution the with here shown are systems orclr vby, n D (14,54) photometric (41,42,45,48) DDO and (vfb,y), four-color 42 430 A E EG H O1 lO x WAVELENGTH 470 510 550 550 510 1 590

630

VO CD * 3 - cr» «-* in o

FLflMBDfl OJ *10 = to OJ j * iue Egtclrbnpse adwr tla spectrum. stellar warm and bandpasses ; Eight-color 2 Figure uevral TOh 8 u 8) Absorption 84). (8 Jun Oph TT variable ture system eight-color the of filters four first The are shown with the spectrum of the warm tempera­ warm the of spectrum the with shown are features from CN and TiO are not evident. not are TiO and CN from features 650610 Ha A EEG H l 0 1 * WAVELENGTH band B 9 730 690 75 band 770 770 1 78 *—I (A) 810

850 to FLRMBDR *10 CO to J O o Figure 3: Eight-color bandpasses and cool stellar spectrum. stellar cool and bandpasses Eight-color 3: Figure 610 TiO are evident in filters '71' and '78', and from CN from and '78', and '71' TiO tofilters in due features evident are absorption 84) (23 May Aql DY nfle '81'. filter in In the spectrum of the cool temperature variable temperature cool the of spectrum the In 5 690 650 Ha AE EG H l 0 1 * WAVELENGTH . B band B . TiO TiO y (0,0) 3 770 730 75 band A i—i TiO 78 i—i (A) 810

850 The RV Tauri stars observed, except R Set, are divided

into two categories according to whether or not TiO was believed to be present. For the variables with TiO an appropriate spectral type is given, based upon the TiO index and comparison with standard stars; this type reflects only the strength of TiO and not necessarily the photospheric spectral type. Several stars not indicating

TiO do have a depressed flux in the first filter due to contamination from CN, as for example V457 Cyg, R Sge, U

Mon, TW Cam, and V362 Aql. The positive monotonic slope of stars such as TT Oph, TX Oph, and UZ Oph indicates hotter temperatures.

The case of R Set is presented separately, the data tak­ en from Wing et al. (1985). Table 8 presents the observed

TiO index and calibrated spectral type along with visual lightrcurve data obtained from the AAVSO covering a period in the light curve from just after primary minimum until nearly the time of secondary minimum. It is during this portion of the light curve that TiO absorption and hydrogen line emission would be most evident. The TiO index is plotted in Figure 5 along with the visual light curve. The primary minimum was remarkable for its depth. R Set is rarely as faint as eighth magnitude. Typically the TiO bands reach a maximum strength corresponding to spectral type M2 or M3 near primary minimum and vanish completely by 53

Variables Exhibiting RV Tauri Stars Comparison StarsOther TIO Absorption

V 564 Oph TT Oph a Aqr, G2 lb

DY Aql, K5 TX Oph

BT Loc, K5 UZ Oph

RV Tou, K5 3 Oct 9 oct 13 Oct V360Cyg IS Aur X M2 CU Del v Vlr M4+ Ml S a b R Sge CN 9 Jun BU Gem EG Lyr TiO MI.O la T M6 13 Oct I mag TiO

U Mon HD 171094 1 6 Oct M3.0 lab

13 Oct BI Cep S Per M6 + M4.5 lab TW Cam

7000 8000 7000 8000 7000 8000 WAVELENGTH (A)

Figure 4: Eight-color photometry spectral classification. A visual representation of spectral classifica­ tion with eight-color photometry (from Wahlgren, Wing, and White 1984). 54 maximum light. However, during this recent cycle the maxi­ mum TiO strength was determined to be M5.4 from the eight- color photometry. At the ensuing light maximum the TiO was still as strong as spectral type Ml and never did complete­ ly vanish during the period of the observations. Previous­ ly only McLaughlin (1939) had recorded a spectral type as late as M5 for R Set.

Table 8

Observations of R Set

Date(UT) JI> V F( 2) TiO Sp.Type 1985 2440000+ (mag.) (mag.) (1-2) (TiO)

Aug 31.111 6308.611 7.7 4.17 1.65 M5.3 Sep 1.079 6309.579 7.6 4.06 1.66 M5.3 Sep 2.045 6310.545 7.5 3.95 1.68 M5.4 Sep 3.058 6311.558 7.4 3.89 1.67 M5.3 Sep 13.212 6321.712 6.5 2.96 1.17 M4.2 Sep 14.141 6322.641 6.4 2.92 1.08 M3.9 Sep 19.063 6327.563 5.9 2.79 0.66 M2.5 Sep 29.070 6337.570 5.5 2.70 0.38 M0.8 Oct 7.040 6345.540 5.6 2.80 0.36 M0.6 55

2.0

R Set M5.0

TiO index - M4.0 (1-2) 1-0 - M3.0

^ — M2.0 0.5 ■ — MI.O - — MO.O • — K5.0

3.0 m(7540) 4.0

5.0 mag.

6.0 85Sep 85 Oct 7.0 V (AAVSO) 8.0

6300 6350 JD 2440000 +

Figure 5 : Photometry of R Set. The variations in F(2), a near-infrared continuum magnitude, and in the TiO index (1-2) are shown together with the vis­ ual light curve. The TiO index is calibrated in terms of spectral type. 56

Suspect Classifications

Several of the variables observed show characteristics that are not consistent with the definition of RV Tauri vari­ ables and therefore may have been incorrectly classified as such. This is not too surprising considering the little attention given to the class as a whole and the remarks in

Chapter 1 concerning the historical problems of their clas­ sification. Most of the variables have had few observa­ tions made within any single cycle to say with certainty whether TiO absorption or hydrogen emission is present. A monitoring of the cooler members would no doubt increase the number known to exhibit TiO. A brief description of the evidence for incorrect classification is given for each of the suspect variables. During the course of this study the fourth edition of the GCVS (Kholopov 1985) became par­ tially available and its contents are incorporated into the discussion.

• IS Aur. Classified in the GCVS as a suspected RV Tauri

variable of period 76.5 days with no previous spectral

classification. The eight-color photometry provides

an M2 spectral type simultaneously with (B-V) = 2.05,

indicative of a moderately reddened M-type star. A

single IDS spectrum obtained three months later shows

TiO bands in the visual region of a strength no less

than M2 and possibly stronger. Because of its strong and possibly persistent TiO, this star is most likely not an RV Tauri variable.

BI Cep. Classified as an RV Tauri star of variable mean brightness with a period of 212 days, longer than any true RV Tauri star. Preston et al. (1963) assigned a type of M5e II from a low-dispersion spectrogram and reclassified it as a gMe star. The eight-color photo­ metry assigns it a type M6+, the latest among all the variables observed. The wide-band color is (B-V) =

1.74, also M-like.

CU Del. Classified in the GCVS as an RV Tauri star of constant mean brightness with a period of 127 days.

Preston et al., from a single spectrogram, observed it at M3 II and reclassified it as an M giant (gM). Our photometry offers a confirmation, designating it as M4+ from the eight-color system with (B-V) = 1.83 .

EG Lyr. This star was reclassified as SRb in the fourth edition of the GCVS. Its period of 236 days is larger than all RV Tauri stars. Preston et al. classified it as M5 III. Dawson (1977) assigned a M5-M6 II—III type using DDO photometry, and our eight-color photometry finds an M6 spectral type.

HQ Mon. The fourth edition of the GCVS lists this star as a suspected RV Tauri variable. However, Lloyd Evans

(1984) reported that its UBV colors are those of a 58

B-type star, and that its spectra show shallow hydrogen

lines. Wahlgren et al. (1985) reported on both photo­

metric and spectroscopic observations. They find spec­

tra with a variable continuum and strong centrally

reversed hydrogen emission profiles. One classifica­

tion made was B5 V. The IDS spectra of that study are

included in the appendix. This star resembles a cata­

clysmic variable with a period of 32 days., half the

assumed RV Tauri period.

Although it is difficult to justify the reclassification of IS Aur, BI Cep, and CU Del based upon the limited data available, they must certainly be considered suspect. All observations of these three stars indicate strong TiO. If these stars were RV Tauri variables, it would be remarkable if we had observed them all at the phase of maximum TiO strength. Therefore, stars with persistently strong TiO are better classified as SRa,b,or c depending upon the characteristics of their light curves and luminosities.

A case of misidentification may have occurred for the variable DS Aqr. The GCVS lists this star as an RV Tauri type RVa with a period of 78.213 days and an F2 II spectral type. The spectral type obtained in this study is K1 III.

Such a large range in spectral type is highly unlikely.

Bidelman (1986) has pointed out that the finding charts of 59

Hoffmeister (1936) and Tsesevich (1954) identify different stars as the variable. The identification used in this study for DS Aqr is that of Tsesevich and appears to be

BD-19°6354. The question still remains as to which one, if either, of these two stars is an RV Tauri variable.

COLOR EXCESSES

The type of data accumulated is conducive to the determina­ tion of the color excess. Knowledge of the color excess is helpful in understanding the extent of circumstellar material and mass loss among these variables. The quantity computed here is the total color excess, E(B-V). It con­ sists of two components: the interstellar, IS, and the cir­ cumstellar, CS, so that we may write

E(B-V) = E(B-V)IS + E(B-V)CS . (1)

Ordinarily there is no CS component and what we determine is due entirely to the IS medium. But the evidence reviewed previously for RV Tauri stars on CS material is compelling enough to require its inclusion in the interpre­ tation of the data. If the IS component can be indepen­ dently determined, for example from observations of early- type stars in the vicinity of the variable, we obtain

E(B-V)c s by eqn.l for the RV Tauri stars. 60

Several techniques have been used in the past to compute the color excess of these variables. Some do not rely on the properties of the stars themselves but rather on other objects in the variable's vicinity or on general relation­ ships for the IS medium. Dawson (1979) used reddening laws from globular clusters and DuPuy (1973) used the galactic extinction formula of Parenago (1945) for deter­ mining E(B-V) . Other techniques rely upon general prop- X b erties of the variables such as a period-luminosity rela­ tion (DuPuy 1973, Erleksova 1974) or an assumed absolute visual magnitude (Preston et al. 1963, DuPuy 1973) to obtain the visual extinction, A v . Then coupled with an assumed value for R (usually 3) from studies of the IS extinction; one obtains

A E(B-V) = (2)

But the most reliable method uses simultaneously obtained photometric and spectroscopic data for individual variables. The peculiarities of each star can then be accounted for. In this study the spectroscopic observa­ tions lead to a spectral classification at the observed epoch. The intrinsic color (B--V)^ is extracted from the compilation of Golay and coupled with the observed (B-V)Q , the color excess is found via

E(B-V) = (B-V)Q - (B-V)i . (3) 61

Two sources of error present themselves. The photome­ tric calibrations of Golay are determined for stars of approximately solar metallicity. As the RV Tauri stars are to some degree all metal-deficient, their (B-V) color would 1 be bluer than a star of similar temperature but of solar metallicity. The difference in (B-V) is approximately 0.2 between stars of metallicity [Fe/H] = 0 and -2 . This may be somewhat offset by their large luminosities, at which the (B-V)-Teff relation appears to be independent of metal­ licity (Bohm-Vitense 1981). Secondly, for several vari­ ables the time between spectroscopic and photometric obser­ vations is a substantial fraction of the period. For example, from Table 7 the time delay for SU Gem amounts to

7 days of the 50-day period, or about 14% of the light curve. The time delay may have no effect on E(B-V) if the observations fall around the time of primary maximum to secondary maximum since the colors tend to change by a lesser amount than around primary minimum, but one should be aware that changes in the color may occur between the times of spectroscopic and photometric data acquistion.

Table 7 lists the data used in determining the color excess. A colon next to the derived E(B-V) implies higher uncertainty. Dawson (1979) has tabulated the results from previous works except for those of Straizhis and Meishtas

(1981) for RV Tau and those of Baird and Cardelli (1985) and Cardelli (1985) for AC Her, U Mon, and R Set. 62

METALLICITY

An initial metallicity estimate is necessary for each RV

Tauri star in the synthetic spectrum analysis. Therefore,

a diagnostic had to bedevised from the data for such a

purpose. Ideally, such a diagnostic would be sensitive

exclusively to changes in elemental abundance, but in prac­

tice the temperature, luminosity, metallicity, and turbu­

lent velocity all affect the observed spectrum. An accep­

table alternative was found among the MK classification

criteria by using(Fel+YII) X4375, Fe I X4383, and a

pseudo-continuum peak near X4360. These features occur in

all spectra obtained with the 1800 1/mm grating.

Two ratios were formed which are primarily sensitive to

luminosity, R , and metallicity , R , defined as 2. m

Fc (4360) - F (4375) R o =------(4) Fc (4360) - F£ (4383)

F„ (4383) Rm = ------(5) Fc (4360)

where Fc is the pseudo-continnum flux and F is the flux at X/ line center. It is assumed that the continuum flux is con­

stant over the region of these features. The ratios were

determined for all of the RV Tauri stars as well as the

standard stars, both photographic and IDS. The temperature dependence is accounted for by plotting these ratios against spectral type. Figure 6 is a plot of the standard star data for . One sees that giant and supergiant stars are for the most part well separated with no apparent temp­ erature dependence. The sample of stars comprising this standard list was not chosen with consideration of metal­ licity; however, since most of them are MK standards in the vicinity of the Sun they are dominated by Population I stars of near-solar composition. Weak-lined and metal- deficient stars are noted in the diagram. In the plot of

versus spectral type (Figure 7), the temperature depen­ dence is clearly visible and the metal deficiency of par­ ticular stars is more pronounced. A slight luminosity effect is noticeable in the hottest stars as the number density of Fe II is enhanced at the expense of Fe I in the more tenuous supergiant atmospheres. In the latter plot the variables would be above and to the right of the super­ giant standards in a region of metal-deficiency. With the known metallicity of BD+30°2611 ([Fe/H] = -1.2) and BD+1°

2916 ([Fe/H] = -1.5) the metallicity of each variable can be estimated by interpolation (or extrapolation) at the appropriate spectral type. Although this is rather crude it does provide the estimation required for the synthetic spectrum program as well as a luminosity classification.

As a further caution remember that the line depths measured 64 are not purely a function of metallicity. Figure 7 accounts for temperature and luminosity but the line depth quantity R includes the effect of turbulent velocity in m addition to metallicity. Thus from this plot alone the metal-deficiency can be underestimated if the turbulence is overestimated. Tables 9 and 10 list the ratio values for the standard stars and variables, respectively.

For the variables in Table 10 with more than one obser­ vation we see that the quantities R„ and R may be either ^ l m ■* fairly stable (R Sge, RV Tau, V Vul) or may change more dramatically (TT Oph, TX Oph). Only two variables (TT Oph,

RX Cap) were observed to have R > 1, indicative of possi- Xr bly extreme luminosities or non-LTE processes. Evidence for the latter comes from the noticeable hydrogen-line emission in the spectra, presumably arising from shock fronts. In fact, of the six stars with R > 0.9, only AC X* Her did not have noticeable hydrogen-line emission. There­ fore, the presence of emission lines and R >0.9 is highly X* correlated. In all, ten variables exhibited emission lines or a filling-in of the hydrogen line profiles when compared to the standard stars. Table 11 lists the variable star spectra with evidence of hydrogen emission.

The eight-color photometry offers an insight into the relationship between the strength of CN and [Fe/H]. Often 65

T— I— I--1 I I I I I I— I-1 I T 1.0

o o „wl o 0.8 o 8 X + _wl jwl

0.6 - X XX X

Luminosity o I 0.4 + IE x in

J I I I I I I I L F5 F8 60 G2 G5 G8 KO Kl K2 K3 K4 K5 MO Ml Spectral Type

Figure 6; R^ versus Spectral Type diagram. The luminosity diagnostic is plotted against spectral type for the spectral standard stars. The positions of weak-lined (wl) stars are noted. 66

0.8

0.6

0 .4

Luminosity

0.2

F5 F8 GO G2 G5 G8 KO Kl K2 K3 K4 K5 MO Ml Spectral Type

Figure 7; versus Spectral Type diagram. The metallici­ ty diagnostic is plotted against spectral type for the spectral standard stars. A slight luminosity dependence is present.

t 67

Table 9

Line Rat i_o_ Pi agnostics for Non-Variables

Star Spectral Type RA *m SAO 84572 F5 III 0.60 0.57 SAO 122182 F6 III 0.76 0.71 SAO 124432 F6 lb 0.75 0.59 SAO 105396 F8 III 0.61 0.65 v Peg F8 III 0.58 0.57 Y Cyg F8 lb 0.83 0.50 BD + 31 3907 F8 la 0.80 0.38 SAO 84189 GO III 0.62 0.66 31 Com GO III 0.78 0.58 3 Aqr GO lb 0.89 0.50 SAO 105624 GO la 0.77 0.42 SAO 84562 G2 V 0.62 0.62 84 Her G2 Illb 0.60 0.52 a Aqr G2 lb 0.89 0.41 SAO 72581 G3 Ib/II 0.92 0.66 HD 32357 gG5: 0.86 0.23 SAO 104534 G5 III 0.60 0.55 SAO 87740 G5 Iab/Ib 0.83 0.40 BD +29°3865 G7 la 0.65 0.41 SAO 84295 G8 III 0.53 0.48 e Vir G8 III 0.72 0.30 HD 25877 G8 Ila 0.70 0.40 e Gem G8 lb 0.77 0.26 HD 12399 G8 lab 0.93 0.28 SAO 47359 G9 III 0.60 0.48 BS 8952 G9 lb 0.75 0.29 3 Gem K0 Illb 0.63 0.22 6 Cet K0 II/IIIb 0.41 0.45 SAO 101952 K1 III 0.55 0.31 < Oph K2 III 0.46 0.37 e Peg K2 lb 0.62 0.30 RW Cep K2 O/Ia 1.00 0.27 SAO 105082 K4/5 II/III 0.64 0.55 SAO 127611 M0+ III/IIIb 0.60 0.34 SAO 29777 Ml III 0.59 0.30 HD 2665 K1 III,Fe-4 0.86 0.78 HD 165195 K2/4 III wl 0.82 0.76 BD +1° 2916 K1 I 0.64 0.72 BD +30° 2611 K0 I 0.67 0.58 68

Table 10

Line Ratio Diagnostics for RV Tauri Variables

Variable Date (UT) R I m DY Aql 23 May 84 0.76 0.53 10 Jun 84 0.58 0.51 23 Jun 85 0.72 0.41 DS Aqr 26 Jun 85 0.69 0.42 IS Aur 6 Jan 85 0.56 0.31 TW Cam 6 Jan 85 0.89 0.54 11 Jan 85 0.78 0.56 RX Cap 27 Jun 85 1.09 0.59 EQ Cas 6 Jan 85 0.63 0.55 DF Cyg 21 Jun 85 0.80 0.50 V360 Cyg 22 Jun 85 0.90 0.76 SS Gem 11 Jan 85 0.80 0.71 SU Gem 11 Jan 85 0.62 0.70 AC Her 10 Jun 84 0.90 0.75 27 Jun 85 0.96 0.74 BT Lac 11 Jan 85 0.77 0.80 EP Lyr 21 Jun 85 0.82 0.74 U Mon 1 Dec 84 0.84 0.65 11 Jan 85 0.71 0.64 TT Oph 26 May 84 0.77 0.56 10 Jun 84 1.08 0.64 21 Jun 85 0.79 0.54 27 Jun 85 0.85 0.51 TX Oph 23 May 84 0.92 0.70 10 Jun 84 0.91 0.64 21 Jun 85 0.74 0.61 UZ Oph 10 Jun 84 0.95 0.58 22 Jun 85 0.91 0.55 V564 Oph 26 May 84 0.63 0.66 10 Jun 84 0.67 0.56 22 Jun 85 0.59 0.48 R Sge 22 May 84 0.73 0.49 10 Jun 84 0.80 0.55 22 Jun 85 0.78 0.51 27 Jun 85 0.76 0.45 RV Tau 6 Jan 85 0.83 0.55 11 Jan 85 0.85 0.55 V Vul 21 May 84 0.79 0.56 10 Jun 84 0.78 0.49 27 Jun 85 0.80 0.40 69

Table 11

Observations of Hydrogen Emission

Variable Date (UT) Comment

DY Aql 24 May 84 shallow H RX Cap 27Jun 85 fairly strong EQ Cas 6 Jan 85 central emission V360 Cyg 22 Jun 85 strong TT Oph 8 Jun 84 strong 9 Jun 84 strong 10 Jun 84 strong 21 Jun 85 fairly strong 27 Jun 85 shallow H TX Oph 24 May 84 fairly strong H 8 Jun 84 Ha absent 21 Jun 85 Hy central emission? UZ Oph 24May 84 strong H 8 Jun 84 shallow H 21 Jun 85 fairly strong V564 Oph 26 May 84 shallow H 8 Jun 84 Ha absent R Sge 24 May 84 weak H emission 9 Jun 84 shallow H lines RV Tau 11 Dec 83 fairly strong emiss. 13 Dec 83 shallow H lines 6 Jan 85 H central emission 11 Jan 85 shallow H lines

the two are used interchangably, as for example in the DDO photometry where the metallicity, designated as [Fe/H], is calibrated in terms of the strength of CN A 4216. To test the relationship, non-variable stars with both eight-color photometry and spectroscopic determinations of [Fe/H], usu­ ally by a curve-of-growth technique, are used.

To account for the temperature dependence of the CN mol­ ecule, average values of the eight-color CN index F(3)-F(4) were computed from giant and supergiant stars having spec- 70 tral types between GO and K5, and were plotted against spectral type. Smooth curves were drawn to the averaged data (Figure 8), which clearly show the CN luminosity effect. From these curves a value of is assigned to each spectral type. For those stars with spec­ troscopically determined [Fe/H] , the quantity Sen was com­ puted from

Sen = < F (3) - F (4) > - ( F(3) - F(4) ) gtar . (6)

Eqn. 6 represents a measure of the CN strength relative to the average value for the star's particular spectral type and luminosity class. Table 12 lists the stars used with their spectral type, CN index, along with [Fe/H] and

6cn if available. The catalogue of Cayrel de Strobel

(1985) served as the source for [Fe/H]. Values of [Fe/H] within <> imply an average was formed after consideration of all values listed in the catalogue. In Figure 9 the CN measure is plotted against [Fe/H] . Positive values of 6cn correspond to stronger than average CN strength. A least- squares straight line fit was computed from the giant star data. One can say that a positive correlation exists between the strength of CN and [Fe/H] for the giants. For supergiants the picture is somewhat different. Their [Fe/H] values are not more metal-deficient than -0.2, owing to the relatively young age of the sample. However, at a given [Fe/H] the CN strength shows considerable scatter.

Errors in the photometric observations or [Fe/H] calcula­ tions are not likely to account for the scatter in the supergiant data. One may then conclude that although CN strength is a useful indicator of stellar luminosity it is not a reliable indicator of [Fe/H] among the supergiants. 72

-0.04

-0.06

-0.08

- 0.10

- 0. 14 ' class III

class I

GO 2 5 8 K0 I 2345 Spectral Type

Figure 8; Eight-color photometry luminosity discrimina­ tion. The luminosity dependence of the eight- color photometry CN measure 5 cn is presented as a function of spectral type. The solid line represents supergiants and the broken line is for giant stars. 73

+ 0.08 Luminosity • Ia/O + 0 .0 6 o Iab/Ib

+ 0 .0 4

+ 0.02 cx 8cn 0.00

- 0.02

- 0 .0 4

- 0 .0 6

- 0 .0 8 + 0.6 +0.4 +0.2 0.0 -0.2 -0.4 -0.6 -0.8 [Fe/H]

Figure 9 : The sen - [Fe/H] diagram. The eight-color pho­ tometry CN measure sen is plotted against spec­ troscopically determined IFe/H] for giant and supergiant stars. The straight line is a least- squares fit to the 'giant data. 74

Table 12

Non-Variable Star Data ; [Fe/Hl - .sen Diagram

Star Sp. Type F(3)-F(4) [Fe/H] sen Name HD#

y Per 26630 GO lb -0.078 <+0.12> +0.004 96918 GO O-Ia -0.052 + 0.32 +0.007 101947 GO la -0.042 B Aqr 204867 GO lb -0.075 <-0.02> +0.001 217476 GO la -0.042 <+0.07> -0.003 104 Aqr 222574 GO lb -0.068 + 0.05 -0.006 57146 G1 Iab-Ib -0.127 59890 G1 lb -0.085 R Pup 62058 G1 O-Ia -0.027 74395 G1 lb -0.128 -0.11 +0.039 19926 cG2 -0.130 67594 G2 lb -0.103 96746 G2 lb -0.040 c^Cen 100261 G2 la -0.032 $ Dra 159181 G2 Ib-IIa -0.094 <+ 0.21> -0.008 167952 G2 lb -0.054 a Aqr 209750 G2 lb -0.107 <+0.13> +0.005 58526 G3 lb -0.091 5 Pup 63700 G3 lb -0.137 <+ 0.26> +0.025 37 LMi 92125 G3 Ib-II -0.097 a1 Cap 192876 G3 lb -0.110 67243 G5 lb -0.095 93306 G5 lb -0.097 159633 G5 lab -0.119 9 Peg 206859 G5 lb -0.156 <-0.02> +0.024 ij> And 223047 G5 lb -0.181 <+0.17> + 0.49 79452 G6 III -0.073 -0.74 -0.073 73155 cG7 -0.143 77912 G7 Ib-II -0.139 k Gem 62345 G8 Ilia -0.122 <-0.10> +0.003 e Vir 113226 G8 IIlab -0.129 <0.0> +0.010 5 Boo A 135722 G8 III -0.089 -0.46 -0.30 e Gem 48329 G8 lb -0.214 <-0.06> +0.058 95393 G8 lab -0.095 224165 G8 lb -0.175 v Aur 39003 G9.5 III -0.147 -0.10 +0.014 a2 Cap 192947 G9 III -0.144 <+0.12> +0.011 a Cas 3712 K0 Ilia -0.165 <-0.1> +0.024 3 Cet 4128 K0 III -0.137 <-0.08> -0.004 a Tau 29139 K0 III -0.136 <-0.19> -0.005 2 Ori 37160 K0 Illb -0.074 <-0.47> -0.067 3 Gem 62509 K0 III -0.127 <-0.04> -0.014 X Hya 88284 KO III,CN1 -0.165 <+0.1> +0.024 46 LMi 94264 KO III-IV -0.119 <-0.22> -0.022 a UMa 95689 KO Ilia -0.138 -0.23 -0.003 75

Table 12 (.continued)

X UMa 102224 KO III -0.105 -0.65 -0.036 1 Cep 216228 KO III -0.129 <+0.12> -0.012 77321 K0 lb -0.162 119796 K0 O-Ia -0.180 + 0.02 +0.012 12 Peg 207089 K0 lb -0.160 + 0.06 -0.006 221861 K0 lab -0.162 i Dra 137759 K2 III -0.138 + 0.30 -0.001 a TrA 150798 K2 IIb-IIIa-0.175 -0.06 +0.036 E Sco 151680 K2.5 III -0.127 -0.30 -0.012 K Oph 153210 K2 III -0.145 <0> +0.006 X Dra 163588 K2 III -0.127 -0.15 -0.012 109 Her 169414 K2.5 IIlab -0.104 -0.38 -0.035 a Set 171443 K2 III -0.158 0.0 +0.019 4817 K2 Ib,CN-2 -0.113 25661 cK2 -0.17 0 !CMa 50877 K2.5 lab -0.235 -0.11 +0.073 12 Pup 65699 cK2 -0.142 -0.20 -0.020 73884 K2 lb -0.182 V Sgr 174974 cK2 -0.129 E Peg 206778 K2 lb -0.182 <-0.04> +0.020 V Psc 10380 K3 III -0.112 -0.3 -0.011 V UMa 98262 K3 III -0.117 <-0.19> -0.006 y Aql 184406 K3 Illb -0.139 <+0.30> +0.016 9366 K3 lb -0.118 17306 K3 lab -0.099 n Per 17506 K3 Ib-IIa -0.161 -0.09 +0.014 17958 K3 lb -0.118 32393 cK3 -0.161 56577 K3 lb -0.098 + 0.15 -0.049 92501 K3 lb -0.076 8 Ara 157244 K3 Ib-IIa -0.207 + 0.50 +0.060 3 Cet 225212 K3 lb -0.199 -0.20 +0.052 11092 K4 + Ib-IIa -0.085 X Vel 78647 K4 Ib-IIa -0.128 + 0.23 +0.009 24 Sgr 171115 cK4 -0.127 185622 K4 lb -0.109 i— o 0 1 . i 5 Cyg 200905 K4.5 Ib-IIa-0.130 + 0.11 63 Cyg 201251 K4 Ib-IIa -0.154 12642 cK5 -0.023 13686 K5 lb -0.132 103999 K5 Ib-II -0.078 170975 cK5 -0.158 219978 K5 lb -0.042 CHAPTER IV

SYNTHETIC SPECTRUM ANALYSIS

INTRODUCTION

The use of synthetic spectrum calculations to study elemen­ tal abundance patterns in stars and to reproduce color indices has been quite widespread in the past fifteen years, and the popularity of this method has undoubtedly been enhanced by the availability of two computer programs,

ATLAS and MOOG. ATLAS (Kurucz 1970) computes model stellar atmospheres, or more exactly the run of temperature, gas pressure, and electron number density with optical depth.

MOOG (Sneden 1974), which requires a model atmosphere among its inputs, solves the problem of the transfer of radiation through the atmosphere at specific wavelengths, thereby allowing a spectrum to be constructed. The synthesized spectrum can then either be convolved with the spectrograph instrumental profile for comparison against observed stel­ lar spectra to derive the elemental abundance, or be con­ volved with filter transmission functions to compute photo­ metric magnitudes and color indices. Both of these programs are quite general in their construction so as to

- 76 - 77 be applicable to a variety of problems involving radiative transfer. They are also not the only such programs; for example, the MARCS code (Bell et al. 1976) also constructs model atmospheres.

Results obtained with synthetic spectra can be very meaningful in interpreting observed spectra and colors pro­ vided that the conditions under which the spectra were com­ puted are commensurate with those of the stars that one is trying to study. It can not be overly stressed that it is inappropriate to extract from the analysis, without quali­ fication, information that is not within the scope of the analysis. Extrapolation is always to be considered less desirable than interpolation as a numerical or analytical tool. An understanding of the method is important not only to its original application but also to any subsequent use of the results.

With a careful choice of observational and theoretical material the method of spectral synthesis can be applied in a meaningful way to the study of the RV Tauri variables.

In this chapter we first briefly review the theoretical aspects of the synthetic spectrum program and its inputs.

The program is then normalized by reproducing the observed spectrum of a standard star, and the sensitivity of the spectrum to variations in the atmospheric parameters is 78 explored. Finally, the atmospheric parameters effective temperature, gravity, turbulent velocity, and metallicity

(Teff/log g/vt /[Fe/H]) are determined for the RV Tauri variables.

THE SYNTHETIC SPECTRUM PROGRAM

The synthetic spectrum program used in this dissertation is

MOOG (Sneden 1974), altered to account for specific items incorporated into this analysis. The main assumptions of the program are the usual ones associated with the con­ struction of model stellar atmospheres; plane-parallel geometry, hydrostatic equilibrium, and local thermodynamic equilibrium (LTE). Each one is of doubtful validity in the case of the atmosphere of a supergiant variable such as those of the RV Tauri stars. However, in what way and to what degree would deviations from the above assumptions be manifested in the observed spectrum? Each assumption will now be addressed.

1. Plane-parallel geometry is appropriate when the thick­

ness of the stellar atmosphere is negligible relative

to the stellar radius. Schmit-Burgk and Scholz

(1975) find two groups of stars which may have their

spectra affected by extended atmospheres: a) red giant

stars with log g < 0 and b) low mass stars of high

luminosity, including some central stars of planetary nebulae and blue halo stars. Such stars have an atmospheric thickness of between ten and fifty percent of the stellar photospheric (a = 1) radius. Watanabe and Kodaira (1978) considered two sets of models with red giant characteristics, ^Teff< 3800K an(* lo9 9 <

0.0), and showed that spherical atmospheric models do not drastically deviate from plane-parallel atmos­ pheres for the lower luminosity limit (log g = 0) but that the temperature-optical depth, T(t), relation is very sensitive to luminosity in the uppermost layers of the atmosphere (log t < -1). As applied to the RV

Tauri stars the use of plane-parallel atmospheres may not pose any special problems since their average luminosity class of lb suggests that their values for log g are probably within the range 1.0 to 2.0 .

Hydrostatic equilibrium is certainly violated in pul­ sating stars but not to the degree that the spectrum is seriously affected. For Cepheid variables, Kraft

(1965) found that he could assign a spectral classifi­ cation based upon non-variable standard stars. Pel

(1978) was able to extract atmospheric parameters from continuum colors of Cepheids in terms of hydrostatic equilibrium model atmospheres. Motions in the atmos­ pheres of the three brightest RV Tauri stars (AC Her,

U Mon, R Set) have been inferred from high-resolution spectra. In all cases data from Fe I lines show lay­ ers of material moving outward over a time interval on the order of half the quoted pulsation period. For U

Mon, Abt (1955) found that the radial velocity varied by as much as 20 km/sec from the average (systemic) value. At the time when the radial velocity of one velocity system attains a maximum positive value, a second velocity system is observed with a comparable negative velocity. The average separation of the doubled lines is about 35 km/sec, or 0.5 A. Then cer­ tainly at those times in the light curve when the Fe I lines appear double, motions in the atmosphere are affecting the appearance of the spectrum. Since the

IDS is operated at a resolution of ^2.5 A, line doub­ ling can not be resolved but spectral features may be broadened. Fortunately, line doubling occurs for only a brief period, from primary minimum until the maximum which immediately follows. It is during this same period that hydrogen-line emission would be observable, if it is seen at all. Spectra showing hydrogen-line emission have been avoided whenever pos­ sible for the synthetic spectrum analysis in an attempt to eliminate the problem of line doubling.

The use of LTE to describe the particles of a gas is appropriate when the populations of the excited states are dominated by collisional processes and can there­ fore be described by the Boltzmann equation. Clear­ ly, the LTE assumption is valid in the interior of stars. In stellar atmospheres, where the density of particles has become so low that radiation accounts for a non-negligible fraction of the population of excited states, LTE is no longer valid. The interpre­ tation of "non-negligible" is not straight-forward.

It is generally recognized that cool stars of high luminosity have atmospheres that violate LTE, but at exactly (or even approximately) what temperature/ gravity combinations this occurs is not obvious. In dwarf stars of spectral types AO to K2 the LTE assump­ tion appears correct, according to spectroscopic grav­ ities determined from the ionization equilibrium of metals such as Fe, Ni, and Cr (Pagel 1971). This method assumes that the metal abundance is the same for neutral and first ionized states at a specific value of the surface gravity. For red giants Pagel points out that discrepancies in abundances are no lower than a factor of two, or 0.3 dex, and conse­ quently it is difficult to determine the role played by non-LTE. Athay and Lites (1972), modeling the iron spectrum of the Sun, noticed significant departures of the ionization equilibrium from that predicted by the Saha equation. Large contributions to the strength of

Fe I ground-state and metastable levels arose high in the photosphere (t = 10-2 to 10-4 ). Auman and Wood­ row (1975) constructed model atmospheres for late-type giants and replaced the LTE assumption with one of strict statistical equilibrium (SE) for metals that contribute significantly to the density of free elec­ trons, namely K, Na, Al, and Mg. Their models showed that departures from LTE became large when Teff<

3000K, but at higher temperatures the electron pres­ sure is essentially identical in both the LTE and SE cases. In recent studies of high-dispersion spectra by Ruland et al.(1980), Brown et al. (1983), and Luck and Bond (1985) a pattern is observed in which low excitation lines of neutral metals yield a lower abun­ dance than that produced by the singly-ionized species or the high-excitation lines of neutral atoms. The separation between high and low excitation was placed at an excitation potential of x = 3.5 eV by Ruland et al.. Apparently, an over-ionization of neutral met­ als occurs high in the atmosphere, at v< 10-3 in the

Sun, where collisional processes are less important than in the deeper layers where the spectral lines of the high-excitation neutral and ionized atomic tran­ sitions are produced. The difference in abundance amounts to 0.2-0.3 dex. In the case of the RV Tauri variables the use of

LTE may not be obviously incorrect. Certainly LTE is

invalid if applied to spectral features arising from shock fronts or chromospheres. We again recall that shock fronts are evident when hydrogen and metal-line emissions are observed. This phase of the light curve is avoided if possible in the analysis, as pre­ viously mentioned. At other phases it is less obvious that shock fronts are a dominant contributor to the spectrum, or even present. Also, RV Tauri stars are hotter and less luminous than those theoretical models which have been shown to require non-LTE physics. A

further precaution can be taken in the application of the synthetic spectra by avoiding, or placing lesser

importance upon, lines attributed to the low-

excitation states of neutral metals. The approach

taken in this dissertation is to find a best fit to an entire region of spectrum of 60 A width rather than

attach an unwarranted importance to specific spectral

features. Most of the transitions are from metals such as Fe and Ti, and depending upon the stellar

temperature, may be predominantly of neutral or first

ionized species. A systematic error could result for

the coolest stars where the spectrum is solely com­ prised of neutral metals. The desired output from the MOOG program is a plot of spectral depth, dx , as a function of wavelength defined as

a* ■ 1 - r* ■ 1 - a) F\ where rx is the residual flux; Fx the net surface flux at wavelength X; and the surface continuum flux at X . In the program the fluxes are expressed in terms of Milne's equations with the source function given by a Planck func­ tion, and E (?) is the second order exponential integral.

= 2 Bx (T( tx)) E2( tx> dxx (8)

Fx ■ 2 V T(tA + Vl ” E2(TA + TX.1> d

The integration variable is the optical depth both in the line, T , and continuum, T , making it the primary focus of X c the calculations. These optical depths can be written in terms of the continuous op a c i t y < and line opacity 1^at wavelength \ : 85

Reference opacities are either read into or computed by

MOOG. Computation of the continuous opacity includes the following sources:

bound-free absorption by the negative hydrogen ion, IT

bound-free absorptions by neutral H and h£

free-free absorptions by H" ,He“ ,H2 ,and H£

Rayleigh scattering by neutral H, He, and

electron scattering .

The H” opacity source is dominant among stars of type Gand

K butits relative importance depends upon the number of free electrons and hence the metallicity of the star.

The form taken by the continuous opacity is

- m t bf , bf , ff bf , ff , ff , Ray KX - H °H + “H- + “H- + “H+ + aH- + “H++ “H

+ 1 + NHe < “Hey+ > + Ne t12> where a's denote the absorption or scattering cross section per neutral H or He atom, and are expressed in terms of the intrinsic atomic absorption coefficient, a , of species y and process x by

x x \ 1 a = a y y (13)

where % is the number density of H and ^ the number den­ sity of species y. Forms employed for the a's are dis­ cussed by Kurucz (1970) and Sneden (1974). The continuous opacity is computed only for the central wavelength of the synthesized spectral region. This necessitates keeping the synthesized region fairly small.

The form taken by the line absorption coefficient, 1 , X is well known in astrophysics to be

i = jl_|2 f N ias^v). X mec 1 - exp (-hv/kT) = lx U(a,v) (14)

with symbol definitions

• f, oscillator strength

• N, number density of the species in the lower state of

transition

• Avd ' the Doppler width of the line

• U(a,v), the normalized Voigt function

• (1-exp(-hv/kT)), correction factor for stimulated emis­

sion

• ne /mec, constants of usual meaning

The Doppler width is defined as

(15) where g0 t the most probable line of sight velocity for a species of atomic mass y , is given by and vt is the line of sight velocity of the gas due to non- thermal motions, otherwise called the microturbulent veloc­ ity. The Voigt function is defined as

a f e"Y U (a,v) = -* ---- S-5----5. dy (17) * I (v-y) + a

with the distance from the line center in units of Doppler width given by

(v-v ) v - 1^— (18) and a dimensionless damping parameter, a , with damping constant r given by

r C (rn + rJ a = 4 it A\> = Tn ~ D 00

In this study the damping constant consists of two compo­ nents: natural, rn , and van der Waals, rw Natural damping of a classical oscillator, or radiation damping, is assumed to be of the classical value, rn = 1 .lxlO8. sec- 1 . Van der

Waals broadening is pressure broadening from collisions of atoms with neutral hydrogen. Following the work of Unsold

(1955) the van der Waals broadening parameter is of the form 88 with v0 , the relative speed of the perturbed species to the perturbing hydrogen atom, given by

v2 = 8kT( - + i ) (21) o y mH

and the interaction constant C. given by 6

J f s 13.5 charge I 13.5 charge C c = 1.61E-33 (22) 6 X • - E. Ai i,u I xi " Ei,l .

The correction to C g of Holweger (1971) is also incorporat­ ed as

C c = 6.3 C c (23) 6 6 which empirically accounts for discrepancies observed in solar data. For each spectral line considered, the quan­ tity 1' is computed at each optical depth. Each model X atmosphere has 35 optical depths or levels. The spectrum depths are then calculated at equally spaced wavelength intervals, the spacing being designated by the input quan­ tity STEP. At each STEP position the line list is searched for all lines that fall within a range of +/- DELTA ang­ stroms, DELTA also being an input parameter. The total line opacity at a given atmospheric depth is formed from the sum of individual line contributions by multiplying the quantity ll by the Voigt function, X

1x (t) = I l x U (a, v) (24) X 89

THE INPUT DATA

A careful glance at eqn. 14, the line opacity equation,

shows that nearly all input data are to some degree repre­

sented within it. One can classify the input data into two

broad categories dictated by the extent to which each is

used. Data which are an integral part of the program and

are therefore not changed from one star to the next (star-

independent) consist of atomic data such as partition func­

tions, atomic line data, relative elemental abundances and molecular dissociation constants. On the other hand, the

star-dependent data entails the model atmosphere, turbulent velocity parameter, and metallicity. A distinction is made between the elemental abundances of the star-independent data and the metallicity of the star-dependent data in so

far as the elemental abundances are the basic or standard

set of element to hydrogen ratios on a scale where log H =

12.00, while the metallicity is a single multiplicative

factor which describes the particular stellar abundance

relative to the standard abundances. In this respect the metallicity can be expressed by the usual formula

Fe Fe H H standard * (25)

An apparent paradox exists within the star-dependent data.

Each atmosphere, consisting of the run of temperature, gas 90 pressure, and electron number density as a function of optical depth, was generated using specific values for microturbulent velocity and metallicity. Yet we input each of the latter two quantities independently, often at dif­ ferent values from those used to generate the atmosphere.

This inconsistency is resolved by knowing that to first approximation, small variations in turbulent velocity and metallicity do not alter the basic structure of the atmos­ phere but do change the observable spectrum. Thus, the turbulent velocity and metallicity are treated as variables of the analysis.

Model Atmospheres

The model atmospheres used in this dissertation were obtained from R.E. Luck (1985) and were generated by the

MARCS code of Gustafsson et al. (1975). They include the atmospheres published by Bell et al. (1976) along with extensions to hotter temperatures and lower surface gravi­ ties. The parameter space covered by the models is bounded by

T eff : 3750 to 7000 K in intervals of 250 K

log g : -0.750 to +4.5 in intervals of 0.375

v : 2, 5 km/sec (5 km/sec only for [Fe/H] = -1,-2)

metallicity,[Fe/H] : +0.5,0.0,-0.5,-1,-2,-3 An important feature of the models is the inclusion of opacity in the near infrared region due to the molecules CN and CO, and in the violet and visual regions due to the molecules MgH, CH, OH, NH, and CN. Gustafsson et al.

(1975) showed that the difference between models with and without the infrared opacity sources can be as great as 200

K depending upon optical depth, metallicity, and effective temperature. The RV Tauri stars fall nicely within the bounds of the models except perhaps in the case of the tur­ bulent velocity, for which some of the variables may have larger values.

Atomic Line Data

The principle source of atomic line data used in this study is the compilation of Kurucz and Peytremann (KP, 1975) for a quarter-million lines. For each transition the wavel­ ength, atomic identification, upper and lower energy lev­ els, ionization potential, and gf-value are given. Only transitions arising from neutral and first ionized species are considered in the analysis owing to the lack of atomic data for doubly ionized species and the fact that the temp­ eratures in the RV Tauri atmospheres are cool enough to render the number densities of doubly ionized species neg­ ligible. The f-values are theoretically derived from a scaled Thomas-Fermi approximation rather than experimental­ ly or empirically obtained. Fuhr et al. (1985) have criti­ 92 cized the work of KP as being too crude and prefer experi­ mentally determined gf-values for their compilation, although they do include theoretical values for some tran­ sitions for which no experimental data are available.

Younger et al. (1978) compared the KP data with experimen­ tal data considered to be reliable for iron-group elements.

They found considerable scatter with 2/3 of the transitions in agreement to within 50%. Experimental data obtained by

Younger from Blackwell for Fe I resonance lines agreed fairly well with those of KP for transitions with well known energy levels and moderate configuration interaction.

The gf-values are quite important, since the line opaci­ ty of eqn. 14 is proportional to it. Therefore, an effort was made to replace in a systematic manner the obviously discordant theoretical values with experimentally deter­ mined values found in the literature. In order to deter­ mine which lines were most important, MOOG was run under conditions reasonable for an RV Tauri star. Those lines which produced obvious depressions of the continuum were considered for comparison. Typically, lines formed at optical depths t < 0.3 fell into this category. The gf- values of KP were replaced by experimental values if either of two criteria was met:

1. the KP gf-value fell outside the range defined by the

experimental value and its quoted accuracy; 93

2. the line was considered very important to the study.

Quoted accuracies for the experimental values were usually from 10 to 50 percent. Very important lines are defined as those having an impact upon classification criteria, such as the luminosity-sensitive lines Ba II X4554 and Y II

X 4375.

For the three spectral regions considered, covering a total of 195 A, a total of 63 lines had their gf-values

replaced with experimental values. If any trend in the comparison can be noted it is that in general the tran­ sitions of neutral species (Ti I, VI) agree well whereas those from ionized species (Ti II, Y II) did not. The fol­

lowing sources of data were used when substitutions were required: Fe I, Fuhr et al. (1985); Fe II, Fuhr et al.,

Kurucz (1981); Cr I, Younger et al. (1978); Y II, Pitts and

Newsom (1986); and other species from the compilation of

Wiese and Martin (1980).

Other necessary atomic data are the partition functions and 'standard' relative elemental abundances. Partition functions are computed from third and fourth order polyno­ mials fit to the data of Drawin and Felenbok (1965), Bolton

(1970), and Kurucz (1970). The abundances of elements rel­ ative to hydrogen are taken to be those of Ross and Aller

(1976). As their data are derived primarily from solar 94 spectra the metallicities derived here can be said to be differential with respect to the Sun. This study, how­ ever, is not strictly a differential one. One normally refers to a differential abundance analysis in the context of a curve-of-growth in which one star's abundance pattern is determined relative to another's. The strength of the differential method is that f-values are not needed. Such is not the case with the synthetic spectrum technique used here. The set of standard relative abundances thus becomes a constant in MOOG. Provision is made to vary the overall metallicity or individual element abundances by scaling factors.

Number Density

The equation for the line opacity requires knowledge of the number density of the atomic species in the lower state of the transition. Deliberate care has been taken in this study to avoid the use of molecules in any aspect of the spectral synthesis, in part because of the nature of these stars. Also, the large range in effective temperature observed for each variable, and for the class as a whole, makes using any single molecular feature difficult. It seems clear that to some extent molecular formation is not associated with the "photosphere" of the star but with higher layers of the atmosphere. It hardly seems appropri­ ate then to construct a metallicity parameter based upon 95

transient molecular features. Also, in Chapter 3 it was

shown that for supergiants of near solar metallicity the

correlation between CN strength and [Fe/H] observed in

giants tends to break down. We would like to look as deep

as possible into the stellar photosphere to avoid obvious

departures from the assumptions on which the models were

generated.

To determine correctly the number of atoms available for

any transition, account must be made of those atoms which

are not in the neutral state, whether they be in molecular

or singly-ionized states. MOOG will first compute the

number density of atoms in molecular states. To do so it

solves the molecular equilibrium equations for all atmos­

pheric levels using specified molecules, thereby yielding

the free atomic number density (neutrals + ions) of the

elements constituting the molecules.

An equation of molecular equilibrium is constructed for

each relevant element with the form

P. = p. + V n . . p . . (26) 1 *1 V 1] '

where

= fictitious partial pressure of element i

p^ = actual partial pressure of element i 96

Pij = actual partial pressure of molecule ij

n^ = number of atoms of element i in molecule ij.

By incorporating the relative number density of element i

to that of hydrogen, eqn. 26 can be expressed as

N. 1 . P. . (27) N PH “ ?! + £ ni H

The atomic and molecular partial pressures are related by means of the molecular dissociation constant (T) :

p. p . *i K. .(T) = (28) iD P ID

thus eliminating molecular pressures in eqn. 27. Two addi­

tional equations are necessary: one relating the total gas pressure, P , to the partial pressures p. (eqn. 29), and g l another accounting for the electron pressure, p_ , arising

from ionizations (eqn. 30).

P = P - ) p. H g i=l l (29)

= 0 (30) pe " i=li pi 1 KI I,± 1

Equations 27, 29, and 30 are solved simultaneously by a

Newton-Raphson technique with initial input parameters specified by 97

K . .(T) , molecular dissociation constants ID K p i , ionization constants

, gas pressure at each level

/ N H , the 'standard' relative elemental abundances

accounting for assumed stellar metallicity

PH , actual hydrogen gas pressure computed initially

from

Pg = PH + %+ + Pe • (3D

The results are the actual partial pressures for each ele­ ment associated with a molecule. . Application of the per­ fect gas law yields the number density of free atoms at each atmospheric level.

The symbolism adhered to in the application of the dis- sociation constants is from Kurucz (1970). The K's can be written in terms of a Saha-type equation,

K . .(T) N. . t±1 (T) = - a = 3 kT N.

(2iry.kT)^ U. (T) u. (T) r -i -1 = i -i 1 |jSxp(-Doij/kT)J (32) h3 uij(T) where D0° is the dissociation energy of molecule ij; y is the reduced mass of the molecule, and the u's are partition functions. As e(T) is solely a function oftemperature it 98

can be rewritten, for the case of neutral diatomic mol­

ecules, as

e (T) = exp -b+cT-dT2+eT3 kTev - f T4 - | In (T) (33)

with the constant 'a' being the molecular dissociation

energy. MOOG stores, for each molecule, the values of the

constants in eqn. 33 thus allowing e(T) to be computed for

any temperature. Constants for most H-C-N-0 molecules have been tabulated by Kurucz (1970). Since this study con­

tends with metals heavier than C,N, and 0, it was necessary

to compute additional constants. The molecular oxides ScO,

TiO, VO, YO, ZrO, and LaO were chosen because of an inter­

est in the constituent metals and because their dissocia­

tion energies are large enough to allow their possible presence in the stellar atmosphere. From the work of Sau- val and Tatum (1984) the dissociation constants K were com­ puted by the equation

log10 K = ^ bn ( l°9lo0 )n - 0 D°(eV) (34) n

where the b coefficients and dissociation energies, D°, o were supplied by the authors. The K's were computed over the temperature range 1000 - 6000 K at intervals of 500 99 degrees and then converted to cgs units. Coefficients to eqn. 33 were determined by a least-squares fitting routine to the computed K(T) data.

In addition to the molecular data it was necessary to include data of a similar nature for important atomic ions such as Ti II, Sc II, and Y II. The inclusion of ions is ( necessary for the correct determination of the number den­ sity of both atoms and molecules. MOOG inherently includes neutral atoms into the molecular equilibrium equations, but not their ions. By ignoring ions in the equilibrium, the number density of neutral atoms and molecules could be artifically inflated.

To input atomic ions, we follow a similar procedure as in the case for molecules. The Saha equation has the form

N tt N 2(2TrmkT)3/2 uTT (T) II e e II e (T) = exP (“Xj mA T ) (35) If” u ^ T )

which can be written similar to eqn. 33, except that the constant 'a' is the ionization potential of the neutral atom. The remaining constants are determined by a least- squares solution to the e(T) data. Table 13 presents the coefficients for eqn. 33 for those molecules and singly 100 ionized atoms which were included in addition to the data of Kurucz .

With the molecular number densities determined from the molecular equilibrium equations MOOG is then prepared to compute number densities for those states required in the line opacity equation. By manipulation of the Boltzmann and Saha equations with the assumption that no ionization stages above the first occur, the population of neutral atoms in lower level is given by

N g. exp(-E.,/kT) N = ±- (36) 1 + Uj (T)

NI while for singly-ionized atoms,

N g1 exp(-E,/kT) N = ±---- #(37) ' N l + -5— un NII

Thus, either or N jj would be substituted for N in eqn. 14. Table 13

Saha Equation Coefficients

a b c d e f Lecule/Ion

ScO 6.960 -47.945 1.8334E-3 -3.6148E-7 3.9705E-11 -1.8382E-15 TiO 6.870 -47.705 1.9401E-3 -4.2595E-7 5.2200E-11 -2.6379E-15 VO 6.410 -47.604 1.0668E-3 -1.6148E-7 1.4670E-11 -0.5676E-15 YO 7.290 -47.291 1.4382E-3 -2.0635E-7 1.1088E-11 +1.8282E-17 ZrO 7.850 -48.815 2.9336E-3 -8.1365E-7 1.1628E—11 -6.4745E-15 LaO 8.230 -46.804 1.2988E-3 -3.5648E-7 5.5106E—11 -3.2886E-15 Na II -5.138 35.351 3.3195E-5 -3.3669E-9 2.6773E-12 -1.4562E-16 Mg II -7.644 36.795 8.3798E-5 -2.6826E-8 3.1751E-12 -2.1554E-16 Al II -5.984 34.921 -1.6800E-4 + 9.7600E-9 1.4005E-12 -1.7108E-16 Si II -8.149 35.776 -1.4837E-5 -1.4357E-8 3.2922E-12 -2.3617E-16 Ca II -6.111 36.243 3.7073E-4 -7.3067E-8 4.6222E-12 -1.7713E-16 Sc II -6.540 35.960 3.9483E-4 -6.7053E-8 4.7208E-12 -1.8944E-16 Ti II -6.820 36.703 1.6352E-4 -4.9902E-8 4.4458E-12 -1.9093E-16 V II -6.740 35.410 2.8298E-4 -4.8417E-8 4.1382E-12 -1.9299E-16 Cr II -6.764 35.216 2.8418E-4 -5.0472E-8 4.1246E-12 -1.9157E-16 Mn II -7.432 35.945 1.9866E-4 -4.0967E-8 4.1252E-12 -2.1220E-16 Fe II -7.870 36.506 9.4865E-5 -3.0304E-8 3.8084E-12 -2.2821E-16 Sr II -5.692 36.457 2.6224E-4 -6.0628E-8 3.9123E-12 -1.6205E-16 Y II -6.380 35.706 2.3565E-4 -3.9386E-8 3.5195E-12 -1.8012E-16 Zr II -6.840 36.593 2.0318E-4 -1.4623E-7 3.0339E—11 -2.1524E-15 La II -5.610 36.615 -3.7469E-5 -1.7448E-8 2.8003E-12 -1.6162E-16 102

PROGRAM INITIALIZATION

Before the spectra of the program stars can be modeled the synthetic spectrum program must be initialized using spec­ tra from star(s) of known atmospheric parameters. The con­ cept of initialization is used here in a rather broad sense, reflecting both the need to determine unknown compu­ tational conditions and to acquire a sense for the effects upon the spectrum by the input conditions and assumptions.

Of particular concern are the matching of the observed spectral resolution by the synthetic spectrum and the rec­ tification of the observed stellar continuum.

Observational Considerations

Of the several spectra obtained with the IDS for stars with known atmospheric parameters, only two were of sufficient quality to be acceptable for initializing the program. To be acceptable the spectra had to reflect a high signal-to- noise level and good reproducibility between the two aper­ tures. Table 14 presents the basic atmospheric data for the two stars. Atmospheric parameters are from Luck and

Bond (1985), who used a model stellar atmospheres technique to reproduce line equivalent widths obtained from echelle spectrograms. 103

Table 14

Parameters for Abundance Standards

Object V Teff log g v. IFe/H) ML (mag) (K) (km/sec)

BD+1° 2916 9.64 4500 1.1 2.5 -1.5 -1.7 BD+30° 2611 9.17 4400 0.9 1.7 -1.2 -2.0

The use of these stars has the added advantage of replicat­ ing conditions in the atmospheres of the RV Tauri variables in terms of effective temperature, surface gravity, metal deficiency, and to some extent absolute visual magnitude.

The turbulent velocity parameter, vt , is smaller than anticipated for the variables. Since both stars have an effective temperature comparable to the cooler variables, they do not provide an additional constraint upon the gf- values for the ionic transitions that dominate the hotter stellar spectra.

Spectrum Rectification

As the synthetic spectrum program normalizes the line flux by the continuum flux it is not possible to compare the observed and synthetic spectra directly until the observed spectra have been similarly normalized. This normalization of the observed spectrum is referred to as spectral recti­ fication. If the continuum is not chosen correctly the synthetic spectrum fits will undoubtedly reflect improperly derived atmospheric parameters, particularly the effective 104 temperature and metallicity. The spectroscopic reduction procedure discussed in Chapter 2 does not include rectifi­ cation. Using the reduced IDS spectra an 'observed' con­ tinuum is fit to several of the highest points, neglecting emission features and instrumental flaws, by a polynomial of usually third or fourth order. The entire spectrum is not necessarily used in the fitting procedure for two rea­ sons:

1. The RV Tauri variables cover a considerable range in

spectral type, and the slope of the continuum in the

spectral region XX 4000-5000 A takes on a wide range of

values. It may not be possible to fit the entire

spectrum in an acceptable manner.

2. For late-type supergiants and stars of near-solar met­

allicity the spectrum is further depressed at the blue

end by CN absorption and a myriad of weak metal lines.

In these regions the continuum at the blue end must be

treated separately from longer wavelength regions.

The observed continuum is depressed from the actual by an amount which depends upon the instrumental resolution and the star’s effective temperature and metallicity. Dif­ ferences in the continuum level between the observed and synthetic spectra are primarily attributed to four factors:

1. incorrect placement of the observed continuum; 2. dif­ ferences in resolution of the observations and computa- 105 tions; 3. unaccounted-for absorption features; and 4. neg­ lected continuous opacity sources.

Incorrectly placing the observed continuum can be mini­ mized to an error of perhaps a few percent if the spectral regions adopted as peaks are carefully chosen. This is related to points 3 and 4 above. Neglecting continuous opacity sources for the moment, the absorption of concern

is due to atoms and molecules. Mention has already been made of CN in the blue region of cool stars, particularly supergiants. Other molecules to be considered are CH, NH,

CR , and TiO. Piccirillo et al. (1981) discovered that the neglect of high angular momentum lines of TiO in stellar models could account for discrepancies between photometri­ cally determined color temperatures and model dependent effective temperatures in M stars.

Atomic line opacity in the blue spectral region of cool stars is mainly composed of weak metal lines. Wildey et al. (1962) showed that line blanketing is a more serious problem shortward of X4500 A and is related to the overall metallicity of the star. It may not be obvious why the opacity of specific lines would affect the apparent contin­ uum. But once the synthetic spectrum is convolved with the

instrumental profile, the individual weak lines lose their

identity and effectively become a continuous opacity. 106

Therefore, not accounting for such opacity would in effect artificially raise the continuum level. This study does not.include molecular lines as opacity sources, making it imperative to avoid choosing continuum 'peaks' which are depressed by such weak lines. The fact that RV Tauri stars are metal-deficient may diminish the gravity of these remarks.

MOOG treats continuous opacity sources only for physical processes arising from hydrogen and helium, as for example

Rayleigh scattering. Neglected are the bound-free and free-free opacities arising from metals found in high abun­ dance such as C, Mg, Al, and Si and others which are included in the model atmospheres program ATLAS. These continuous opacities are generally at least two to three orders of magnitude smaller than the continuous opacity sources from H and He.

Computational Resolution

The computational resolution refers to all aspects of the computational process which come to bear upon matching the observed spectral resolution. Two problems present them­ selves: optimization of the generation of MOOG runs, and determination of the instrumental profile that must be con­ volved with MOOG output in order to reproduce the observed spectral resolution. The quantities STEP and DELTA, both expressed in units of angstroms, have been mentioned previously. STEP defines the interval at which the total line opacity is computed while ±DELTA is the distance from each STEP posi­ tion within which lines are considered to contribute to the total line opacity. Although it is possible to limit the spectral resolution by a judicious choice of these two quantities, this procedure would ignore the true instrumen­ tal profile. The alternate choice, and the one chosen, is to generate spectra with the best possible resolution and then match the observed resolution with an appropriate instrumental profile. After running MOOG with various com­ binations of STEP and DELTA, the values settled upon were

0.05 A and 1.0 A, respectively. These values did not com­ promise the resolution while also providing for acceptable execution times of the program. Lines outside the range

±DELTA were found not to contribute noticeably to the total line opacity.

The instrumental profile of the IDS was determined from the emission lines of the helium and iron-neon hollow cathode tubes used to determine the wavelength scale.

Crenshaw (1985) found that for this instrument the emission lines are well represented by a gaussian profile except in the far wings where the observed profile rises above that of a gaussian. The resolution is also known to degrade by 108 more than 50% near the ends of the spectral interval scanned. The resolution can be characterized by the full width at half maximum (FWHM) of the instrumental profile.

For the 1800 1/mm grating the resolution of the unsmoothed

He X4471 A line was measured to be 2.6 A, a fairly typical value for classification spectrograms. If we can qualita­ tively explain the term 'resolution' of the synthetic spec­ trum as our ability to distinguish intensity variations in contiguous STEP points, then the instrumental profile is a gaussian with FWHM = STEP x n , where n is the number of

STEP points. For a FWHM of 2.5 A and a STEP of 0.05 A, we have n =50 as the number of STEP points, or spectrum depths, which are used in the convolution at each STEP position.

Analysis

The star BD+1°2916 was used as the primary test example since its atmospheric parameters exactly matched those of one of the model atmospheres. Three bandpasses were chosen to be modeled: XX4220-4280, 4360-4425, and 4510-4580 A.

Each of these bandpasses contains features known to be luminosity dependent. Convolution of the synthesized spec­ trum with a gaussian profile characterized by n = 5 0 pro­ vided the best fit. Figure 10 shows these fits. The greatest number of discrepancies between observed and syn­ thetic spectra occur in the region of shortest wavelength. 109

To a large degree the discrepancies can be attributed to the absence of molecular lines in the synthetic spectrum.

The positions and identifications of molecular lines for

Figure 10 can be identified from the high resolution spec­ tral atlas of the Sun by Beckers et al. (1976). The over­ all fits to the other two regions, which are relatively free of molecular lines, are quite good. One can speculate as to the cause of the remaining discrepancies. It is most probable that the differences do not arise from computa­ tional resolution, incorrect atmospheric parameters, or placement of the continuum. More probable scenarios include observational (IDS) problems, f-values of individu­ al lines, missing lines (opacity sources) and a failure of the assumptions of the model atmospheres (LTE, plane- parallelism). It is interesting to note that differences between the spectra exist at some of the strongest absorp­ tion features, such as Cal X 4226, Fel X 4383, and Ball X 4554

A.

In lieu of a formal error analysis we can get a sense for the magnitude of the discrepancies observed by varying each of the atmospheric parameters independently of the others. Figure 11 compares the standard model for BD+f*

2916 with the results from atmospheric models representing deviations from the standard model in effective tempera­ ture, surface gravity, turbulent velocity, and metallicity. 110 BD+l 2916 (Te ff/l0S 8/ V ^ e/H] * <4500/1.125/2.5/ -1.5 )

2^0985726498328621

C422Q .00 4240.OG 4250.00 4230.00 4200. WAVELENGTH (A)

^

A$/A

C42Su.O o 4440 WAVELENGTH fA)

Figure 10 : Synthetic spectra for BD+1°2916. Synthetic spectrum (thick line) fits to the observed spectrum (thin line) of the star BD+1° 2916. From these figures and the equations for continuum and line opacities we can deduce the following points regarding the effects of the variation of atmospheric parameters upon the spectrum:

• Variations in the surface gravity affect the depths of

specific lines, particularly strong neutral and ionized

lines. The regionxx 4510-4580 A is relatively insensi­

tive to changes in the surface gravity. The luminosity

criterion ( x4376/ x4383) is gravity sensitive, prima­

rily in its contribution from Fel X4383. The continuum

does not appear to be affected over the range of gravi­

ties considered.

• Variations in the effective temperature manifest them­

selves in both the continuum and line opacities. Of

the several continuum opacities that are temperature

dependent, the strongest is most probably the H- bound-

free opacity in the visual region which has a T-1

dependence. The line opacity temperature dependence is

quite complicated; for neutral atoms,

exp(-E^/kT) U(a,v) 1 - exp(-h\)/kT) (38) ■ N UX (T) Av, II 1 + For small changes in temperature most of these quanti­

ties also vary slowly and we can approximate the temp­

erature dependence by

exp(-E^/kT) exp (-*1- /kT) a (39)

For ions a similar approximation is obtained. Both the

line and continuum opacities vary in the same sense.

This is borne out in Figure 11 where we see variations

in line depths and peaks, here representing the contin­ uum.

Variations in the turbulent velocity only affect the

line opacity as there is no vt dependence in the con­

tinuum opacity equations and small changes in vt do not

appreciably alter the temperature structure in the

atmosphere. The dependence of line opacity upon vt

lies within the Doppler parameter and the Voigt pro­

file,

2 U(a,v) exp{-[ (v -v q )/Av d ] } a (40) AV D where the Voigt profile is expressed by the initial

term in an expansion appropriate in the astrophysical

case when a « l (Cowley 1970). From Figure 11 we see that the line opacity appears to be increasing along with vt . But from eqn. 40 for line center the opacity decreases with increasing vt . This conflict is

resolved by realizing that microturbulence does

increase the equivalent width, W-^, of a line, with cen­

tral absorption decreasing, by increasing the contribu­

tion to from frequencies further away from v . In

essence the frequency space for absorption is increased

by the additional Doppler motion imparted by the micro­

turbulence. Figure 11 represents a degrading of the

resolution by convolution of the true spectrum with a

gaussian of FWHM = 2.5 A. Increased absorption, even

at line center, is due to this degradation process

coupled with the increase in from an increase of the

turbulent velocity.

Variation in the metallicity appears to affect both the

continuum level and the line depths as did the tempera­

ture variation. The computed continuum opacity depends

upon the metallicity through the number density of free

electrons. In cool stars, such as the Sun, the domi­

nant continuum opacity arises from the dissociation of

the IT ion. In metal-deficient stars, such as the RV

Tauri stars, the number density of free electrons is

smaller as is then the H“ opacity. The H" opacity is

also frequency dependent. In the X 4500 A region it is only fifty percent of its peak value (Mihalas 1978).

The apparent continuum level is also affected through

the line opacity. When one remembers that the line

density is approximately 30 lines/A it is easy to see

how a simple scaling of the metallicity will affect the

continuum level at a spectral resolution of 2.5 A. The

line opacity lx is directly proportional to the number

density of the element in question.

• Each of the atmospheric parameters affects the spectrum

in a distinct manner, thereby making it possible to

attribute specific spectral peculiarities to one of the

parameters. Only two of the parameters, effective

temperature and metallicity, affect the continuum level

to a noticeable degree, with the metallicity showing

the greater effect for the particular parametric inter­

vals chosen. An error in the temperature of +250

degrees corresponds to an error in the metallicity on

the order of [Fe/H] = ±0.2 .

To judge from the case of BD+1° 2916, the agreement between observed and synthetic spectra is quite good. But, because of the stronger than anticipated molecular contri­ bution in the XX4220-4280 A region as well as the question­ able nature of the continuum fits in. the bluest region

(XX4000-4300 A), only the two longer wavelength regions will be used in the synthetic spectrum analysis of the RV 115

(Teff/log g/vfc/[Fe/H ])

(4500/1.125/2.5/-1.5)

Te f f ! 4750 K 4500 4250

D/.:++/+.+./.:++/+.:+:/^^

log g : 0.750 1.125 1.500

vfc : 1 .5 km /sec 2.5 3.5

[Fe/H] : -1.5

- 1.0

c

o ft

ft I e 510.GO 4520.00 4550.00 WP.VELENG7H (S)

Figure 11: Synthetic spectra parameterization. The effects of atmospheric parameter variations upon the synthetic spectrum of BD+1°2916. 116

Tauri variables. Results from the W4360-4425 A region are more reliable when the observed spectrum is set to the bluer setting (AA4000-4880 A), as opposed to the redder setting (XX4300-5100 A), because of its more centered posi­ tion and the longer continuum baseline shortward of this region.

APPLICATION TO RV TAURI VARIABLES

The extraction of the atmospheric parameters from the observed spectra resembles an iterative process. The ini­ tial values (Teff /log g/ vt /[Fe/H])o were arrived at empirically and serve as a guide in the proper choice of an initial representative atmospheric model. For each star a four-dimensional grid centered on the initial model was formed, comprised of a pair of models flanking the initial model in each of the four parameters. A grid is therefore composed of eight models plus the initial. Additional MOOG runs were made, usually for distinguishing between the effects of vfc and [Fe/H] , until the most satisfactory fit was achieved to the observed rectified spectrum. An alter­ nate approach would be to simply generate synthetic spectra for all possible combinations of the atmospheric parame­ ters, thus bypassing the need to derive empirical initial conditions. The latter approach was not feasible. The large range of these variables in Teff and log g would 117

require on the order of 103 MOOG runs for each wavelength

region, without discriminating in the metallicity parameter

to better than ±0.5 dex. This latter shotgun-type approach

to generating synthetic spectra is not without merit. Sev­

eral groupings of variables, particularly among the hotter

ones, did allow for models common to several stars, thereby

increasing the efficiency of generating MOOG runs. It must

be pointed out that the most satisfactory fit, much like

the process of spectrum classification, was based upon the

entire spectral region and not solely on specific lines or blends.

The first step of the analysis, the spectral classifica­

tion, has been previously discussed. From the spectral

type and luminosity class initial values for Te f f ,log g,

and vt were assigned. The effective temperature and sur­

face gravity transformations were made using the calibra­

tions of Flower (1977) and Allen (1973), respectively.

These calibrations were chosen for their completeness and

overall agreement with other published works for the later

type stars. Flower's calibrations are constructed for

stars of solar-like metallicity. As the RV Tauri stars are metal-deficient their atmospheric parameters can not

strictly be described by ones of solar composition. To

approximate the discrepancy in the effective temperature we

assume that the spectral classifications are with respect 118 to solar-type stars and that a unique spectral type - (B-V) color correspondence exists. According to Table 4 of

Bohm-Vitense (1981) for a color of (B-V) =+1.0, a solar- composition star is 240 degrees hotter than a star with a metal composition of one-hundredth solar. Since few RV

Tauri variables have compositions as metal-deficient as

O.OIZo, the error in temperature resulting from an incor­ rect metallicity should be less than 200 K. To account for the possibility of choosing a (Teff ) which is too high, the Teff derived from Flower is rounded down to the nearest

250 K interval when choosing a grid temperature. In addi­ tion to (Teff )0 , for each star values of Teff are used at

intervals of (Teff )0 ±250 , and the atmospheric models themselves had been constructed for metallicities of [Fe/H]

= 0 .0 , -1 , -2 .

An initial value for the velocity parameter is also extracted from the spectral classification. The interpre­ tation of the spectrum relies critically upon vfc since its effect on the line spectrum is somewhat similar to that of abundance for small variations. In non-variable stars v

is more commonly known as the microturbulent velocity and has historically been incorporated as a non-thermal contri­ bution to Doppler broadening necessary to match line equiv­ alent widths in the curve-of-growth technique. The lumi­ nosity dependence of v is well documented. In the Sun its value is approximately 1.4 km/sec (Gray 1976) and it

increases with luminosity in a non-linear fashion. Most cool giants have values for v between 2 and 3 km/sec.

Late-type supergiants are generally around v = 4-7 km/sec.

In the case of variable stars the relationship between microturbulence and the dynamics of the envelope are uncer­

tain but probably related. The term 'velocity parameter'

is used in this dissertation to reflect a more general

notion of non-thermal velocities than one might infer for non-variable stars. In its application in MOOG the veloc­

ity parameter is considered to be similar to classical microturbulence in being depth and species independent.

Parsons (1967) determined a depth dependence in the stars o

Per (F5 lb) and 3 Aqr (GO lb) with v increasing with height in the atmosphere, for optical depths t < 0.5 .

Among variable stars the phase variations of v have been determined for Cepheids by Abt (1954), Schmidt et al.

(1974), and Luck and Lambert (1981), and for RR Lyr by Benz

and Stellingwerf (1985). For RV Tauri variables v was

found to be 3-7 km/sec for U Mon (Abt 1955), 4.4-9.5 km/sec

for AC Her (Baird 1981), and 4 km/sec for R Set (Luck

1981). Baird's v includes the thermal motion in addition

to the non-thermal. For choosing an initial v the compi­

lations of Wright (1955) and Glebocki (1973), based upon

non-variables, are most useful. The majority of initial 120 values chosen vere 4 or 5 km/sec since the RV Tauri vari­ ables were predominantly classified as supergiants.

The initial metallicity, [Fe/H] , was estimated from the strength of the X4383 A feature relative to the continuum peak at X4360 A using Figure 7 . Most of the RV Tauri stars are assigned moderate metal deficiencies by this technique, in the range -0.3 < [Fe/H] < -0.8 with an accu­ racy of approximately ±0.4 dex. The final synthetic spec­ trum fits use the [Fe/H] formalism although an entire spec­ tral region is employed, composed of line absorption from several metallic species. However, the predominant absorp­ tion does originate from the iron-peak elements, particu­ larly Fe and Ti. During the course of this analysis there was no indication that the use of a single scaling factor of the standard composition is incorrect, or that systemat­

ic differences exist for any star between the relative abundances of Fe and Ti.

With the initial estimates to the atmospheric parameters now determined, a model atmosphere can be chosen which best matches these conditions. The observed spectra are recti­ fied by the polynomial fitting procedure previously dis­ cussed. Figure 12 shows the spectrum and determined con­ tinuum for the variable TT Oph. Division of the spectrum by its continuum defines the rectified spectrum. For the 121 stars TX Oph and V564 Oph, Figures 13 and 14 display the best fits of their synthetic to rectified spectra. The spectrum of TX Oph is dominated by singly-ionized metal lines and V564 Oph by neutrals. Tables 15 through 18 list the strongest transitions contributing to synthetic spectra of RV Tau and TX Oph in the two spectral regions. The quantity TAUONE in the tables is an indication of the rela­ tive strengths among lines in the same spectrum. More pre­ cisely, TAUONE is computed to be the level of the atmos­ phere, increasing inward from the surface, at which the optical depth in the line becomes greater than unity. The number of levels in a model atmosphere is defined at the time it is generated. From the MARCS code, all atmospheres used in this study have 35 levels spanning a range in opti­ cal depth from 10-5 to 101 . The strongest lines will then have the smallest values of TAUONE.

Table 19 presents the atmospheric parameters indicative of the best fits for all observations of RV Tauri stars.

The data are presented as follows: column 1, star name; column 2, pulsation period; column 3, observation date

(UT); columns 4-7, derived atmospheric parameters (Teff/log g/vt/[Fe/H]); column 8, photometric [Fe/H] from Dawson

(1979); and column 9, spectroscopic [Fe/H] when available

in the literature. Tj- 04 CL CD CQ CL Li_ co

IS 03 4000 4160 4320 4480 4640 4800 4960 WAVELENGTH Figure 12: The observed spectrum and derived continuum of TT Oph. Relative Flux 03 (Sf CD Figure 13: TX Oph, observed and synthetic spectra. The rectified The spectra. synthetic and observed Oph, TX 13: Figure 4360 temperature variable TX Oph. TX variable temperature (thin) and synthetic (thick) spectra for the warm the for spectra (thick) synthetic and (thin) 4046 4600 4560 4400 4440 VRVELENGTH (A) 4480 ( 5 7 5 0 /1 .1 2 5 /- 0 .8 / 5 ) 5 / .8 0 /- 5 2 .1 /1 0 5 7 5 ( 4520 A 1984 MAY 3 2 TX Oph TX

123 V564 Oph 22 JUNE 1985 (4250/2.250/-I.05/3) CN

4360 4400 4440 4480 4520 4560 4600 WAVELENGTH (A) Figure 14: V564 Oph, observed and synthetic spectra. The rectified (thin) and synthetic (thick) spectra for the cool temp­ erature variable V564 Oph. 125

Table 15

Atomic Transitions in RV Tau

Strongest transitions in the cool star RV Tau (4250/1.125/-1.0/4) in the region >.*4360-4425 A.

Lambda(A )' ID EP(eV) TAUONE Lambda(A)' ID EP(eV) TAUONE

4359.61 Cr I 0.983 3 4395.04 Till 1.084 5 4365.90 Fe I 2.990 14 4395.23 V I 0.267 3 4367.58 Fe I 2.990 8 4398.02 Y II 0.120 13 4367.90 Fe I 1.608 3 4399.59 Ni I 3.847 14 4369.77 Fe I 3.047 5 4399.78 Till 1.237 13 4371.26 Cr I 1.004 3 4400.38 Till 0.605 7 4373.25 Cr I 0.983 13 4400.59 V I 0.262 5 4373.56 Fe I 3.017 12 4400.86 Ni I 3.655 11 4374.46 Till 0.618 6 4401.28 Fe I 3.602 11 4374.94 Y II 0.400 7 4401.45 Fe I 2.831 8 4375.93 Fe I 0.000 2 4401.54 Ni I 3.193 10 4375.99 Fe I 3.047 13 4404.75 Fe I 1.557 2 4379.23 V I 0.301 2 4405.02 Fe I 0.052 4 4382.76 Fe I 3.573 13 4406.65 V I 0.301 4 4383.55 Fe I 1.485 2 4407.64 V I 0.287 3 4384.96 Cr I 1.030 3 4407.71 Fe I 2.176 4 4387.89 Fe I 3.071 10 4408.20 V I 0.275 3 4388.39 Fe I3.602 10 4408.42 Fe I 2.198 3 4389.25 Fe I 0.052 2 4408.51 V I 0.262 4 4389.98 VI 0.275 2 4415.12 Fe I 1.608 2 4390.95 Fe I 3.017 10 4415.54 Till 0.595 7 4391.05 Till 1.231 11 4416.47 V I 0.267 10 4391.74 Cr I 1.004 14 4417.72 Till 1.165 9

A formal error analysis would be quite difficult to con­ duct due to the strong interrelation among the four atmos­ pheric parameters. However, a useful indication of the effect of each parameter has been examined with a paramet­ ric analysis performed on the stars TX Oph and V564 Oph.

Each of the four atmospheric parameters was varied indepen­ dently by an amount equivalent to one grid spacing in Teff and log g and the realistic amounts of +1 km/sec for vt and 126

Table 16

Atomic transitions in RV Tau

Strongest transitions in the cool star RV Tau (4250/1.125/-1.0/4) in the spectral region AA4510-4580 A.

Lambda(A) ID EP(eV) TAUONE Lambda(A) ID EP(eV) TAUONE

4512.73 Ti I 0.836 9 4540.48 Cr I 2.544 17 4514.19 Fe I 3.047 13 4542.42 Fe I 3.640 17 4515.33 Fell 2.844 16 4544.60 Cr I 2.544 17 4517.53 Fe I 3.071 12 4544.69 Ti I 0.818 9 4518.02 Ti I 0.826 7 4545.94 Cr I 0.941 3 4518.69 Ti I 1.430 12 4547.02 Fe I 1.557 9 4520.25 Fe I 3.071 15 4547.83 Ca I 1.899 7 4521.86 Ni I 3.740 17 4547.85 Fe I 3.546 11 4522.62 Fell 2.844 14 4548.76 Ti I 0.826 7 4522.79 Ti I 0.818 7 4549.46 Fell 2.828 13 4524.69 Till 1.231 15 4549.62 Till 1.548 9 4525.14 Fe I 3.602 9 4552.45 Ti I 0.836 7 4526.44 Cr I 2.544 16 4554.03 Ball 0.000 2 4526.93 Ca I 2.709 13 4555.48 Ti I 0.848 9 4527.30 Ti I 0.813 9 4555.88 Fell 2.828 15 4527.33 Cr I 2.544 17 4556.09 Fe I 2.949 16 4528.61 Fe I 2.176 2 4558.11 Fe I 3.641 17 4528.82 Fe I 3.017 14 4559.92 Ti I 1.460 11 4530.73 Cr I 2.544 16 4560.26 Fe I 2.831 16 4531.15 Fe I 1.485 2 4562.62 Ti I 0.021 17 4533.24 Ti I 0.848 2 4563.76 Till 1.221 8 4533.96 Till 1.237 7 4565.50 Cr I 0.983 7 4534.78 Ti I 0.836 3 4571.09 Mg I 0.000 2 4535.57 Ti I 0.826 4 4571.67 Cr I 2.544 16 4535.69 Cr I 2.544 16 4571.95 Till 1.572 9 4535.86 Ti I 1.443 12 4574.72 Fe I 2.278 12 4535.91 Ti I 0.818 5 4576.33 Fell 2.844 17 4536.04 Ti I 0.813 6 4577.17 V I 0.000 9 4538.75 Fe I 2.278 14

±0.2 for [Fe/H] . Table 20 shows the change in the line depth as a percentage of the continuum for specific lines in the AA4510-4580 A region. Positive values in the table correspond to increased absorption relative to the nominal atmosphere. The primary atomic species contributing to the 127

Table 17

Atomic, Trans it ions. JiLJEX-Pp.h

Strongest transitions in the warm star TX Oph (5750/1.125/- 0.8/5) in the spectral region XX 4360--4425 A

Lambda(A) ID EP(eV) TAUONE; Lambda(A)' ID EP(eV) TAUONE

4359.61 Cr I 0.983 19 4395.04 Till 1.084 5 4359.74 Zrll 1.230 19 4395.86 Till 1.243 18 4367.58 Fe I 2.990 18 4398.02 Y II 0.120 17 4367.66 Till 2.590 17 4398.30 Till 1.224 15 4367.90 Fe I 1.608 17 4399.59 Ni I 3.847 19 4369.77 Fe I 3.047 15 4399.78 Till 1.237 12 4371.26 Cr I 1.004 19 4400.38 Till 0.605 8 4374.46 Till 0.618 8 4400.86 Ni I 3.655 17 4374.82 Till 2.061 19 4401.28 Fe I 3.602 19 4374.94 Y II 0.400 9 4401.45 Fe I 2.831 18 4375.93 Fe I 0.000 9 4401.54 Ni I 3.193 17 4379.23 V I 0.301 19 4404.75 Fe I 1.557 4 4383.55 Fe I 1.485 3 4407.71 Fe I 2.176 17 4384.32 Fell 2.657 16 4408.42 Fe I 2.198 15 4384.81 Till 0.595 16 4409.25 Till 1.243 17 4385.37 Fell 2.778 10 4409.53 Till 1.231 14 4386.85 Till 2.598 18 4411.92 Till 1.224 16 4387.89 Fe I 3.071 19 4413.60 Fell 2.676 19 4388.39 Fe I 3.602 17 4415.12 Fe I 1.608 8 4389.25 Fe I 0.052 19 4415.54 Till 0.595 9 4390.95 Fe I 3.017 19 4416.81 Fell 2.778 10 4391.05 Till 1.231 10 4417.72 Till 1.165 9 4394.06 Till 1.221 15 4418.34 Till 1.237 18

spectral feature is listed under the wavelength. The X 4

A feature is a peak in the spectrum. The results are soi what unrealistic since the four parameters are not indepen­ dent. If we compare the variations to those resulting from metallicity changes, we see that for the hotter star the spectrum is most sensitive to changes in metallicity, regardless of ionization state. For the cooler star the spectrum appears to be equally sensitive to metallicity and Table 18

Atomic Transitions in TX Oph

Strongest transitions in the warm star TX Oph (5750/1.125/-0.8/5) in the spectral region AA4510-4580 A.

Lambda(A) ID EP(eV) TAUONE

4515.33 Fell 2.844 10 4520.21 Fell 2.806 13 4522.62 Fell 2.844 8 4524.69 Till 1.231 14 4525.14 Fe I 3.602 17 4526.93 Ca I 2.709 19 4528.61 Fe I 2.176 10 4529.46 Till 1.572 19 4531.15 Fe I 1.485 13 4533.24 Ti I 0.848 19 4533.96 Till 1.237 7 4534.16 Fell 2.855 16 4541.51 Fell 2.855 12 4547.83 Ca I 1.899 17 4547.85 Fe I 3.546 18 4549.46 Fell 2.828 7 4549.62 Till 1.584 8 4549.81 Till 1.180 19 4554.03 Ball 0.000 3 4555.88 Fell 2.828 9 4558.64 Cr I 4.073 15 4563.76 Till 1.221 8 4571.09 Mg I 0.000 17 4571.95 Till 1.572 8 4576.33 Fell 2.844 12

temperature changes. A gaussian estimate of the error in metallicity due solely to errors in T eff» log 9» an

’ 2 2 2 l/i a [Fe/H] “ °Teff + aiog g + °vt Table 19

Synthetic Spectrum Parameters

Variable Period Date (UT) Atmospheric Parameters Previous Fe/H (days) T log g V Fe/H Photom.(l) Spec. 0 00 1 DY Aql 131.42 23 May 84 4500 1.125 5 -0.90 • 23 Jun 85 4250 1.125 5/6 -0.90 DS Aqr 78.21 26 Jun 85 4500 2.625 2 -0.40 TW Cam 85.6 6 Jan 85 5000 1.125 8 -0.75 -1.06 RX Cap 67.92 27 Jun 85 5750 0.750 8 -0.30 -0.33 EQ Cas 58.31 6 Jan 85 5750 3 8 -0.30 -0.75(class I) +0.20(classIII) DF Cyg 49.81 21 Jun 85 4750 1.500 5 -0.30 -0.28 V360 Cyg 70.45 21 Jun 85 6250 1.875 8 -1.00 -0.87 SS Gem 89.31 11 Jan 85 5250 2 4 -0.40 -0.39 SU Gem 50.12 11 Jan 85 5750 1.125 5 -0.70 -1.00 AC Her 75.46 27 Jun 85 6000 1.875 5 -1.10 -0.56(class I) +0.20(classlII) -1.22 (2 ) -1. (3) EP Lyr 83.32 21 Jun 85 5250 1.500 6 -1.70 -1.9 U Mon 92.26 11 Jan 85 4750 1.875 3 -0.40 -0.27 -2.93 TT Oph 61.08 21 Jun 85 5000 1.500 6 -0.80 -0.66 TX Oph 135. 23 May 84 5750 1.125 5 -0.80 -0.68 UZ Oph 87.44 22 Jun 85 5750 0.750 8 -0.50 -0.77 V564 Oph 70.6 22 Jun 85 4250 2.250 3 -1.05 -1.37 R Set 140.2 -0.48 -0.9 129 -0.4 Table 19 (continued)

Variable Period Date (UT) Atmospheric Parameters Previous Fe/H (days) T log g V Fe/H Photom. (1) Spec.

R Sge 70.59 22 May 84 4750 1.875 5 -0.50 -0.52 RV Tau 78.70 6 Jan 85 4250 1.125 4 -1.00 -0.63 V Vul 75.72 27 Jun 85 4750 1.125 4 -0.30 -0.30

References: (1) Dawson (1979) (2) Baird (1981) (3) Yoshioka (1979) (4) Aliev (1967) (5) Luck (1981) (6) Preston (1962) where gx is the variation in a [Fe/H] <*ue to atmospheric parameter x. For the hotter star, using the Fe \4529 A line, a [Fe/H] = *0-2, and for the cooler star, using the Fe

X4531 A line, o[Fe/H] = ±0.3. The synthetically derived

[Fe/H] values in Table 19 have an error of magnitude ±0.3, excluding errors of observation, continuum placement and f-values, which are not necessarily negligible. 132

Table 20

Variations in Spectral Line Depth

Positive values correspond to increased absorption relative to the nominal atmosphere in units of % of continuum inten­ sity.

TX Oph (5750/1.125/-0.8/5)

X 4529 X 4534 X 4541 X 4554 X 4538 Parameter Fe I Till Fell Ball •Peak'

AT = +250 -1.8 -2.3 -0.9 -0.8 -0.9 -250 + 2.0 ♦2.8 ♦1.3 ♦1.3 ♦1.4 Alog g=+0.375 -1.0 -0.9 -0.8 -1.5 -0.3 -0.375 ♦0.4 0.0 ♦0.4 ♦1.0 ♦0.3 Av = +1.0 ♦1.5 ♦1.6 ♦1.3 ♦2.8 0.0 t -1.0 -1.5 -2.0 -1.4 -2.8 0.0 A[Fe/H] = +0.2 ♦3.1 ♦ 3.4 ♦2.6 ♦ 3.0 ♦1.8 -0.2 -2.9 -3.3 -2.0 -2.5 -1.1

V564 Oph (4250/2.250/-1.05/3)

X 4527 X 4531 X 4535 X 4554 X 4565 X 4538 Parameter Ti I Fe I Ti I Ball Cr I 'Peak

AT = +250 -5.8 -4.5 -5.5 -3.8 -4.0 -2.2 -250 ♦6.8 ♦5.0 ♦6.0 ♦3.8 ♦3.9 ♦1.8 Alog g=+0.375 ♦ 1.0 ♦0.3 -0.1 -1.0 -1.0 -0.8 -0.375 -0.5 -0.3 ♦0.3 ♦0.9 ♦1.0 ♦0.8 Av = +1.0 ♦3.3 ♦3.0 ♦5.5 ♦3.9 ♦2.2 ♦1.3 t -1.0 -3.3 -3.3 -5.0 -4.4 -2.8 -1.4 A[Fe/H] = +0.2 ♦5.3 ♦4.0 ♦3.4 ♦4.4 ♦4.4 ♦2.8 -0.2 -4.5 -3.7 -3.3 -3.9 -3.9 -2.3 CHAPTER V

THE NATURE OF RV TAURI VARIABLES

INTRODUCTION

When assessing the data and derived properties of an indi­ vidual variable star one is naturally inclined to compare it to some preconceived notion of the average properties of its class. This sort of mental averaging appears valid for stars such as the classical Cepheids and RR Lyrae variables which are quite regular and predictable in their proper­ ties. Such a simple model does not exist for RV Tauri variables as common denominators are more difficult to define. Of the variables observed in this study, formally classified as RV Tauri, nearly twenty percent may have been misclassif ied.

The heterogeneity of the class members can be inferred from the observations; ten variables show evidence of hydrogen Balmer-line emission, and eight were found to have photometric indices that reflect the presence of TiO absorption. These samples are probably incomplete since the observations were made at random phases in the light curve and in some cases only a single spectrum was

- 133 - 134 obtained. The range in [Fe/H] as determined from the syn­ thetic spectra is quite large, extending from -0.3 to -1.7, and by itself might indicate different stellar populations, ages, or masses for the variables.

To investigate the nature of the RV Tauri stars we draw upon our knowledge of their metallicity, galactic distribu­ tion, location in the H-R diagram, and the few applicable theoretical models that exist. Because of the apparent heterogeneity of the individual members, a credible expla­ nation of the evolutionary state of the class as a whole may be difficult to formulate.

METALLICITY

This study has been primarily concerned with the determina­ tion of metallicity among the RV Tauri variables. The syn­ thetic spectrum fits seem quite satisfactory except for a few spectra in which the hydrogen emission was particularly strong. Few spectroscopic [Fe/H] determinations exist that allow direct comparisons to check the results. The only such case is AC Her for which three independent determina­ tions, including this study, yield [Fe/H] between -1.0 and

-1.2, a rather good agreement. When comparing the [Fe/H] from this work to those photometrically determined with the

DDO system (Dawson 1979), an overall agreement is found in terms of the range of [Fe/H] and most individual variables 135 show agreement within the quoted errors. However, eight of the nineteen variables in Table 19 show differences of about a factor of two in the iron abundance in a non- systematic manner. Besides the errors of observation and reduction discussed by Dawson and the problems of synthetic spectra previously mentioned, there are fundamental differ­ ences in the two techniques that affect the interpretations in indeterminable ways. These differences include:

• The DDO measure of [Fe/H] is obtained through the

observation of the CN A 4216 band and its calibration

with respect to iron abundance in normal stars. But CN

strength is phase dependent in RV Tauri stars, and fur­

thermore it has been shown that the correlation between

CN strength and [Fe/H] for field supergiant stars is

weak, perhaps due to a mixture of stellar populations.

Also, the formation of molecules such as CN and TiO may

not occur in the same atmospheric layers as in non­

variable stars. In contrast to the DDO photometry the

synthetic spectrum fits are made to atomic line blends

composed primarily of Fe and Ti.

• The occurrence of hydrogen Balmer-line emission contam­

inates the DDO filters "41" and "48", affecting the

derived effective temperature and metallicity.

• Spectroscopy can distinguish between contributions to

the line depths from elemental abundance and turbulent 136

velocity, but photometry does not. From Tables 11 and

19 we see that a strong correlation exists between tur­

bulent velocity and hydrogen line emission. With the

single exception of TW Cam, all variables having deter­

mined turbulent velocities of 6 or 8 km/sec also show

hydrogen emission to some degree. Therefore, a large

turbulent velocity could be photometrically misinter­

preted as higher metallicity or cooler temperature. In

general, there is more information in spectral lines

than in intergrated light.

• The final values of [Fe/H] quoted by Dawson represent

an averaging of the observations, common in variable

star work, whether or not they are equally spaced in

phase or represent the entire magnitude range. On the

other hand, a synthetic spectrum represents the atmos­

phere at a specific epoch. Since the metallicity of a

variable star does not change with phase and can, in

principle, be determined at any phase, it seems prefer­

able to make the determinations at the specific times

of the observations rather than to use average proper­

ties which may not represent the star at any phase.

For all these reasons, the determinations of metallici- ties of RV Tauri variables based on DDO photometry must be considered uncertain and should be checked by other meth­ ods. There is, of course, no guarantee that the method of 137 spectrum synthesis employed here will give the "true" val­ ues of [Fe/H], or even that those values are free from sig­ nificant systematic errors. It is, however, a method that is almost completely independent of the assumptions of the photometric method, and as we have seen it avoids several specific problems of the latter method.

In view of the differences between the photometric and spectroscopic techniques it is remarkable that their results for [Fe/H] agree to extent that they do. Five of the variables are in excellent agreement between the meth­ ods, to within 0.1 dex for [Fe/H], These stars have not displayed TiO absorption and only one of them, RX Cap, shows significant hydrogen emission. On the other hand there are eight variables with poor agreement, with differ­ ences for [Fe/H] greater than 0.25 dex. This latter group contains all three of the stars that have ever displayed

TiO absorption and for which a spectroscopic analysis was done. In addition, five variables displayed hydrogen emis­ sion, although weakly in some cases, and two (EQ Cas, AC

Her) were not given unambiguous luminosities by photometry.

The '48' filter of the DDO system is susceptible to both

TiO absorption and hydrogen emission, whereas the synthetic spectra avoided regions of TiO and hydrogen lines. As both of these phenomena are transient in nature and the observa­ tions with both techniques were made rather randomly, it is 138 not possible to say definitely what their effect was upon the DDO photometry. However, it is of legitimate concern that the agreement was least good for the variables dis­ playing TiO and/or hydrogen emission.

ABSOLUTE MAGNITUDES

Our understanding of the mass and evolutionary state of the

RV Tauri stars depends critically upon the correct determi­ nation of their luminosities, or absolute magnitudes. This has proven to be a difficult observational task for the field variables. No RV Tauri star is close enough to have had its distance determined by trigonometric parallax, and none is associated with objects such as binary stars or open clusters for which fairly reliable distance- determining techniques exist. From their spectral type we can classify them as bright giants and lower luminosity supergiants but the transformation from spectral type to Mv is complicated by not knowing their masses. This has left the problem to be decided by the few RV Tauri stars in globular clusters.

DuPuy (1973) constructed a period-luminosity (P-L) rela­ tion, eqn. 42, based primarily upon four variables in as many clusters:

Mv = -5.3 + 0.021 P(days) . (42) Although this relation was derived from the best avail­ able data (Sawyer 1955) and ideas concerning the correct­ ness of the classification of the individual variables, there is good reason to consider it dubious at best. Fur­ ther observations of one of the variables, AP Set (Sandage et al. 1966), lead to a change in its observed lightcurve amplitude. According to the procedures followed by DuPuy this places the star about a full magnitude lower in M . v where it could not be represented by the P-L relation.

Neglecting this variable altogether would not alter the P-L relation significantly, as noted by DuPuy,but would cast considerable doubt upon a relation based on only three stars. New observations of any of the three variables or changes in the cluster distance moduli or the absolute mag­ nitude of the cluster RR Lyrae stars could drastically change the relation. Wehlau et al. (1985) present light­ curve data obtained over forty years for the RV Tauri vari­ able in the cluster M56. One clearly sees that the average magnitude can vary by an amount which would considerably affect the form of the P-L relation.

Lloyd Evans (1983) has described the globular cluster variable NGC 6626 #17 as an RV Tauri star. From its peri­ od, average magnitude, and an estimation of its color it appears that eqn. 42 would over-estimate its luminosity when compared with that computed from the distance modulus 140 of the cluster. Including it to formulate a P-L relation would add considerable scatter to the slope of the rela­ tion.

Theoretically, the P-L relation of eqn. 42 contradicts those of all other stars in the instability strip in that the luminosity increases with a decreasing pulsation peri­ od. Yet the RV Tauri stars in globular clusters appear to be more luminous than the shorter-period Population II

Cepheids. This would suggest that the slope of the P-L relation in the Population II instability strip changes near a period of 60 days. This seems unlikely, particular­ ly in view of the fact that the P-L relation for Population

I Cepheids, including extragalactic members, is continuous to periods of 200 days (Sandage and Tammann 1968). Rosi- no's (1978) Figure 10 does suggest that the globular clus­ ter P-M relation turns over in the region of the RV Tauri v * stars. However, he speculates that this may occur as a result of the relative metal-deficiency of the clusters containing RV Tauri stars compared with those clusters con­ taining the red variables. Also, if infrared colors are used, the globular cluster P-L relation appears to be lin­ ear for all periods. With the exception of the variable of longest period in Rosino's sample of RV Tauri stars, those remaining form an extension, at M = -3, to the W Vir stars in the P-L relation. It is easy to see from his figure how 141 a possibly misleading P-L relation of negative slope can be constructed for the RV Tauri stars if the longest period variable is also included.

A theoretical P-L relation can be constructed from the definitions of average mass density, effective temperature, and pulsation constant, Q,

M " (43) 4 d3 ■j it R

L = 4ttR2 aT4 (44)

Q = P(

/

q )1/2 (45) resulting in an expression requiring the period to increase with increasing luminosity:

log (P) = 12.71 + log(Q) - 0.5 log(M )

- 0.30(Mv + BC) - 3 log(Teff) . (46)

In eqn. 46, M is the pulsational mass and the value of the hr constant results from expressing the equation relative to the Sun. The period is that for pulsation in the fundamen­ tal mode. Higher modes differ from this by a constant which would not affect the slope of the relation. As none of the quantities on the right hand side of eqn. 46 is accurately known, particularly the mass, this expression is of little use at this time in determining a P-L relation. 142

An alternate procedure for computing Mv is obtained from the synthetic spectrum data and the combination of equa­ tions defining the effective temperature (eqn. 44) and gravity (eqn. 47): G M g = (47)

Again, the derived expression can be formulated with respect to solar quantities as

M =2.5 log(g) - log(M/Mq) - 41og(Teff) v

+12.49 - BC (48)

If we presuppose the RV Tauri masses to be solar, then eqn.

48 becomes

Mv = 2.5 log(g) - 41og(Teff) + 12.49 - BC . (49)

We now have an expression dependent upon two quantities

(Teff,log g) resulting from the spectral fits and a third

(BC) that can be estimated from the spectral classifica­ tion. Table 21 presents the comparison of absolute magni­ tudes as determined from the P-L relation (eqn. 42) and the spectral fits (eqn. 49). Data for Teff and log g are taken from Table 19 and the bolometric corrections are interpo­ lated using the compilation of Flower (1977). Figure 15 graphically displays this comparison, with the individual 143 absolute magnitudes from eqn. 49 plotted along with the P-L relation of eqn. 42, represented by the solid line. Also depicted is a straight line 'chi-by-eye' fit to the majori­ ty of variables found around Mv = -2, and serves only to suggest an alternate plausible relation derived from the field RV Tauri stars.

Table 21

Luminosity: P-L vs. Synthetic Fit

Star Period(days) M (P-L) Mv (syn) Date (UT) V DY Aql 131.42 -2.54 -1.79 23 Jun 85 DS Aqr 78.21 -3.66 + 1.71 26 Jun 85 TW Cam 85.6 -3.50 -2.81 6 Jan 85 RX Cap 67.92 -3.87 -4.50 27 Jun 85 EQ Cas 58.31 -4.08 + 1.16 6 Jan 85 DF Cyg 49.81 -4.25 -1.54 21 Jun 85 V360 Cyg 70.45 -3.82 -2.13 21 Jun 85 SS Gem 89.31 -3.42 -0.83 11 Jan 85 SU Gem 50.12 -4.25 -3.60 11 Jan 85 AC Her 75.46 -3.72 -1.91 27 Jun 85 EP Lyr 83.32 -3.55 - 2 . 1 1 21 Jun 85 U Mon 92.26 -3.36 -0.55 11 Jan 85 TT Oph 61.08 -4.02 -1.81 21 Jun 85 TX Oph 135. -2.47 -3.66 21 Jun 85 UZ Oph 87.44 -3.46 -4.60 22 Jun 85 V564 Oph 70.6 -3.82 + 1.37 22 Jun 85 R Sge 70.59 -3.82 -0.73 26 Jun 85 RV Tau 78.70 -3.65 -1.58 6 Jan 85 V Vul 75.72 -3.71 -2.48 27 Jun 85

According to Figure 15, the majority of variables are underluminous when compared to the P-L relation. One explanation for the disparity could be that the one solar- mass assumption is invalid. . Forcing the variables to fit 144

- 5

- 4

- 3 P-L

-2 o —

+ 2

60 80 100 120 140 Period (days)

Figure 15; The Mv - Period diagram. The absolute visual magnitude, as determined from the synthetic spectra data and eqn. 49, is plotted against pulsation period. The solid line represents the P-L relation of DuPuy (1973) and the broken line suggests a different relation, approximat­ ed to the variables centered around M v = -2. 145

the P-L relation, however, would require an increase in mass of up to ten solar masses. Dawson (1979) pursued the determination of RV Tauri masses through the use of eqn. 48

using the P-L relation of DuPuy and, indeed, his masses

fell between one and ten solar masses. Equally distressing masses can be obtained using the data from this study if we

continue to use the P-L relation of DuPuy (1973).

Another possible explanation is associated with a subtle

systematic effect. It was observed in the spectroscopic

studies of AC Her and U Mon that the gravity can appear to

vary by at least a factor of ten over the light-cycle. In

Figure 15 the most luminous stars are associated with

noticeable hydrogen emission in the spectrum. That more

of the variables with emission are not noted is a result of

discriminating against the use of such spectra in the syn­

thetic spectrum analysis. Spectroscopic evidence from U

Mon (Abt 1955) suggests that the effective gravity has its

smallest value nearest maximum radial expansion, corre­

sponding to a range in the light-curve phase from prior to

primary minimum to the approach of primary maximum. It is

during this period that hydrogen emission appears to be

strongest. Therefore, it seems likely that the absolute

magnitudes obtained spectroscopically at these phases are

too bright and should be ignored. If that is correct then

all of the variables observed are less luminous than the 146 values given by DuPuy's relation. It is possible that the globular cluster members used by DuPuy are more luminous than the field RV Tauri stars, and that his P-L relation should not be applied to the field variables.

If the true pulsational period of the variables is half that of the formal period, as suggested from radial veloci­ ty studies, then the luminosity from the P-L relation is increased along with the disparity. Also note that the P-L relation of eqn. 42 is obtained from stars of mass less than solar and that high mass stars are not consistent with the RV Tauri metallicities and galactic distribution.

Again, it appears that the P-L relation is either incorrect or not applicable to the RV Tauri variables found among the field stars.

GALACTIC DISTRIBUTION AND POPULATION TYPES

We can address the distribution of RV Tauri stars in the

Galaxy using both galactic coordinates and their distance above the plane. The latter requires knowledge of the

interstellar reddening and absolute magnitude. In terms of galactic coordinates the RV Tauri stars are not unlike oth­ er old-disk objects such as the W Vir stars, novae, and planetary nebulae. Most lie within thirty degrees of the plane with a majority also found in the direction of the galactic center. Other types of variables have markedly 147 different distributions; for example the RR Lyrae stars are homogeneously distributed in both galactic longitude and latitude while the classical Cepheids are restricted to the plane (Plaut 1965).

The distance, |z| , from the galactic plane in an abso­ lute sense can be computed from the equations

(V - Mv ) = 51og(d) - 5 + 3E(B-V) (50)

!z| = | d-sin(b) | (51)

where d and z are in units of parsecs, b is the galactic latitude, and the assumption has been made that the visual absorption can be represented as three times the color excess in (B-V). The observations of this study provide V and E(B-V) at specific epochs rather than an average over the light-cycle. The remaining unknown is the absolute magnitude.

We compute | z(pc)| from eqns. 50 and 51 using deter­ mined from the P-L relation and synthetic spectrum data.

We expect that the latter values of |z| will tend to be smaller because of the lower luminosities obtained spectro­ scopically. In either case the color excesses employed may also lead to lower than correct values of |z| since it will 148 be assumed that the excess is due solely to the interstel­

lar medium. Thus, the interstellar contribution is over­ estimated if any sizeable circumstellar component exists.

The results are presented in Table 22. Data for V and

E(B-V) are from this study unless otherwise noted. As expected |z| tends to be larger when Mv is computed from

the P-L relation. Few of the variables lie within 160 parsecs of the plane, as would be expected for Population I objects (Blaauw 1965). Likewise, few are as far as 2 kpc

from the plane, which would be suggestive of the Halo Popu­

lation.

Population types can also be inferred for the variables

from their determined metallicities. Certainly the most

extreme deficiencies found are representative of Population

II objects, having masses less than solar. The more metal-

rich variables can not be population-typed solely from

their metallicity. The lower limit to the metallicity of

the older Population I stars such as the Sun is about

[Fe/H] = -0.2, whereas the globular clusters, representing the Halo Population, have an observed metallicity range of

-2.2 < [Fe/H] < -0.5 .

The upper limit of the globular cluster metallicity scale is a problem which has received much attention in

recent years. The metallicity [Fe/H] determined from low- 149

Table 22

Distance from the Galactic Plane

Star V E(B-V) b N

lz l 1 1 1 syn ►V t-< DY Aql 9.80 .17 -17.12 477 674 DS Aqr 9.98-10 ,9.48 *3> - 6.91 66-126 737-1403 DF Cyg 12.41 .42 + 8.62 517 1803 V360 Cyg 11.08 .26 -11.78 624 1360 SS Gem 8.73 .46: + 1.29 1 33 SU Gem 13.09 .45: + 4.80 982 1325 AC Her 7.55 .14 +14.25 158 363 EP Lyr 10.60 .17 + 6.95 329 638 tJ Mon 7.18 .03: + 4.14 24 88 TT Oph 9.79 .14 +28.64 824 2281 TX Oph 9.99 .40 +26.13 1358 785 UZ Oph 10.27 .45 +23.03 1980 1171 V564 Oph 10.22 .26 +16.80 119 1296 RV Tau 9.49 .07 -12.20 314 814 V Vul 8.86 .31 - 8.51 178 314

Notes: (1) B mag range from the GCVS, with (B-V) = +1.1 for K1 III spectral type (2) Burstein and Heiles (1982) (3) Dawson (1979)

resolution techniques, such as DDO photometry and low-

resolution spectroscopic analyses, is less metal deficient

than when obtained from high-resolution spectroscopic anal­

ysis of iron-peak elements. For example, the cluster M71

by low-resolution techniques is relatively metal-rich with

[Fe/H] = -0.5, whereas at high resolution its metalicity is more deficient, [Fe/H] = -1.2 (Burstein et al. 1986). Sim­

ilar evidence that the ‘upper limit of the globular cluster

[Fe/H] scale should be lowered to around -1 has been

obtained from other clusters. 150

The best we can say with regard to stellar population based upon metallicity is that the RV Tauri variables appear to span the range from Disk Populations to Halo Pop­ ulation, with the preponderance being Intermediate Popula­ tion II. The population types referred to here are those outlined at the Vatican Conference (O'Connell 1957) which categorized the populations according to the kinematics and chemical compositions of specific classes of objects.

EVOLUTIONARY STATUS

From the location of the RV Tauri stars in the H-R diagram and theoretical stellar models we can place limits on their mass. The upper limit is set at about eight solar masses

(Iben 1967), as stars of higher mass would have higher luminosities at all stages of their evolution than the max­ imum observed luminosities of the globular cluster RV Tauri stars, which are log(L/L o ) = -3.5. The lower limit is approximately 0.6 M q. Stars as low as 0.51 never appear to reach luminosities above log (L/L0) = -2.9 (Sweigart et al.1974), by-passing altogether the asymptotic-branch phase of evolution. This lower mass limit says nothing about the progenitor star mass as the total amount of mass lost throughout its evolution is not accurately known. These mass limits are not very constrictive. 151

Further constraints on mass are obtained by incorporat­ ing the results from their metallicity and galactic distri­ bution. In the Galaxy, stars as massive as the classical

Cepheids (5-8 MQ) are not found to be more metal-deficient than [Fe/H] = -0.2 and are restricted to the plane. Stars less than four solar masses, crossing the instability strip for the first time on their vay to becoming giants, are found at luminosities lower than the cluster RV Tauri stars. However, at subsequent stages in their evolution they may re-enter the instability strip at higher luminosi­ ties while at presumably lower mass due to mass loss pro­ cesses. From the high-resolution spectral analyses of AC

Her (Baird 1979) and R Set (Luck 1981) no enhancement of the s-process elements was observed, as expected for evolved stars of mass greater than three solar masses (Iben and Truran 1978). Finally, for the variables in globular clusters the 0.6 M 0 AGB-models of Gingold (1974,1976) pro­ vide a reasonable way to account for the RV Tauri variables as stars which are in the post-AGB phase or are undergoing their final blueward movements in the H-R diagram.

Considering the evidence outlined above, the conclusion one draws regarding the evolutionary state of the RV Tauri variables is that they belong to an older stellar popula­ tion having masses of about one solar mass or less. Their high luminosities place them on or above the AGB phase of 152 evolution. Further observations regarding the s-process elements and mass-loss would be most useful in advancing our .knowledge of their masses. Appendix A

SPECTRA OF THE RV TAURI VARIABLES

- 153 - s p ----- .------1------'------1------'------1------r------1------•------1 T ID

\

(3 Ln _J______|______1______i______|______i______|______|______|______i______I__ 4160 4320 4480 4640 4800 4960 5120 WRVELENGTH 154 Figure 16 : The spectrum of DY Aql on 23 May 1984. m f i CN C I FLAMBDfl *10 CD O C (a 6100 iue 17 Figure 1 h setu fD q n 4My 1984. May 24 on Aql DY of spectrum The 6500 90 7300 6900 WAVELENGTH 7700 I 8100 I 8500

I 55 1 I . I ■ I . I . » t I 3900 4300 4700 5100 5500 5900 6300 WAVELENGTH Figure 18 : The spectrum of DY Aql on 9 Jun 1984. CO

CO CO .—I

CO CN CE □ CD 2! CE oo

CSJ oo 4320 4480 4640 48004160 4960 5120 WAVELENGTH 157 Figure 19 : The spectrum of DY Aql on 10 Jun 1984. FLflMBDR *10 “U

00 10 30 40 60 4800 4640 4480 4320 4160 4000 10.0 16.0 22.0 28.0 I iue 0 Tesetu fD q n2 u 1985. Jun 23 on Aql DY of spectrum : The 20 Figure ____ i ____ I ____ i ____ 1 ____ WAVELENGTH i ____ i I ____ I ____ i ____ I _

4960 158 Q

co

s i CD

Q CN CO CE

CE i El Ll j CD

S> ta I __Li 4000 4180 4320 4480 4640 4800 4980 WAVELENGTH 159 Figure 21 : The spectrum of DS Aqr on 26 Jun 1985. SI 03

V «SJ CD Si *

SJ xl- CE

CE s CN

(S3 S3 I . I. 4160 4320 4480 4640 4800 4960 5120 WAVELENGTH Figure 22 : The spectrum of IS Aur on 6 Jan 1985. FLRMBDR *10 oo CD 10 50 90 30 70 10 8500 8100 7700 7300 6900 6500 6100 I — iue 3 Te pcrmo WCmo 1 e 1983. 11Dec on Cam TW of spectrum : The 23 Figure ----- 1 ------1 ______I ______I ______WAVELENGTH I ______I ______I ______I ______I ______I ______I ______I _ 03

03

CN n CE Q CQ CE

Li_ CD

3900 4300 4700 5100 5500 5900 6300 WAVELENGTH 162 Figure 24 : The spectrum of TW Cam on 13 Dec 1983. cn FLRMBDfl *10 oo 4240 iue2 : h setu f WCmo a 1985. Jan 6 on Cam TW of spectrum : The 25 Figure 404560 4400 WAVELENGTH 4720 4880 5040 5200 oo cn

CD CD

oo

CE CD QD CE OD

00 1 I______11______I______1I______I_____ 1I_____ I______I______I______I______1______I_____ I_ 4160 4320 4480 4640 4800 4960 5120 WAVELENGTH

Figure 26 : The spectrum of TW Cam on 11 Jan 1985. Q cn

i si

S cn CE

CE _) (S Ix j co

ca I _L __U 4000 4100 4320 4480 4040 4800 4900 WAVELENGTH. 165 Figure 27 : The spectrum of RX Cap on 27 Jun 1985. S3

CN

I (S3 CN El

(S3 CD

(X a

CE ^ i-1 S. Lu CN

(Si GO I 4160 4320 4480 4040 4800 4960 5120 WAVELENGTH 166 Figure 28 : The spectrum of EQ Cas on 6 Jan 1985. FLGMBQG *10 4000 iue 9 Te pcrmo D y n2 u 1985. Jun 21 on Cyg DF of spectrum : The 29 Figure 4160 30 40 4640 4480 4320 WAVELENGTH 4800 4960 (S3 T ta IN

ca i CD IS i—i m s t oi 4 r CE 1 = 1 CD CE _J S3 L l j CO

S3 N" I 4000 4100 4320 4480 4040 4000 4900 WAVELENGTH 168 Figure 30 : The spectrum of V360 Cyg on 22 Jun 1985. CO »*■ t CN I FLflMBDR *10 CD —I *— tSJ 90 30 70 10 50 90 6300 5900 5500 5100 4700 4300 3900 iue 1 Te pcrmo S e n 3Dc 1983. Dec 13 on Gem SS of spectrum : The 31 Figure

WRVELENGTH 169 cn i—t FLRMBDA *10 LO cn 10 30 40 60 80 90 5120 4960 4800 4640 4480 4320 4160 iue 2 Tesetu f SGmo 1 a 1985. 11Jan on Gem SS of spectrum : The 32 Figure

WAVELENGTH 170 FLRMBDfl *10 ' 14

106500 6100 10.0 20.0 30.0 40.0 50.0 iue3 : h setu f UGmo 1 e 1983. 12Dec on Gem SU of spectrum : The 33 Figure 6900 WAVELENGTH 307700 7300 8100 8500 CN

CD

CE cm Od x: CE —I CD

__L j 3900 4300 4700 5100 5500 5900 6300 . WAVELENGTH 172 Figure 34 : The spectrum of SU Gem on 13 Dec 1983. I . I . I I . I . I 4240 4400 4560 4720 4880 5040 5200 WAVELENGTH

Figure 35 : The spectrum of SU Gem on 1 Dec 1984. in —I *— I FLRMBDfl *10 CN cn in in cn cn 10 4320 4160 iue 6 Te pcrmo S e n 1 a 1985. 11 Jan on Gem SU of spectrum : The 36 Figure i 40 4640 4480 WAVELENGTH 80 4960 4800 A 5120

T 174 2 U I I L_ I . I , 1 , 1 4160 4320 4480 4640 4800 4960 5120 WAVELENGTH

Figure 37 : The spectrum of AC Her on 10 Jun 1984. cn T T -1 I FLRKBJDR *10 G) CN cn CN cd m rj- CD - 4000 iue 8 Te pcrmo CHr n 7 u 1985. Jun 27 on Her AC of spectrum : The 38 Figure 4100 30 4480 4320 I I WAVELENGTH 4840 JL 4800 __ 4960

u 176 cn I — * i FLRKBQfl * 10 cn CD CN CO

10 30 40 60 80 4960 4800 4640 4480 4320 4160 30.0 36.0 42.0 48.0 54.0 i — iue 0 Te pcrmo E y n2 a 1984. 26 May on Lyr EP of spectrum : The 40 Figure ---- 1 ---- 1 ---- 1 ____ 1 ____ WAVELENGTH. i ____ I ____ i ____ I ____ i ____ | _ EJ

CE ca Lu (N

CO 40,0 0. 4180 4320 4480 4040 4800 WAVELENGTH

Figure 41 : The spectrum of EP Lyr on 21 Jun 1985. oo

00

CD CE

2C C E ^

Li_jr 1 cn • in

----- 11----- 1----- x1----- 1----- 1_____ I_____ I_____ I_____ 1_____ I_____ ,_____ LJ 4240 4400 4560 4720 4880 5040 5200 WAVELENGTH H Figure 42 : The spectrum of U Mon on 1 Dec 1984. § FLflKBDfl * 10 in CN CN cn cn 10 30 40 60 80 90 5120 4900 4800 4640 4480 4320 4160 1 iue 3 Te pcrmo UMno 1 Jn 1985. Jan 11 on Mon U of spectrum : The 43 Figure _____ x i _____ I _____ i i _____ I _____ WRVELENGTH x i _____ I _____ i _____ I _____ i _____ I _____ i _____

I _ 181 FLRHam * 2 0 10 4320 4160 iue 4 Te pcrmo QMno 1 a 1985. 11Jan on Mon HQ of spectrum : The 44 Figure 40 4040 4480 WAVELENGTH. 4800

90 5120 4960 182 tn r- i I FLAMHDA *10 N C r^ co to 10 4320 4160 Figure 45 Figure ± h setu f QMno 2 e 1985, Feb 23 on Mon HQ of spectrum The 40 4040 4480 WAVELENGTH _L

80 90 5120 4960 4800 183 S p------i------1------1------1------r------1------.------1------1------1 •3- LO

ta id I 1 i I i I i I i I i I I 1_ 4160 4320- 4480 4640 4800 4960 5120 . WAVELENGTH 184 Figure 46 : The spectrum of TT Oph on 26 May 1984. r -1 OQ cn

to CM CL Q CD CL _l Li_

CN 6100 6500 6900 73007700 8100 8500 WAVELENGTH 5 8 1 Figure 47 : The spectrum of TT Oph on 8 Jun 1984. ] I I I . I . I I 3900 4300 4700 5100 5500 5900 6300 WAVELENGTH

Figure 48 : The spectrum of TT Oph on 9 Jun 1984. FLFIMBDA *10 ~ U

10 4320 4160 14.0 26.0 38.0 50.0 62.0 iue4 : h setu fT p n 0Jn 1984. 10Jun on Oph TT of spectrum : The 49 Figure 40 4640 4480 WAVELENGTH 80 4960 4800

5120 187 FLRMBDR *10 N — CN 00 10 30 40 60 80 4960 4800 4640 4480 4320 4160 4000 I — iue5 : h pcrmo T p n 1Jn 1985. 21Jun on Oph TT of spectrum : The 50 Figure ----- 1 ----- 1 ----- 1 _____ I _____ WAVELENGTH i _____ L _____ i _____ I _____ i _____ I _____ i _____

L_ 188 _JJ 4160 4320 4480 4640 4800 4960

WAVELENGTH 189

Figure 51 The spectrum of TT Oph on 27 Jun 1985, i 1------1------•------r

?,n . i ■ i .___ i___ i i u 4160 4320 4480 4640 4800 4960 5120

. WAVELENGTH 190

Figure 52 : The spectrum of TX Oph on 23 May 1984 FLRMBDR *10 "H

10 6500 6100 16.0 32.0 48.0 64.0 iue 3 Te pcrmo XOho 2 a 1984. 24May on Oph TX of spectrum : The 53 Figure 90 7300 6900 WAVELENGTH M

70 108500 8100 7700 191 in ■tf

in cn

in CN CE o CO

in 6100 6500 73006900 7700 8100 8500

WRVELENGTH 2 9 1

Figure 54 : The spectrum of TX Oph on 8 Jun 1984. S3 (S

f t p

/'A (Si I (S3 CO

*

(SI (S3 CN ac cn an a: ^ Lir 1 s •

is s J. I. Jl I I u 3900 4300 4700 5100 5900 6300 WAVELENGTH

Figure 55 : The spectrum of TX Oph on 9 Jun 1984. FLRKBDfl *10 C'i KJ

10 3048 4640 4480 4320 4160 20.0 28.0 36.0 44.0 iue 6 Te pcrmo T p n 0Jn 1984. 10Jun on Oph TX of spectrum : The 56 Figure 1 .L WAVELENGTH 80 4960 4800 5120 !______.______I__ 4000 4160 4320 4480 4640 4800 WAVELENGTH

Figure 57 : The spectrum of TX Oph on 21 Jun 1985 FLRMBDR *10

1060 90 7300 6900 6500 6100 16.0 28.0 40.0 52.0 iue5 : h setu fU p n2 a 1984. May 24 on Oph UZ of spectrum : The 58 Figure J. WAVELENGTH L_L _L 7700

108500 8100 196 FLRMBDR *10 CD 18.0 30.0 42.0 54.0 iue5 : h setu fU p n8Jn 1984. Jun 8 on Oph UZ of spectrum : The 59 Figure 65006100 WAVELENGTH 7300 708100 7700 8500 i

3900 4300 4700 5100 5500 5900 6300

WAVELENGTH 198

Figure 60 : The spectrum of UZ Oph on 9 Jun 1984. FLAMBDR *10 "H

10 4320 4160 12.0 20.0 28.0 36.0 44.0 iue 1 Te pcrmo U p n 0Jn 1984. 10Jun on Oph UZ of spectrum : The 61 Figure 40 4640 4480 WAVELENGTH 80 4960 4800 U _ 5120 T ts

(3 i OJ cn

*

«s

CN CE O cn CE ( 3 CD

(3 CO I 4000 4160 4320 4480 4640 4800 4960 WAVELENGTH 200

Figure 62 The spectrum of UZ Oph on 22 Jun-1985. CO in

CM co CE □ 0Q CE _

- J S. Li_ ® CM

CO 4160 4320 4480 4640 4800 4960 5120 WAVELENGTH

Figure 63 : The spectrum of V564 Oph on 26 May 1984. CN

inCO

CE O CQ CE 'd- CN

00 6100 6500 69007300 7700 8100 8500

. WAVELENGTH 202

Figure 64 : The spectrum of V564 Oph on 8 Jun 1984. oo

CD cn

CE O CD CE

Ll CN

3900 4300 4700 5100 5500 5900 6300

WAVELENGTH 203 Figure 65 : The spectrum of V564 Oph on 9 Jun 1984. PM cn

CN

CD cn o CD CE 11 • CD

__u 4240 4400 4560 4720 4880 5040 5200 WRVELENGTH 204 Figure 66 : The spectrum of V564 Oph on 10 Jun 1984. ta cal I ■ I ■ I , I , 1 , I I 4000 4160 4320 4480 4640 4800 4960

WAVELENGTH 205

Figure 67 : The spectrum of V564 Oph on 22 Jun 1985. FLRMBDR *10 ' H CD

10 30 40 60 80 90 5120 4980 4800 4640 4480 4320 4160 12.0 18.0 24.0 30.0 iue 8 Te pcrmo R g n 2My 1984. May 22 on Sge R of spectrum : The 68 Figure

WRVELENGTK 206 O C I I I FLRMBDR *10 1060 90 7300 6900 6500 6100 iue 9 Te pcrmo g n2 a 1984, 24May on Sge R of spectrum : The 69 Figure WAVELENGTH 7700 8100

8500 207 L 3900 4300 4700 5100 WAVELENGTH 208 Figure 70 : The spectrum of R Sge on 9 Jun 1984. — I---- 1----- 1-----1-----1_____I_____I_____ 4160 4320 4480 4640 4800 4960 5120 WAVELENGTH 209 Figure 71 : The spectrum of R Sge on 10 Jun 1984. CO *—I I

I_____ i_____ I_____ i_____ I_____ i_____ I__ I . I 4000 4160 4320 4480 4640 4800 WAVELENGTH

Figure 72 : The spectrum of R Sge on 22 Jun 1985. FLRMBDA *10 00 10 30 40 60 4800 4640. 4480 4320 4160 4000 —I iue 3 Te pcrmo g n 7Jn 1985. Jun 27 on Sge R of spectrum : The 73 Figure --- 1 ---- 1 ____ i ____ T I ____ WAVELENGTH i ____ I ____ i ____ I ____ i ____ I

4960 211 FLRMBDR *10 ei CD 10 50 90 30 70 10 8500 8100 7700 7300 6900 6500 6100 F —I iue 4 Te pcrmo VTuo 1 e 1983. 11Dec on Tau RV of spectrum : The 74 Figure ------1 ______I ______I ______I ______WAVELENGTH I ______I ______t ______I ______I ______1 ______I ______

I _ 212 CO FLRHBDA *10 cn CM co co 90 30 70 10 50 90 6300 5900 5500 5100 4700 4300 3900 iue 5 Te pcrmo VTuo 1 e 1983. 13Dec on Tau RV : of 75 spectrum -Tie Figure I _____ i _____ l _____ i _____ | _____ WAVELENGTH i _____ I _____ i _____ i _____ i _____ I _____ i _____

! _ 213 cn I • i FLAMBDR *10 4160 iue7 : h setu f VTuo a 1985. Jan 6 on Tau RV of spectrum : The 76 Figure 4320 40 60 4800 4640 4480 WAVELENGTH 4960

5120 214 T—1 CO FLRMBDR *10 CO CN CO 4160 iue 7 Te pcrmo R a n 1Jn 1985. 11Jan on Tau RV of spectrum : The 77 Figure 4320 4480 WAVELENGTH 4040 4800 4900

5120 215 cn i—i FLRMBDA *10 CN CD co CN CN 00 CS 4160 iue 8 Te pcrmo u n 1My 1984. 21May on Vul V of spectrum : The 78 Figure 4320 4480 WAVELENGTH 4640 804960 4800 5120 cn r CN I 1 FLHKBDR *10 CD CO K> 104320 4160 Figure 79 : The spectrum of V Vul on 10 Jun 1984, Jun 10 on Vul V of spectrum : The 79 Figure 40 4640 4480 . 1 . WAVELENGTH 804960 4800 5120 1------r------r

I— J______I______I______I______I______I______I______—I----- 1 I l 1 4000 4160 4320 4480 4640 4800 4960 WAVELENGTH 218 Figure 80 : The spectrum of V Vul on 21 Jun 1985. FLRMBDR *10 00 10 30 40 B0 4800 4B40 4480 4320 4160 4000 —I I— iue8 : h setu fVVlo 2 Jn 1985. Jun 27 on Vul V of spectrum : The 81 Figure ------1 ------1 ------1 ------1 ------WAVELENGTH 1 ______1 ___ ! ___ I i ______i ______I __

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