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A STUDY OF ATTENUATION EFFECTS IN HIGHLY INCLINED SPIRAL GALAXIES
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of The Ohio State University
By
Leslie E. Kuchinski, M.S.
*****
The Ohio State University
1997
Dissertation Committee: Appro^^ by
Professor Donald M. Terndrup, Adviser 7A /J ^
.-Vdviser Professor Kristen Sellgren Department of Astronomy DMI Number: 9 801728
UNn Microform 9801728 Copyright 1997, by UMI Company. All rights reserved.
This microform edition is protected against unauthorized copying under Title 17, United States Code.
UMI 300 North Zeeb Road Ann Arbor, MI 48103 ABSTRACT
This dissertation presents a quantitative study of the attenuation of stellar light by
dust in highly inclined spiral galaxies. BVRIJHK images of 15 Sab-Sc galaxies with
inclination angles greater than 65° are used to explore which properties of radiative
transfer models are required to describe the reddening of optical and near-infrared
(NIR) colors across galaxy dust lanes. The models are then used to predict line-of- sight and face-on optical depths through these systems. Preliminary comparisons of the dust lane color gradients to predictions from models with simple slab or spherical shapes and several different relative dust-star geometries demonstrates that no single model of this type adequately describes the observed reddening over the entire optical-
NIR spectral baseline. The NIR colors are best fit by screen geometries and are not well reproduced by models with mixed dust and stars that have unextinguished light sources near the edge of the dust distribution. However, only those models with a mixture of dust and stars produce the saturation of reddening observed in the dust lane optical colors. More sophisticated disk galaxy radiative transfer models with exponential stellar and dust disks, bulge components, multiple scattering, and both homogeneous and clumpy dust distributions provide much better simultaneous agreement to the optical and NIR dust lane color gradients. I use several of the
11 radiative transfer models to infer values for the V’-band optical depth ry through these galaxies and find the result to be highly dependent on the adopted dust-star geometry. When compared to the extent of reddening predicted by the disk galaxy models, which are the most physically plausible ones used here and provide the best prediction of galaxy color gradients, the maximum dust lane color excesses imply central face-on optical depths of rv.o = 0.5 — 2.0. I find no evidence from the galaxy colors to support the recent claim that spiral disks are opaque out to D0 5 . Finally, I briefly discuss implications of the model comparisons and inferred optical depths for some techniques used to study spiral galaxy structure and stellar content.
Ill ACKNOWLEDGMENTS
I cannot thank by name every individual whose support made this thesis possible, but there are numerous people whose contributions have been substantial.
Many thanks to my adviser, Don Terndrup, for keeping this thesis going as it evolved rapidly from what was originally planned. Also for understanding how as tronomy is just one part of life. I am grateful to Adolf Witt and Karl Gordon, whose efforts to model attenuation effects in galaxies were not only invaluable to this project but are also a significant contribution to astronomy. I am also grateful to many (most?) members of the OSU Astronomy Department. Special thanks to .Jay
Frogel and Kris Sellgren, who kept in touch and were always available for advice and critiques. Rick Pogge, Alice Quillen, Brad Peterson, and Darren DePoy provided a great deal of intellectual and moral support. I thank my fellow graduate students, especially Glenn, Bob, and Anita, for celebrating and commiserating with me.
Finally, I acknowledge with deep gratitude the support of my family. I thank my parents for encouraging an interest in science and the beauty of the universe from a very young age. And of course a huge thanks to Kevin, Ryan, and K2, whose love, companionship, support, and sacrifices over the past several years have kept me going and have shown me some of the happiest times of my life.
IV VITA
March 13,1969 ...... Born — Madison, VVI
1991 ...... B.S. (Physics), Duke University, Durham, North Carolina 1991 ...... Multiple Year University Fellowship, The Ohio State University 1993 ...... M.S. (Astronomy), The Ohio State University 1991-present ...... Graduate Fellow, Teaching and Re search Associate, The Ohio State Uni- versitv
Publications
Research Publications (refereed)
Quillen, A.C., Kuchinski, L.E., Frogel, .J.A., k. DePoy, D.L. 1996, "Discovery of a Boxy Peanut-Shaped Bulge in the Near-Infrared”, The Astrophysical Journal 481. 179.
Kuchinski, L.E. & Terndrup, D.M. 1996, "Infrared Photometry and Dust .-Absorption in Highly Inclined Spiral Galaxies”, The Astronomical Journal 111, 1073.
Kuchinski, L.E. k Frogel, 1995, "Infrared .Array Photometry of Metal Rich Globular Clusters III: Two More Clusters and an .Analysis of U — K Colors”, The Astronomical Journal 110, 2844.
Frogel, J..A., Kuchinski, L.E., k Tiede, G.P. 1995, "Infrared .Array Photometry of Metal Rich Globular Clusters IT. Filler 1 - The Most Metal Rich Cluster?”, The Astronomical Journal 110, 1154.
Kuchinski, L.E., Frogel, J.A., Terndrup, D.M., k Persson, S.E. 1995, “Infrared .Array Photometry of Metal Rich Globular Clusters I: Techniques and First Results”, The Astronomical Journal 110, 1131. Quillen, A.C., Frogel, J.A., Kuchinski, L.E., & Terndrup, D.M. 1995, “Multiband Images of the Barred Galaxy NGC 1097” , The Astronomical Journal. 110, 156.
Research Publications (unrefereed abstracts)
Kuchinski, L.E., Terndrup, D.M., Witt, A.N., & Gordon, K.D. 1996 “The Impact of Dust on Photometric Studies of Spiral Galaxies”, Bulletin of the American Astro nomical Society, 28, no.4, 1303.
Kuchinski, L.E. & Terndrup, D.M. 1995, “Infrared Photometry and Dust Absorption in Edge-On Spiral Galaxies”, Bulletin of the American Astronomical Society, 27. no.4, 1353.
Kuchinski, L.E. & Terndrup, D.M. 1995, “Infrared Photometry and Dust Absorption in Edge-On Spiral Galaxies”, New Extragalactic Perspectives in the New South Africa, ed. D.L. Block &: J.M. Greenberg, (Dordrecht: Kluwer), 178.
Fields of Study
Major Field: .A.stronomy
Studies in: .■Vttenuation Eflfects in Spiral Galaxies Prof. D.M. Terndrup Near-Infrared Studies of Globular Clusters Prof. .LA. Frogel Spiral Galaxy Structure and Formation Prof. D.M. Terndrup
VI TABLE OF CONTENTS
Page
A b stra c t ...... ii
Acknowledgments ...... iv
V i t a ...... V
List of T a b le s ...... ix
List of Figures ...... x
Chapters:
1 Introduction ...... 1
1.1 Interstellar Dust and Relevant Physical Processes ...... 1 1.2 Implications of Dust for Photometric Studies of Spiral Galaxies . . 5 1.3 Previous Studies of Opacity and .Atténuation Eflfects inSpirals . . . 6 1.4 Overview of this thesis ...... 11
2 Acquisition and Reduction of D a ta ...... 14
2.1 The S a m p le ...... 14 2.2 O b se rv a tio n s ...... 15 2.3 Near-Infrared D ata Reduction ...... 16 2.4 Optical Data Reduction ...... 19 2.5 Photometric Calibration of the Near-Infrared D ata ...... 19 2.6 Photometric Calibration of the Optical D ata ...... 21 2.7 Optical and NIR Color Maps and Profiles ...... 22
3 Radiative Transfer Models ...... 35
3.1 Simple Slab Models ...... 38 3.2 Numerical Models with Spherical G eom etry ...... 39
vii 3.3 Disk Galaxy M o d e ls...... 41
4 Comparison of Galaxy Colors to Model Predictions ...... 49
4.1 M e th o d ...... 49 4.2 Comparison of Data to Slab and Spherical Models ...... 51 4.3 Disk Radiative Transfer Model Comparisons ...... 54
5 Estimates of the Optical Depth through Spiral Galaxies ...... 98
5.1 Optical Depths from Slab and Spherical M odels ...... 98 5.2 Optical Depths from Disk Radiative Transfer M odels ...... 100 5.3 Uncertainties in Optical Depth Estimates ...... 102 5.4 .A.re Spiral Disks O paque? ...... 105 5.5 Implications for the Study of Spiral Galaxies ...... 107
6 Conclusions ...... 117
6.1 Summary of T h e sis ...... 117 6.2 Future Directions ...... 121
Bibliography ...... 124
Vlll LIST OF TABLES
Table Page
2.1 Sample galaxy properties and log of observations ...... 25
2.2 Comparison to published JHK aperture photometry ...... 26
2.3 Comparison to published BVRI aperture photometry^ ...... 27
3.1 Properties of dust grains in radiative transfer models ...... 43
4.1 .A.dopted Unreddened Bulge Colors ...... 60
5.1 Line-of-sight optical depths in galaxy dust lanes from slab and spher ical radiative transfer models 109
5.2 Face-on central optical depths from disk radiative transfer models. . . 110
IX LIST OF FIGURES
Figure Page
2.1 /-band images of the sample galaxies, shown on a logarithmic intensity scale. Galaxy types and inclinations are given above each image. . . . 28
2.2 Magnitude residuals for photometric calibration of the near-infrared data, in the sense standard values on the CTIO/CIT system minus our values ...... 29
2.3 Magnitude residuals for the photometric calibration of the 1995 opti cal data, in the sense standard values on the .Johnson-Kron-Cousins system minus our values ...... 30
2.4 Minor axis B — V color profiles for sample galaxies. Errorbars represent uncertainties due to photon statistics; they do not include calibration errors. Galaxy inclination angles are given at the lower right corner of each panel ...... 31
2.5 Minor axis V — I color profiles for sample galaxies. Errorbars represent uncertainties due to photon statistics; they do not include calibration errors. Galaxy inclination angles are given at the lower right corner of each panel ...... 32
2.6 Minor axis V —K color profiles for sample galaxies. Errorbars represent uncertainties due to photon statistics; they do not include calibration errors. Galaxy inclination angles are given at the lower right corner of each panel ...... 33
2.7 Minor axis J — K color profiles for sample galaxies. Errorbars represent uncertainties due to photon statistics and sky noise; they do not include calibration errors. Galaxy inclination angles are given at the lower right corner of each panel ...... 34
X 3.1 Dust-star geometries in simple plane-parallel models ...... 44
3.2 Extinctions and color excesses as a function of V'-band optical depth for slab and spherical radiative transfer models with different dust-star geometries ...... 45
3.3 Dust-star geometries in the radiative transfer models of VVTC92. . . 46
3.4 Components of disk galaxy radiative transfer models from Witt et al. (1997)...... 47
3.5 Fraction of observed light that has been scattered into the line of sight as a function of wavelength for models from WTC92 ...... 48
4.1 Comparison of our adopted unreddened bulge colors to spiral bulge colors from Peletier & Balcells (1996) ...... 61
4.2 Color-color diagrams for IC 2531 minor axis colors and reddening tra jectories for slab and spherical radiative transfer models ...... 62
4.3 Color-color diagrams for NGC 3390 minor axis colors and reddening trajectories for slab and spherical radiative transfer models ...... 63
4.4 Color-color diagrams for NGC 1886 minor axis colors and reddening trajectories for slab and spherical radiative transfer models ...... 64
4.5 Color-color diagrams for ESQ 489-29 minor axis colors and reddening trajectories for slab and spherical radiative transfer models ...... 65
4.6 Color-color diagrams for NGC 3717 minor axis colors and reddening trajectories for slab and spherical radiative transfer models ...... 66
4.7 Color-color diagrams for IC 2469 minor axis colors and reddening tra jectories for slab and spherical radiative transfer models ...... 67
4.8 Color-color diagrams for NGC 1515 minor axis colors and reddening trajectories for slab and spherical radiative transfer models ...... 68
4.9 Color-color diagrams for A 0908-08 minor axis colors and reddening trajectories for slab and spherical radiative transfer models ...... 69
XI 4.10 Color-color diagrams for NGC 2613 minor axis colors and reddening trajectories for slab and spherical radiative transfer models ...... 70
4.11 Color-color diagrams for NGC 1888 m inor axis colors and reddening trajectories for slab and spherical radiative transfer models. Only the minor axis colors for the obscured side of the galaxy are shown; there is a close companion near the unobscured side ...... 71
4.12 Color-color diagrams for NGC 1589 minor axis colors and reddening trajectories for slab and spherical radiative transfer models ...... 72
4.13 Color-color diagrams for NGC 1325 minor axis colors and reddening trajectories for slab and spherical radiative transfer models ...... 73
4.14 Color-color diagrams for NGC 1055 minor axis colors and reddening trajectories for slab and spherical radiative transfer models ...... 74
4.15 Color-color diagrams for NGC 1964 minor axis colors and reddening trajectories for slab and spherical radiative transfer models ...... 75
4.16 Color-color diagrams for NGC 2713 minor axis colors and reddening trajectories for slab and spherical radiative transfer models ...... 76
4.17 Variations in disk radiative transfer model reddening trajectories as a function of inclination angle for B/D = 0.50, rv,o = 2.0, and homoge neous dust ...... 77
4.18 Variations in disk radiative transfer model reddening trajectories as a function of bulge-to-disk ratio (B/D) for i = 80°, rv = 2.0, and homogeneous dust ...... 78
4.19 NGC 1886 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 90°, B /D = 0.20, and rv,o = 0.5. . 79
4.20 NGC 1886 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 90°, B/D = 0.20, and rv.o = 10. . 80
X ll 4.21 NGC 1886 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 90°, B /D = 0.20, and rv,o = 2.0. . 81
4.22 NGC 1886 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 90°, B /D = 0.20, and ry,o = 4.0. . 82
4.23 NGC 1886 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 90°, B /D = 0.20, and rv,o = 10.0. . 83
4.24 NGC 3390 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 90° and B/D = 0.50 ...... 84
4.25 IC 2531 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 90° and B/D = 0.50 ...... 85
4.26 ESO 489-29 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 85° and B/D = 0.40 ...... 86
4.27 NGC 3717 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 85° and B/D = 0.50 ...... 87
4.28 IC 2469 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 80° and B/D = 0.50 ...... 88
4.29 NGC 1515 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 80° and B/D = 0.40 ...... 89
4.30 A 0908-08 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 80° and B/D = 0.50 ...... 90
xm 4.31 NGC 2613 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 75° and B/D = 0.20 ...... 91
4.32 NGC 1888 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 80° and B/D = 0.30. Only the minor axis colors for the obscured side of the galaxy are shown; there is a close companion near the unobscured side ...... 92
4.33 NGC 1589 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 80° and B/D = 0.40 ...... 93
4.34 NGC 1325 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 75° and B/D = 0.10 ...... 94
4.35 NGC 1055 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 75° and B/D = 1.00 ...... 95
4.36 NGC 1964 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 70° and B/D = 0.10 ...... 96
4.37 NGC 2713 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 70° and B/D = 0.75 ...... 97
5.1 Reddening produced by changes in age (points in left-hand panels) and metallicity (points in right-hand panels) compared to slab and spheri cal radiative transfer model reddening trajectories (same line types as in Figures 4.2-4.16.) ...... I l l
5.2 Reddening produced by changes in age (points in left-hand panels) and metallicity (points in right-hand panels) compared to disk radiative transfer model reddening trajectories (solid lines) ...... 112
XIV 5.3 Color-color diagrams for IC 2531 minor axis colors (points) and disk model reddening trajectories (lines) assuming a metallicity gradient similar to that of the Milky Way bulge. The model has i = 90° and B /D = 0.50...... 113
5.4 Maximum J — K color excess in cuts across the dust lane as a function of distance of that cut from the galaxy center (along the major axis). 114
5.5 Color-color diagrams for IC 2531 minor axis colors (points) and red dening trajectories for models that are optically thick over most of the disk (lines) ...... 115
5.6 Radial color gradients across face-on disk radiative transfer models and spiral galaxy radial color gradients from de Jong (1996a). Solid lines represent de Jong’s data, dashed lines are color gradients for a model with rv,o = 2.0. and dotted lines are gradients for a model with W,o = 1.0. The models have clumpy dust, z = 0°, and B/D=0.30. . . 116
XV CHAPTER 1
INTRODUCTION
1.1 Interstellar Dust and Relevant Physical Processes
Interstellar dust consists of tiny (< l^m) solid grains found mixed with gas in the space between stars in a galaxy. Together, the dust and gas comprise the interstellar
medium (ISM). The existence of dust in the Milky Way Galaxy was first demonstrated conclusively by R.J. Trumpler (Trumpler 1930), who determined that the relationship between the distance to a star cluster and its apparent brightness was being affected by absorption occurring somewhere between the cluster and the sun. Trumpler also observed that the amount of absorption as a function of wavelength was inversely proportional to the wavelength itself, suggesting that the absorbing material consists of solid particles with size about equal to the wavelength of visible light (Whittet
1992). In external spiral galaxies, the presence of absorbing material was thought to be responsible for the dark lanes observed in systems viewed edge-on {e.g.,, Curtis
1918). Based on spectral studies of the light absorbed and emitted by dust grains and on measured element depletions in interstellar gas with respect to solar abundances, these dust particles are believed to consist mainly of silicates, carbon-rich materials. and graphite (Mathis 1990; Whittet 1992). The most likely origin of dust grains is in
the extended atmospheres of evolved stars, where temperatures and densities favor
the formation of solid particles and stellar winds transport these particles out into
the interstellar medium (Whittet 1992). Although dust grains contribute only a tiny
fraction of the mass of a typical galaxy, they play a significant role in determining the
radiative transfer of stellar light through the ISM (Whittet 1992.) The role of dust
in altering the emitted stellar light from galaxies is the subject of this thesis.
The primary physical processes by which dust affects continuum light from stars
and galaxies are absorption and scattering of stellar light and re-radiation of the
energy absorbed by dust grains. Emission by dust grains of the energy they have
absorbed is not an important contributor to the optical and near-infrared (NIR) light
used to study the stellar component of galaxies and thus will not be considered in
this thesis. (This emission typically peaks at far-infrared wavelengths (A > 30/j.m),
with some contribution to the mid-infrared light (5^m < A < 30^m) from non
equilibrium heating of very small grains (Sellgren 1984; Whittet 1992).) .Absorption
and scattering of the stellar light are together referred to as attenuation because the
net effect of a dusty medium is most often to diminish the energy of light passing
through it. In order to determine quantitatively the attenuation of incident light as a function of frequency or wavelength, it is necessary to solve the radiative transfer equation:
dit, where is the intensity of light, ds is the path length, is the absorption coefficient and jj, is the emission coefficient. Loss of light from the line of sight is represented in the absorption term, while sources of light are taken into account by the emission term.
At optical and NIR wavelengths, the primary effect of dust is to remove light from the line of sight, a process referred to as extinction. Photons traveling through in terstellar dust may be absorbed by dust grains with a probability determined by the wavelength of the photon and the size and chemical composition of the dust grain.
Alternatively, photons may be scattered off dust particles, again with a probability dependent on wavelength and grain properties, and thus redirected out of the original line of sight. We define the extinction optical depth, denoted as r, to be a dimension- less parameter that gives the probability of a photon suffering from extinction while traversing a given path length:
dr^ -- at,ds
Photons will likely escape a medium with r
^ = - c + s, cLT i/ where = y„/o„ is called the source function. The extinction optical depth r can be used to express the ratio of observed light to incident light I^q '.
■ p = f{ru) where the function /(r^) depents on the relative geometry of light sources and dust and the frequency or wavelength dependence of r incorporates the dust grain proper ties (Whittet 1992). The wavelength dependence of is called the extinction law and appears to be similar for many lines of sight in the Milky Way and nearby galaxies at optical and NIR wavelengths (Mathis 1990).
In addition to its role in extinction, scattering contributes to the emission term or source function in the radiative transfer equation when light emitted in directions away from the line of sight is scattered off dust grains into the line of sight. The term will depend on the likelihood of a photon being scattered and the direction in which it is likely to be scattered. The former probability is parameterized by the grain albedo:
^ ^scattering
^extinction where Qscattering Is the scattering efficiency of dust grains and ^extinction, the extinction efficiency, is the sum of absorption and scattering efficiencies ( (^absorption 4- ^scattering)
(Whittet 1992). Thus an albedo of zero indicates a purely absorbing grain, while an albedo of one indicates pure scattering. The probable direction of scattering is parameterized by the phase function asymmetry g:
g = < cosd > where 6 is the angle between the directions of the incoming and outgoing (scattered) photon (Whittet 1992). If the dust grains scatter light isotropically, g = 0: values of g between 0 and 1 indicate forward-directed scattering. Like the optical depth r, both the albedo and phase function asymmetry depend on wavelength, grain size distribution, and chemical composition. The total amount of light scattered into the line of sight in a galaxy also depends sensitively on the relative geometric distributions of dust and stars (Witt et al. 1992; Witt & Gordon 1996). 1.2 Implications of Dust for Photometric Studies of Spiral Galaxies
It is desirable to understand the magnitude and wavelength-dependence of attenua tion effects in spiral galaxies because the modification of stellar light by dust com plicates many techniques used to analyze broad-band images. Several recent works have demonstrated the importance of correctly treating attenuation effects. Dust obscuration in optical images is known to hide morphological features such as bars and inner rings and produces a generally patchy appearance that makes it difficult to measure feature strengths like the amplitudes of spiral arms {e.g., Heraudeau et al. 1996; Knapen et al. 1995; Rix & Rieke 1993; Quillen et al. 1995). While surface brightness profiles can be fit to obtain parameters such as disk scale lengths, the pres ence of dust makes these measurements sensitive to wavelength (Byun et al. 1994;
Evans 1994; Peletier et al. 1995). Studies of color gradients to infer changes in stellar populations are extremely sensitive to dust: it is difficult to disentangle attenuation effects from the reddening produced by increased stellar age or higher metallicity
{e.g., Peletier & Balcells 1996). de Jong (1996a) uses color-color plots to compare galaxy color profiles to those predicted by stellar population models and radiative transfer models, but Witt et al. (1992, hereafter WTC92) show that the behavior of colors in these plots as optical depth increases depends sensitively on the adopted dust geometry and the treatment of scattering. The use of surface photometry to es timate galaxy mass distributions and understand the dynamical influences of various structural components implies a knowledge of the mass-to-light (M/L) ratio, usually assumed to be constant in the NIR. However Jansen et al. (1994) and Kuchinski &: Terndrup (1996) find .4k- ~ 0.25 — 0.3 in the dust lanes of highly inclined galaxies,
which implies that only 75-80% of the /v-band light from these regions escapes along
the line of sight on which it was emitted and therefore the local mass density will
be underestimated. Light blocked by dust can also exacerbate disagreements with
kinematical mass estimates and thus suggest the presence of more dark matter than
is actually required to explain the rotation curve (Barnaby & Thronson 1994). Op
tical depth effects may complicate kinematical studies: spectra taken across a dust
lane at wavelengths in which the dust is optically thick will show stellar motions in an outer layer of the disk rather than near the center (Bosma et al. 1992, Bureau &
Freeman 1997). Because highly inclined spirals are valuable sources of information about the structure, kinematics, and stellar content of spiral bulges and their relation to the disk component, it is critical to understand attenuation effects even in the high opacity dust lanes of these systems. .Although in principle one can also study these basic galaxian properties with spectral data, which are less susceptible to attenuation effects, it is far more efficient to obtain broad-band images than spectra for large samples of galaxies and/or for very distant systems.
1.3 Previous Studies of Opacity and Attenuation Effects in Spirals
The optical depth through spiral galaxies has been a subject of considerable con troversy in recent years. .A. significant factor contributing to ambiguous results in extinction studies is that neither the quantity of dust nor its distribution with re spect to the stellar component is precisely determined for spiral galaxies. However, the discussion in the previous section clearly indicates the critical need for further
quantitative study of attenuation effects. A suitable representation of the dust should
be able to explain the observed extinction and reddening over a long spectral baseline
in order to facilitate the use of broad-band colors in studies of spiral galaxies.
While the traditional view stated by Holmberg (1958), de Vaucouleurs (1959)
and Heidmann et al. ( 1972a,b,c) is that face-on spiral disks are optically thin, or
transparent, several recent works claim that these systems behave as though they are
optically thick even out to the Holmberg radius D 2 0 and thus that only the outer
layers of stars are observable (Valentijn 1990, Burstein et al. 1991, Choloniewsky
1991). All of these conclusions are drawn from statistical tests of parameters such as
galaxy surface brightnesses and isophotal diameters versus inclination: in the optically
thin case a galaxy has higher surface brightness and larger D 2 0 at high inclination,
while optically thick galaxies have the same surface brightness and isophotal diameter
at any orientation (Huizinga 1995). Yet more recent statistical studies of surface
brightnesses by Huizinga & van Albada (1992). Giovanelli et al. (1994), and Burstein
et a/. (1995) reaffirm the view that face-on spirals are mostly transparent. Boselli
k. Gavazzi’s (1994) statistical analysis of the behavior of galaxy integrated colors
with inclination suggests average V'-band optical depths of 1.0 to 1.8, just barely optically thick. Huizinga (1994) finds that his sample of spirals must be opaque in their central regions but optically thin on the outer parts in order to explain his results that total magnitudes get fainter and diameters increase at increasing inclination angles. Trewhella’s (1997) statistical analysis of luminosity functions suggests that on average, spirals are optically thick in blue light and would have a peak B-band central optical depth of ~ 2.5 when viewed face-on assuming that the dust is distributed in an exponential disk. Several reasons have been proposed to explain the ambiguities
in results of these tests, including selection effects {e.g., Davies 1990, Huizinga k. van
Albada 1992), significant contributions of light from the bulge (Davies 1990), and
the fact that because both extinction and emission are highest in spiral arms, these
optically thick regions dominate the overall appearance of the galaxy (White k Keel
1992). Further complications have been discussed by Disney et al. (1989) and Jones
et al. (1996), who find that properties of realistic star and dust distributions cause
galaxies to behave as if they are optically thin in these statistical tests regardless of
the true opacity of their dust layers.
In light of the confusing results of statistical tests, recent approaches have focussed
on individual galaxies and have used a variety of techniques to determine the opacity.
W hite et al. (1996a, 1996b, see also White k Keel 1992) and Beriind et al. (1997)
investigate overlapping galaxy pairs and find that while dust lanes associated with
spiral arms are opaque, face-on disks in general are transparent over most of their
surfaces. Ronnback k Shaver (1997) find the foreground spiral of another overlapping galaxy pair to be optically thin even as close as half a disk scalelength from the center.
However, James k Puxley (1993) find evidence from the Balmer decrements of HII
regions that the foreground spiral in one of the White et al. (1996a) pairs is optically
thick in B-band as far as two disk scale lengths from the center. Trewhella (1997) calculates extinctions and optical depths for the face-on spiral NGC 6946 and finds that the data do not necessarily rule out the possibility that much of the disk is optically thick. Sodroski et al. (1997) analysis of the COBE DIRBE maps suggest that the Milky Way would have a B-band optical depth ranging from ~ 0.5 —1.2 over the disk if it were observed face-on. Studies of asymmetries in the light distribution
8 of highly inclined galaxies suggest that if seen face-on, these systems may be optically
thick in their central regions but not at large radii (Jansen et al. 1994; Byun 1993)
Evidence from the ratios of galaxy disk scalelengths at different wavelengths (Peletier
et al. 1995; van Driel 1995), fitting radiative transfer models to individual galaxy light
distributions (Kylafis & Xilouris 1996; Kylafis & Bahcall 1987), and the behavior of
optical rotation curves (Bosma et al. 1992) all support the view that face-on spiral
disks are mostly transparent. Clearly a coherent picture of spiral galaxy opacity is yet to be obtained.
.A. third approach to the problem has been to study numerical models of radia
tive transfer through systems that resemble spiral galaxies. Models for plane-parallel and spherically symmetric geometries predict that the amount of dust needed to produce a given reddening depends sensitively on whether the dust lies in front of the luminosity sources or is mixed with them in various ways (Jansen et al. 1994;
WTC92). Plane-parallel and spherical geometry models including scattering effects demonstrate that light scattered into the line of sight partially compensates for ab sorption and reddening, thus reducing extinction effects (WTC92; Bruzual et al.
1988). The plane-parallel models of Bruzual et al. (1988) predict that attenuation corrections are strongly dependent on disk inclination only for optically thin disks.
These authors conclude that the lack of inclination dependence in Kent’s (1986) sur face brightness profiles suggests spirals are optically thick (Bruzual et al. 1988).
Radiative transfer calculations for systems consisting of a bulge, a disk, and a disk absorbing layer show that the observed extinction depends on both the optical depth in dust and the structural parameters of the absorption layer (Kodaira & Ohta 1994;
Ohta Kodaira 1995). Similar calculations by Byun et al. (1994), which include the effects of scattering, find that while disk scale length ratios (at different wavelengths) and color gradients are sensitive diagnostics of the opacity in spirals, central surface brightnesses are not. Bianchi et al. (1996) model both attenuation and polarization for spiral galaxy geometries with scattering; they confirm previous results about the role of scattering in reducing the observed extinction and find the amounts of extinc tion and polarization to be only loosely correlated. Models of the sort described here are powerful tools to study opacity in spirals because they use realistic treatments of geometry- and dust grain properties to predict trends in observable parameters that can be compared to galaxy data.
Most previous comparisons of spiral galaxy light distributions and colors to ra diative transfer calculations have used models with simplifications that may not be physically plausible. The studies of Bruzual et al. (1988) and Jansen et al. (1994) represent spiral disks as plane-parallel slabs of uniformly mixed dust and stars rather than having an exponential distribution of stars and a layer of dust that is thinner than the stars, as is observed in many edge-on spiral galaxies {e.g., Ohta & Kodaira
1995; Kylafis & Bahcall 1987; Kylafis &: Xilouris 1996; Wainscoat et al. 1989). Many authors {e.g., Evans 1994; Kodaira &: Ohta 1994; Disney et al. 1989) neglect scatter ing in order to reduce computational requirements. Others model pure disks but do not include the bulge component, which may contribute a great deal of light in the central regions of the galaxies and appears behind a large part of the dusty disk in highly inclined systems {e.g., Disney et al. 1989; de Jong 1996a).
10 1.4 Overview of this thesis
The goal of this thesis is to provide a framework for quantitative understanding of opacity and attenuation effects in spiral galaxies. Multicolor BVRIJHK data for
15 highly inclined spiral galaxies are compared to several different radiative transfer models to investigate the wavelength-dependence of attenuation effects and to predict the line-of-sight and face-on optical depths through the systems. By making use of a long spectral baseline from B to K bands, we study the effects of dust on colors and investigate whether or not the models predict a reasonable effective extinction curve, or more properly an attenuation curve, over optical and NIR wavelengths. The investigation is carried out via the following procedures:
• Explore the usefulness of different radiative transfer models to describe the atten uation of stellar light by dust in the optical-NIR wavelength regime. The models differ from each other in the relative geometric distributions of dust and stars and the treatment of physical processes such as absorption and scattering. They range in sophistication from analytical representations with simple dust-star geometries and pure absorption to numerical calculations that include exponential disk geometries for dust and stars, exponential bulge components, and the effects of scattering and dumpiness in the dust distribution. Through this investigation we aim to identify the required characteristics of a model that could be used to measure and correct for these effects in broad-band images and color maps of spiral galaxies.
• Use a radiative transfer model with the required characteristics (determined as described above) to constrain the V'-band optical depth through spiral galaxies. Note that we will select a single class of models (with a range of optical depths) to describe
11 all galaxies in the sample rather than try to solve the radiative transfer problem separately with different parameters for each galaxy. This part of the study will investigate the range of optical depths typically seen in intermediate and late-type spirals and will shed light on the controversy over the transparency of disk galaxies.
• Investigate quantitatively uncertainties in the studies of both attenuation and stellar populations that are introduced by degeneracy in their effects on broad-band colors.
Implications of the optical depth values derived here for studies of metallicity and age gradients in spiral galaxies will be given particular attention.
Our general approach of applying one class of models to 15 galaxies complements both the statistical approach, which requires a large and carefully selected sample, and the detailed modeling of individual galaxies, in which many parameter values must be redetermined for each specific case and computational requirements may be substantial {e.g., Kylafis & Xilouris 1996).
The organization of this thesis is as follows: Chapter 2 describes the galaxy sample and the acquisition and reduction of the data. Chapter 3 contains details of the various radiative transfer models with which the data are compared. Detailed comparisons of the reddening observed in galaxy dust lanes to that predicted by the models are presented in Chapter 4. In Chapter 5, the models are used to constrain the V'-band optical depth through these galaxies and uncertainties in the derived values of ry are discussed in some detail. Implications of the optical depth results for future studies of spiral galaxies are also included in Chapter 5. Chapter 6 highlights the main conclusions of the thesis and presents some possible directions for future study.
12 Portions of the material in this thesis were previously published as: Kuchinski,
L.E. & Terndrup, D.M. 1996, “Infrared Photometry and Dust Absorption in Highly
Inclined Spiral Galaxies”, The Astronomical Journal, 111, 1073.
13 CHAPTER 2
ACQUISITION AND REDUCTION OF DATA
2.1 The Sample
Our sample consists of 15 highly inclined galaxies with prominent dust lanes or fea tures in which to study attenuation effects. Because this sample was originally se lected to study spiral bulge morphology' and stellar populations in late-type galaxies, we included eight galaxies that have been identified in the literature as having boxy or peanut-shaped bulges (Jarvis 1986; de Souza & dos Anjos 1987; Shaw et al. 1990)
The remaining seven were selected from the Third Reference Catalogue of Bright
Galaxies, hereafter the RC3 (de Vaucouleurs et al. 1991), to span a similar range of inclinations, absolute magnitudes, and major-axis dimensions as the boxy-bulge sys tems. The galaxies have Hubble types in the range Sab through Sc and inclinations of i > 65° to facilitate study of the bulge component. (Inclinations are estimated from the formula given by Bottinelli et al. 1983: cos^i = — go)/(l ~ 9o)’ where q is the observed axis ratio 6/a, — log % = 0.60 H- 0.045T, and T is the Hubble type parameter.) They range in distance from 10 to 50 Mpc, (calculated using velocities from the RC3 and Hg = 75 km/s/Mpc), yielding a scale of 50 to 250 pc/pixel on
14 our images. Some of these systems exhibit sharp dust lanes through or near their
centers, while in others, dust obscures one entire side of the bulge. Most have enough
reddening in the dust features to see color changes even in the NIR, which allows
us to extend the analysis over a large wavelength range. The basic properties of the
sample galaxies are given in Table 2.1. Greyscale images of our /-b an d data for these
galaxies are shown in Figure 2.1.
2.2 Observations
Near-infrared [JHK] images of the bulge and inner disk regions of sample galaxies
were obtained from 20-21 and 27-31 December 1993 with the Ohio State Infrared
Imager and Spectrograph (OSIRIS) on the 1.5 m telescope at CTIO. Details of the
instrument are described by DePoy et al. (1993). OSIRIS has a 256 x 256 NICMOS
3 array detector and was employed in its wide-held mode, which yielded a field of
view of 4.5' at a scale of % 1.1 arcsec pixel" .A.11 observations were obtained under photometric conditions.
We observed each galaxy using an alternating sequence of sky and on-source po sitions. The sky and galaxy frames were taken with positional dithering so that bad pixels in the array could be filtered out when the frames were combined. Exposure times were set to % 4.9 sec in each filter, so that the count level of the sky plus galaxy nucleus was always less than half the saturation level of 32,000 counts. For these exposure times, the typical sky levels in the J, H, and K filters were 1000, 1500, and
5000 counts respectively. The total integration time on the sky was approximately
2/3 of the total time on the source; sky observations were made at intervals of 90 s
15 during the galaxy observations. Table 2.1 gives the total on-source integration times
for each galaxy in each filter.
BVRI broad-band images of the sample galaxies were obtained on 22-24 Decem
ber 1993 and 24-25 January 1995 at CTIO using the 0.9m telescope in direct imaging
mode. A Tek 1024^ CCD detector with a platescale of 0.40 arcsec/pixel was used
in 1993, and a Tek 2048^ detector with a platescale of 0.39 arcsec/pixel was used in
1995. All of the observations were obtained under photometric conditions. During
each night, multiple twilight sky frames were obtained in each filter to use as flatfields.
The total exposure times for each galaxy are given in Table 2.1.
2.3 Near—Infrared Data Reduction
We performed all steps in the JHK data reduction using the VIST.A. package (Stover
1988). The first step was to apply a linearity correction to each raw data frame,
which was a quadratic polynomial in pixel intensity amounting to less than 2 % at the
brightest typical exposure levels. .A.11 frames were then scaled to a common exposure
time using the true integration time for each exposure. The length of sequential
exposures in OSIRIS varies by % 0.1 s. OSIRIS records the exact exposure time
for each image, storing it as the value of a designated pixel. The extraction of the
exposure time was performed before the linearity correction.
We obtained multiple exposures of the nightly twilight sky in each filter to serve as
Hatfield corrections. .A zero-exposure bias frame was subtracted from each twilight sky
frame, then they were multiplicatively scaled to match intensity levels and combined.
Initial tests of the flatfields did not yield satisfactory results because there were small.
16 but significant, amounts of scattered light on one part of the detector. We corrected for this scattered light using multiple observations of a standard star on a grid of positions over the detector. We then fit a quadratic surface to the difference between the instrumental magnitude of the star at each point on the grid and the average instrumental magnitude measured on the unaffected parts of the detector. The r.m.s. residual in the photometry after correction with the polynomial was 3%: this was only slight larger than the scatter (2.5%) measured from observations of photometric standards (see Section 2.5), suggesting that the corrected flat fields were good to about 1%. Subsequent tests of the constancy of the sky level on the galaxy frames indicated that the accuracy of the flattening process was significantly better than this
(below).
We created average sky frames for each sequence of galaxy observations from the sky exposures which immediately preceded and followed the galaxy frames. These were combined using a median operation to remove stellar images. The appropriate average sky frame was subtracted from each galaxy frame, which effectively removed not only the sky emission but also the dark current and some gross additive features caused by scattered light. The sky-subtracted frames were then divided by the cor rected twilight flat fields and multiplied by a bad pixel mask to remove recurring bad pixels from subsequent analysis. To retain the correct count levels for error calcula tions, a constant equal to the mean of the subtracted sky frame was added back onto each galaxy frame. Note that the mean of the subtracted sky frame is not necessarily identical to the sky value on the galaxy frame because sky levels can fluctuate rapidly in the NIR. Determination of a sky value to subtract from the final processed galaxy image is discussed below.
17 All the frames for an individual galaxy were then aligned to a single reference position using the centroids of 3 to 4 bright stars on the frames. No rotation or difference in scale between the J, H, and K images was evident in a comparison of stellar centroids, so only row and column shifts were required. The alignment was performed using bilinear interpolation with masked bad pixels excluded from the calculation. Tests of the alignment routine using artificial stars showed slight smoothing in the direction of the shift but no significant change in the full width at half maximum (FWHM) of the stellar point spread function. The aligned galaxy frames were additively scaled to match the sky levels, then combined using a weighted average based on the photon statistics and detector read noise. At each pixel position, individual pixel values that were more than 5cr from the mean of all others in the stack were rejected from the calculation.
The final reduction step before photometric calibration was to determine and subtract an accurate sky value for each galaxy image. None of the galaxies fill the frames and most have only a few bright stars in the field. Thus we could determine the overall sky level by averaging the modal sky values taken in four different boxes on blank regions of the frame. The r.m.s. scatter in the sky levels in different portions of the frame, which is a measure of the accuracy of flat fielding and scattered-light removal, were % 0.2% of the sky level at J and H (corresponding 21.1 and 20.7 mag arcsec"- respectively) and 0.1% at K (corresponding to 19.7 mag arcsec"-).
1 8 2.4 Optical Data Reduction
Reductions of the BVRI data were carried out using the IRAF and VISTA (Stover
1988) packages. All frames were corrected for readout bias (using the overscan),
trimmed, and zero-level bias subtracted. Twilight sky frames for each night in each
filter were multiplicatively scaled and median combined to produce a flatfield, then
each object frame was divided by the appropriate flatfield. Cosmic rays on the galaxy
frames were identified with the IRAF ccdred.cosmicrays package and were replaced
with an average of surrounding pixel values. For cases in which there was more than
one data frame for a galaxy, a zeropoint offset was applied to match the background
on all frames, then the images were averaged (for two frames) or median combined
(for three frames). The r.m.s. scatter in sky levels across the final reduced galaxy
frames was typically less than 0.5% of the sky value. Finally, the B, V', R. and I
images for each galaxy were aligned to the nearest pixel using the centroids of .3-4
bright stars. No rotation or difference in scale was evident between the images in the
four filters.
2.5 Photometric Calibration of the Near—Infrared Data
All of our calibrated magnitudes and colors are on the CTIO/CIT system. Because
nearly all of the faint Elias et al. (1982) CTIO/CIT standards were too bright to be observed with OSIRIS, we observed the faint UKIRT standards (Casali & Hawarden
1992). We then converted these onto the CTIO/CIT system using the transformation of Casali &: Hawarden (1992). The UKIRT standards do not span a large enough range in color to determine the color term between OSIRIS and the CTIO/CIT system,
19 so we determined a color term from observations of the IR standards of Carter &
Meadows (1994) and red stars in the Coalsack obtained on 26 and 28 January 1994
at CTIO with the same telescope and instrumental set-up (Jones et al. 1980; Ali
1995).
Holding the color term (derived above) fixed, we obtained zero points, airmass
terms, and where appropriate, a UT term for each night of our galaxy observations.
•A.lthough all nights were photometric, software problems on the first two nights of the
run resulted in an inaccurate record of exposure times. Snapshots of galaxies observed
on these two nights were taken later in the run and used for calibration. The airmass
terms on the remaining five nights did not varv' significantly and weather conditions
were relatively constant, so we used the same average airmass term on all nights. The
transformation equations for each night are of the form:
K = k + 0.011( J - K) + Cl - 0.054A'
J-K = 0.952(j-A:) + C2-0.017A[+c*TT]
H - K = 0.894(/i - A:) + C3 + 0.014.Y where capital letters denote magnitudes on the CTIO/CIT system, small letters de note OSIRIS instrumental magnitudes, Ci, cg, and C 3 are the zero points, and X is the airmass. The zero points remained constant within the errors from night to night, and a UT term was required only on 28 December for the J filter. Figure 2.2 shows the residuals in K, J — /v, and H-K vs. color and magnitude for all nights. The r.m.s. residuals in the transformations are < 0.025 mag, which we take to be the error in the calibration.
2 0 We compared photometr\' in synthetic apertures on our calibrated images to pub lished aperture photometrj' available in the literature for several galaxies in our sample
(Aaronson et al. 1982; Devereux 1989; Aaronson et al. 1989; Bothun & Gregg, 1990).
Table 2.2 gives the differences in aperture magnitudes in the sense ours minus pub lished. Our photometry agrees with the previous values to within a few hundredths of a mag for most of the apertures larger than 10". Discrepancies in the large aperture
(> 10") photometry for NGC 2613 and NGC 3717 are likely due to difficulties in correcting for the presence of bright stars within the aperture. For apertures less that
10" in diameter, our photometry is consistently brighter than the aperture values.
Photometry in small apertures can be subject to significant seeing and alignment effects; Terndrup et al. (1994) also note disagreement between synthetic aperture measurements from arrays and single channel photometrj' for apertures < 10".
2.6 Photometric Calibration of the Optical Data
Calibrations of the BVRI frames were carried out using observations of standard stars from Graham (1982) and Landolt (1992). For each night, we determined a zeropoint, color term, and airmass term for each filter to serve as coefficients Cq, Ci, and C2 in transformation equations of the form:
B = 6 4- Cq + Ci(B - 1 ) 4 - C2 A
V = u 4- Co 4" Cl (B — 1)4" C2 A
R — r 4 - Cq 4" Cl (1 — R) 4" C2 AT
I = z "f" Co 4" Ci(V — /) 4" C2 A'
21 where capital letters denote magnitudes on the standard system, small letters denote instrumental magnitudes, and X is the airmass. Inspection of the residuals in these transformations, which are shown in Figure 2.3 for the 1995 data, showed no evidence for a dependence on UT or higher order color or airmass terms. We estimate the uncertainty in the calibration to be ~0.02 mag for the 1993 data and ~0.01 mag for the 1995 data based on the r.m.s. residuals in the transformations.
We compare our BVRI photometry for these galaxies to published aperture pho tometry by taking synthetic apertures centered on the apparent A'-band galaxy center
(determined from JHK data and transformed to optical coordinates as described be low). B and V photometry are taken from Longo & de Vaucouleurs (1983) and Frueh et al. (1996); VRI photometry is from Buta & Williams (1995) and Lauberts (1987).
Table 2.3 gives the differences in aperture magnitudes in the sense ours minus pub lished. In general, our photometry agrees with the published values to within a few hundredths of a magnitude. The serious discrepancy for .A. 0908-08 is probably due to the presence of a foreground bright star, which is severely saturated on our images.
Larger-than-average differences for NGC 2613 may be due to the presence of several moderately bright stars in the aperture; we did not attempt to remove these stars before calculating synthetic aperture magnitudes on our images.
2.7 Optical and NIR Color Maps and Profiles
In order to make optical and NIR color maps and profiles, it was first necessary to transform the coordinates of the optical galaxy images onto the coarser scale of the NIR data, align all images of an individual galaxy, and smooth all frames for
22 that galaxy to the same stellar FWHM. During prior stages of the data reduction
(see above), all of the optical images for a galaxy were aligned to the /-band image position and all of the NIR frames to the /C-band position. We used the centroids of
10-20 stars on the I and K images to determine a linear coordinate transformation
(scaling, rotation, and translation) between the optical and NIR data. The scaling and rotation coefficients of the transformation were determined separately for each galaxy and were found to be nearly identical for all galaxies observed with the same optical detector (the 1993 and 1995 data sets had different transformations to the NIR coordinates). We applied the transformation to the BVRI images and then measured stellar FWHM on all the galaxy frames. The images for each galaxy were smoothed by convolution with a circular gaussian to the largest FWHM for that galaxy, usually measured on the J image but occasionally on the B image.
-•Vfter the BVRIJHK images for each galaxy were aligned, smoothed, and cali brated in units of magnitudes arcsec"-, we made color maps by aligning the appropri ate pairs of images for each galaxy and computing the colors at each pixel. Minor axis color profiles were extracted assuming that the minor axis position angle is 90° from the major axis position angle given in the RC2. The galaxy center was determined from the //-band image to minimize the effects of dust, then colors were determined at one-pixel intervals on a cut through this center at the minor axis position angle.
Because the galaxy axes were not necessarily aligned with those of the detector, each point along the minor axis was not typically centered on a pixel. The color at each location was therefore taken as the average of surrounding pixels weighted by the distance of each pixel from the non-integer position at which the color is desired.
Errors on the colors were estimated from photon statistics, including sky noise from
23 the JHK images. These errors do not include uncertainties in the photometric cal
ibration. We note that in two cases we had to take profiles parallel to the minor
axis at a distance of ~ 5 arcsec from the center; A 0908-08 has a foreground star
that is severely saturated (with diffraction spikes) in our images and NGC 1964 has
a foreground star overlapping the center of the galaxy.
Color profiles for the sample galaxies are shown in Figures 2.4-2.7. The zero
position on the x-axis of each plot is the center of the galaxy as determined from the
i\-band image (see above). The color maps and profiles show distinct red features in
areas affected by absorption from dust in the disk, but the bulge colors in regions away
from the dust lanes and galaxy nuclei remain relatively constant. The most highly
inclined systems in our sample - NGC 1886, IC 2531, and NGC 3390 - have red dust
lanes along the major axis, bisecting the bulge. These dust lanes are identifiable as central peaks in the minor axis color profiles. In systems at slightly lower inclinations, such as NGC 1055, NGC 1589. and A0908-08, the red dust lane is displaced from the major axis and/or one side of the bulge appears to be reddened by disk dust.
The minor axis profiles of these galaxies show broad, off-center red peaks at the location of the dust lane. Galaxies at even lower inclinations, such as NGC 1325 and
NGC 2713, show very little reddening along the minor axis. The various dust lane signatures described here are seen quite clearly in the I ' — I and V' — K color profiles in Figures 2.5 and 2.6 and are noticeable but less dramatic in the J — K profiles of
Figure 2.7. The B — V color profiles shown in Figure 2.4 show the same features but tend to be noisy in very red regions due to low signal-to-noise on the B-band images, where there is simply not very much light due to absorption by the dust.
24 G alaxy Type" incl.*^ 0 r" log Dos r R / JHK N G C 105.3 SBb 72 11.40 1.88 25.0 18.0 18.0 18.0 9.75 9.75 11.67 NGC 1325 Sbc 73 12.22 1.67 20.0 15.0 15.0 16.0 9.75 9.75 11.67 NGC 1515 Sbc 82 12.05 1.72 20.0 15.0 15.0 16.0 9.75 9.75 11.67 N G C 1589 Sab 75 12.80 1.50 15.0 15.0 15.0 15.0 9.75 9.75 11.67 N G C 1886 Sbc 90 13.60 1.49 40.0 30.0 30.0 30.0 6.50 6.50 11.67 N G C 1888 SBc 77 12.83 1.48 23.0 18.0 18.0 18.0 9.75 9.75 11.67 N G C 1964 Sb 70 11.58 1.75 20.0 16.0 15.0 15.0 9.75 9.42 11.67 ESO 489-29 Sbc 90 13.33 1.47 15.0 15.0 15.0 15.0 9.75 9.75 13.67 NGC 2613 Sb 80 11.16 1.86 36.0 25.0 25.0 26.0 5.25 5.25 11.67 N G C 2713 SBab 68 12.72 1.56 20.0 15.0 15.0 15.0 9.75 9.75 11.67 .A 0908-08 Sb 81 11.91 1.63 16.67 16.67 16.67 16.67 9.75 9.75 11.67 IC 2469 SBab 85 — 1.67 20.0 15.0 15.0 16.0 6.50 5.25 11.67 IC 2531 Sc 90 12.90 1.84 60.0 30.0 30.0 32.0 9.75 9.75 11.67 NGC 3390 ' Sb 90 12.85 1.55 42.0 30.0 30.0 20.0 11.67 11.67 17.50 N G C 3717 Sb 88 12.24 1.78 23.0 15.0 15.0 15.0 9.75 9.75 13.67
“ D ata from the RC3.
‘ Inclinations in degrees estim ated from Equations I and 2 in Bottinelli el al. (1983).
" Log D-2S in units of 0.1 arcmin.
Total exposure time in minutes for each filter.
' Sandage & Bedke (1994) classify NGC 3.390 as either SO3 (SO with dust lane) or Sb. This is the only galaxy in the sample for which they give 2 classifications and which differs greatly from the RCZ classification.
Table 2.1: Sample galaxy properties and log of observations.
25 Galaxy Aperture “ AJ" AA" NGC 1055': 81.2 — -0.05 —
110.6 — -0.01 —
NGC 1325': 55.8 — -0.02 —
70.1 — -0.01 — NGC 1964':'' 3.6 — —0.05 -0.14 5.3 — --- -0.18 7.2 — --- -0.25 9.3 — -0.22 -0.29
53.4 — -0.03 —
81.2 — -0.10 —
105.0 — -0.05 — 110.6 — -0.10 — NGC 2613': 83.6 — -0.17 — 110.0 — -0.19 — IC 2531= 59.2 — -0.07 —
69.5 — -0.09 — NGC 3390/ 10.0 -0.18 -0.19 -0.20
NGC 3717= 50.4 — -0.15 — 81.2 — -0.15 —
“ Aperture diameter in arcsec.
* A mag in the sense (ours-published) .
^ Aaronson et al. 1982.
Devereux 1989.
® Aaronson et al. 1989.
^ Bothun &c Gregg 1990.
Table 2.2: Comparison to published JHK aperture photometry.
26 Galaxy Aperture** AV A{B - V) A{V - R) A{V - 1)
NGC 1055"': 33.0 0.04 0.04 ——
68.9 -0.09 -0.04 —— 154.0 —— 0.00 0.01 NGC 1325" 15.4 0.00 0.02 —— 92.9 -0.22 0.22 — — NGC 1515" 10.9 -0.03 0.00 ——
16.5 -0.09 0.02 — —
20.8 0.06 0.04 —— 44.5 0.02 -0.01 ——
NGC 1589" 48.8 -0.07 -0.03 —— 82.8 -0.05 0.00 —— NGC 1888" 31.5 -0.20 —0.08 —— 61.3 -0.17 -0.07 ——
NGC 1964" 31.5 0.05 0.02 ——
61.3 0.12 -0.01 ——
NGC 2613"'" 15.4 -0.47 0.14 —— 25.0 -0.93 0.29 ——
68.9 -0.53 0.11 ——
134.0 —— 0.24 -0.36
NGC 2713" 25.0 -0.04 0.03 —— 114.3 -0.44 0.07 —— NGC 3390"’^ 20.8 0.17 0.03 —— 41.5 0.07 0.02 ——
64.0 —— 0.20 0.06
NGC 3717"-'' 15.4 0.01 0.18 ——
23.3 0.06 0.11 ——
47.7 -0.01 0.02 ——
15.5 —— 0.00 0.05
22.9 —— -0.03 -0.01
31.2 —— -0.01 0.04
60.8 —— 0.00 0.06
A 0908-08" 261.9 -2.17 -0.50 ——
“ Aperture diameter in arcsec.
* BV photometry from Longo & deVaucouleurs 1983.
VRI photometry from Buta & Williams 1995.
VRI photometry from Lauberts 1987.
Table 2.3: Comparison to published BVRI aperture photometry.
27 IC 2531 Sc i=aO° IC 2469 SBab ^ 5° NGC 1589 Sab i=75' • • . •
NGC 3170 Sb (=90° NGC 1515 Sbc (=82‘ NGC 1325 Sbc (=73°
NGC 1886 Sbc é=90‘ A 0908-08 Sb (=81° NGC 1055 SBb ^72° ♦ V
ESO 489-29 Sbc (=90° NGC 2613 Sb (=80° NGC 1964 Sb (=70°
NGC 3717 Sb (=88° NGC 1888 SBc (=7T NGC 2713 SBab (=68‘
Figure 2.1: /-band images of the sample galaxies, shown on a logarithmic intensity scale. Galaxy types and inclinations are given above each image.
28 .1 1 1 1 1 1 M 1 1 1 1 1 i 1 1 1' r 1 j 1 1._p 1 i 1 1 1 1 n 1 1 II 1 T r 1 j 1 1 i_ .05 2 0 ÿ ...... 1 1 .• 1 J L « I , i ! : E E • !l ! : -.0. _1“1 M !1 1 1 1 1 M 1 1 1 1 1 I1 1M 1 ( ? rlM 1 1 I 1rul"I J 1 M1 1 1 I1 rr1 1 [1 1 1 1 j1 rrt1 I 1 [1 1 1 p i- L S ' 05 J, i l l 2 ° 1 l i i 3 2 -.05 — 1 ^ H H I1 1 1 j1 M1 1 1 1 I1 1 1 rt1 1 1 I1 rri1 1 1 1 i1 iT«1"I 1 1 I1 1 1! tI 1M ! 1 f1 1 1 ]1 Tt,1 ! ! ]1 1 1 L|-
- • t - - * . * ! * I * ' n1 0 'eo n ; L- : 1 ' • J 2 -.05 t j
“ I p 1 1 1 1 r 1 1 ! 1 1 r 1 i 1 1 1 1 1 1 r-1 1 1 1 p ! p 1 1 1 1 1 1 1 1 1 1 1 1 1 r 10 11 12 0 .2 .4 .6 .8 1 K J -K
Figure 2.2: Magnitude residuals for photometric calibration of the near-infrared data, in the sense standard values on the CTIO/CIT system minus our values.
29 1 1 1 M 1 1 1 1 M 1 1 IT 1 1 1 1 \ 1 l_- 1 1 I 1 1 1 1 1 1 1 1 1 1 _ .04 g .02 j: . . . Ï -•...... «.....• • * - 2m 0 -.02 L* • . i z_ # _z £ I • • I -.04 T 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ! |-- 1 1 1 1 1 1 ! 1 1 1 J 1 r I 1 1 1 M 1 1 1 II tTil t t IL^ 1 1 1 1 1 1 1 1 1 I 1 1 1 - .04
S ' .02 _ .....#,...... -3L * %.’.! • • • ,.-E - • • : V* #£ -.02° -.04 “ 1 I » t 1 1 1 1 1 1 1 I " T111 1 M rin1 1 1 I 1 1 1 1 M1 M 1 1 1 1 1 Lr_ 1 1 1 1 1 i pt 1 1 i 1 _ .04
.02 T . . Î, T ^ ^ ï 0 Êi...... :...... " ...... ' r : £ -.02 r h ' A f -. J E. • x* . *J -.04 T 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 III-- 1 1 1 1 r 1 1 1 1 1 1 1 1 - 12 13 14 15 16 0 .5 V B -V
Figure 2.3: Magnitude residuals for the photometric calibration of the 1995 optical data, in the sense standard values on the Johnson-Kron-Cousins system minus our values.
30 ci - 10 2531 90 IC 2469 85" -i-NGC 1589 75 KfhllH-lkHFhlII
•* *• t ci NGC 3390 90 NGC 1515 82 NGC 1325 73
ci -NGC 1886 90 A 0908-08 81 NGC 1055 72
k, . r - . i t e v ci 4 # i ^ ESC 489-29 90 NGC 2613 80 NGC 1964 70
ci NGC 3717 88' --I NGC 1888 77° - - NGC 2713 68°
I I I I I I I I I I I I I I I I I 1 1 I I I 1 1 I I I I I I 1 1 I I I M ill 11 1 1 I I I I I I I I I I I -10 G 10 -10 0 10 -1 0 G 10 r (arcsec) r (arcsec) r (arcsec)
Figure 2.4: Minor axis B — V' color profiles for sample galaxies. Errorbars represent uncertainties due to photon statistics; they do not include calibration errors. Galaxy inclination angles are given at the lower right corner of each panel.
31 -t 1111111'lmnrrrp rriTri 111 i-h 111'l 1111111 n 1111 t-H'i 11 ri i ri'i i n 11111 h 2 ■V
1 2 IC 2531 90° + IC 2469 85° + NGC 1589 75' 0 HfE 2
1 -NGC 3390 90° 4 - NGC 1515 82° NGC 1325 73° - 0 H 4 f liH II I W I+W fH +3 2 I
1 - NGC 1886 90° - - A 0908-08 81' NGC 1055 72° 0 ] iii n il Mil IIIÜIII Mil n il iiin i ii n il
2 ♦ —
1 - ESO 489-29 90° NGC 2613 80° NGC 1964 70° 0 III! IIIÜ III INI 2 *•**% .32
* 11—I, i,_ 1 -NGC 3717 88° + NGC 1888 77° 4 - NGC 2713 68° ; ~ M I I I I I I I I I I I I I I M M I I I I I I I I I I I I I I I I I 1 1 1 1 11 1 1 1 11 1 1 11111 r -10 0 10 -10 0 10 -1 0 0 10 r (arcsec) r (arcsec) r (arcsec)
Figure 2.5: Minor axis V — I color profiles for sample galaxies. Errorbars represent uncertainties due to photon statistics; they do not include calibration errors. Galaxy inclination angles are given at the lower right corner of each panel.
32 ■H 111111 II 111111111 i-M 11111 '11111 ri 11111 i-j-t l'i 1111111111111111- 6
4 zi 2 IC 2469 NGC 1589 75 0 6
4
2 NGC 3390 90“ NGC 1515 82“ - - NGC 1325 73“ 0 f h Æ i i i i I i f h I i i i i fl+E 6
4 zi ^ -H 2 : NGC 1886 90' A 0908-08 81“ * NGC 1055 72“ : 0 I fH-lH I ll-lin l fHffi 6
zi 4 2 - ESO 489-29 90“ - - NGC 2613 80“ - - NGC 1964 70' 0 ] H il l II I I U lll l I [ ] U lIlH I f E 6
— zi 4 2 : NGC 3717 88° NGC 1888 77“ NGC 2713 68“ ~i I I I I I I I I 1 1 i l I I I I I I I I I I I I 1 I I I I I I I I I I I I I I I I I I M I I I I I -1 0 G 10 -10 0 10 -10 0 10 r (arcsec) r(arcsec) r (arcsec)
Figure 2.6: Minor axis V — K color profiles for sample galaxies. Errorbars represent uncertainties due to photon statistics; they do not include calibration errors. Galaxy inclination angles are given at the lower right corner of each panel.
33 P * ‘*‘ Hfjtf
2531 90 IC 2469 85 NGC 1589 75 t l H H l l ffflllJlJ
i*; J) *++ J NGC 3390 90 NGC 1515 82° NGC 1325 73
4, _ NGC 1886 90° A 0908-08 81 NGC 1055 72 s
_ ESO 489-29 90 NGC 2613 80 NGC 1964 70 5
"++++++K
I NGC 3717 88° NGC 1888 77° NGC 2713 68°
i I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I -1 0 0 10 -10 0 10 -10 0 10 r (arcsec) r (arcsec) r (arcsec)
Figure 2.7: Minor axis J — K color profiles for sample galaxies. Errorbars represent uncertainties due to photon statistics and sky noise; they do not include calibration errors. Galaxy inclination angles are given at the lower right corner of each panel.
34 CHAPTER 3
RADIATIVE TRANSFER MODELS
In recent years, sophisticated efforts to model attenuation effects in spiral galaxies have shed a great deal of light on the necessary components of such models (see
Huizinga 1995 for a review). The relative geometric distribution of dust and stars is of critical importance; many authors have shown that different geometries produce significant variations in reddening and the optical depth inferred from single-band absorptions A\ or color excesses E { \ 2 — Ai) {e.g., Disney et al. 1989; WTC92;
Kuchinski k Terndrup 1996). Although many previous modeling efforts consider an idealized smooth distribution of dust, observations show patchiness in the absorbing material in real galaxies (Rix & Rieke 1993; Quillen et al. 1995). Witt & Gordon
(1996) have shown that the local structure of the dust can have a large effect on the transmitted and scattered photons from an embedded source. These authors, as well as Natta k Panagia (1984), Hobson k Scheuer (1993), and Berlind et al.
(1997) demonstrate that clumpy structure in the interstellar medium affects both the wavelength dependence of extinction and the total optical depth inferred from a color excess: clumpy dust produces a grayer attenuation curve and requires a greater
35 dust column density than the simple foreground screen model to produce a given
reddening.
Although scattering is often neglected in favor of retaining simplicity in dust
models, it may have considerable effects on the observed attenuation characteristics
and is thus worthy of further consideration. VVTC92, Emsellem (1995), and Bruzual
et al. (1988) find that scattering by dust grains plays an important role in reducing the amount of reddening caused by a given quantity of dust because the color of the light scattered back into the line of sight is usually bluer than that of the star light, thus compensating for some of the reddening caused by extinction. The importance of scattering depends on the relative geometric distributions of dust and stars and the dust grain albedos and angular scattering properties. The introduction of clumpy structure in the dust distribution reduces the fraction of emergent light that is due to scattering because photons scattered in dense clumps of dust are likely to be subsequently absorbed rather than escaping from the system (Boissé 1991; Witt &:
Gordon 1996).
Figure 3.5 shows the percentage of observed light that is due to scattering into the line of sight as a function of wavelength for three of the WTC92 model geometries at several different optical depths, again calculated from data tabulated in that paper.
Contrary to what may be expected, scattering effects are not largest at very high optical depths because so much light is absorbed in these cases that there is little left to be scattered (WTC92). This is evident from comparing the three panels of
Figure 3.5. The scattered light fraction is always less than 10% in the H and K bands for rv < 5, indicating that scattering is not expected to be significant at these wavelengths. The effects of scattering are often more pronounced at shorter
36 wavelengths as extinction optical depths t\ are higher, scattering is less isotropic, and dust grain albedos may be somewhat higher (WTC92). However, we note that recent models and observations (Lehtinen & Mattila 1996; W itt et al. 1994; Kim et al. 1994) suggest more forward-directed scattering (higher g) and higher albedos in the near-infrared. The K albedo may be as high as 60 to 70%, rather than the value of 20 to 30% in the standard dust mixture of Draine & Lee (1984). The higher JHK albedos and scattering phase function asymmetry parameters were not used in the
WTC92 calculations shown in Figure 3.5 but were used for the disk galaxy model calculations (see Table 3.1).
Byun et al. (1994) find that scattering effects can be ignored for disk galaxies with inclinations i > 85° because little light is scattered into the plane of the disk.
However, even at inclinations as high as 70°, neglect of scattering can contribute to errors of several x 0.1 mag in the predicted total B band magnitude (Byun et al.
1994). Emsellem (1995) finds that scattering effects are necessary to simultaneously explain the B, V, R, and / band attenuation in the dust lane of NGC 4594 (i = 84°) and that much more dust is required to explain the observed extinction if scattering is considered than if it is neglected. In general, the above discussion suggests that estimates of the total extinction must be based on models with both absorption and scattering unless it is certain that a particular galaxy has a dust geometry or inclination for which scattering is unimportant.
The minor axis color profiles of our galaxies are compared to reddening predic tions from several different radiative transfer models in order to investigate which model elements are required to represent attenuation in the optical and NIR wave length range. Representations of the dust distribution can be divided into two types:
37 simple models with analytical solutions of the radiative transfer equation and sophis ticated ones require a full numerical solution. Simple models consider absorption but not scattering and can only be constructed for a few specific dust geometries. The complex models considered here treat both absorption and scattering for various dust geometries that represent different environments in galaxies. Model calculations yield values for total extinctions and color excesses as a function of some measure of dust column density, here the total V^-band optical depth t\- along the line of sight through the center of the galaxy.
3.1 Simple Slab Models
The simplest representation of dust in galaxies is the plane-parallel foreground screen model, in which an obscuring layer of dust absorbs light from a source behind it. In the absence scattering, the radiative transfer equation can be solved analytically to vield:
h = h.oe-T\ where is the unattenuated intensity from the source and t\ is the optical depth.
The total extinction at any wavelength is then given by
-1a = “ 2.5 logjo-p-^,
= I.OSGta.
Because the wavelength dependence of absorption by dust grains in other galaxies is poorly known, it is common to assume a Galactic reddening law to express the optical depth r as a function of wavelength {e.g., .Jansen et al. 1994). Here we adopt
38 the Galactic extinction law of Rieke & Lebofsky (1985), given in Table 3.1. Color excesses EfAg — Ai) = .Aa, — -4^, can then be computed from the adopted reddening law. Extinctions in the V and K bands (.4v and .4k) and color excesses E{B — V) and
E{J — K) for the foreground screen model are shown in Figure 3.2. The foreground screen model predicts a large degree of reddening even when the optical depth through the system is low because all of the light must pass through the dust layer.
Another dust model with an analytic solution to the transfer equation is that of a uniformly mixed slab of dust and stars (again neglecting scattering). Walterbos &
Kennicutt (1988) derive:
.4a = -2.5logio r;r— j ■
for this model. We compute extinctions .4a and color excesses E(A -2 — Ai) as a function of rv for the BVRIJHK passbands, again using the Galactic extinction law to express
Ta. Extinctions and color excesses for this model are also shown in Figure 3.2. For the same total optical depth through the slab, this model produces less reddening than the foreground screen because light from sources near the edge of the mixture escapes with little or no extinction.
3.2 Numerical Models with Spherical Geometry
WTC92 calculate Monte Carlo models of radiative transfer in spherically symmetric systems and include the effects of both absorption and scattering. With Monte Carlo techniques (Witt 1977), photons are followed through a dust distribution and their interaction with the dust is parameterized by the dust optical depth ( t a ) , albedo
( o a ) , and scattering phase function asymmetry ( ^ a ) - The optical depth determines
39 the probability distribution for where the photon interacts, the albedo gives the prob
ability the photon is scattered from a dust grain, and the scattering phase function
determines the probability distribution for the angle at which the photon scatters.
The values of these dust grain properties used by WTC92 are given in Table 3.1.
The fraction of light observed directly and the fraction scattered into the line of
sight are tabulated in VVTC92 for several wavelengths ranging from the ultraviolet to
near-infrared. The extinction at a wavelength A is then given by the relation
.4, = -2.3log,„(%2 + %^). (3.1)
Extinctions and color excesses were calculated as a function of total V'-band optical
depth through the sphere using this relation; some results are shown in the right-hand
panels of Figure 3.2.
We select three of the WTC92 dust geometries for use in our quantitative com
parison of model and observed color excesses; these are called the "dusty galaxy,”
“starburst galaxy,” and "dusty galactic nucleus” models. The dusty galaxy is a
sphere of uniformly mixed stars and dust that differs from the simple uniform mix
ture model due to the spherical geometry and the inclusion of scattering. Because
light is scattered into the line of sight and because sources near the surface suffer
little extinction, there is much less reddening at each Ty than is produced by the simple foreground screen. (Recall that it is the extinction as a function of optical depth which distinguishes the various models.) The starburst galaxy has a centrally concentrated spherical distribution of stars with a uniform sphere of dust embedded in it. Most of the light in this model comes from the central dusty regions, so red dening effects are more pronounced than for the dusty galaxy. The dusty galactic
40 nucleus model contains a sphere of stars surrounded by a spherical shell of dust, with
no mixing of dust and light sources in either region. This model differs from the sim
ple foreground screen mainly due to the inclusion of scattering, which compensates
for some of the absorption to produce slightly less reddening than the screen model.
These models are not ideal representations of spiral galaxies because of their spheri
cal shape and smooth dust distributions, but they provide valuable insight into how
different assumptions about the distribution of the dust yield different color changes
as a function of total optical depth.
3.3 Disk Galaxy Models
We have also compared the galaxy data to recently calculated Monte Carlo simula
tions of radiative transfer in spiral galaxies (Witt 1977; Gordon et al. 1997a; W itt et
ai. 1997). We use the physical properties of dust in our Galaxy as a template for the dust in other spiral galaxies. Thus, the wavelength dependence of t\ is that of the
average Milky Way extinction curve (W hittet 1992). The wavelength dependences of
the dust albedo (oa) and scattering phase function asymmetry (^a) were determined by Gordon et al. (1994) from smooth curves drawn through many empirical determi nations taken from the literature (see also Calzetti et al. 1995; Lehtinen & Mattila
1996). Values for T\, a\, and gx are tabulated in Table 3.1.
Because the dust in our Galaxy is known to be very clumpy, we consider both locally homogeneous and clumpy dust distributions with our model. The two-phase clumpy dust case is characterized by the ratio of inter-clump to clump medium density
(^2 /^ 1 ), the filling factor (//) of the high density clumps, and the size of the clumps
41 compared to the system size (W itt & Gordon 1996). Again, we use our Galaxy as a template for the clumpy case and choose ko/ki = 0.01, f f = 0.15, and cubic clumps with sides of 44 pc.
The Monte Carlo technique allows us to represent the complicated geometry of a spiral galaxy and to view the model disk at an arbitrary inclination angle. The model spiral galaxy possesses a disk component made up of stars and dust and a bulge component containing only stars. The spatial distribution of dust and stars in the disk is a double exponential density distribution:
z) = D j ( 0 , (3.2) where hn is the scale length and is the scale height. The dust scale length and height are 3000 pc and 110 pc, respectively. The stellar scale length is 3000 pc, and the stellar scale height varies from 115 pc at the B band to 250 pc at the K band (Mihalas &: Binney 1981). This variation in stellar scale height is necessary to account for the different types of stars which dominate the flux of a galaxy at different wavelengths. The physical radius of the model disk is 4 scale lengths, or 12,000 pc.
The stellar distribution of the bulge is described by an exponential distribution:
D&(r) = £>6(0)6-'-/'*^ (3.3) where hr is the bulge scale length. We select a value of 300 pc for hr, which corre sponds to projected value of 225 pc (Courteau et al. 1996). The geometry of these models, as well as the inclusion of locally clumpy dust distributions and the care taken to use realistic values of the dust optical properties t\, a\, and g\, make them more plausible representations of spiral galaxies than the slab and spherical radiative transfer models discussed in the previous sections.
42 Analytic" Spherical* Disk" Passband r\lrv txI tv a\ 9\ txI tv a\ PA B 1.32 1.32 0.66 0.59 1.32 0.61 0.63 V 1.00 1.00 0.60 0.50 1.00 0.59 0.61 R 0.75 0.76 0.53 0.40 0.76 0.57 0.57 I 0.48 0.48 0.45 0.29 0.48 0.55 0.53 J 0.28 0.28 0.36 0.15 0.28 0.53 0.47 H 0.18 0.17 0.28 0.04 0.17 0.51 0.45 K 0.11 0.10 0.20 0.00 0.10 0.50 0.43
“ Reddening law from Rieke and Lebofsky (1985).
^ Dust optical properties from Table 1 of WTC92.
Dust optical properties from Table 1 of Gordon et al. (1997).
Table 3.1: Properties of dust grains in radiative transfer models.
43 Foreground Screen
Uniformly Mixed Slab
r:x:*:x r:x:*:x: r:x:*:x:
Figure 3.1: Dust-star geometries in simple plane-parallel models.
44 5
4
3 ,Nucleus < dusty 2 uniform slab Ô starburst 1
0 1 .8 starburst .6 < uniform slab nucleu .4 * ...A' dusty .2 0 .8 nucleus ST .6 1 c& .4 LU .2 uniform slab starburst 0
1.5 e 1 starburst LU *nucleus .5 uniform s ab A- ...... ^ dusty I
0
Figure 3.2: Extinctions and color excesses as a function of V'-band optical depth for slab and spherical radiative transfer models with different dust-star geometries.
45 Dusty Galaxy
.@ism@gg;a^^gsg.
SSSSBSSSSSSSSSSSiSS 'ïsæsswssssæssæ* ^saasggggBP
Dusty Galactic Nucleus
Starburst Galaxy
jMiliiii|fe
l a i B p
Figure 3.3: Dust-star geometries in the radiative transfer models of WTC92.
46 Exponential Disk of Dust
Exponential Stellar Disk
Exponential Stellar Bulge
Figure 3.4; Components of disk galaxy radiative transfer models from Witt et al. (1997).
47 nucleus 0 — starburst - A- - dusty
nucleus 0 — starburst A - dusty
I
nucleus 9— starburst A dusty
I
Figure 3.5: Fraction of observed light that has been scattered into the line of sight as a function of wavelength for models from WTC92.
48 CHAPTER 4
COMPARISON OF GALAXY COLORS TO MODEL
PREDICTIONS
4.1 M ethod
In this chapter, the reddening of optical and NIR colors predicted by various radiative transfer models is compared to color variations across the dust lanes of the sample galaxies. We take minor axis color cuts (perpendicular to the disk dust lane) as described in Chapter 2. For each point in the galaxy that experiences reddening, the intrinsic color, e.g., [B — l')o, would be observed at a redder color. For each model, the reddened color is given by {B — V')o 4- E{B — V), where the color excess is a function of the V'-band optical depth t\-. In the simple foreground screen model, the ratio of any two color excesses is a constant yielding a traditional reddening vector in a color-color plot. However, complex dust geometries and scattering produce ratios between any two color excesses which depend on rv and thus yield curved reddening trajectories in color-color plots. We select several different color combinations to investigate the wavelength dependence of extinction effects. Plots of optical vs. NIR colors provide a good separation between the color trajectories predicted by different
49 models, while plots of two optical or two NIR colors show the eflFects of attenuation in particular wavelength regimes.
We estimate unreddened bulge colors for each galaxy by assuming that extinction is negligible in the outer bulge (away from the plane of the disk). This assumption is supported by the color profiles of Figures 2.4 - 2.7, in which the bulge colors are typically constant with minor-axis distance away from the dust lane. We use the minor axis profiles and color maps to select a location away from the plane in each galaxy which has constant colors and small errors; the colors at this point are taken to be the unreddened bulge colors {B — V')o, (V — A')o etc. In galaxies that are almost edge-on, for example IC 2531 and NGC 3390, the dust lane bisects the bulge along the major axis and bulge colors are equal (within the errors) on both sides. For these systems we average the outer bulge colors on either side of the dust lane. Galaxies that are not edge-on exhibit more reddening on the side obscured by the dusty disk. In these cases we adopt colors from outer bulge regions on the unobscured side. Table 4.1 summarizes the adopted unreddened bulge colors for each galaxy. Figure 4.1 gives a comparison of these unreddened colors to bulge colors measured by Peletier &: Balcells (1997) in highly inclined galaxies of similar Hubble type. Although we do not have any individual galaxies in common with the Peletier k. Balcells (1997) study, the samples show substantial overlap. We set ry = 0 for each radiative transfer model at the adopted unreddened colors, then compare the model reddening trajectory to the reddening observed across the galaxy dust lanes.
50 4.2 Comparison of Data to Slab and Spherical Models
Color-color diagrams of galaxy and model reddening trajectories are shown in Fig ures 4.2 - 4.16. The figures are in order of decreasing inclination angle i (using the estimates of i given in Table 2.1). In the following discussion, note that this esti mated inclination does not totally determine the observed reddening features of an individual galaxy: this is probably due in part to uncertainties in the inclination val ues themselves (which are estimated from a general formula as noted in Chapter 2) and in part to variations in galaxy dust content or dust lane thickness.
Galaxies seen at inclinations close to edge-on, such as IC 2531, NGC 3390,
NGC 1886, ESO 489-29, NGC 3717, and .A. 0908-08, feature prominent red dust lanes. The NIR colors {J — H and H — K) get red enough to rule out the trajec tories of all slab and spherical models presented here except the foreground screen and possibly the uniformly mixed slab. The optical colors, on the other hand, show a saturation of reddening that is characteristic of geometries with mixed dust and stars: at high optical depth, only the outer layer of stars is visible and thus the addition of more dust does not result in further reddening. Optical-optical color plots are not very useful for these galaxies, a.s B — V and V — I both appear to suffer this saturation of the reddening. We speculate that the different behavior of the optical and IR colors may arise from a combination of line-of-sight optical depth effects and stellar population differences between the bulge and disk. In the IR, where the optical depth is lower and we see further into the galaxy, we expect to see light primarily from red bulge stars located behind the dusty disk. This effect may also explain why dust geometries with a significant fraction of light sources located near the edges of
51 the system never produce enough reddening to match the extremely red dust lane colors observed in the nearly edge-on galaxies. At optical wavelengths, we see only part of the way into the edge-on disk and thus observe primarily light from young blue stars embedded in the dust layer.
Galaxies at slightly lower inclination angles, such as IC 2469, NGC 1515, NGC-
2613, NGC 1888, NGC 1589, NGC 1325, NGC 1964, and NGC 2713, do not show extremely red dust features. The NIR colors do not get red enough to distinguish between the trajectories of different models, which all follow similar paths at low optical depths. The line-of-sight optical depth does not appear to be large enough to cause saturation of the reddening in BVI colors.
We discuss NGC 1055 separately because its minor axis colors are quite different on the obscured and unobscured sides of the bulge. The blue and red sides are shown as closed and open points respectively in Figure 4.14. The curved trajectory of the
JHK colors on the blue side of NGC 1055 resembles the behavior of the dusty galactic nucleus model at high ry, where it deviates from the other models by curving in the opposite direction. .A.s described in Chapter 3, the dusty galactic nucleus model is basically a foreground screen with the inclusion of scattering. It is possible that in this case, we are observing disk stars through a dust lane at an angle at which scattering effects are important. The outer-bulge colors we measured may not be completely free of reddening even for the blue side of the bulge; this would explain why the model diverges from the simple foreground screen at high Ty while our data diverge at what we have called ry = 0 . The optical colors on the blue side of NGC 1055 show only slight evidence for saturation of the reddening. On the red side of the galaxy, the extremely red J — H and H — K colors suggest heavy obscuration. Here we select a
52 second location for rv = 0 of the models at the bluest point of the red side. Clearly
this point is not actually free of reddening, but this is not important because we are
interested in the change in color across the dust feature. However, the reddening
trajectory of the galaxy color gradient does not appear to follow any of the models.
The optical colors over much of the red side of the galaxy are relatively constant,
perhaps because the dusty disk is so opaque that only the outer layer of stars can be
seen anywhere in this region.
.A.lthough the dusty galactic nucleus and dusty galaxy models of VVTC92 differ
from the simple analytical screen and uniform models only in the inclusion of scatter
ing and the spherical (rather than plane parallel) geometry, they predict veiy different
JHK colors as t\- increases. The simple uniform model appears to be a much better
fit to the observations than the analogous dusty galaxy model of WTC92, which has
a trajectory that curves sharply blueward \u J — H at high r\-. Likewise, the simple
foreground screen model lies along the observed color trajectories while the analo
gous dusty galactic nucleus model of WTC92 has a color trajectory that curves away
from the observations and the other models considered here. This lack of agreement
between the models with scattering and the NIR dust lane colors of highly inclined galaxies suggests that in the NIR, scattering effects are not significant for the ob jects that make up our sample. These results are not surprising: scattering is not expected to be important in the NIR for the highly inclined galaxies in our sample because most of the light is from red bulge stars located behind the “screen” of the dusty disk and thus little is scattered towards the observer. However, we note that the mixture of dust and light sources that would be seen in a face-on system or in an edge-on galaxy at blue wavelengths (where the young stars in the spiral arms are
53 visible) would likely produce more scattering and would also require a different model
geometry.
None of the idealized slab or spherical models considered here accurately describes
the galaxy reddening trends over the optical-NIR baseline. We therefore conclude
that more sophisticated and realistic radiative transfer models are required to predict
attenuation effects and make plausible estimates of the optical depth through spirals.
4.3 Disk Radiative Transfer Model Comparisons
The disk radiative transfer models produce simulated images of disk 4- bulge compo
nents with various bulge-to-disk (B/D) ratios, viewed at several selected inclination
angles. We smooth these images with a circular gaussian of FWHM = 2 pixels to
represent seeing effects, then we take minor axis color profiles from the model images
with the same procedure used on the galaxy images. The models have colors equal to
zero in the unreddened regions; we adjust the zeropoints of the color-color plots so
that the model zero colors coincide with the unreddened bulge colors for each galaxy.
We then plot both model and galaxy reddening trajectories on color-color diagrams as was done for the slab and spherical models in the previous section.
We consider in particular how just a few of the numerous disk model parameters affect our comparison of model and galaxy colors. A grid of models was calculated for specific values of inclination angle, B/D, and central face-on optical depth rv,o- At each point on this 3-D parameter grid, the model calculations yield a set of simulated images at BVRIJHK bands. The entire grid was calculated twice, once with a homogeneous dust distribution and once with clumpy structure in the dust, in order
54 to explore the role of dumpiness in producing observable attenuation effects. For
the clumpy dust models, rv,o is the central, face-on optical depth of a homogeneous
model with the same total dust mass; the optical depth along any line of sight in
a clumpy model depend on how many clumps it passes through. The models have
Tv,o of 0.50, 1.0, 2.0, 4.0, 10.0, and 20.0 all the way through the galaxy at the central
point (or half these values if measured from surface to center). The grid of inclination angles considered for our galaxy sample ranged from i = 65° — 90° in 5° increments.
Input B/D values for the model calculations are 0.01, 0.02, 0.05, 0.10, 0.20. 0.30, 0.40.
0.50, 0.75, 1.0. It is important to note that the B/D ratio measured on the model's output image is not necessarily equal to the input value due to the absorption of disk light by dust.
Unlike the slab and spherical model comparisons, we need here to select appro priate values for the model inclination and B/D ratio to match each galaxy in our sample. We wish to understand the effects of varving these parameters. We first round the inclination estimate for each galaxy from Table 2.1 to the nearest 5° and select a model with that inclination for comparison. However, in some cases the minor axis color profile suggests that these inclination estimates require revision. Although we estimate i = 90° for ESO 489-29, its off-center reddening over one side of the bulge suggests a lower inclination (only edge-on galaxies have a dust lane through the center of the disk), and thus we chose the i = 85° model. For the same rea son we use the i = 85° model for NGC 3717 even though its estimated inclination of 88° rounds to 90°. Color maps of NGC 1589 show a well-defined, very red dust lane across one side of the disk, implying a slightly higher inclination than the es timated 75° (at which one entire side of the galaxy is typically reddened). Jansen
55 et al. (1994) estimate i ~ 83° for this galaxy; we select a model w ith i = 80° for
comparison. Images of NGC 2613 show more disk and spiral arm structure than we
see in other galaxies with i ~ 80°: we thus adopt the lower value of i = 75° given by
Fisher k Tully (1981). Likewise, the IC 2469 disk structure and reddening suggest
that it should be modeled with a lower inclination that the estimate of 85°, we select
i = 80° and i = 75° models. The uncertainties arising from comparison to models
viewed at different inclinations are summarized in Figure 4.17, in which model color
trajectories at different viewing angles are shown on the same plot. By observing the
spacing between adjacent lines and the difference in their maximum reddenings on
Figure 4.17, one can estim ate the change in color trajectory associated with an error of ~ ±5° in i.
We measure the B/D ratio on both galaxy images and the simulated images pro duced by the radiative transfer model in order to determine the appropriate model
B/D to match each galaxy. The B/D ratio is measured with Kent’s (1986) method, which assumes no functional form for the light distribution but simply relies on the difference in ellipticity between the bulge and disk components when viewed at high inclination. Details of the B/D measurements and results will be presented in a sub sequent paper; here we simply use these values to match each galaxy to a model with similar measured B/D (recall from the discussion above that the measured ratio may not be equal to the input ratio due to extinction). We note that the use of B/D measurements is probably more reliable than simply assigning a B/D value based on a galaxy’s Hubble type: recent studies {e.g., de Jong 1996b; Simien & de Vaucouleurs
1986) find a significant spread in B/D with Hubble type. We present model color trajectories for different B/D values in Figure 4.18, which demonstrates that the tra
56 jectories and red extents of the colors are not highly sensitive to errors in B/D of up
to ~ 20%.
Figures 4.19 - 4.37 show galaxy and disk model reddening trajectories for many of
the same color combinations analyzed in the previous section. For each galaxy in our
sample, we select the closest values of i and B/D from the parameter grid for which
models were calculated and take color profiles from the simulated images at each
available value of rv,o for both homogeneous and clumpy dust cases. This method
is demonstrated in Figures 4.19 - 4.23 for the edge-on galaxy NGC 1886. which
features a very red dust lane. Figure 4.19 shows the .NGC 1886 minor axis color
data compared to the rv,o = 0.5 model for homogeneous dust in the left-hand panels
and clumpy dust in the right-hand panels. The same galaxy colors are repeated in
Figures 4.20 - 4.23, shown each time with model trajectories for a different ry.o-
It is clear from Figures 4.19 - 4.23 that the models with ty^q = 0.5 do not get as
red as the observed minor axis colors for any color shown; this is the signature of a
model with central face-on optical depth lower than that of the galaxy. Models with
Tv,o > 4.0 get redder than the NIR colors of the galaxy and predict a saturation in
the reddening of the optical colors at values that are too blue. These discrepancies
indicate that the model optical depth is too high: the models produce too much
reddening in the NIR and do not ’’see” far enough into the dusty disk at optical
wavelengths to include light from stars that experience reddening. We carry out similar analyses to that of NGC 1886 for each galaxy in the sample to determine
which model values of rv,o are neither obviously too small or too large to match the galaxy color profiles. Ideally, it would be possible to identify a single rv,o (at the i and
B/D we have selected for an individual galaxy) that best matches the galaxy data
57 in both, shape of trajectory and maximum reddening in all four color-color plots. In
practice, there are often two adjacent model values of rv,o that cannot be ruled out
as being obviously too low or too high. Figures 4.24 - 4.37 show, for each galaxy,
the two models whose central optical depths produce the closest agreement between
model and galaxy reddening trajectories.
The agreement between the data and models is quite good for V' — K and redder
colors and is often satisfactory for V — I as well. The B — V colors of NGC 1886,
NGC 1888, and IC 2469 agree well with the models, but for others the B — V and
occasionally V — I colors appear redder than the model values when plotted versus
.7 — K. One possible explanation for the discrepancies in the optical colors is a bulge
metallicity gradient, to which the optical colors are more sensitive than the NIR ones.
We investigate this possibility in more detail in Chapter 5. Another possibility is that
the unreddened color in the dust lane region is strongly influenced by the disk, which
has similar NIR colors to the bulge but may have slightly bluer optical colors (Peletier
k Balcells 1997; Terndrup et al. 1994). In IC 2531, ESO 489-29, NGC 3717, and
.A. 0908-08, the galaxy B — V and V — I colors " turn over” and get bluer than the
models in regions of high and increasing NIR reddening. It is possible that regions of
very high optical depth, which would have extremely red J — K colors, are dominated
by recently-formed stars and thus have bluer colors. Witt and collaborators (Witt
1997) find preliminary evidence of the latter phenomenon from Ha spectra: very dusty regions also contain a significant number of early-type stars that contribute to
the observed blue light in these spots.
The disk radiative transfer models investigated here provide markedly better agreement than the simplified geometries for galaxy colors in the V' through K bands.
58 We therefore suggest that some or all of the components that are included in the disk models but not in the others are required to model attenuation effects in spiral galaxies. The most obvious difference is in the geometry; the multi-component disk radiative transfer model bears a closer resemblance to real galaxies than a slab or sphere. We did not directly test the importance of treating multiple scattering by considering models with disk geometry but no scattering, but most theoretical work suggests that scattering does play an important role in modifying the reddening (see the discussion in Chapter 3) and thus is a necessary component of a plausible radiative transfer model. Although theoretical work (Witt & Gordon 1996, Natta & Panagia
1984) suggests that dumpiness may strongly influence reddening, we do not find any cases among these galaxies in which either the clumpy or homogeneous dust model would be strongly favored over the other. This result is not unexpected because of the high inclination angles at which the sample galaxies are observed. The line of sight through a highly inclined clumpy dust disk will intersect a significant number of clumps, rendering it little different from the homogeneous case. We emphasize that at lower inclinations, where some lines of sight may intersect clumps and other may not, dumpiness will likely be an important consideration. It is clear that modeling attenuation effects in spiral galaxies requires a more rigorous treatment than the sim ple foreground screen model that has been invoked often since the work of Holmberg
(1958).
59 G alaxy B-V e rro r V - I e rro r I ' - K e rro r J-K erro r J-H e rro r H -K error N G C 10.55 0.91 0.05 1.31 0.04 .3.15 0.00 0.91 0.04 0.61 0.03 0..30 0.04 .NGC 1325 0.91 0.23 1.31 0.10 .3.10 0.00 0.84 0.11 0.68 0.08 0.16 0.09 N G C 1515 0.88 0.03 1.23 0.02 3.22 0.00 0.96 0.02 0 .6 9 0.01 0 .27 0.03 NGC 1589 0.98 0.02 1..38 0.02 3.48 0.00 0.92 0.05 0.70 0.02 0.22 0.04 NG C 1886 0.88 0.13 1.27 0.06 3.01 0.00 0.82 0.08 0.61 0.09 0.21 0.04 NGC 1888“ 0.99 0.12 1.75 0.07 4.49 0.01 1.16 0.09 0.88 0.12 0.28 0.10 N G C 1964 " 0.91 0.05 1.23 0.01 3.37 0.00 0.95 0.02 0.68 0.02 0.27 0.02 ESO 489-29 0.79 0.02 1.27 0.01 3.32 0.00 0.92 0.03 0.68 0.03 0.23 0.03 N G C 2613 1.07 0.03 0.90 0.02 .3.13 0.00 0.92 0.11 0 .6 5 0.13 0 .27 0.09 NGC 2713 0.98 0.02 1.33 0.01 3.36 0.00 0.98 0.03 0 .7 5 0.02 0.23 0.03 .AG908-08* 0.97 0.02 1.43 0.01 3.69 0.00 0.97 0.01 0 .7 2 0.01 0.25 0.01 IC 2469 1.03 0.02 1.40 0.01 3.63 0.00 1.02 0.02 0 .7 6 0.03 0.26 0.02 IC 2531 0.86 0.06 1.23 0.02 3.22 0.00 0.90 0.02 0.66 0.02 0.24 0.02 N G C .3390 0.95 0.03 1.29 0.01 3.43 0.00 0.92 0.02 0.66 0.02 0.22 0.02 N G C 3717 0.93 0.02 1.21 0.01 .3.22 0.00 0.85 0.02 0.66 0.02 0.19 0.02
“ Colors are taken from the bluest points of the obscured side of tlie galaxy due to the presence of a. close companion on the unobscured side,
* Colors are taken from profiles offset 5 arcsec from the minor axis due to the presence of bright stars.
Table 4.1: Adopted Unreddened Bulge Colors.
60 2
■ Unreddened Bulge Colors O Peletier & Balcells Data 1.8
1.6 QC ci ■ O 1.4
1.2
1 2 2.2 2.4 2.6 2.8 3 3.2
■ Unreddened Bulge Colors O Peletier & Balcells Data O 3 —
it: oc ■ S » 2.5 —
J I L J I I I I I I I I I I I I I I I I .7 .8 .9 1 1.1 1.2 J-K
Figure 4.1: Comparison of our adopted unreddened bulge colors to spiral bulge colors from Peletier & Balcells (1996).
61 IC 2531 1.6
1.4 Foreground Screen /- Uniform Mixture b. 1.2 ci Starburst (WTC92) 1 Dusty (WTC92) .8 Nucleus (WTC92)
.6 1.5 2 2.5 V -l 2.5
1.4 2 ^ 1-2 ci 1.5
1 1.5 2 11.5 2 J-K J-K 7 ■* : 1.4 6 1.2 5 ï J) 1 4 .8
3 .6
1 1.5 2 .2 .4 .6 J-K H-K
Figure 4.2: Color-color diagrams for IC 2531 minor axis colors and reddening trajec tories for slab and spherical radiative transfer models.
62 NGC 3390 1.6
1.4 Foreground Screen /: 1.2 Uniform Mixture Starburst (WTC92) 1 Dusty (WTC92) 8 Nucleus (WTC92)
6 1.5 2 2.5 V -l 1.6 2.5
1.4
' // ■
1 1.5 2 1 1.5 2 J-K J-K 7 1.4 6 1.2 5 Z J) 1 4 8
3 6
1 1.5 2 .2 4 6 J-K H-K
Figure 4.3: Color-color diagrams for NGC 3390 minor axis colors and reddening trajectories for slab and spherical radiative transfer models.
63 NGC 1886 1.6
1.4 Foreground Screen Uniform Mixture Starburst (WTC92) ------Dusty (WTC92) Nucleus (WTC92)
1.5 2 2.5 V -l 1.6 2.5
1.4
1 1.5 2 1 1.5 2 J-K J-K 7 1.4 6 1.2 5
4
3
1 1.5 2 2 .4 .6 J-K H-K
Figure 4.4: Color-color diagrams for NGC 1886 minor axis colors and reddening trajectories for slab and spherical radiative transfer models.
64 ESO 489-29
1.4 ------Foreground Screen Uniform Mixture Starburst (WTC92) Dusty (WTC92) Nucleus (WTC92)
1.5 2 2.5 V -l 1.6 2.5
1.4
^ 1.2
1 1.5 2 1 1.5 2 J-K J-K 7 1.4 6 1.2 5 Z J. 1 4 .8
3 .6
1 1.5 2 2 4 .6 J-K H-K
Figure 4.5: Color-color diagrams for ESO 489-29 minor axis colors and reddening trajectories for slab and spherical radiative transfer models.
65 NGC 3717 1.6
1.4 Foreground Screen Uniform Mixture is. 1.2 c6 Starburst (WTC92) 1 Dusty (WTC92) 8 Nucleus (WTC92)
6 1.5 2 2.5 V-\ 2.5
1.4 2 oi ' // 1.5
1 1.5 2 1 1.5 2 J-K J-K 7 1.4 6 1.2 5 Z J, 1 4 8
3 6
1 1.5 2 2 4 .6 J-K H-K
Figure 4.6: Color-color diagrams for NGC 3717 minor axis colors and reddening trajectories for slab and spherical radiative transfer models.
66 IC 2469 1.6
1.4 Foreground Screen Uniform Mixture ^ 1.2 Starburst (WTC92) 0 6 Dusty (WTC92) Nucleus (WTC92)
1.5 2 2.5 V-l 2.5
1.4
.8 —
1 1.5 2 1 1.5 2 J-K J-K 7 1.4 6
5
4 8 —
3
1 1.5 2 .2 .4 6 J-/C H-K
Figure 4.7: Color-color diagrams for IC 2469 minor axis colors and reddening trajec tories for slab and spherical radiative transfer models.
67 NGC 1515 1 .6
1.4 Foreground Screen /- Uniform Mixture 1.2 Starburst (WTC92) 06 1 ------Dusty (WTC92) 8 Nucleus (WTC92)
.6 1.52 2.5 I/-/ 2.5
1.4 2
, // 1.5
1 1.5 2 1 1.5 2 J-K J-K 7 1.4 6
5
4
3
1 1.5 2 .2 .4 6 J-K H-K
Figure 4.8: Color-color diagrams for NGC 1515 minor axis colors and reddening trajectories for slab and spherical radiative transfer models.
68 A 0908-08 1.6
1.4 ------Foreground Screen Uniform Mixture 1.2 ci Starburst (WTC92) 1 ------Dusty (WTC92) 8 Nucleus (WTC92)
6 1.5 2 2.5 I/-/ 1.6 2.5
1.4 2
1.5
1 1.5 2 1 1.5 2 J-K J-K 7 1.4 6 1.2 5 y. J) 4 .8
3 6
1 1.5 2 2 4 6 J-K H-K
Figure 4.9; Color-color diagrams for A 0908-08 miner axis colors and reddening trajectories for slab and spherical radiative transfer models.
69 NGC 2613 1.6
1.4 Foreground Screen Uniform Mixture 1.2
06 Starburst (WTC92) 1 Dusty (WTC92) 8 Nucleus (WTC92)
.6 1 1.5 2
1.6 LT'I I 2 J/ ' ' '/ ' ' 1.4 i tT . _ ------— 1.2 1.5 oil 1 1 .8
.6 I I I I I I I I I I I I I 1 1.5 2 1 1.5 2 J-K J-K 7 1.4 6
5
4
3
1 1.5 2 ,2 .4 6 J-K H-K
Figure 4.10: Color-color diagrams for NGC 2613 minor axis colors and reddening trajectories for slab and spherical radiative transfer models.
70 NGC 1888 1.6
1.4 ------Foreground Screen ------Uniform Mixture b. 1.2 oil Starburst (WTC92) 1 ------Dusty (WTC92) .8 Nucleus (WTC92)
,6 1.5 2 2.5 V -l 1.6 2.5
1.4
1.2 ci 1
8
6 1 1.5 2 1 1.5 2 J-K J-K 7 1.4 6 1.2 5 4, 1 ■■ 4 8
3 .6
1 1.5 2 2 ,4 6 J-K H-K
Figure 4.11: Color-color diagrams for NGC 1888 minor axis colors and reddening trajectories for slab and spherical radiative transfer models. Only the minor axis colors for the obscured side of the galaxy are shown; there is a close companion near the unobscured side.
71 NGC 1589 1.6
1.4 Foreground Screen
1.2 Uniform Mixture ci Starburst (WTC92) 1 Dusty (WTC92) 8 Nucleus (WTC92)
6 1.5 2 2.5 V-l 2.5
1.4
1 1.5 2 1 1.5 2 J-K J-K
1.4
1.2
8
3 - 6
1 1.5 2 .2 .4 6 J-K H-K
Figure 4.12: Color-color diagrams for NGC 1589 minor axis colors and reddening trajectories for slab and spherical radiative transfer models.
72 NGC 1325 1.6
1.4 Foreground Screen /- Uniform Mixture 1.2 ci Starburst (WTC92) 1 ------Dusty (WTC92) .8 Nucleus (WTC92)
6 1.5 2 2.5 V -l 2.5
1.4 2
' // 1.5
1 1.5 2 1 1.5 2 J-K J-K 7 1.4 6 1.2 5
4
3
1 1.5 2 .24 6 J-K H-K
Figure 4.13: Color-color diagrams for NGC 1325 minor axis colors and reddening trajectories for slab and spherical radiative transfer models.
73 NGC 1055 1.8
1.6 Foreground Screen 1.4 Uniform Mixture /_ 1.2 Starburst (WTC92) c i 1 ■ ■ Dusty (WTC92) .8 Nucleus (WTC92) 6 1.5 2 2.5 V -l 1.8 2.5 1.6 1.4
ci 1.2 // 1 f - 8 6 1.5 21 1 1.5 2 J-K J-K 7 1.6 1.4 6 ./■ a— 1.2 5 Z J 1 4 8 3 6 1.5 2 .2 4 6 J-KH-K
Figure 4.14: Color-color diagrams for NGC 1055 minor axis colors and reddening trajectories for slab and spherical radiative transfer models.
74 NGC 1964 1.6
1.4 /- Foreground Screen Uniform Mixture 1.2 Starburst (WTC92) c i 1 ------Dusty (WTC92) 8 Nucleus (WTC92)
.6 1.5 2 2.5 y-\ 2.5
1.4
-//
1 1.5 2 1 1.5 2 J-K J-K 7 1.4 6 1.2 5 // 4
3
1 1.5 2 2 .4 6 J-K H-K
Figure 4.15: Color-color diagrams for NGC 1964 minor axis colors and reddening trajectories for slab and spherical radiative transfer models.
75 NGC 2713 1.6
1.4 /_ ------Foreground Screen Uniform Mixture 1.2 ch Starburst (WTC92) 1 ------Dusty (WTC92) .8 Nucleus (WTC92)
6 1.5 2 2.5 V-l 2.5
1.4
^ 1.2 C6 '' //
1 1.5 2 1 1.5 2 J-K J-K 7 1.4 6 1.2 5 1
4 .8
3 .6 1 1.5 2 2 4 6 J-KH-K
Figure 4.16; Color-color diagrams for NGC 2713 minor axis colors and reddening trajectories for slab and spherical radiative transfer models.
76 1
.4 8
,6 c i .2 ,4
.2 0 0 0 5 1 05 1 J-K J-K
3
2
1
0 0 5 01 2 4 .6 J-K H-K
Figure 4.17: Variations in disk radiative transfer model reddening trajectories as a function of inclination angle for B/D = 0.50, rv,o = 2.0, and homogeneous dust.
77 .4 — 1
QÎj .2 — :L B/D=1.00 5 B/D=0.50 B/D=0.30 - - B/D=0.05 0 I I I I I I I I I I I I I I I I I I I 0 .2 .4 .6 .8 1 0 .2 .4 .6 .8 1 J-K J-K
3 .6
2 .4
1 2
0 0 0 .2 .4 .6 .8 1 0 1 2 .3 .4 J-K H-K
Figure 4.18: Variations in disk radiative transfer model reddening trajectories as a function of buige-to-disk ratio (B/D) for i = 80°, rv = 2.0, and homogeneous dust.
78 NGC 1886 + x„,=0.5 NGC 1886 + Tv 0=0.5 1.6 1.4 1.2 1 .8 .6 1 1.5 2 2.5
2.5
2 2 -V t " 1.5 1.5 'I I I Fi i I I I I I I I I I I I r 1 1.5 2 2.5 1 1.5 2 2.5 J-K J 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1- 7 J li 1 M 1 1 1 II 1 T|”n 1 iz 6 ^ = z M q : = z z 4
-III 1 1 1 1 1 1 1 1 1 1 1 1 1 IZ 3 =1 !*^h 1 1 1 1 1 1 1 1 1 1 1 il= 1 1.5 2 2.5 1 1.5 2 2.5 J-K J-K -1 1 1 r 1 1 II 1 1 1 I 1 1 r II- -1 1 1 1 1 1 Ti 1 1 1 r T p 1 1- 1.4 1.4
1.2 1.2 a: L ; J L _= 1 ? ' = . - E 1 ^ . = .8 .8 = - " = .6 .6 -1 |l| 1 1 1 1 1 1 1 1 1 1 1 III- ^|T| 1 1 1 1 1 1 1 1 1 1 1 1 1 1- .2 .4 .6 .8 1 .2 .4 .6 .8 1 H-K H-K
Figure 4.19: NGC 1886 minor eixis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 90°, B/D = 0.20, and rv,o = 0.5.
79 NGC 1886+ Tv 0=1.0 NGC 1886+ Tv 0=1.0
ci
-I 11111 1111 I I I I IIII- - I I I I I I I I I I I I I I I I 1 I - 1 1.5 2 2.5 1 1.5 2 2.5 J-K 2.5 J I rpri'i I I I I il I I I IL
2 y. 1.5
1.5 2 2.5 J-K 7 -Il I I i I I I I I Tr ni 1-4 6 it: 5 y. 4 3 1 1.5 2 2.5 J-K 1.4 1.4 1.2 1.2 z J, 1 1 .8 .8 .6 .6 .24 6 8 1 24 6 8 1 H-K H-K
Figure 4.20: NGC 1886 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 90°, B/D = 0.20, and rv,o = 1.0.
80 NGC 1886 + Tv.o=2-0 NGC 1886 + Xv.o=2-0 1.6 -1 1 1 1 1 r r r | ’m i | i i i i_ 1.6 -M 1 1 1 1 I'l 1 1 1 II 1 II II- 1.4 1.4 ^ 1.2 ^ 1.2 li 1 ci 1 L- IP i Æ * — " f* J .8 — 1 — .8 .6 - I 1 1 1 1 1 1 r 1 1 1 1 1 1 1 I I I - .6 - I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 - 1 1.5 2 2.5 J-K 2.5
2
1.5
1.521 2.5 J-K 7 6 5 4 3 1 1.5 2 2.5 J-K urrri' i i i i i ri n i i i u 1.4 1.4 1.2 1.2 a: 4, 1 4> .8 .6 - I I I I I I I I I I I I I I I I H ZL .2 .4 .6 .8 1 .2 .4 6 .8 1 H-K H-K
Figure 4.21: NGC 1886 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 90°, B/D = 0.20, and rv,o = 2.0.
81 NGC 1886+ 0=4.0 NGC 1886+ Ty 0=4.0
1 1.5 2 2.5 1 1.5 2 2.5 J-K 2.5 2.5 LI 1 1 I I I I 1 I I I I I I ri 1 L
2
1.5
1 1.5 2 2.5 J-K 7 7 I! II I II M II II- 6 6 5 5 y. 4 4
3 3 ËLLL I I I I li I I I I I I I g 1 1.5 2 2.5 1 1.5 2 2.5 J-K 1.4 1.4 1.2 1.2 z J) 1 J, 1 .8 .8
.6 h-l i Ml 11 I I I I I I I I I I I I I l - i .6 .2 .4 .6 .8 1 2 .4 6 8 1 H-K H-K
Figure 4.22: NGC 1886 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 90°, B/D = 0.20, and ry o = 4.0.
82 NGC 1886 + Tv 0=10.0 NGC 1886 + tv 0=10.0 1.6 -1 II 1 1 1 rr I' rrn |i i i u 1.6 -1 1 1 1 1 I 1 T I" 1 1 1 1 1 1 1 1 l_ 1.4 1.4 ^ 1.2 1.2 cij 1 (i 1 W - f ! ...^ i .8 .8 E - M -= .6 -1 1 1 1 II II 1 1 1 1 1 1 1 III- .6 -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1- 1 1.5 2 2.5
2.5 2.5
2
1.5 1.5 'II I Fi I I I I I I I I I I I I r 1 1.52 2.5 1 1.5 2 2.5 J-K 7 7 - m T II I I I 1 II I I I I I I- 6 6 5 : ® 4 4 3 3 g I I I I I I II I I I I I I iig 1 1.52 2.5 J-K 1.4 1.2 1 .8 .6 .2 4 .6 8 1 H-K
Figure 4.23: NGC 1886 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 90°, B/D = 0.20, and rv,o = 10.0.
83 NGC 3390 + Tvo=1.0 NGC 3390 + t,,„=2.0 1.6 -1 1 1 1 1 1 1 1 1 1 1 1 t 1- 1.6 -1 1 1 1 I 1 i”l 1 I 1 1 1 1- 1.4 1.4 1.2 ^ 1.2 odi 1 — ^ QÎ1 1 .8 .8 .6 -1 1 1 1 1 1 1 1 1 1 1 1 1 1- .6 -1 1 1 1 1 1 1 1 1 1 1 1 1 1- 1 1.5 1 1.5 J-K 2.5 2.5
2 2 y. 1.5 1.5
1 1.5 2 1.5 21 J-K J-K 7 7 6 6 5 5 y. 4 4 3 3 1 1.5 2 1.5 21 J-K J-K 1.4 1.4 1.2 1.2 a: 1 .8 .6 •6 — 2 4 .6 .2 .4 6 H-K H-K
Figure 4.24: NGC 3390 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 90° and B /D = 0.50.
84 1C 2531 +Tv o=1.0 10 2531 + Xv.o=2-0 1.6 - r n 1 1 1 1 i|j 1 1 1 1 |_ 1.6 -1 1 1 1 1 1 1 1^ 1 T 1 1 |- 1.4 1.4 ^ 1.2 ^ 1.2 ci 1 ti 1 .8 .8 .6 -1 1 1 1 1 1 1 1 1 1 1 1 1 1- .6 -1 1 1 1 1 1 1 1 1 1 1 1 1 1- 1 1.5 2 1 1.5 J-K 2.5 2.5
1.5 —
1 1.5 2 1 1.5 2 J-K 7 7 6 6 5 5 4 4 3 3 1 1.5 2 1 1.5 2 J-K J-K 1.4 1.4 1.2 1.2 1 .8 •6 Et .6 .2 4 .6 2 .4 6 H-K- H-K
Figure 4.25: IC 2531 minor axis colors (points) and reddening trajectories from ho mogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 90° and B /D = 0.50.
85 ESO 489-29 + 1^0=1.0 ESO 489-29 + Xv,o=2-0
_l i 1 1 1 1 1 1 1 1 I 1 1 l_ 2.5 _r 1 T 1 r 1 1 1 1 1 1 1 1 |_
2 2 r ^ i
1.5 — —1.5 — _* — "I 1 n 1 1 1 1 1 1 1 1 1 1“ "1 1 1 1 1 1 1 1 1 1 1 1 1 1“ 1 1.5 1 1.5 2 J-K J-K 7 6 5 zl 4 3 Ë1. 1 L I I I 1 1.5 1 1.5 2 J-K J-K n I I I I I - 1.4 1.4 1.2 1.2 3; 3: J, 1 4, 1 .8 .8 .6 .6 I I I I I I I I I I -I 2.4 6 .2 .4 .6 H-K H-K
Figure 4.26: ESO 489-29 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 85° and B/D = 0.40.
86 NGC 3717+ t^ 0=1.0 NGC 3717 + %^ 0=2.0 1.6 1.4 1.2 c i 1 .8 .6 11.5 2 J-K 2.5 2.5
2 2
1.5 1.5
1.5 21 1 1.5 2 J-K J-K 7 7 6 6 «- 5 5 4 4 3 3 1 1.5 2 1 1.5 2 J-K J-K 1.4 1.4 1.2 Ï I 4, 1 .8 .6 rr .6 .2 .4 .6 2 .4 6 H-KH-K
Figure 4.27: NGC 3717 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 85° and B /D = 0.50.
87 IC 2469 + Xyg=0.5 10 2469 + 1^ 0=1.0
0&
2.5
2
1.5
1 1.5 1 1.5 2
7 6 5 4 3 1 1.5 2 J-K 1.4 1.2 3: 1 .8 .6 .2 .4 .6 H-K
Figure 4.28: IC 2469 minor axis colors (points) and reddening trajectories from ho mogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 80° and B/D = 0.50.
88 NGC 1515 + Tv.o=0-5 NGC 1515 + T„„=1.0 1.6 1.4 1.2 J li .8 I I I I I 1 1.5 J-K 2.5
2
1.5
1 1.5 2 J-K 7 6 5 4 3 1 1.5 2 J-K 1.4 1.2 = z 1 .8 .6 2 4 6 H-K
Figure 4.29: NGC 1515 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 80° and B/D = 0.40.
89 A 0908-08+ T„„=1.0 A 0908-08 + Xv.o=2-0
1.4
1.5 21
2.5
1.5 —
1 1.5 2 J-K 7 7 6 6 5 5 y. 4 4 3 3 1 1.5 2 1 1.5 2 J-K J-K 1.4 1.4 1.2 1.2 a: 1 J, 1 .8 .8
.6 .6 -t I .2 4 .6 1 .2 .3 .4 .5 .6 H-K H-K
Figure 4.30: A 0908-08 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 80° and B/D = 0.50.
90 NGC 2613 + Ty 0=0.5 NGC 2613+ Ty 0=1.0 I, I I I I -
2
1.5
1
11.5 2 J-K 7 7 6 6 5 5 4 4 3 3 1 1.5 2 1 1.5 2 J-K 1.4 1.2 a: J, 1 .8 .6 2 .4 6 H-K
Figure 4.31: NGC 2613 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 75° and B/D = 0.20.
91 NGC 1888 + x„„=1.0 NGC 1888 + 0=2-0 1.6 %T 1.4 1.2
1 1.5 2
2.5
2
1.5
1 1.5 2
- I '
1.4 1.4 1.2 1.2 X 1 1 .8 .8 .6 .6 .2 .4 .6 2 4 6 H-K H-K
Figure 4.32: NGC 1888 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 80° and B /D = 0.30. Only the minor axis colors for the obscured side of the galaxy are shown; there is a close companion near the unobscured side.
92 NGC 1 5 8 9 + 0=0.5 NGC 1589+ 0=1.0 1.6 -r r 1 1 1 1 1 1 1 1 1 1 1 1- 1.6 1.4 1.4 1.2 1.2 oil 1 ti 1 -F T# I i . 8 . 8 .6 - 1 1 1 1 1 1 1 1 1 M i l l - .6 1 1.5 2 J-K 2.5 2.5
2 2
1.5 1.5
1 1.5 2 1 1.5 2 J-K J-K -iiiiiiiirriiii- 7 -1 1 1 1 1 1 1 1 1 1 1 1 1 |- 6 5 f 5 4 4 1 i 3 "1 1 1 1 1 1 II 1 II II T= 3 =1 1 1 1 1 1 1 1 1 1 1 1 1 T= 1 1.5 1 1.5 2 J-K J-K p i III m Ti'i 1111111111111 |_u 1.4 1.2 I a: J) 1 4. .8
.6 II I I I I I I II IT .2 4 .6 H-K
Figure 4.33: NGC 1589 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 80° and B /D = 0.40.
93 NGC 1325 + Xv 0=0.5 NGC 1325+ Xv 0=1.0 1.6 I I I I I I 1p -T I -rxI I ^ : 1-6 i-i I I I r r I I I I I 1.4 1.4 E- i» 1.2 1.2 ci 1 ci 1 .8 .8 .6 -I I I I I I I I I I I I I .6 hJ .1 l-l I. L I I I I I. 1 I |-j 1 1.5 1 1.5 J-K 2.5 2.5
2
1.5
1 1.5 2 1 1.5 2 J-K J-K 7 6 z ^ 5 i 4 3 1 1.5 2 J-K 1.4 1.4 1.2 1.2 Z 1 J, 1 .8 .8 .6 .6 .2 4 6 .2 4 6 H-K H-K
Figure 4.34: NGC 1325 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 75° and B/D = 0.10.
94 NGC 1055 + Tv 0=2.0 NGC 1055 + Tvo=4.0
0 6 cij
_i 1 1 1 1 rr 1 L1 1 1 I 1 L 2.5 _i 1 1 1 1 1 1 1 ] 1 M r I' i_ : " a : 2 E . / - # ♦ zL !: IT T + + T - 1.5
“ 1 1 rVi 1 1 1 1 1 1 1 1 1 i~ "1 1 1 1 1 1 1 1 1 1 1 1 1 1 l~ 1 1.5 2 1 1.5 J-K J-K 7 7 T: 6 6 5 5 4 4 3 3 1 1.5 2 1 1.5 2 J-K J-K 1.6 1.4 I = Î 1.2 j 1 .8 .6 2 .4 6 H-K
Figure 4.35: NGC 1055 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 75° and B/D = 1.00.
95 NGC 1964 + 1^0=0.5 NGC 1964+ T^ 0=1 0 1.6 -I I I I I I I I I I I I - 1.4 1.2 oil 1 E- 8 1-1 I I I I I I I I I I I 1 1.5 2 J-K 2.5 _i I I I I "rr r I i i "i i i 2.5
2 F- > 2
1.5 1.5 I I I I I I I I I I I I 1 1.5 2 1 1.5 2 J-K / -1 1 1 1 1 1 1 1 1 1 1 1 1 |- 7 -1 1 1 1 1 1 1 1 1 1 1 1 1 |- 6 E- -E 6 E- -E
5 r ~ A ^ 4 4 r 1 ^ i ? 1 3 =1 1 1 1 1 1 1 1 1 1 1 1 1 3 =_i_ 1 1 ! 1 1 1 1 1 1 1 1 1 T=
Figure 4.36: NGC 1964 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 70° and B/D = 0.10.
96 NGC 2713 + Tvo=0.5 NGC 2713 + 1^ 0=1.0
J-K 2.5
2
1.5
1 1.5 2
z J)
Figure 4.37: NGC 2713 minor axis colors (points) and reddening trajectories from homogeneous dust (solid lines) and clumpy dust (dotted lines) disk radiative transfer models with i = 70° and B /D = 0.75.
97 CHAPTER 5
ESTIMATES OF THE OPTICAL DEPTH THROUGH SPIRAL
GALAXIES
In principle, it is possible to infer a value for vy along any line of sight given an observed color excess and a choice of model. However, in practice the inferred optical depth is extremely model-dependent and may also be uncertain due to degeneracies in the reddening produced by dust and changes in the stellar population. In this chapter, we explore the usefulness of the radiative transfer models discussed in Chapter 3 to predict line-of-sight and face-on optical depths for the sample galaxies. The factors contributing to uncertainties in the optical depth are considered in some detail.
Finally, some implications of the derived optical depths for the spiral disk opacity controversy and for studies of galaxy stellar content and structure are discussed.
5.1 Optical Depths from Slab and Spherical Models
We measure maximum color excesses in galaxy dust lanes to estimate the range of total V band optical depth predicted by the slab and spherical geometry radiative transfer models. We consider only those galaxies with clearly defined dust lanes and
JHK colors that follow the model reddening trajectories from the unreddened bulge
98 colors out to the reddest values. We do not estimate ry from optical color excesses
because of problems introduced by the saturation of the reddening noted in the reddest
dust lanes. Columns 3-5 of Table 5.1 give the maximum E{J — K), E{H — K) and
E{J — H) measured along the minor axis. Corresponding V band optical depths at
each color for each appropriate dust model are given in Columns 6 - 8 of Table 5.1. The
values of ry predicted from the three different colors of a single galaxy are similar,
as is expected if the model adequately describes the observed colors. We take an
average of these three values as the estimated ry for the galaxy and present this and
the corresponding K band extinction for each case in columns 9-10 of Table 5.1.
It is clear from Table 5.1 that the total optical depth in dust needed to produce
the observed reddening is highly sensitive to geometry (the models all have similar
dust properties, and thus differ primarily in geometry). In Chapter 4, vve stated that
the foreground screen, uniform mixture, and starburst galaxy models all produce
reddening trajectories that match the NIR dust lane colors of many of the sample
galaxies. Because three different models each provide a satisfactory description of
the colors, we cannot derive a single value for the optical depth. Instead, we use
the three results to place limits on this quantity. In all cases, the simple foreground
screen model that is traditionally used to estimate extinction provides a lower limit
on Ty because the light sources interact with all of the dust and there is no scattering
into the line of sight to compensate for absorption. For the highly inclined galaxies in
Table 5.1 that are not edge-on, the predicted ry from the screen model ranges from
1.6 to 2.7, while corresponding ry from the uniform mixture and starburst galaxy models are much higher; 3.7 to 7.5. For two of the edge-on galaxies, NGC 1886 and
IC 2531, only the screen model produces enough reddening and the predicted values
99 of Tv are % 4.5. The colors of NGC 3390 can be represented by either the screen or uniform mixture models: the screen model predicts rv ~ 4.5 and the uniform mixture yields ry % 15. All of these values imply that the dusty regions of highly inclined galaxies are optically thick at visible wavelengths, but whether or not they would be optically thin at face-on inclinations depends on which model is used to predict Ty and the assumed ratio of dust scale height to disk scale length.
The limits we derive from the slab and spherical models provide guidelines for understanding galaxy optical depths, but they can be narrowed to more precise val ues only with a better understanding of the geometry and scattering properties of the dust. Because the disk radiative transfer models more accurately describe the observed dust lane reddening trends (see Chapter 4), we speculate that they may also yield better estimates of the optical depth through the sample galaxies.
5.2 Optical Depths from Disk Radiative Transfer Models
We use the model and galaxy reddening trajectories to constrain the central face-on optical depth, rv.o, for each galaxy by determining which models produce enough reddening to describe the observed colors. Because the models have set values of Ty o and the red extent of galaxy colors usually lies between that of two different models, we actually delineate a range of ry,o for most of the sample galaxies. For each galaxy, we use only the color-color plots in which models and data agree to estimate ry,o.
Table 5.2 lists value or range of ry o inferred for each galaxy, as well as the incli nations and B/D values of the models used for comparison. The two galaxies with profiles taken parallel to the minor axis are noted in Table 5.2 (see Chapter 2). We
100 find that all of the galaxies in our sample fall in the range rv,o = 0.5 — 2.0 all the way through the galaxy at the central point. There do not appear to be any galaxies that have much higher or lower optical depths; recall from Figures 4.19 - 4.23 that the reddening trajectories of models with rv.o much too low or high show distinct departures from the galaxy color profiles. These results suggest that face-on spirals are in general just barely optically thick in their central regions and are optically thin over large parts of the disk.
The comparison of galaxy colors to the family of disk radiative transfer models provides some useful insights into the observable effects of attenuation. We have done this analysis over a long spectral baseline, and we find that the inferred optical depth does not depend strongly on the colors or wavelengths used as long as the data and model reddening trajectories agree: i.e., we do not see cases in which two different color-color plots both match the data well but yield very different estimates of rv,o- We have performed tests with some individual galaxies by matching each to several models of slightly different inclination and optical depth. The results of these comparisons are included in Table 5.2. .A.S suggested by Figure 4.18, the inferred optical depth does not appear to be sensitive to small uncertainties in B/D.
Not surprisingly, the value of rv,o is somewhat dependent on the choice of model inclination: models viewed at higher inclinations have lines of sight passing through larger physical distances in the dusty disk. Because of this dependence we exercised extreme caution in determining i for each galaxy, as described above.
101 5.3 Uncertainties in Optical Depth Estimates
There are several uncertainties in the procedure we adopt to infer galaxy optical
depths; perhaps the most significant of these lies in our assumption that the outer
bulge color (which we have been calling the “unreddened” color) is identical to the
unreddened color of the galaxy in the region obscured by the dust lane. A gradient
in the mean metallicity or age of bulge stars will produce a color gradient across the bulge, in w^hich case the unreddened colors of the inner and outer bulge would indeed be different. Figures 5.1 and 5.2 compare the reddening predicted by the slab, spher ical, and disk models to the color changes produced by stellar population differences, taken from the calculations of Worthey (1992). The color gradients produced by age, metallicity, and attenuation are quite similar; thus it is nearly impossible to disentan gle the effects of dust and stellar populations using broad-band colors. Note also that the difficults of using colors as population indicators is exacerbated by degeneracies in the changes produced by metallicity and age. Spectral line studies, rather than colors, appear to be a more effective tool to disentangle all of these effects and to study stellar population gradients in spiral bulges.
Because galaxy minor axis color gradients are in good agreement with the disk model reddening trajectories, which are quite similar to the color changes produced by increased stellar age or metallicity, it follows that the galaxy color gradients could also be due to stellar population variations. We may estimate the size of these effects on our results by using the Milky Way bulge as a model: the metallicity change across the Galactic bulge is ~ 0.4 dex/kpc declining from the center outward (Terndrup et al. 1990, Tiede et al. 1995). Assuming a central mean [Fe/H] of the solar value and
102 using Worthey’s (1992) models, the corresponding color changes would be ~ 0.12 mag at [B — V), ~ 0.60 mag at {V — K), and ~ 0.13 mag at (,/ — K) over a distance of one kpc. We note that the {J — K) color change is comparable to or larger than that measured across several bulges of external galaxies by Peletier & Balcells (1997). This is much smaller than the total color change across the dust lanes of edge-on galaxies
(see Figures 2.4 - 2.7), suggesting that the observed reddening is for the most part due to attenuation effects.
We carry out a preliminary investigation of the effect of a bulge population gra dient on our results using the edge-on galaxy IC 2531, in which color changes due to a vertical or radial population gradient would be directly observable along the minor axis. The optical colors in the dust lane of this galaxy tend to be redder than the model trajectories in Figure 4.25: we speculated in Chapter 4 that this could be due to stellar population gradients. Assuming a distance of 30 Mpc to IC 2531
{Hq = 75 km/s/Mpc), we measure the color gradient in this galaxy over ~ 1 kpc. We can therefore use the color changes calculated above for the Milky Way metallicity gradient and align the zero reddening points of the models to a color that is redder than the adopted outer bulge color by those amounts. This is done by offsetting the zero colors from their locations in Figure 4.25 by the amounts given above. This shift in the model reddening trajectories causes the inferred rv,o for IC 2531 to change from ~ 2 . 0 to somewhere in the range 1 . 0 — 2 . 0 and also produces slightly better agreement between the models and galaxy colors on the V — K vs. J — K diagram.
We emphasize that the presence of a bulge color gradient in the typically observed sense, in which colors are redder at the center, would cause us to overestimate the
103 optical depth because some of the reddening towards the center would be due to
population effects rather than dust.
Along with the possible presence of stellar population gradients, there are other
sources of discrepancy between the unreddened colors of the inner and outer bulge.
Young disk stars may contribute a significant amount of light to the dust lane region
but not to the part of the bulge away from the plane, causing the unreddened color
of the dust lane to be bluer than the unreddened color of the bulge alone. Light
scattered from the part of the disk located behind the bulge might cause bluing on
the unobscured side of the bulge. Thus our adopted unreddened color, which is
measured on this unobscured side, would be too blue. It is also possible that there is
some component of dust mixed throughout the bulge that could cause reddening even
in the outer bulge. Based on the smoothness of our galaxy color maps and profiles
outside the observed dust lanes, we find this latter possibility somewhat unlikely.
In addition to the uncertainties introduced by the choice of model inclination
angle and B/D that were investigated in Chapter 4, several other components of the disk radiative transfer models may also contribute to errors in the inferred rv,o. The model assumes the stellar population to be identical throughout the galaxy, neglecting possible differences between bulge and disk stars and variations in the mean stellar properties between very dusty star-forming regions and the rest of the disk. As noted in Chapter 4, Witt and collaborators (Witt 1997) suggest that very dusty regions contain a significant fraction of young stars that contribute alot of blue light in these spots. The clumpy distribution of dust in the models is not necessarily realistic, both because the model clump size is limited by available computing power and because the clumpy structure of dust in real galaxies is not known on all size scales (Witt
104 & Gordon 1996). It is not known whether accurate, realistic dumpiness is even required to describe galaxies on the scales we observed (each pixel has sides of 50
- 250 pc). Finally, there are some uncertainties in the physical characteristics of dust grains, including NIR albedoes (ax), the scattering phase function asymmetry parameter and the possibility that dust grains in dense clumps may have different characteristics than those in the interclump medium (Boissé 1991, Witt et al. 1994;
Lehtinen & M attila 1996; W itt & Gordon 1996). In the future, we may investigate the addition of a simple stellar population gradient to the model and variations in the clumpy structure or physical properties of the dust to determine in more detail how these factors affect the predicted reddening trajectories.
5.4 Are Spiral Disks Opaque?
We use dust lane colors from the galaxies in our sample to investigate whether or not these systems could be optically thick over large parts of their disks when viewed face-on, as suggested by Valentijn (1990) and Burstein et al. (1991). Because we find rv,o not much greater than one for most of the sample galaxies, they would only be optically thick over most of the disk if the thickness of the dust layer did not drop off away from the galaxy center. We investigate this possibility by taking color profiles on several cuts parallel to the minor axis of four sample galaxies that are almost exactly edge-on and have well-defined dust lanes; the cuts intersect the major axis at intervals of 5 arcsec from the major axis. We measure the maximum reddening in J — iv, E{J — K)max: along each of these cuts by determining the color difference between the reddest point on the cut and the unreddened bulge color given for the
105 galaxy in Table 4.1. (We use an NIR color because it is less likely to have saturated
reddening than the optical colors. Although many of these cuts pass primarily through
the disk rather than the bulge, we note that our color maps show similar J — K colors
for bulge and disk. Terndrup et al. (1994) and Peletier &c Balcells (1997) also find
that bulges and disks have similar J — K colors.) E{J — K)max is shown as a function
of distance from the galaxy center along the major axis in Figure 5.4. These galaxies
show a strong central peak in the reddening; this could be due to a concentration of
dust and/or an extremely red nuclear stellar population. There is a slight tendency
for the maximum reddening to decrease with increasing galactocentric distance away
from the very red central regions. This decrease is consistent with the fall-off of
an exponential disk of dust. Using Av,ma.x instead of £’(,/ — K)max, Jansen et al.
(1994) find a rapid drop in the maximum dust lane extinction at increasing distance
from the center for several highly inclined galaxies, further supporting the idea that galaxies with rv,o not much greater than one in the center would not be optically
thick throughout their disks.
We also investigate the possibility of an optically thick disk with an exponential disk of dust. One can estimate the face-on optical depth at a distance R from the center of a homogeneous exponential disk of dust to be:
Tv = where rv,o is the face-on optical depth at the center and is the disk scale length.
Assuming that D 25 for a galaxy is located 3-4 disk scale lengths from the center
{e.g., Elmegreen & Elmegreen 1984; Evans 1994), a value of ry,o > 20 is required to produce optical depths greater than one in the outer disk (it is generally assumed
106 that the dust and stellar disk scale lengths are the same.) Figure 5.5 shows the color trajectories for IC 2531 compared to a model with rv,o = 20; it is clear that the model reddening is much greater than the observed NIR color change and that the reddening of the optical colors saturates at nearly the outer bulge color. Thus we can rule out agreement between the observed galaxy color gradients and disks that are opaque over most of their surfaces when viewed face-on.
5.5 Implications for the Study of Spiral Galaxies
The results presented in this paper have implications for the study of radial color gradients in face-on spirals, which are often used to infer clues about stellar age and abundance gradients across the disk component {e.g., de Jong 1996a). For galaxy disks that are optically thick in the central regions but transparent over the rest of their disks, we expect to see a color gradient produced by attenuation. We calculate radial color gradients due solely to attenuation for our disk radiative transfer model viewed face-on by calculating surface brightness profiles from ellipse fitting in each passband and subtracting the appropriate pairs of profiles to make color profiles. In
Figure 5.6 we plot these model color gradients along with radial color changes mea sured by de Jong (1996a) for two face-on spiral galaxies. For purposes of comparison we have set the model outer disk colors to the values of the individual galaxies (re call that model colors are zero in the absence of dust and that we are looking at relative color changes due to attenuation). It is clear that the model color gradients, which were computed for optical depths similar to those presented in Table 5.2, are substantially smaller than the color changes in de Jong’s (1996a) sample. Thus, as
107 de Jong (1996a) concludes, it seems likely that changes in the stellar population are
responsible for a significant fraction of the radial color gradients observed in face-on
spirals.
Our investigation of galaxy opacities also can help pinpoint where mass models
based on the light distribution are likely to be inaccurate, an important step in
understanding dynamical influences on the bulge and inner disk. Using the slab and
spherical models, we predict values of .4/^ — 0.5—0.6 at the centers of edge-on galaxies
and 0.2 — 0.3 in the dust lanes of highly inclined galaxies that are not seen exactly
edge-on (see Table 5.1). For the more sophisticated geometry' of an exponential disk
of dust, we can estimate the line-of-sight optical depth through the center of the disk
as follows (Kylafis & Xilouris 1996):
_ _ fha, Ai'.edge — ^VJace ( ^ j
where hn is the disk scale length and h, is the disk scale height. For rv,o = 0.5 — 2.0.
the corresponding edge-on values for our disk radiative transfer models are rv.edge =
14 — 55. Clearly the dust lanes of highly inclined galaxies are opaque even in the
NIR, where optical depths are typically a few tenths of the V'-band values. Thus the
assumption of constant mass-to-light ratio (M/L) in uncorrected light distributions
for highly inclined galaxies will result in mass models that are inaccurate. .Addition
ally, spectra taken in regions of extremely high line-of-sight optical depth will only sample kinematics and stellar populations in the outer parts of the galaxy. For dusty spiral galaxies, it is particularly important to understand where in the galaxy the observed light originates before making any interpretation of the data.
108 Galaxy .Model EjK" £^hk“ tv,j k * tv.hk* T v,JH ^ {tvY
Edge-On Galaxies
NGC 1886 screen 0.80 0.31 0.50 4.36 4.49 4.29 4.38 0..53
IC 2531 screen 0.81 0.30 0.52 4.40 4.33 4.44 4.39 0.53
NGC 3390 screen 0.79 0.35 0.44 4.29 5.07 3.82 4.39 0.54 NGC 3390 uniform 0.79 0.35 0.44 14.89 15.37 14.24 14.84 0.78
Highly Inclined Galaxies
NGC 1589 screen 0.31 0.11 0.20 1.65 1.55 1.71 1.64 0.20 NGC 1589 uniform 0.31 0.11 0.20 3.77 3.37 4.04 3.73 0.22 NGC 1589 starburst 0.31 0.11 0.20 3.98 3.57 4.20 3.92 0.24
ESQ 489-29 screen 0.43 0.15 0.28 2.31 2.18 2.38 2.29 0.28 ESQ 489-29 uniform 0.43 0.15 0.28 5.63 4.94 6.17 5.58 0.32 ESQ 489-29 starburst 0.43 0.15 0.28 6.02 4.97 6.91 5.97 0.36
-A. 0908-08 screen 0.49 0.18 0.31 2.66 2.66 2.66 2.66 0.32 -A. 0908-08 uniform 0.49 0.18 0.31 6.78 6.24 7.21 6.75 0.38 .A. 0908-08 starburst 0.49 0.18 0.31 7.33 6.41 8.18 7.31 0.43
“ EjK = E{J - AT), £hk = E{H - A'), Ajh = E{J - H).
* tv,jk = Tv determined from E{J — K, likewise for other colors.
Values for (r v ) and ( . 4 k ) are averages of the values determined for each of the 3 colors.
Table 5.1: Line-of-sight optical depths in galaxy dust lanes from slab and spherical radiative transfer models.
109 Galaxy i B/D TV.O, CD“’'> rv,o, HD^’** IC 2531 90° 0.50 2.0 2.0 90° 0.30 2.0 2.0 NGC 3390 90° 0.50 1.0 - 2.0 1.0 - 2.0 NGC 1886 90° 0.20 2.0 2.0 90° 0.10 2.0 2.0 ESQ 489-29 85° 0.40 0.5 - 1.0 0.5 - 1.0 NGC 3717 85° 0.50 1.0 - 2.0 1.0 - 2.0 80° 0.50 2.0 2.0 IC 2469 80° 0.50 0.5 - 1.0 0.5 - 1.0 80° 0.75 0.5 - 1.0 0.5 - 1.0 75° 0.50 1.0 1.0 NGC 1515 80° 0.40 0.5 - 1.0 0.5 - 1.0 75° 0.40 0.5 0.5 A 0908-08= 80° 0.50 1.0 - 2.0 1.0 - 2.0 NGC 2613 75° 0.05 1.0 - 2.0 1.0 - 2.0 75° 0.10 1.0 1.0 NGC 1888 80° 0.50 1.0 - 2.0 1.0 - 2.0 80° 0.30 1.0 - 2.0 1.0 - 2.0 NGC 1589 80° 0.40 0.5 - 1.0 0.5 - 1.0 75° 0.20 1.0 1.0 NGC 1325 75° 0.10 0.5 - 1.0 0.5 - 1.0 70° 0.05 0.5 - 1.0 0.5 - 1.0 75° 0.10 0.5 - 1.0 0.5 - 1.0 NGC 1055 (models do not match data well enough to estimate rv.o-) NGC 1964C 70° 0.20 0.5 - 1.0 0.5 - 1.0 NGC 2713 70° 1.00 0.5 0.5 70° 0.75 0.5 0.5
“ CD = clumpy dust, HD = homogeneous dust.
^ rv.o is optical depth all the way through the center of the (face-on) disk.
Color profile offset 5" from major axis due to star.
Table 5.2: Face-on central optical depths from disk radiative transfer models.
110 [Fe/H] = 0.0 Age = 12.0 Gyr 5 < t < 17 Gyr -1.0 < [Fe/H] < 0.25 :n7|-nn|yn[n^.jjjL 1.2 1.2
cil 1 ci 1 .8 8 II1111111111111111111 .6 .8 1 1.2 1.4 1.6 J-K 11111 U11 2 I / ' ' 1 1.8 - 1.6 — 1.4 - 1.2 — 1 FÎTI 1 1 1 1 1 1 1 11 1 l.l 1 1 1 It .6 .8 1 1.2 1.4 1.6 J-K 5 5
4 4 zl zl 3 3
.6 .8 1 1.2 1.4 1.6 6 .8 1 1.2 1.4 1.6 J-K J-K J IIII IIIIIIIIIIWIL 2]11111111111111111 1 .2 1.2
3: ^
.8 .8 — — .6 .6 T1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1r ^ 1 1 1 1 1 1 M 1 1 1 1 M 1 1 1 1 r .1 .2 .3 .4 .5 .1 .2 .3 .4 .5 H-K H-K
Figure 5.1: Reddening produced by changes in age (points in left-hand panels) and metallicity (points in right-hand panels) compared to slab and spherical radiative transfer model reddening trajectories (same line types as in Figures 4.2-4.16.)
I l l [Fe/H] = 0.0 Age = 12.0 Gyr 5 < t < 17 Gyr -1 .0 < [Fe/H] <0.25
1.2 1.2
1 1
8 .8
6 .8 1 1.2 1.4 1.6 6 .8 1 1.2 1.4 1.6 J-K J-K HjTjn I 11 ri I n r| rn 2 1.8 1.6 1.4 1.2 1 .6 .8 1 1.2 1.4 1.6 J-K 5
4
3
.6 .8 1 1.2 1.4 1.6 .6 .8 1 1.2 1.4 1.6 J-K J-K 1.2 1.2
X 1 J) .8 .6 2 3 .41 5 .1 .2 .3 ,4 .5 H-K H-K
Figure 5.2: Reddening produced by changes in age (points in left-hand panels) and metallicity (points in right-hand panels) compared to disk radiative transfer model reddening trajectories (solid lines).
112 IC 2531 + Tv 0=1-0 10 2531 + Tv 0=2.0 1.6 1.6 1.4
1.2
1 .8 1 1.5 2 1 1.5 2 J-K 2.5 2.5
2
1.5
1 1.5 2 1 1.5 2 J-K J-K 7 7 6 6 5 5 4 4 3 3
1 1.5 2 1 1.5 2 J-K J-K 1.4 1.4 1.2 1 .8 .6 .2 4 .6 .8 .24 6 8 H-K H-K
Figure 5.3: Color-color diagrams for IC 2531 minor axis colors (points) and disk model reddening trajectories (lines) assuming a metallicity gradient similar to that of the Milky Way bulge. The model has i = 90° and B/D = 0.50.
113 NGC 1886 8 E e UJ .4
0
10 2531 .8 E e
UJ .4
0
NGC 3390 8
.4
0
ESO 489-29 8 e
UJ 4
0 -20 -10 0 10 20 Major Axis R(arcsec)
Figure 5.4: Maximum J — K color excess in cuts across the dust lane as a function of distance of that cut from the galaxy center (along the major axis).
114 1.6 /•=90° 1.4 B/D = 0.50 Tyo = 20.0 — Homogeneous Dust Clumpy Dust
1.5 2 2.5 V-\ 1.6 2.5
1.4 i» oil 1.2
1
8 1 1.52 2.5 1.5 2 2.5 J-K J-K
1.4
4 —
1 1.5 2 2.5 .2 .4 .6 .8 1 J-K H-K
Figure 5.5: Color-color diagrams for IC 2531 minor axis colors (points) and reddening trajectories for models that are optically thick over most of the disk (lines).
115 .6 .4 UGC 1305 UGC 1455 > CO .2 0 6 .4
2
0
.4
.2
0
1 2 3 1 2 3 Disk Scale Length Disk Scale Length
Figure 5.6: Radial color gradients across face-on disk radiative transfer models and spiral galaxy radial color gradients from de Jong (1996a). Solid lines represent de Jong’s data, dashed lines are color gradients for a model with rv,o = 2.0, and dotted lines are gradients for a model with rv.o = 10. The models have clumpy dust, i = 0°, and B/D=0.30.
116 CHAPTER 6
CONCLUSIONS
6.1 Summary of Thesis
We compare optical and NIR color gradients across the dust lanes of highly inclined galaxies to the reddening predicted by several different radiative transfer models ranging from the simple, purely absorbing foreground screen to physically plausi ble constructions with exponential stellar and dust disks, bulge components, multiple scattering, and optional clumpy dust distributions. The galaxy sample consists of 15 spirals of Hubble type Sab-Sc with inclinations greater than 65°, all of which show prominent red dust lanes or features in which to study attenuation effects. The com parisons are carried out by making color-color plots of minor axis color profiles across galaxy dust lanes and the reddening trajectories predicted by the models. We use several combinations of the optical and NIR colors on the plots to explore the agree ment between model and galaxy color gradients over a long spectral baseline from B to K bands. The primary goal of this project is to identify which types of models can adequately predict the observed optical and NIR reddening in galaxy dust lanes and to use such models to the optical depth through spirals.
117 No single one of the simplified slab and spherical radiative transfer models de scribes the colors of galaxies over the spectral range investigated here: the optical colors appear to follow different model reddening trajectories than the NIR ones. In the NIR, the foreground screen model provides the best description of the reddening in edge-on galaxies, and dust-star geometries with a significant fraction of unobscured light sources at the edge of the system never produce enough reddening to match the reddest galaxy dust features. However, at optical wavelengths, models with mixed dust and stars are required to produce the observed saturation of reddening in the
B — V and V — I colors: in regions of high optical depth, only the outer layer of stars are visible in blue light, so the addition of more dust does not significantly change the observed color of the system. Although the dusty galactic nucleus and dusty galaxy models of WTC92 differ from the foreground screen and uniformly mixed slab mod els only in the inclusion of scattering and the spherical (rather than plane parallel) shape, they predict very different JHK colors as Ty increases. The lack of agreement between the models with scattering and the NIR dust lane colors of highly inclined galaxies suggests that scattering effects do not play a significant role in determining the NIR colors of highly inclined galaxies. It is likely that scattering effects will be significant in the optical due to higher dust grain albedoes at these wavelengths. .At tempts to infer a V'-band optical depth along the line of sight using the slab and spherical models yield a large range of results. Combined with a general understand ing of the importance of geometry, scattering, and dumpiness in the dust distribution based on previous work in this field (see Chapters 1 and 3), these inadequacies point to the need for more physically plausible radiative transfer models for spiral galaxies.
118 Of the handful of radiative transfer models that we compare to galaxy dust lane colors, the sophisticated disk galaxy representation provides the most realistic predic tions of the reddening. Its reddening trajectories provide markedly better agreement than the simplified geometries for galaxy colors in the V' through K bands. The disk galaxy models are used to infer a range of the central face-on optical depth rv,o for each galaxy by comparing the maximum extent of reddening in galaxy dust lanes to that of models with specific rv.o- Excluding some cases in which the {B — V) color does not follow the model reddening trajectories, we find that both optical and NTR colors yield the same optical depth values. Central face-on optical depths in the 15 galaxies studied here fall in the range rv.o = 0.5 — 2.0. These results do not appear to be highly sensitive to the presence of a clumpy versus homogeneous dust distribution in the optical-NlR wavelength range, which is not unexpected in a highly inclined galaxy because nearly any line of sight through an edge-on disk will intersect at least one, and usually many, clumps. The rv,o values are somewhat sensitive to the choice of model viewing angle, so we are careful to match each galaxy to a model viewed at similar inclination. We also consider the effect of a gradient in the bulge stellar population on our results. A metallicity gradient in the sense of that observed in the
Milky Way bulge would cause us to overestimate rv,o, but we note that the maximum color change across galaxy dust lanes is much larger than the one expected from such a change in metallicity and thus that much of the observed dust lane color gradient is probably indeed due to attenuation effects.
The galaxy opacities that we find are consistent with much of the previous work on individual galaxies noted in Chapter 1, as well as some of the statistical studies of galaxy properties as a function of inclination. We suggest that the extinction appears
119 to decline away from the center of the disk by analyzing the major axis reddening trends in several galaxies. Combined with the fact that we infer the central optical depth to be not much greater than one, this implies that spirals are not optically thick over large parts of their disks when viewed face-on, as was suggested by Valentijn
(1990). We also demonstrate that a model with very high rv,oi which would be opaque over 3-4 disk scalelengths, produces colors that do not agree with our galaxy data.
We briefly discuss the implications of the optical depth results for some common techniques used to analyze images of spiral galaxies. The radial color gradients due to attenuation that would be associated with the rv,o values we derive are much smaller than those measured across face-on spirals {e.g., de Jong 1996a), which suggests that the observed radial color gradients are mostly due to changes in the stellar population across the disk. The line-of-sight optical depths through the dust lanes of highly inclined galaxies that are implied by the face-on optical depths we derive range from
14 - 55 in the V'-band. Thus these dust lanes are likely to be optically thick even in the NIR K-band (tv = O.IOtk, Whittet 1992), which is often assumed to be relatively free of extinction. Therefore, observations of the high opacity dust lanes will only sample light from outer regions of the galaxy. The implications of this effect must be considered when determining mass distributions from light distributions and when analyzing spectra to study kinematics and stellar populations.
The good agreement we find between galaxy and model color trajectories and the favorable comparison of our inferred optical depths to published values obtained from a variety of different methods suggests that this set of disk radiative transfer models is a useful tool to diagnose attenuation effects in highly inclined, intermediate to late type spiral galaxies. Although broad-band photometry is hampered more than
120 spectroscopy by the effects of dust, it remains the most efficient tool for studying large samples of galaxies and very distant objects. A better understanding of attenuation effects in these data will be valuable for efforts to disentangle the effects of dust and stellar populations on the surface brightness distributions and colors that hold clues about galaxy structure, stellar content, and evolution.
6.2 Future Directions
There are several avenues of investigation that are logically related to the work pre sented in this dissertation. Broadly stated, the ultimate goal of any of these suggested areas of research is to understand and correct for attenuation effects in broad-band images of spiral galaxies. The attenuation of galaxy light by dust is a significant con tributor to uncertainties in many common analysis techniques. This list of ideas is certainly incomplete; it is simply intended to represent a sample of possible projects that would make significant contributions to the problem of understanding attenua tion effects.
• Extend this project to galaxies at lower inclinations to assess the importance of dumpiness and scattering and further test that disk radiative transfer models predict the observed reddening. Clumpy structure in the dust distribution is likely to play an increasing role in determining attenuation effects at lower inclination angles because some lines of sight will encounter no clumps and others may encounter one or more.
.A.t high inclinations, all lines of sight are likely to encounter several clumps and thus a homogeneous dust distribution is expected to work well in predicting reddening.
Scattering may also become more important at lower inclinations. Light scattered
121 from disk dust grains is most easily observable if it is scattered out of the plane (a photon scattered into the plane is likely to be absorbed or scattered again when it encounters more dust), and while this light is not in the line of sight for edge-on galaxies, it is emitted directly towards the observer at face-on inclinations.
• Use disk galaxy radiative transfer models to produce optical depth maps. These maps would identify the galaxy locations and inclinations at which disk dust lanes become optically thick and thus would provide a great deal of insight into where the observed galaxy light originates as a function of wavelength. The attenuations asso ciated with these optical depths, which are also part of the model calculations, can be used to correct broad-band images of galaxies for the effects of dust. These correc tions would help disentangle the reddening produced by dust from stellar population gradients to give an improved picture of a galaxy's star formation history. They could also be used to understand how M/L changes over galaxy dust features or even to crudely correct the light distribution so that a constant M/L can be invoked. .A. bet ter understanding of the stellar light distribution in the inner regions of spirals, when combined with kinematical data, will shed light on the interaction between disks and bulges, the history of bulge and disk components, the relationship between bars and bulges, and why some galaxies have boxy or peanut-shaped bulges.
• Investigate the role of dust in determining the apparent morphology of galaxies at various wavelengths. Morphological features hold valuable clues about the structure and evolution of galaxies and are easily obtainable for large samples and out to great distances. Traditional morphological classifications have been carried out mainly on
B and V images of galaxies, but recent surveys in the NIR {e.g., Heraudeau et al.
1996) find that features such as bars are often obscured by dust at optical wave
122 lengths. Extinction in the disk is known to affect measurements of disk scalelength as a function of wavelength and may also affect the determination of B/D ratios (Evans
1994). As a first step in understanding the interplay between dust and apparent mor phology, one could study the variation of B/D as a function of wavelength in both real galaxies and simulated model images. A comparison of the galaxy and model wavelength dependences of B/D would also help disentangle the stellar population differences between bulge and disk from the effects of attenuation.
• .A.dd plausible features such as bulge population gradients, radial population gradi ents in the disk, etc. to the radiative transfer models to see if these features improve the model reddening predictions. Features such as these have been observed in our own and nearby galaxies {e.g., Tiede et al. 1995, de Jong 1996a), so their addition would make the models more realistic. However, we wish to find the simplest model that adequately describes attenuation effects, and it may not be necessary to add every observed physical detail of galaxies to the models.
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