Dark and Luminous Matter in Bright Spiral

DISSERTATION

Presented in Partial Fulfillment of the Requirements for

the Degree Doctor of Philosophy in the

Graduate School of The Ohio State University

By

Susan Alice Joan Kassin

*****

The Ohio State University

2004

Dissertation Committee: Approved by

Professor Richard Pogge, Adviser

Professor Bradley Peterson Adviser Astronomy Graduate Program Professor Christopher Kochanek

Professor Jay Frogel ABSTRACT

I present photometrically calibrated images and surface photometry in the

B, V, R, J, H, and K-bands of 26, and in the g, r, and K-bands of 5 nearby bright

o (BT < 12.5 mag) spiral galaxies with inclinations between 30–65 degrees spanning the Hubble Sequence from Sa to Scd. Data are from The Ohio State University

Bright Spiral Survey, the Two Micron All Sky Survey, and the Sloan Digital

Sky Survey Second Data Release. Radial surface brightness profiles are extracted, and integrated magnitudes are measured from the profiles. Axis ratios, position angles, and scale lengths are measured from the near-infrared. A 1-dimensional bulge/disk decomposition is performed on galaxies with a non-negligable bulge component.

Radial stellar mass distributions are estimated by applying color-M/L relations derived from spectrophotometric evolution models to the photometry.

When available, radial gas masses are added to the radial stellar mass distributions to produce radial baryonic mass distributions. For each galaxy, a rotation curve due to its radial baryonic mass distribution is calculated, taking into account both the bulge and disk components when necessary. All of the galaxies have high-quality

ii rotation curves available in the literature which allows us to calculate radial distributions for each galaxy by comparison with the baryonic mass rotation curves. Most galaxies are found to have maximal stellar disks, but seven are found to be submaximal in their inner parts (inner five scale radii). The following quantities are derived to characterize the radial baryonic and dark matter content of galaxies, and are found to correlate with Hubble Type: the peak velocity of the baryonic rotation curve (V∗,max), the radius at which the dark matter contributes 10% to the observed rotation curve (R10), and the radius at which dark matter contributes 50%

2 2 (RX ). From the radial distribution of β(r) ≡ V∗ (r)/Vtot(r), I find that although the behavior of the dark matter distributions are qualitatively similar from galaxy to galaxy, there is systematic scatter among them to argue against a universal rotation curve. The general qualitative shape the β(r) curves is what is expected from an exponential baryonic disk and a rotation curve that is nearly flat at large radii.

iii Dedicated to Prof. Joe Patterson who knew enough to send a

freshman to Chile.

iv ACKNOWLEDGMENTS

I would like to thank my adviser Dr. Richard Pogge for his untiring advice, patience, and, of course, computer support. I would also like to thank Dr. Roelof de

Jong for his advice, patience, productive collaboration in Baltimore, and for that memorable dinner with N, F, and W. Thank you Dr. Jay Frogel for creating the

Ohio State University Bright Spiral Galaxy Survey, for providing me with some good scotch to make it go down easier, and for marrying Dr. Susana Deustua who made me visit the AAS Job Center in Atlanta which ultimately got me my job at UCSC

(thanks Susanna).

I would like to thank my closest friends for their untiring love and support: the Rasta Chimweme “Silver Bullet” Mphande, Robert “Laphroaig 20-yr” Farrell,

Geraldine “Barbie” O’Brien, the one and only Brad Neuberg, and Mme. Louise

Powers (in order of response time to my phone-mail messages-ha!).

Thanks to Drs. Joe Patterson and Marc Kamionkowski for your inspiration at

Columbia.

I would also like to thank The Ohio State University Department of Astronomy, especially Dr. Brad Peterson and James Pizagno for their support and encouragement

v and Dr. Andy Gould for admitting me to the graduate program. Thank you Benne

Holwerda for your friendship, encouragement, and Benne-breaks. I wouldn’t have survived Baltimore without you! Thanks to Dr. Carol Christian, Prof. C.D., and

Sra. Summer for letting me stay at the “resort” in Baltimore. Thank you Nicole

Marie for letting me watch Sibyl in your beautiful apartment! Thank you Yoni

Hucke Atan and of course Mahina. And, thank you Blackie’s chai and the gang at

Shi-sha for keeping me out of trouble.

I would like to thank the astronomers who provided copies of their galaxy rotation curves in tabular form via email: Kor Begeman, Gianfranco Gentile, Thilo

Kranz, Povilas Palunas, Stuart Ryder, Michele Thornley, and Wilfred Walsh. I would also like to thank Marc Verheijen for making available his high-quality imaging and rotation curves of galaxies in the cluster.

I thank the CTIO TAC for generous allocation of time for the OSU Galaxy

Survey and the many people over the years who helped collect these observations.

Funding for the OSU Bright Spiral Galaxy Survey was provided by grants from

The National Science Foundation (grants AST-9217716 and AST-9617006), with additional funding by The Ohio State University.

I would like to acknowledge financial support from The Space Science

Institute Director’s Discretionary Research Fund (DDRF) which was invaluable in allowing me to study with Roelof de Jong at Space Telescope.

vi This research makes use of data from both the and the Two Micron All Sky Survey. The Two Micron All Sky Survey was a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National

Aeronautics and Space Administration and the National Science Foundation.

Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National

Aeronautics and Space Administration, the National Science Foundation, the

U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck

Society. SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions: The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University,

Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University,

University of Pittsburgh, Princeton University, the United States Naval Observatory, and the University of Washington.

I also made use of NASA’s Astrophysics Data System, the NASA/IPAC

Extragalactic Database (NED), the HyperLeda database, and the VizieR catalog.

NED is operated by the Jet Propulsion Laboratory, California Institute of

Technology, under contract with NASA, and HyperLeda database and VizieR are operated by the CDS in Strasbourg, France.

vii VITA

November 18, 1977 ...... Born – Manhasset, New York

1999 ...... B.A. Physics, Columbia College, Columbia University

1999 – 2000 ...... Distinguished University Graduate Fellow, The Ohio State University

2002 ...... M.S. Astronomy, The Ohio State University

2000 – 2004 ...... Graduate Teaching and Research Associate, The Ohio State University

PUBLICATIONS

Research Publications

1. S. A. Kassin, J. A. Frogel, R. W. Pogge, G. P. Tiede, and K. Sellgren, “Stellar Populations in NGC 4038/39 (the Antennae): Exploring a Galaxy Merger Pixel by Pixel”, AJ, 126, 1276, (2003).

2. J. P. Halpern, R. Uglesich, N. Mirabal, S. Kassin, J. Thorstensen, W. C. Keel, A. Diercks, J. S. Bloom, F. Harrison, J. Mattox, and M. Eracleous, “GRB 991216 Joins the Jet Set: Discovery and Monitoring of Its Optical Afterglow”, ApJ, 543, 697, (2000).

FIELDS OF STUDY

Major Field: Astronomy

viii Table of Contents

Abstract ...... ii

Dedication ...... iv

Acknowledgments ...... v

Vita ...... viii

List of Tables ...... x

List of Figures ...... xii

1 Introduction 1

1.1 Dark and Luminous Matter in Galaxies ...... 1

1.2 Relation to Previous Work ...... 5

1.3 Scope of the Dissertation ...... 8

2 Data Sample and Analysis 9

2.1 Data Sets ...... 9

2.2 Observation and Reduction of the OSUBSGS Galaxies ...... 11

2.3 Photometric Calibration ...... 13

2.3.1 OSUBSGS & 2MASS Galaxies ...... 13

2.3.2 SDSS DR2 Galaxies ...... 16

3 Surface Brightness Profiles and Physical Properties of the Galaxies 22

ix 3.1 Axis Ratios & Position Angles ...... 22

3.2 Radial Surface Brightness Profiles ...... 23

3.2.1 Bulge/Disk Decompositions ...... 25

3.3 Distances ...... 26

4 Radial Distributions of Baryonic and Dark Matter in Galaxies 43

4.1 Baryonic Matter ...... 44

4.1.1 Radial Baryonic Surface Mass-Density Distributions ...... 44

4.1.2 Baryonic Rotation Curves ...... 46

4.1.3 Uncertainties in Baryonic Rotation Curves ...... 47

4.1.4 Effects Due to Dust ...... 48

4.2 Dark Matter ...... 51

4.2.1 Observed Rotation Curves ...... 51

4.2.2 Dark Matter Rotation Curves ...... 53

4.2.3 Uncertainties in Dark Matter Rotation Curves ...... 53

5 Baryonic and Dark Matter Properties 68

5.1 Maximal and Non-Maximal Disks ...... 68

5.2 Dark and Baryonic Matter Correlations ...... 70

5.3 Radial Behavior of Dark Matter ...... 72

6 Conclusions 81

Bibliography 82

x List of Tables

2.1 Basic parameters of the sample galaxies...... 17

2.1 Basic parameters of the sample galaxies...... 18

2.2 Observational Details for the OSUBSGS Galaxies ...... 19

2.2 Observational Details for the OSUBSGS Galaxies ...... 20

2.2 Observational Details for the OSUBSGS Galaxies ...... 21

3.1 Measured Galaxy Parameters ...... 34

3.1 Measured Galaxy Parameters ...... 35

3.1 Measured Galaxy Parameters ...... 36

3.1 Measured Galaxy Parameters ...... 37

3.1 Measured Galaxy Parameters ...... 38

3.1 Measured Galaxy Parameters ...... 39

3.1 Measured Galaxy Parameters ...... 40

3.2 Bulge/Disk Parameters for K-band Images ...... 41

3.2 Bulge/Disk Parameters for K-band Images ...... 42

4.1 Sources of Rotation Curve Data ...... 66

4.1 Sources of Rotation Curve Data ...... 67

5.1 Parameters Derived From Observed, Baryonic Matter, and Dark Matter Rotation Curves ...... 79

xi 5.1 Parameters Derived From Observed, Baryonic Matter, and Dark Matter Rotation Curves ...... 80

xii List of Figures

3.1 Surface brightness profiles and B and K-band images for the sample galaxies (1 of 11)...... 27

3.2 Surface brightness profiles and B and K-band images (2 of 11). . . . 28

3.3 Surface brightness profiles and B and K-band images (3 of 11). . . . 29

3.4 Surface brightness profiles and B and K-band images (4 of 11). . . . 30

3.5 Surface brightness profiles and B and K-band images (5 of 11). . . . 31

3.6 Surface brightness profiles and B and K-band images (6 of 11). . . . 32

3.7 Surface brightness profiles and B and K-band images (7 of 11). . . . 33

4.1 Color-M/L relation for the B − R color and M/L at K...... 55

4.2 The rotation curve for NGC 1090 due to the stellar mass component is compared with the rotation curve due to and gas...... 56

4.3 Observed, baryonic, and dark matter rotation curves (1 of 6). . . . . 57

4.4 Observed, baryonic, and dark matter rotation curves (2 of 6). . . . . 58

4.5 Observed, baryonic, and dark matter rotation curves (3 of 6). . . . . 59

4.6 Observed, baryonic, and dark matter rotation curves (4 of 6). . . . . 60

4.7 Observed, baryonic, and dark matter rotation curves (5 of 6). . . . . 61

4.8 Observed, baryonic, and dark matter rotation curves (6 of 6). . . . . 62

4.9 The effects of various systematic uncertainties on the baryonic rotation curves derived for NGC 157...... 63

xiii 4.10 A demonstration of the first-order effects of dust in NGC 157. . . . . 64

4.11 Baryonic rotation curves for both sides of NGC 4062 and 7083. . . . . 65

5.1 Relations between basic physical parameters of galaxies and Hubble T-type ...... 75

5.2 Relations for Vtot,max and V∗,max ...... 76

5.3 Relations for RX/hK ...... 77

2 2 5.4 β(r) ≡ V∗ (r)/Vtot(r) is plotted for galaxies with an appreciable dark matter contribution ...... 78

xiv Chapter 1

Introduction

1.1. Dark and Luminous Matter in Galaxies

One of the most persistent mysteries in modern astronomy is the observation that most of the matter in our Universe is unaccounted for if Newtonian and

Einsteinian theories of gravity are correct. Evidence for this “dark matter” is varied, with the most direct evidence coming from observations of galaxies in the local Universe. In these galaxies, the mass due to the visible stars and gas is only

∼ 10% of their total mass calculated from dynamics. The other ∼ 90% is either a form of matter that does not emit light (hence “dark matter”), or a sign that the theory of Newtonian gravity is invalid on the scale of galaxies. In this paper, as in most of the field of astronomy, I will presume the former. Not much is known about the properties of the postulated dark matter, even though it seems to pervade the Universe. Little is known about how much of it exists in galaxies, or even its distribution in galaxies (i.e., where it is located relative to the luminous stellar mass that we can see).

1 Typical bright galaxies are composed of around ten to one hundred billion stars that orbit about a common center. Using Newtonian gravity, astronomers can measure the total amount of matter in a galaxy by measuring the orbital speeds of the stars in it. To measure the combined mass of all the stars in a galaxy, astronomers usually measure how bright a galaxy is in one wavelength of light (e.g., blue, red, yellow, infrared, etc.) and infer how many stars of different types are needed to produce this light. Then, using information previously determined about the masses of different types of stars, they estimate how much mass is present in the galaxy in the form of stars. When one compares the amount of matter in stars

(stellar mass) to the total amount of matter in a galaxy inferred from the orbital speeds of its stars (dynamical mass), the stellar mass is found to contribute only about ∼ 10% to the total dynamical mass.

These numbers are the result of an empirical estimate of the distribution and amount of stellar mass that ignores the fact that different types of stars shine predominately at different wavelengths. For example, hot young stars emit primarily at ultraviolet wavelengths, while older, cooler stars that make up the majority of stars emit primarily at infrared wavelengths. Thus, by using only one wavelength, an astronomer must make simplifying assumptions about the different contributions from all of the different types of stars present. Using multiple wavelengths gives a more accurate census of the stellar populations present in galaxies, and in principle should result in a more robust estimate of their total stellar mass.

2 In this work, I have eliminated some of these assumptions by using images of galaxies in six different wavelength bands, ranging from the visible to the near-infrared (λ = 0.4–2.2µm). The galaxies in this sample come mainly from The

Ohio State University Bright Spiral Galaxy Survey (OSUBSGS), a collection of about 200 galaxies with images in 6 bands (BVRJHK). Observed galaxy rotation curves were taken from data in the literature for the final sample of 36 galaxies. Due to the difficulty of obtaining and calibrating such a sample of galaxies of comparable image quality in six wavebands for which dynamical information is available, this is the first time such an analysis has been done for a homogeneous galaxy sample.

Recently, Bell & de Jong (2001) combined models of the evolution of stars and galaxies with existing photometric data for galaxies to derive empirical relations between the photometric colors brightness and mass-to-light ratios (M/L) of galaxies. A mass-to-light ratio measures the amount of stellar mass (in solar units of 1.98 × 1030 kg) corresponding to each interval of stellar luminosity (also in solar units of 3.826 × 1026 watts). Their analysis used images of galaxies in multiple bands. For example, they found a strong correlation between the B − R colors of galaxies and M/L measured in the near-infrared K-band (λc = 2.2µm). This has been found to give a more accurate result than simply “counting” stars detected in different bands, since it takes into account important factors such as very dim stars that cannot be detected in any band (i.e., those described in Kranz 2002). I apply the B − R vs. M/LK relation from Bell & de Jong (2001) to my sample of galaxies

3 in order to map the amount and distribution of stellar mass present in them and create a more accurate calculation of the stellar mass of galaxies than was previously done.

The OSUBSGS images have a combination of high photometric quality

(generally < §4%) and good angular resolution (1–2 arcsec) that allows a precise measurement of the radial distribution of the light in galaxies. These data, when combined with the empirical color-M/L relations of Bell & de Jong (2001), allow an accurate determination of the radial distributions of stellar mass in these galaxies.

When available, radial gas masses are added to the radial stellar mass distributions to produce radial baryonic mass distributions. From the detailed radial baryonic mass distribution and the observed dynamical masses determined at different radii,

I calculate a detailed distribution of the dark matter in these galaxies. These distributions are presented in Chapter 4.

Cosmological theories of galaxy formation make specific predictions about the distribution of dark matter in galaxies. A measurement of this distribution serves as an empirical test of these theories. For example, if dark matter is distributed similarly in all galaxies, we can infer the properties that candidate dark matter particles must have and the conditions necessary in the early Universe to produce such a distribution. Similarly, we can infer information about the physical properties of dark matter and the conditions necessary in the early Universe if there are

4 relations between the distributions of dark matter in galaxies and their morphological or other structural properties.

1.2. Relation to Previous Work

Much of the previous work on this problem has concentrated on the analysis of correlations between dynamical and photometric quantities evaluated at the approximate optical edge of the galactic disks, usually defined as Ropt ≡ 3.2h for an exponential disk where h is the scale length (Persic, Salucci, & Stel 1996).

This radius roughly corresponds to R25 for a Freeman disk (Freeman 1970). These quantities were measured under the assumption that little baryonic matter exists beyond R25 that can contribute to a rotation curve. In particular, the most telling correlations at Ropt are: (1) A linear relation was given in Persic & Salucci (1990) between the ratio of the mass of the dark matter to the total mass present MDM /Mtot and the mean slope of the rotation curve. This relation is such that galaxies with steeper slopes have greater dark matter fractions. (2) The slope of a galaxy’s rotation curve was found to be proportional to both the log of its luminosity and the log of the velocity of rotation curve due to the baryonic matter (Persic et al. 1996). These relations are such that rotation curve velocities are very steep at low luminosities and become gradually flat at greater luminosities and velocities (Persic et al. 1996).

2/3 (3) Also in Persic & Salucci (1990), it was found that Mdisk/Mhalo ∝ LB (where

5 Mdisk is the mass of the disk, Mhalo is the mass of the , and LB is the luminosity in the B-band) such that bright spirals have more baryonic than dark matter (and vice-versa for low-luminosity spirals). (4) The quantity β is defined in

2 2 Salucci (2001) as VLum/Vtot, and was termed the “disk mass fraction.” It was found to correlate tightly with the slope of the rotation curve (Salucci 2001). (5) The total

0.5 halo mass was found to scale as LI (Persic, Salucci, & Stel 1996). (6) The slope of the dark matter rotation curves at Ropt (as derived by using a fixed baryonic rotation curve slope for all galaxies), was found to be constant over the entire sample without much scatter. This slope was found to be steeply increasing with a mean of 0.8 § 0.1

(Salucci 2001). In short, these authors discovered that the profile and amplitude of rotation curves have a strong dependence on luminosity. Moreover, they found that the rotation curves of spiral galaxies are determined by a single parameter (i.e., luminosity).

Persic et al. (1996) found that higher luminosity spirals have a small dark matter content within Ropt, and show a kinematic signature of a transition from a luminosity-dominated to a dark-matter dominated region. They found that low-luminosity spirals are nearly entirely dominated by dark matter, and that the transition from baryonic to dark matter dominance occurs within Ropt, before the disk half-mass radius, and without a feature marking the transition. Furthermore,

−1 1.2 Salucci (2001) defined a radius RIBD ≤ 2Rd(Vopt/200 km s ) (“Radius of Inner

Baryon Dominance”) such that for R < RIBD, dark matter begins to significantly

6 contribute to the gravitational potential, which is similar to Rt which is defined as the innermost radius at which the baryonic mass fails to account for a galaxy’s rotation by greater than 4 times the typical observational error (Persic et al. 1996).

RIBD was found to be a function of galaxy luminosity (Ratnam & Salucci 2000).

Adding to this picture, Casertano & van Gorkom (1991) measured the slopes of

2 the rotation curves of 28 galaxies between /3R25 and the radius of last measurement of the rotation curve. Similarly, they observed that these slopes are correlated with the maximum total mass, rotation velocity, scale length, central surface brightness, and Hubble T-type. These relations are such that the more positive the slope (rising rotation curve), the slower the maximum rotation velocity, the shorter the scale length, the fainter the central surface brightness, and the earlier the Hubble type of the galaxy.

Another question I will address is whether maximal disks are present in bright spiral galaxies. See Chapter 7.1.3.1 of Kranz (2002) for a thorough discussion of the various different approaches to this issue and their results; here I summarize the main points. Studies that used high resolution rotation curves have argued for maximal disks (Blais-Ouellette et al. 2004). Authors which have modeled the rotation curves of galaxies have found maximal disks in addition to evidence for lower disk mass fractions (Erickson, Gottesman, & Hunter 1999; Pignatelli et al.

2001). Dynamical studies of bars in galaxies have long supported the maximum disk scenario (Englmaier & Gerhard 1999; Weiner 2001) . On the other hand,

7 Bottema (1997) used stellar velocity dispersion measurements to argue for a greater dark matter contribution. Courteau & Rix (1999) and Maller et al. (2000) use the residuals of the Tully-Fisher relation and gravitational lensing, respectively, to investigate this question and both find evidence for lighter disks. Finally, Kranz

(2002) dynamically modeled the stellar disks of five galaxies. He finds that the two most massive galaxies in his sample have maximal disks, while the other three have a dark matter mass that was found to at least match the stellar mass.

1.3. Scope of the Dissertation

The outline of this dissertation is as follows: In Chapter 2, I discuss the data sample. I describe each data set that was incorporated, particularly The Ohio State

University Bright Spiral Galaxy Survey. In Chapter 3, I present the imaging data and measure the photometric and structural properties of the sample galaxies. In

Chapter 4 I present the kinematic data and combine these with the photometric data from Chapter 3 to calculate the baryonic and dark matter distributions. In

Chapter 5 I discuss the baryonic and dark matter properties. Finally, in Chapter 6,

I summarize the results of this work and propose some directions for future research.

8 Chapter 2

Data Sample and Analysis

2.1. Data Sets

My sample includes 31 galaxies from The Ohio State University Bright Spiral

Galaxy Survey (OSUBSGS; Esrkidge (2003)), the Two Micron All Sky Survey

(2MASS; Jarrett et al. (2000); Cutrie et al. (2000); Jarrett et al. (2003)), and the second data release of the Sloan Digital Sky Survey (SDSS DR2; Abazajian et al. (2004)) which span the Hubble Sequence of spirals from Sa to Scd for bright

o galaxies (BT < 12.5 mag). One of these galaxies has B and R profiles from Verheijen

(1997), and another has H and K profiles from de Jong (1996). Furthermore, this sample is supplemented with five bright galaxies from a sample of galaxies in Ursa

Major (Verheijen 1997) to create a final sample of 35 galaxies. Table 2.1 1 lists

−2 all the galaxies in my sample, the morphological class, the µB = 25 mag arcsec isophotal diameter (D25) from de Vaucouleurs et al. (1991) (hereafter, RC3), the heliocentric (Vhel), and the adopted distance in Megaparsecs. I also list the parameters of galaxies from the Verheijen (1997) sample that will be used in the subsequent analysis. Additional galaxies were selected from the SDSS DR2

9 and 2MASS surveys if they had (1) sufficient quality imaging to create a high signal-to-noise surface brightness profiles at g, r, and K, (2) a rotation curve in the literature, (3) an inclination between 29.5 and 66.4 degrees in order to reduce the effect of dust extinction while still being able to obtain accurate dynamical

o information, (4) BT < 12 mag to satisfy the selection criterion of the OSUBSGS, and (5) a galactic latitude where the absorption due to our Galaxy is known from

Schlegel, Finkbeiner, & Davis (1998). The selected galaxies would have been in the

OSUBSGS, but are either too large (D25 > 6.5 arcminutes) to fit in the field-of-view of the infrared array cameras of the time that the survey was carried out or were not observable during the OSUBSGS observing runs.

The OSUBSGS is a sample of nearly 200 nearby bright spiral galaxies.

Twenty-five of the galaxies studied in this dissertation have imaging in at least one band from the OSUBSGS, 12 have at least one band from 2MASS, and five from the SDSS DR2. I use 2MASS K-band data to calibrate the OSUBSGS near-infrared images, and in some cases, to replace them. Galaxies in the OSUBSGS were chosen from the RC3 to have 1 ≤ TRC3 ≤ 7 where TRC3 is the mean numerical Hubble

o stage index as tabulated in the RC3, BT ≤ 12, D25 ≤ 6.5 arcminutes where D25

−2 the apparent major isophotal diameter measured at µB=25 mag arcsec , and

−80 < δ < +50 degrees where δ the declination (due to the pointing limits of the Cerro Tololo Interamerican Observatory (CTIO) 1.5-meter and the Lowell

Observatory Perkins 1.8-meter ). I imposed a few additional criteria to

10 select galaxies from the OSUBSGS: (1) As with the SDSS DR2 selection, galaxies were required to be non-interacting and within an optimal inclination range (30–65 degrees), (2) candidate galaxies were also selected to have Galactic latitudes where the absorption due to our Galaxy is known from Schlegel, Finkbeiner, & Davis

(1998), (3) galaxies were required to have a photometric optical calibration in the

OSUBSGS, (4) galaxies were also required to have a photometric near-infrared calibration in the OSUBSGS or the 2MASS, (5) and, they were required to have a rotation curve available from the literature.

2.2. Observation and Reduction of the OSUBSGS

Galaxies

Data for the OSUBSGS were obtained during a large number of observing runs with six telescopes of apertures between 0.9 and 1.8 meters during the period

1993–2000. Table 2.2 lists the telescope, instrument, and detector used for each

final image in my sample, along with the date each image was taken. For details about the telescopes and instruments used see Esrkidge (2003). The observations were made by the OSUBSGS team and their students, as well as by a professional observer (Roberto Aviles) hired by the project at CTIO. I did not make any new observations for this present work.

11 The optical images were taken through Kron-Cousins B, V and R filters. For each galaxy, three images were acquired per filter, giving total on-source integration times of approximately 20–30 minutes for B, 10–15 minutes for V , and 5–10 minutes for R on both photometric and non-photometric nights. Even though different telescopes and instruments were used, exposure times were adapted to create images that achieved similar limiting surface brightness levels for each galaxy. A combination of twilight sky and illuminated dome screen images were used to provide a flat-field calibration in the optical.

The near-infrared images were taken through standard J, H, and K filters.

Typically, a set of five 20-second integrations were taken in an ×- or a +-shaped pattern, interspersed with comparable exposures of off-target sky fields. Dithering in this way permitted removal of bad pixels and detector blemishes. The total on-source integration times per galaxy for deep images at J and H were typically 10–15 minutes, and at K typically 20–30 minutes. For galaxies with deep exposures on non-photometric nights, additional “snapshot” images were acquired on photometric nights, with the same unit exposures as the deep images, but only one set instead of five. As in the optical, exposure times were adapted to create images that reach similar surface brightness levels for each galaxy. Dome flats with the lights on and off were used to create the near-infrared flat-field calibration.

12 2.3. Photometric Calibration

2.3.1. OSUBSGS & 2MASS Galaxies

Nights were judged to be photometric in three stages. First, at the telescope the observer would make a decision based on the weather and acquire standard images if the night was apparently photometric. Second, the standard star data were reduced and it was verified that the residuals between the observed and cataloged standard star magnitudes did not change during the night. Finally, the photometric zero-points for contiguous nights were checked for consistency. If the zero-points for a night were not consistent with adjoining nights and there was no change to the observing set-up (i.e., instrument changes between nights) that could account for the difference, then the night was judged to be non-photometric, and images from those nights had to be excluded from further consideration.

For optical photometric calibration, equatorial standard star fields from Landolt

(1992) were observed at a range of airmasses to derive photometric transformations onto the Kron-Cousins BV R system. Photometric zero-points, airmass terms, and

B − V color terms were calculated for each night with the fitparams task in IRAF.

For each night, a photometric solution was fit to the standard star observations which included both airmass and B − V color terms. Standard star observations which were outliers to this solution were examined and generally were found to

13 be problematic due to factors such as cosmic ray contamination, bad pixels, bad columns/rows, or because some stars were imaged near the edges of the detectors.

For galaxies with deep optical images taken on photometric nights, the calibration solution calculated for that night was directly applied to the BV R surface brightness profiles. For galaxies whose deep optical images were taken during non-photometric conditions, shallow images were taken on photometric nights, and surface brightness profiles calculated from the shallow images were calibrated with the photometric solution for those nights. Profiles calculated from deep images taken on non-photometric nights are then calibrated with a “bootstrap” zero-point determined by comparing the shallow calibrated profiles to the deep profiles (extraction of profiles is described in §3.2). The internal consistency of my photometric solutions was checked by comparing adjacent nights in observing runs with the same detector/camera/telescope configuration.

OSUBSGS J, H, and K-band images are photometrically calibrated with data from 2MASS. I apply the zero-points to the 2MASS images that are listed in their image headers. An attempt was made to use standard stars from the list of Carter

& Meadows (1995), but due to ambiguities in the data I decided to calibrate them against the 2MASS database instead. JCIT , HCIT , and KCIT were transformed to

J2MASS, H2MASS, and KS,2MASS using the transformations tabulated on the 2MASS

14 website3:

(KS)2MASS = KCIT − (.019 § 0.004) + (0.001 § 0.005)(J − K)CIT (2.1)

(J − KS)2MASS = 1.068 § 0.009(J − KCIT ) − 0.020 § 0.007 (2.2)

(H − KS)2MASS = 1.000 § 0.023(H − KCIT ) + 0.034 § 0.006 (2.3)

KCIT transforms to KS,2MASS with a zero-point shift and no color term to within

0.005 mag, JCIT transforms to J2MASS with a dependence on K, and HCIT transforms into H2MASS with a dependence on J.

I calibrated the near-infrared surface brightness profiles from my sample by

finding the best-fit combination of a sky determination and magnitude zero-point that allows for the smallest difference between the profiles. I chose to use the

OSUBSGS profiles for a number of galaxies, even though they generally have poorer sky measurements, since they have higher signal-to-noise ratios throughout, and extend to larger galactocentric radii essential for the subsequent analysis. On average, the OSUBSGS infrared images have limiting surface brightnesses of ∼ 2 mag arcsec−2 fainter than those from 2MASS. The calibration is done by plotting the calibrated flux from a 2MASS profile against the instrumental counts from an

OSUBSGS profile. A straight line is fit to these data; its slope determines the bootstrap zero-point necessary to calibrate the OSUBSGS image, and the intercept determines the sky offset multiplied by the zero-point. This procedure works

3http://www.astro.caltech.edu/∼jmc/2mass/v3/transformations/

15 because for a typical galaxy in the sample, the color terms are small (∼ 1%). The photometric zero-point calibration of the 2MASS galaxies is accurate to §2%–3%

(Cutrie et al. 2000). However, as warned in Appendix A of Jarrett et al. (2000), a small fraction of the galaxies may be affected by high-frequency background variations, causing the photometric error to increase. This does not appear to be the case in those galaxies presented here.

2.3.2. SDSS DR2 Galaxies

For the SDSS DR2 images, the zero-point calibration is accurate to §2% in both SDSS r and SDSS g − r (Lupton et al. 2001). For these SDSS DR2 galaxies,

I apply the zero-points and extinction terms as given in the “best TsField” FITS table.

16 Table 2.1. Basic parameters of the sample galaxies.

D25 Vhel Distance Galaxy RC3 Type (00) (km s−1) (Mpc)

NGC 157 SAB(rs)bc 250 1668 21.6 NGC 289 SAB(rs)bc 308 1628 19.9 NGC 488 SA(r)b 315 2272 31.0 NGC 908 SA(s)c 362 1498 18.9 NGC 1087 SAB(rs)c 223 1519 20.7 NGC 1090b SB(rs)bc 239 2758 37.9 NGC 1241 SB(rs)b 169 4052 55.5 NGC 1385 SB(s)cd 203 1493 19.3 NGC 1559 SB(s)cd 208 1292 15.8 NGC 1832 SB(r)bc 154 1937 27.3 NGC 2090 SA(rs)b 294 931 12.3c NGC 2139 SAB(rs)cd 158 1843 26.2 NGC 2280 SA(s)cd 379 1906 27.5 NGC 2841b SA(r)b 488 638 14.1c NGC 3198b SB(rs)c 511 663 14.5c NGC 3223 SA(r)bc 244 2895 43.6 NGC 3319 SB(rs)cd 370 739 14.3c NGC 3521b SAB(rs)bc 658 805 9.4 NGC 3726 SAB(r)c 370 866 21.7 NGC 3893 SAB(rs)c 268 967 23.6 NGC 3949a SA(s)bc 173 · · · 20.7 NGC 3953a SB(r)bc 415 · · · 20.7 NGC 3992a SB(rs)bc 455 · · · 20.7

(cont’d)

17 Table 2.1—Continued

D25 Vhel Distance Galaxy RC3 Type (00) (km s−1) (Mpc)

NGC 4051 SAB(rs)bc 315 · · · 5.2 NGC 4062 SA(s)c 244 769 10.8d NGC 4138a SA(r)0+ 154 · · · 20.7 NGC 4580 SAB(rs)a pec 125 1034 28.3d NGC 4651 SA(rs)c 239 805 18.3d NGC 4698 SA(s)ab 239 1002 19.1d NGC 5371 SAB(rs)bc 262 2553 45.1 NGC 5806b SAB(s)b 185 1359 26.4 NGC 6300 SB(rs)b 268 1110 14.5 NGC 7083 SAB(rs)c 233 3109 40.5 NGC 7217 (R)SA(r)ab 233 952 15.9 NGC 7606 SA(s)b 322 2233 29.4

aAll imaging is from Verheijen (1997)

bAll imaging is from SDSS DR2 & 2MASS cDistance measured from observations of Cepheid variable stars dGalaxies which have a triple-valued solution for the infall calculation. The chosen solution is the one that is the closest to the calculated Tully-Fisher distance

(given Wr and H−0.5 from Tully (1988).

18 Table 2.2. Observational Details for the OSUBSGS Galaxies

Galaxy Bands Date Telescope Camera Detector

NGC 157 BVR 1995 Oct 29 CTIO 0.9m CFCCD Tek1K#2 JH 1995 Oct 08 Perkins 1.8m OSIRIS NICMOS3 K 2MASS · · · · · · · · · NGC 289 BVR 1995 Oct 26 CTIO 0.9m CFCCD Tek1K#2 JK 1996 Oct 01 CTIO 1.5m CIRIM NICMOS3 H 1996 Oct 02 CTIO 1.5m CIRIM NICMOS3 NGC 488 BVR 1994 Oct 11 Perkins 1.8m IFPS NCCD JHK 1995 Oct 18 Perkins 1.8m OSIRIS NICMOS3 NGC 908 BVR 1995 Oct 26 CTIO 0.9m CFCCD Tek1K#2 JHK 1996 Sep 30 CTIO 1.5m CIRIM NICMOS3 NGC 1087 BVR 1993 Sep 17 Perkins 1.8m IFPS NCCD J 1995 Oct 15 Perkins 1.8m OSIRIS NICMOS3 H 1995 Oct 06 Perkins 1.8m OSIRIS NICMOS3 K 2MASS · · · · · · · · · NGC 1241 BVR 1995 Oct 29 CTIO 0.9m CFCCD Tek1K#2 JH 1995 Oct 10 Perkins 1.8m OSIRIS NICMOS3 K 2MASS · · · · · · · · · NGC 1385 BVR 1995 Oct 27 CTIO 0.9m CFCCD Tek1K#2 JHK 2MASS · · · · · · · · · NGC 1559 BVR 1995 Oct 26 CTIO 0.9m CFCCD Tek1K#2 JHK 1995 Mar 10 CTIO 1.5 m CIRIM NICMOS3 NGC 1832 BVR 1994 Nov 01 CTIO 0.9m CFCCD Tek2K#3 JHK 2MASS · · · · · · · · · NGC 2090 BVR 1995 Mar 07 CTIO 1.5m CFCCD Tek1K#2 JHK 1995 Mar 08 CTIO 1.5m CIRIM NICMOS3 NGC 2139 BVR 1994 Apr 09 CTIO 0.9m CFCCD Tek1K#2 JHK 2MASS · · · · · · · · ·

(cont’d)

19 Table 2.2—Continued

Galaxy Bands Date Telescope Camera Detector

NGC 2280 BV 1995 Mar 08 CTIO 1.5m CFCCD Tek1K#2 R · · · · · · · · · · · · JH 1995 Mar 09 CTIO 1.5m CIRIM NICMOS3 K 1995 Mar 15 CTIO 1.5m CIRIM NICMOS3 NGC 3223 BVR 1994 Apr 07 CTIO 0.9m CFCCD Tek1K#2 JHK 1994 Feb 25 CTIO 1.5m OSIRIS NICMOS3 NGC 3319 BVR 2000 Apr 22 MDM 1.3m MIS Echelle JH 1995 Apr 25 Perkins 1.8m OSIRIS NICMOS3 K · · · · · · · · · · · · NGC 3726 BVR 2000 Apr 26 MDM 1.3m MIS Echelle JH 1996 Mar 08 Perkins 1.8m OSIRIS NICMOS3 K 1997 Mar 15 Perkins 1.8m OSIRIS NICMOS3 NGC 4051 BR Verheijen · · · · · · · · · V · · · · · · · · · · · · JH 1996 Mar 31 Perkins 1.8m OSIRIS NICMOS3 K 2MASS · · · · · · · · ·

(cont’d)

20 Table 2.2—Continued

Galaxy Bands Date Telescope Camera Detector

NGC 4062 BVR 1996 Feb 15 Perkins 1.8m IFPS NCCD J 2MASS · · · · · · · · · HK 1995 Mar 27 Perkins 1.8m OSIRIS NICMOS3 NGC 4580 BVR 1997 Mar 11 USNO CCD TI800 JH 1996 Apr 29 Perkins 1.8m OSIRIS NICMOS3 K 1997 Mar 30 Perkins 1.8m OSIRIS NICMOS3 NGC 4651 BVR 1997 Mar 11 USNO CCD TI800 J 2MASS · · · · · · · · · HK de Jong · · · · · · · · · NGC 4698 BVR 1998 Mar 24 MDM 2.4m MIS Templeton JH 1996 Apr 29 Perkins 1.8m OSIRIS NICMOS3 K 1997 Apr 07 Perkins 1.8m OSIRIS NICMOS3 NGC 5371 BVR 1996 Feb 15 Perkins 1.8m IFPS NCCD JHK 1995 Mar 23 Perkins 1.8m OSIRIS NICMOS3 NGC 6300 BVR 1996 Apr 12 CTIO 0.9m CFCCD Tek2K#3 JHK 2MASS · · · · · · · · · NGC 7083 BVR 1995 Oct 26 CTIO 0.9m CFCCD Tek1K#2 JHK 1996 Sep 26 CTIO 1.5m CIRIM NICMOS3 NGC 7217 B 1994 Oct 10 Perkins 1.8m IFPS NCCD VR 1993 Sep 18 Perkins 1.8m IFPS NCCD JH 1995 Oct 18 Perkins 1.8m OSIRIS NICMOS3 K 2MASS · · · · · · · · · NGC 7606 BVR 1994 Oct 11 Perkins 1.8m IFPS NCCD JHK 1994 Oct 25 CTIO 1.5m CIRIM NICMOS3

21 Chapter 3

Surface Brightness Profiles and Physical Properties of the Galaxies

In this chapter, I describe how the radial surface brightnss profiles and distances are calculated. These data will be used to create radial surface mass profiles in

Chapter 4.

3.1. Axis Ratios & Position Angles

In order to create surface brightness profiles, I first need to measure the axis ratio and position angle of each galaxy. Axis ratios and position angles are measured from the galaxies’ H-band images. For galaxies with SDSS DR2 and 2MASS images,

I adopt the position angles and axis ratios used in the literature for measuring their rotation curves. The H-band is chosen to measure physical parameters because near-infrared wavelengths trace most of the stellar mass in galaxies, and my H-band images generally have higher signal-to-noise than my J or K images. For each galaxy’s H-band image, ellipses are fit with increasing semi-major axis from the

22 galaxy’s center. This is done with the profile command in the XVista4 package, which uses a modification of Kent (1983)’s implementation of the azimuthal Fourier moments technique as described by Lauer (1985). The resulting plots of position angles and axis ratios of the ellipses versus radius are examined by eye, and a position angle and inclination are chosen for each galaxy at radii where the galaxy’s disk is exponential (usually between 2 and 3 scale lengths). As a check on the adopted parameters, an ellipse with the chosen axis ratio and position angle is plotted over the H-band image and is visually inspected. This procedure is repeated until the parameters derived for each galaxy passes a visual inspection. The measured axis ratio is converted into an inclination angle, i, assuming that the disks are intrinsically circular (q = cosı, where q is the ratio of minor and major axes). The final position angles and inclinations adopted for the galaxies are presented in columns 6 and 7 of

Table 3.1.

3.2. Radial Surface Brightness Profiles

To extract surface brightness profiles for each of my sample galaxies I used the

XVista command annulus. The SDSS DR2 galaxies are first aligned to the World

Coordinate System so that they are aligned with their respective 2MASS images.

The annulus command computes a radial surface brightness profile by finding the

4XVista is based on Lick Observatory Vista and maintained by a loose consortium of die-hard users at http://ganymede.nmsu.edu/holtz/xvista.

23 median surface brightness per pixel in elliptical annuli of increasing distance from the center of a galaxy. I choose to calculate the median (instead of the mean) surface brightness in order to avoid foreground stars and effects such as bad pixels which tend to corrupt the average statistic. Ellipse parameters are pre-determined for each galaxy, as discussed in §3.1, and centers are defined as the pixel in the nucleus with the highest surface brightness.

The resulting surface brightness profiles for each galaxy are presented in

Figures 3.1–3.7, alongside B and K-band images (KS for 2MASS images) for each galaxy to allow for comparison of surface brightness profiles with morphological properties. The profiles have been corrected for Galactic extinction using Schlegel et al. (1998) (see Fukugita et al. 1996 for the SDSS bands). The galaxies NGC 1090,

NGC 2841, and NGC 3198 have SDSS DR2 images in which slightly less than half of the galaxy is not present, as can be observed in the g-band images in Figures 3.2,

3.3, 3.4. This is also this case, but to a much lesser extent, for NGC 3521.

−2 Total magnitudes within the µB = 25 mag arcsec isophotal radius (R25) are measured by extrapolating surface brightness profiles with an exponential function, and integrating the galaxy’s light to R25. The resulting magnitudes are listed in column 4 of Table 3.1 along with magnitudes from the literature in column 5 for comparison. Note that Verheijen (1997)’s K0-band measurements have not been converted to KCIT for this comparison, though the difference is small (∼ 0.05 mag for typical mean J − H colors).

24 3.2.1. Bulge/Disk Decompositions

The radial surface brightness profiles in the H or K-band for each of the galaxies were decomposed into bulge and disk components following de Jong (1996ba) and

Knapen et al. (2003) (see also MacArthur, Courteau, & Holtzman (2003)). The bulge component was fit using a generalized Sersic (1968) profile of the form

R 1/n µ(R) = µe + 2.5bn − 1 (3.1) "µRe ¶ # where n is the bulge shape parameters (n = 4 for a deVaucouleurs r1/4 law, n = 1 for an exponential disk), Re is the effective radius, µe is the surface brightness at

Re, and bn is a normalization factor depending on n that ensures that half of the integrated light is within Re. Only n, Re, and µe are free parameters. The disk was

fit with a standard exponential surface brightness profile of the form

µ(R) = µ0 + 1.086(R/h) (3.2)

where µ0 is the central surface brightness of the disk and h is the disk scale length.

The results for the 5-parameter bulge/disk fits to our near-infrared radial surface-brightness profiles are summarized in Table 3.2. The scale sizes (Re and h) have been converted into kiloparsecs using the adopted distances from Table 2.1.

For 20 galaxies, there was no significant bulge component (i.e., the added bulge component did not significantly change the rotation curve derived from assuming

25 that the galaxy ws composed only of a disk), and so I re-fit these galaxies with just an exponential disk, as noted in Table 3.2. Not surprisingly, these are all among the latest Hubble types in this sample. Finally, the bulge-to-disk ratio (B/D) was derived from integrating the best fit bulge and disk profiles, and is listed in Table 3.2.

3.3. Distances

Table 2.1 lists the distances for each of the galaxies in Megaparsecs (Mpc).

These were calculated under the assumption of Hubble flow, after correction for

Virgocentric infall, following the formalism of Aaronson et al. (1982). Four galaxies were found to have triple-valued solutions for their distances in the Virgocentric infall solution. For these galaxies, NGC 4062, NGC 4580, NGC 4651, and NGC 4698, a distance was adopted based on H-band Tully-Fisher distances. For NGC 4580, I adopted the distance calculated by Tully (1988), corrected to my adopted H0 = 70 km s−1 Mpc−1.

In addition, 4 galaxies in the sample have distances measured by Hubble Space

Telescope observations of Cepheid variable stars: NGC 2090 (Phelps et al. 1998),

NGC 2841 (Macri et al. 2001), NGC 3198 (Kelson et al. 1999), and NGC 3319 (Sakai et al. 1999). In all 4 cases, I have adopted these Cepheid distances, which are listed in Table 2.1.

26 Fig. 3.1.— Surface brightness profiles and B and K-band images for the sample galaxies. In this and subsequent figures, surface brightness curves run B-to-K bottom- to-top; see Table 2.2 for the observed bands. The B image is on the left, K on the right, and the scale bar indicates 6000. Orientation is North=Up, East=Left.

27 Fig. 3.2.— Surface brightness profiles and B and K-band images for the sample galaxies (continued). See Figure 3.1 for details.

28 Fig. 3.3.— Surface brightness profiles and B and K-band images for the sample galaxies (continued). See Figure 3.1 for details.

29 Fig. 3.4.— Surface brightness profiles and B and K-band images for the sample galaxies (continued). See Figure 3.1 for details.

30 Fig. 3.5.— Surface brightness profiles and B and K-band images for the sample galaxies (continued). See Figure 3.1 for details.

31 Fig. 3.6.— Surface brightness profiles and B and K-band images for the sample galaxies (continued). See Figure 3.1 for details.

32 Fig. 3.7.— Surface brightness profiles and B and K-band images for the sample galaxies (continued). See Figure 3.1 for details.

33 Table 3.1. Measured Galaxy Parameters

Seeing Magnitude (< R25) P A i Galaxy Band (00) This Work Literature (◦) (◦)

NGC 157 B 1.3 10.97§0.015 11.00§0.12b 43 45.6 V 1.1 10.38§0.011 · · · R 1.0 9.89§0.011 · · · J 2.6 8.46 · · · H 2.6 7.81 · · · K 2.9 7.59 · · · NGC 289 B 2.0 11.00§0.009 11.72§0.13b 148 49.1 V 1.8 10.41§0.009 10.99§0.03b R 1.4 9.99§0.013 · · · J 1.9 8.82 · · · H · · · 8.25 · · · K · · · 7.99 · · · NGC 488 B 1.6 11.40§0.061 11.15§0.13b 10 47.2 V 1.5 10.14§0.027 · · · R 1.8 9.57§0.047 · · · J 2.4 7.89 · · · H 2.6 7.11 · · · K 2.4 6.98 · · · NGC 908 B 1.6 11.00§0.009 10.83§0.13b 80 59.3 V 1.1 10.34§0.009 10.18§0.13b R 1.2 9.81§0.013 · · · J 1.9 8.20 · · · H 2.0 7.56 · · · K 2.0 7.33 · · · NGC 1087 B 1.9 11.61§0.015a 11.46§0.12b 12 50.4 V 2.1 11.04§0.011a · · · R 1.7 10.60§0.011a · · · J 2.4 9.29 · · · H 2.6 8.78 · · · K 1.9 8.48 · · ·

(cont’d)

34 Table 3.1—Continued

Seeing Magnitude (< R25) P A i Galaxy Band (00) This Work Literature (◦) (◦)

NGC 1090 g · · · 12.35 · · · 98 56.6 r · · · 11.58 · · · · · · K · · · 9.24 · · · · · · NGC 1241 B 3.1 12.49§0.015 11.99§0.13b 128 51.7 V 3.6 11.74§0.011 · · · R 2.5 11.21§0.011 · · · J 2.6 9.67 · · · H 2.6 8.92 · · · K 1.9 8.67 · · · NGC 1385 B 1.2 11.59§0.015a 11.45§0.10b 170 47.2 V 1.0 11.05§0.011a · · · R 1.2 10.61§0.011a · · · J 2.0 9.28 · · · H 1.9 8.68 · · · K 1.9 8.44 · · · NGC 1559 B 2.1 11.02§0.009 11.00§0.30b 66 57.3 V 1.8 10.57§0.009 10.65§0.30b R 1.6 10.15§0.013 · · · J 1.9 8.85 · · · H 2.0 8.26 · · · K 2.0 8.06 · · · NGC 1832 B 1.6 11.84§0.061 11.96§0.13b 20 48.7 V 1.3 11.32§0.025 · · · R 1.3 10.85§0.047 · · · J 2.0 9.27 · · · H 1.9 8.64 · · · K 1.9 8.38 · · ·

(cont’d)

35 Table 3.1—Continued

Seeing Magnitude (< R25) P A i Galaxy Band (00) This Work Literature (◦) (◦)

NGC 2090 B 1.5 11.90§0.032 11.99§0.13b 14 63.3 V 1.4 11.08§0.018 · · · R 1.3 10.42§0.010 · · · J 2.0 8.88 · · · H 2.0 8.26 · · · K 1.9 8.03 · · · NGC 2139 B 2.0 12.10§0.034 11.99§0.13b 80 39.2 V 2.2 11.69§0.025 · · · R 2.0 11.31§0.035 · · · J 1.8 10.19 · · · H 1.9 9.59 · · · K 1.9 9.35 · · · NGC 2280 B 1.2 11.52§0.011 10.90§0.20b 157 66.4 V 1.2 10.90§0.012 · · · R · · · · · · · · · J 2.0 9.03 · · · H 2.0 8.41 · · · K 2.0 8.19 · · · NGC 2841 g · · · 9.81 · · · 148 56.63 r · · · 9.05 · · · K · · · 6.16 · · · NGC 3198 g · · · 11.50 · · · 30 60 r · · · 10.97 · · · K · · · 8.03 · · ·

(cont’d)

36 Table 3.1—Continued

Seeing Magnitude (< R25) P A i Galaxy Band (00) This Work Literature (◦) (◦)

NGC 3223 B 1.2 11.28§0.029 11.79§0.14b 134 40.5 V 1.1 10.59§0.017 · · · R 1.2 10.10§0.017 · · · J 1.9 8.46 · · · H 1.9 7.79 · · · K 1.9 7.58 · · · NGC 3319 B 1.3 11.69§0.038a 11.48§0.17b 40 60.0 V 1.3 11.32§0.020a 11.07§0.18b R 1.4 10.98§0.022a · · · J 2.4 10.08 · · · H 2.4 9.43 · · · K 2.4 · · · · · · NGC 3521 g · · · 9.32 · · · 163 53.13 r · · · 8.65 · · · K · · · 5.91 · · · NGC 3726 B 1.9 10.92§0.097 10.91§0.07b 9 54.6 V 1.5 10.26§0.039 10.62d R 1.1 9.83§0.057 9.97 J 2.4 8.65 · · · H 2.6 7.97 · · · K 2.6 7.81 7.96 NGC 3949 B · · · 11.61 · · · 128 R · · · 10.77 · · · K · · · 8.58 · · · NGC 3953 B · · · 11.08 · · · 120 R · · · 9.70 · · · K · · · 7.05 · · ·

(cont’d)

37 Table 3.1—Continued

Seeing Magnitude (< R25) P A i Galaxy Band (00) This Work Literature (◦) (◦)

NGC 3992 B · · · 10.69 · · · 124 R · · · 9.44 · · · K · · · 7.12 · · · NGC 4051 B · · · 11.53 § 0.03 10.83§0.10b 131 V49 V · · · · · · · · · R · · · 10.40 § 0.04 9.88 J 2.4 8.97 · · · H 2.4 8.41 · · · K 2.6 8.06 7.86 NGC 4062 B 2.6 11.82§0.016 11.9§0.40b 97 63.9 V 1.3 11.15§0.028 11.20d R 1.3 10.59§0.026 · · · J 2.5 9.01 · · · H 2.6 8.39 · · · K 2.6 8.15 · · · NGC 4138 B · · · 12.39 · · · 124 R · · · 10.84 · · · K · · · 8.27 · · · NGC 4580 B 2.1 12.74§0.038 12.78,c 11.83§0.15b 159 43.5 V · · · 11.84§0.020 11.94c R · · · 11.32§0.022 · · · J · · · 9.73 · · · H · · · 9.06 · · · K · · · 8.83 · · · NGC 4651 B 2.0 11.49§0.038 11.57,c 11.39§0.08b 82 47.9 V 1.9 10.78§0.020 10.81,c 10.78d R 1.9 10.28§0.022 · · · J 2.6 8.81 · · · H 2.4 · · · K 2.4 8.12 · · ·

(cont’d)

38 Table 3.1—Continued

Seeing Magnitude (< R25) P A i Galaxy Band (00) This Work Literature (◦) (◦)

NGC 4698 B 1.0 11.59§0.025 11.48,c 11.46§0.08b 168 51.3 V 1.0 10.66§0.012 10.56c R 0.9 10.14§0.015 · · · J 2.7 8.40 · · · H 2.6 7.79 · · · K 2.4 7.56 · · · NGC 5371 B 2.1 11.29§0.016 11.32§0.14b 16 49.8 V 2.0 10.51§0.028 R 2.0 9.94§0.026 · · · J 2.4 8.51 · · · H 2.4 7.86 · · · K 2.4 7.59 · · · NGC 5806 g · · · 11.91 · · · 170 58 r · · · 11.24 · · · K · · · 8.46 · · · NGC 6300 B 1.1 10.45§0.013 10.98§0.05b 123 51.7 V 1.1 9.74 §0.006 · · · R 0.9 9.14 §0.012 · · · J 1.9 7.71 · · · H 1.9 7.08 · · · K 1.9 6.86 · · · NGC 7083 B 2.4 11.72§0.009 11.87§0.13b 10 58.0 V 1.0 11.13§0.009 · · · R 1.1 10.65§0.013 · · · J 2.0 9.42 · · · H 2.0 8.10 · · · K 1.9 8.46 · · ·

(cont’d)

39 Table 3.1—Continued

Seeing Magnitude (< R25) P A i Galaxy Band (00) This Work Literature (◦) (◦)

NGC 7217 B 0.9 10.98§0.044 · · · 90 29.5 V 0.9 10.19§0.033 · · · R 0.9 9.58§0.043 · · · J 2.4 7.88 · · · H 2.4 7.18 · · · K · · · 6.98 · · · NGC 7606 B 2.0 11.60§0.044 11.51§0.14b 146 63.9 V 1.9 10.88§0.033 10.98,d 10.75§0.14b R 2.0 10.35§0.043 · · · J 2.0 8.61 · · · H 2.0 7.82 · · · K 2.0 7.69 · · ·

abased on a secondary calibration obtained from a short “snapshot” image taken on a photometric night bfrom the RC3 cfrom Gavazzi et al. 2003

dfrom H´eraudeau & Simien 1996

40 Table 3.2. Bulge/Disk Parameters for K-band Images

Bulge Disk

Re µe h µ0 Galaxy B/D n (kpc) (mag/arcsec2) (kpc) (mag/arcsec2)

NGC 157a · · · · · · · · · · · · 2.79 16.33 NGC 289 0.10 1.10 0.36 15.74 1.76 15.94 NGC 488 0.20 2.20 1.40 16.36 5.78 16.62 NGC 908a · · · · · · · · · · · · 3.11 16.26 NGC 1087a · · · · · · · · · · · · 2.45 16.83 NGC 1090a · · · · · · · · · · · · 3.78 17.09 NGC 1241 0.20 1.30 1.01 16.02 4.68 16.78 NGC 1385a · · · · · · · · · · · · 2.40 17.19 NGC 1559 0.02 1.20 0.26 17.13 1.94 16.33 NGC 1832 0.15 1.20 0.34 14.94 2.00 15.98 NGC 2090a · · · · · · · · · · · · 1.04 15.27 NGC 2139a · · · · · · · · · · · · 2.09 17.25 NGC 2280 0.35 1.30 1.62 16.87 3.63 16.68 NGC 2841 0.19 1.10 0.61 14.96 2.70 15.64 NGC 3198a · · · · · · · · · · · · 2.73 17.18 NGC 3223a · · · · · · · · · · · · 5.33 16.57 NGC 3319a · · · · · · · · · · · · 5.00 19.79 NGC 3521 0.13 1.40 0.31 14.67 1.48 15.05 NGC 3726a · · · · · · · · · · · · 4.75 17.37 NGC 3893 0.29 1.50 1.54 17.54 3.17 16.88 NGC 3949a · · · · · · · · · · · · 1.61 16.08 NGC 3953a · · · · · · · · · · · · 3.93 16.57 NGC 3992a · · · · · · · · · · · · 5.61 17.27 NGC 4051 0.18 3.70 0.19 14.71 2.82 17.41 NGC 4062a · · · · · · · · · · · · 1.39 16.29 NGC 4138a · · · · · · · · · · · · 1.40 15.6 NGC 4580a · · · · · · · · · · · · 2.16 16.39

(cont’d)

41 Table 3.2—Continued

Bulge Disk

Re µe h µ0 Galaxy B/D n (kpc) (mag/arcsec2) (kpc) (mag/arcsec2)

NGC 4651a · · · · · · · · · · · · 1.39 15.66 NGC 4698 0.28 3.10 0.68 16.25 2.26 16.23 NGC 5371 0.11 1.30 1.04 15.74 8.11 17.03 NGC 5806 0.20 1.40 0.47 15.34 2.37 16.28 NGC 6300 0.09 1.20 0.45 15.91 2.51 16.21 NGC 7083 0.06 1.50 0.48 15.70 3.13 15.83 NGC 7217 · · · · · · · · · · · · 1.83 15.67 NGC 7606 · · · · · · · · · · · · 4.46 16.26

aFor galaxies with a negligable bulge component we fit an exponential disk, and hence I only list the central surface brightnesses and scalelengths of the disks.

42 Chapter 4

Radial Distributions of Baryonic and Dark Matter in Galaxies

In this chapter, the distributions of baryonic and dark matter are derived for 35 bright spiral galaxies. In §4.1 I derive the baryonic mass surface density profiles of the galaxies, and compute the component of the galaxies’ observed rotation that is due to the baryons (stars and gas). These are called the “baryonic rotation curves,” to distinguish them from the observed rotation curves taken from the literature.

In §4.2 I will introduce the term “dark matter rotation curves,” to denote the contribution from dark matter to the observed rotation curve. My results will be discussed in Chapter 5.

43 4.1. Baryonic Matter

4.1.1. Radial Baryonic Surface Mass-Density

Distributions

To measure a galaxy’s radial surface mass-density distribution, I apply a color-M/L relation to its surface brightness profiles. These relations show a relatively tight correlation (∼ 0.1 dex spread for the color range where my galaxies lie) between the optical color of a galaxy and its stellar mass-to-light ratio, (M/L)∗.

Color-M/L relations are most useful when applied to (M/L)∗’s in the near-infrared since they are the least affected by dust obscuration, as discussed in Bell & de Jong

(2001). Specifically, I choose to use the relation between B − R color and (M/L)∗ at K. This relation is composed of the optical color with the largest wavelength baseline and the reddest near-infrared band. This relation is reproduced in Figure 4.1 where reddening vector is plotted for an AV = 1 mag. The galaxies in my sample are plotted in Figure 4.1 as filled circles according to their integrated R25 colors and luminosities. Note that for NGC 2280 I use the B − V color, and for NGC 3319 I use the H-band luminosity because good quality imaging was unavailable in the R and

K-bands, respectively. The scatter in these relations is also ∼ 0.1 dex.

For those galaxies without a significant bulge contribution, I apply a color-M/L relation directly to their azimuthally averaged radial B − R color profiles to derive

44 radial (M/L)∗ profiles at H or K. The LH or LK profile for each galaxy is then multiplied by the galaxy’s (M/L)∗ profile to derive a radial surface mass-density profile. For those galaxies with a significant bulge component, a bulge-disk decomposition is performed. A characteristic B − R color is adopted for each component based on the average colors of the bulge and disk. The variation in

B − R color from galaxy-to-galaxy for bulge and disk components argues strongly that a bulge/disk decomposition is required, combined with good photometry to set the M/L for each component of each galaxy. However, within a galaxy, systematic variations within the disk component have a much smaller effect upon the derived stellar rotation curves.

When available from the literature, I use radial H I 21 cm measurements to determine the contribution of interstellar gas to the radial baryonic surface-mass densities. There are gas measurements available for NGC 1090, NGC 3949,

NGC 3953, and NGC 3992. The neutral gas component is included by scaling the H I surface mass-density by a factor of 1.32 to account for the abundance of helium. For those galaxies without gas mass measurements, I assume that a galaxy Hubble Type

Sa–Scd has a gas mass that is typically MHI /LB ≈ 0.32 (Roberts & Haynes 1994) and hence does not greatly affect their baryonic mass. Figure 4.2 demonstrates the effect of including the interstellar gas component in the baryonic matter rotation curve of NGC 1090. Here, the rotation curve due solely to stars (solid line) is plotted alongside a rotation curve computed by including H I data from Gentile et al. (2004)

45 to the stars (dashed line). The difference between these two rotation curves is within the errors of the stellar mass rotation curve, as will be discussed in §4.1.3. Therefore, by not including interstellar medium contributions in the analysis only a minor systematic effect is introduced.

4.1.2. Baryonic Rotation Curves

Baryonic rotation curves are calculated for each galaxy from their radial baryonic surface mass-density distributions. They are plotted in Figures 4.3–4.8 as solid lines. This calculation is done with the rotmod task in the GIPSY software package (van der Hulst et al. 1992), which calculates rotation curves assuming a truncated exponential disk (via the formalism of Casertano (1983)) and a spherical bulge. Exponential disks in this calculation are assumed to have a scale height of 0.3 kpc, which is typical of bright spirals. Note that the difference between using a different scale height for each galaxy of 0.1 × h kpc (where h is the disk exponential scale length), as in Sparke & Gallagher (2000), and 0.3 kpc for every disk is negligible.

46 4.1.3. Uncertainties in Baryonic Rotation Curves

The three primary sources of systematic error in the determination of the baryonic surface mass-density distributions are the galaxies’ distances1, the 0.1 dex spread in the color-M/L relations, and the zero-point of these relations.

Secondary sources of error generally have a negligible effect on the baryonic rotation curves. They include photometric zero-point calibrations, secondary photometric

(“bootstrap”) calibrations, and the neglect of interstellar gas content. Note that the transformations of 2MASS and SDSS DR2 photometry to the Kron-Cousins system introduce negligible uncertainties, as shown in Chapter 2.

As an illustration, Figure 4.9 shows the effects of two of the primary sources of systematic error on the baryonic rotation curve of NGC 157. Figure 4.9a shows the effect of systematic errors of §20% in the distance, and Figure 4.9b shows the effect of a systematic change of §0.1 dex in the color-M/L relation. However, the largest source of uncertainty lies in the behavior of the stellar initial mass function

(IMF) at low-mass, as this sets the normalization of the color-M/L relation. Since the faint end of the IMF is relatively unconstrained, there may exist many low-mass, low-luminosity stars that can contribute significantly to the mass budget of a stellar population without creating a detectable increase in luminosity or change in color.

Bell & de Jong (2001) and Bell et al. (2003) adopted a “diet Salpeter” IMF which

1Of the 35 galaxies in my sample, 4 have distances estimated from Cepheid variables for which the uncertainties are much less than other distance measurements.

47 derives from the constraint applied in Bell & de Jong (2001) that baryonic rotation curves should not over-predict observed rotation curves for spirals in Ursa Minor

(the Verheijen (1997) sample). With this constraint, they predict fewer low mass stars than a Salpeter IMF, hence diet Salpeter. These relations thus give an upper limit to the stellar mass present.

In Figure 4.9c,d the effects of introducing systematic errors in the photometric zero-point calibrations on the derived baryonic rotation curves are shown. In

Figure 4.9c the effect of the actual zero-point errors for NGC 157 is shown:

σB = 0.015, σR = 0.011, σK = 0.03. This secondary source of uncertainty does not have a particularly noticeable effect on the baryonic rotation curve at the resolution of the figure. To show the effect of a photometric calibration that is not as good as NGC 157’s, in Figure 4.9d I show what would happen to the rotation curve if I arbitrarily assign systematic photometric zero-point errors of §10%. Whereas most of my photometric zero-points are good to < 4%, the worst error in a zero-point calibration for any of the surface brightness profiles that I use in this analysis is

§6%, as shown in Table 3.1.

4.1.4. Effects Due to Dust

Since the reddening vector in Figure 4.1 lies nearly parallel to the color-M/L relation, to first order errors in foreground dust reddening estimates should not

48 strongly affect the final relative derived masses of the stellar populations, as foreground dust will both systematically redden and extinguish galactic light.

However, a dust effect is observed in our data.

A simple foreground screen model is used to describe to first order the dust content of the galaxies in the sample. It is very likely that more complex dust models are needed, along the lines of those of Disney (1989) and Gordon et al. (2001), where the effects of dust depend on star/dust geometry. However, I choose to leave this approach to a future analysis, since the detailed radiative transfer codes are not publicly available and are difficult to apply to real galaxies. The simple screen model is likely to be warranted as a first order approximation, as colors and luminosities are radial averages in which any discrete effects due to dust would be smoothed out. If this analysis was done on a pixel-by-pixel or an area-by-area basis, a more complicated dust treatment would likely be needed, but that is however beyond the scope of the present work.

In Figure 4.10 demonstrates the effect of dust on the baryonic rotation curve of NGC 157. In Figure 4.10a,b the galaxy’s radial B − R color is plotted alongside the ratio of the galaxy’s radial surface mass densities as derived from its K and

R-band (M/L)∗’s, respectively. (Note that the K-band surface mass-density is generally greater than that derived from the R-band.) The correlation between these two quantities (Figure 4.10a,b) shows that whatever it is that causes the difference between the radial surface mass densities, it is likely to be correlated with the

49 galaxy’s radial B − R color. A simple screen model for dust extinction is correlated with B − R color, I apply that, and I apply it by deriving the radial AV distribution necessary to match the R-band radial surface mass-density to that calculated from the K-band. The AV resulting distribution is plotted in Figure 4.10c; it is consistent with that measured for nearly face-on galactic disks by Holwerda et al. (2004).

Furthermore, in Figure 4.10d I plot the baryonic rotation curves calculated from

NGC 157’s radial B − R color and the radial (M/L)∗ at B, V, R, J, H, and K. They increase in rotation speed from B to K, as is expected if their differences are due to dust. If the calculated AV distribution is applied to the K-band surface mass-density profile, its effect on the K-band baryonic rotation curve is negligible. In light of this,

I do not correct the K-band baryonic rotation curves for dust.

To examine the screen model in a different manner, I cut the images of two galaxies (NGC 4062 and NGC 7083) in half along their major axes and compare the baryonic rotation curves calculated from the R and K-band (M/L)∗’s for each side. The idea is that the far side of the disk should show more of a dust effect because it is inclined away from the plane of the sky and hence has a longer path length through its disk. In Figure 4.11 I plot the baryonic rotation curves, without bulge-disk decompositions, for both halves of the two galaxies. For both galaxies, the K-band baryonic rotation curve for one side is plotted as a solid line, and the other side as a dotted line. Similarly, the B-band rotation curve for both galaxies is plotted as a long dashed line for one side, and for the other side as a short dashed

50 line. In NGC 7083 the effect of an inner star-formation region is observed where the

R-band baryonic rotation curve is faster than the rotation curve derived from the

K-band. Beyond this region, one side of the galaxy rotates systematically faster than the other, as is expected from the effects of dust obscuration. In NGC 4062 there is particularly patchy dust throughout the disk in addition to a star-forming inner ring. The effect of the inner ring is seen in the K and R-band rotation curves: for this inner part the R-band baryonic rotation curves for both sides are faster than those derived from the K-band. An effect of the dust is that for one side of the galaxy the R-band baryonic rotation curve falls beneath the K-band baryonic rotation curve, but for the other side these rotation curves approximately match.

4.2. Dark Matter

For each galaxy, I compare its baryonic rotation curve derived in §4.1 with its observed rotation curve from the literature to derive a “dark matter rotation curve.”

4.2.1. Observed Rotation Curves

Observed rotation curves for the galaxies are plotted in Figures 4.3–4.8 as open triangles if they came from from single-slit or Fabry-Perot Hα observations and as open circles if they came from H I observations. Table 4.1 lists the tracer and literature reference for each rotation curve; the notation “FP Hα” is used for

51 rotation curves derived from Fabry-Perot measurements of Hα. Note that the 2–3 innermost points of the H I rotation curves and the last few outer points of the

Hα rotation curves have a greater uncertainty than the other points due to beam smearing and low signal-to-noise, respectively. Some galaxies have two rotation curves, one from Hα observations which traces the inner parts, and another from H I observations which traces the outer parts. Those galaxies marked with the reference

“Mathewson & Courteau” in Table 4.1 are rotation curves that were originally presented in Mathewson, Ford, & Buchhorn (1992) and were modeled by Courteau

(1997). For these single-slit Hα rotation curves, I plot the model rotation curve as a dashed line and the Mathewson, Ford, & Buchhorn (1992) data as open triangles in

Figures 4.3–4.8. I adopt the modeled rotation curves for these galaxies in order to avoid much of the fine structure inherent to the actual rotation curve data for these galaxies, since I am primarily interested in large-scale trends.

For many of the rotation curves, I have obtained data from the authors, but for a handful I could not. For those few galaxies, rotation curves are extracted from plots in the literature with the DataTheif program (Tummers 2000) and are noted in Table 4.1. Errors inherent to the extraction of a rotation curve vary from plot to plot, but tend to be ≤ §5 km s−1.

52 4.2.2. Dark Matter Rotation Curves

At those radii where a galaxy’s observed rotation speed is faster than that derived from its baryonic component, the additional gravitational component is assumed to be due to dark matter. A dark matter rotation curve is derived as the square root of the difference of the squares of the observed velocity and the baryonic velocity at each radius (Binney & Tremaine 1987). Dark matter rotation curves for each of the galaxies are plotted as dashed lines in Figures 4.3–4.8. In doing this, it is assumed that the halos of galaxies are axially symmetric and that the disk and halo are aligned, which is reasonable for tidally undisturbed normal galaxies.

4.2.3. Uncertainties in Dark Matter Rotation Curves

Uncertainties in the dark matter rotation curves arise from a number of effects.

The most important, however, are those uncertainties inherent to the determination of the baryonic mass component, as discussed in §4.1.3. Other uncertainties inherent to the observed rotation curves include: non-circular motions that perturb the underlying potential (i.e., spiral arms, bars, substructure), statistical errors from the measurement of velocities in radial bins, systematic errors in measuring the velocity (i.e., beam smearing and slit position angle error), and uncertainties in the measurement of the dynamical centers of the galaxies. There may be differences between the centers of galaxies determined from photometry and those determined

53 from the observed rotation curves. However, these measurements should not differ much since the photometric centers were always chosen to be the brightest pixel in the nucleus, and since there does not exist much star-formation in the galaxies’ nuclei, the centers tend to match from galaxy to galaxy. It should be noted that for those galaxies with rotation curves derived from Fabry-Perot observations, the position angles and dynamical centers should be the most certain; these galaxies are noted in Table 4.1.

54 Fig. 4.1.— Color-M/L relation for the B − R color and M/L at K from Bell & de Jong (2001) (solid line). The galaxies in the sample are plotted as filled circles and a reddening vector is plotted for AV = 1.

55 Fig. 4.2.— The rotation curve for NGC 1090 due to the stellar mass component (solid line) is compared with the rotation curve due to stars and gas (dotted line). The total observed rotation curve from Gentile et al. (2004) due to all mass components (baryonic and dark) is shown by open circles.

56 Fig. 4.3.— Observed rotation curves (circles for H I, triangles for Hα, dashed lines for models), baryonic rotation curves (solid lines), and dark matter rotation curves where applicable (dotted lines) for each galaxy in the sample.

57 Fig. 4.4.— Observed rotation curves (circles for H I, triangles for Hα, dashed lines for models), baryonic rotation curves (solid lines), and dark matter rotation curves where applicable (dotted lines) for each galaxy in the sample.

58 Fig. 4.5.— Observed rotation curves (circles for H I, triangles for Hα, dashed lines for models), baryonic rotation curves (solid lines), and dark matter rotation curves where applicable (dotted lines) for each galaxy in the sample.

59 Fig. 4.6.— Observed rotation curves (circles for H I, triangles for Hα, dashed lines for models), baryonic rotation curves (solid lines), and dark matter rotation curves where applicable (dotted lines) for each galaxy in the sample.

60 Fig. 4.7.— Observed rotation curves (circles for H I, triangles for Hα, dashed lines for models), baryonic rotation curves (solid lines), and dark matter rotation curves where applicable (dotted lines) for each galaxy in the sample.

61 Fig. 4.8.— Observed rotation curves (circles for H I, triangles for Hα, dashed lines for models), baryonic rotation curves (solid lines), and dark matter rotation curves where applicable (dotted lines) for each galaxy in the sample.

62 Fig. 4.9.— The effects of different systematic uncertainties on the derived baryonic rotation curve of NGC 157. The derived baryonic rotation curve is plotted as a solid line and the uncertainties are plotted as dotted lines. (a) the effect of an error of §20% in its distance; (b) the effect of a change of §0.1 dex in the color-M/L relation; (c) the effect of the actual zero-point errors for the photometry for NGC 157; (d) the effect of 10% errors in the photometry

63 Fig. 4.10.— First-order effects of dust extinction on the derived stellar mass surface density. (a) the radial B − R distribution (b) the ratio of the surface mass densities calculated from the K and R-band M/L∗’s; (c) the derived AV distribution needed to match the the R-band radial surface density to that calculated from K (d) the baryonic rotation curves calculated from the B − R color and the M/L∗ at B, V, R, J, H, and K which are plotted from the bottom to the top of the plot; the B and V -band rotation curves overlap.

64 Fig. 4.11.— Baryonic rotation curves derived from R and K-band M/L’s for both halves of (a) NGC 4062 and (b) NGC 7083. For both galaxies, the K-band rotation baryonic rotation curve for one side is plotted as a solid line, and the other side as a dotted line. Similarly, the B-band rotation curve for both galaxies is plotted as a long dashed line, and for the other side as a short dashed line.

65 Table 4.1. Sources of Rotation Curve Data

Galaxy Tracer Reference(s)

NGC 157 FP Hα, HI Fridman et al. (2001), Ryder et al. (1998) NGC 289 HI Walsh (1997) NGC 488 Hα Peterson (1980)a NGC 908 Hα Mathewson et al. 1992 NGC 1087 Hα Rubin et al. (1985) NGC 1090 Hα, HI Courteau (1997), Gentile et al. (2004) NGC 1241 Hα Mathewson et al. 1992 NGC 1385 Hα Mathewson et al. 1992 NGC 1559 Hα Mathewson et al. 1992 NGC 1832 Hα Mathewson et al. 1992 NGC 2090 Hα Mathewson et al. 1992 NGC 2139 Hα Mathewson et al. 1992 NGC 2280b Hα Mathewson et al. 1992 NGC 2841 FP Hα, HI Blais-Ouellette et al. (2004), Giraud (1998)a NGC 3198 HI Giraud (1998)a NGC 3223 Hα Mathewson et al. 1992 NGC 3319c HI Moore & Gottesman (1998) NGC 3521 HI Sanders (1996)a NGC 3726 HI Verheijen (1997) NGC 3893 Hα, HI Kranz (2002), Verheijen (1997) NGC 3949 HI Verheijen (1997) NGC 3953 HI Verheijen (1997) NGC 3992 HI Verheijen (1997)

(cont’d)

66 Table 4.1—Continued

Galaxy Tracer Reference(s)

NGC 4051 HI Verheijen (1997) NGC 4062 Hα Rubin et al. (1985) NGC 4138 HI Verheijen (1997) NGC 4580 Hα Rubin et al. 1999 NGC 4651 Hα Rubin et al. 1999 NGC 4698 Hα Rubin et al. 1999 NGC 5371 HI Begeman (1987)a NGC 5806 Hα Courteau (1997) NGC 6300 FP Hα, HI Buta et al. (2001), Ryder et al. (1996) NGC 7083c Hα Mathewson et al. 1992 NGC 7217 Hα Rubin et al. (1985) NGC 7606 Hα Mathewson et al. 1992

aThe rotation curve for this galaxy has been removed electronically from a plot in the referenced paper. bThe B −V color is used instead of B −R to derive the stellar mass surface density distribution. c (M/L)∗,H is used instead of (M/L)∗,K to derive the stellar mass surface density distribution.

67 Chapter 5

Baryonic and Dark Matter Properties

I begin with a discussion of the general properties of the baryonic and dark matter rotation curves, followed by a derivation of quantities that describe the relative baryonic and dark matter distributions. Then I show how these quantities correlate with general galaxy properties. Finally, I investigate the radial behavior of the dark matter rotation curves themselves.

5.1. Maximal and Non-Maximal Disks

The rotation curves in Figures 4.3–4.8 are presented in order of decreasing observed rotational velocity, reading from left-to-right then top-to-bottom. From these figures one can discern the general trend that faster rotating galaxies (which tend to be more massive and brighter) are dominated by baryonic matter in their inner regions (e.g., Persic et al. (1996)). However, there are exceptions to this trend. In particular, NGC 2841, NGC 4651, and NGC 7606 are among the faster rotators in the sample, but have a measurable dark matter contribution within their inner 5 scale-lengths. (They all have Hα rotation curves which are important for

68 measuring the dark matter contribution in their inner parts). These three galaxies, along with the comparatively slower rotators NGC 2139, NGC 4580, NGC 4051, and NGC 4062, have a dark matter behavior more like what is seen in low-surface brightness galaxies (e.g., Persic et al. (1996)), even though they are all manifestly high surface brightness galaxies.

It is important to note that the population synthesis M/L values used in this paper rely on disk dynamics that were calibrated to maximum disk for galaxies in the . This means that the stellar mass determinations in this dissertation are upper limits to the actual stellar mass present in galaxies.

With this in mind, it is even more intriguing that they are bright galaxies that are observed to be dark-matter dominated in their inner parts. Furthermore, for some galaxies the baryonic rotation curve over-predicts the observed rotation curve in the inner parts. Six galaxies over-predict their observed rotation curves: NGC 1559,

NGC 2139, NGC 4698, NGC 5371, NGC 6300, and NGC 7083 (I exclude galaxies that over-predict only the inner points of their H I rotation curve). In three of these cases, the over-prediction is likely to be due to irregular morphology: NGC 1559 and NGC 2139 both have a slightly disturbed appearance, and NGC 6300 has a significant bar and ring (see Figures 3.2, 3.3, and 3.6). One could re-scale the color-M/L relations to avoid over-predicting the observed rotation curve in the three galaxies with more regular morphologies, however that would not change the qualitative results of this work.

69 5.2. Dark and Baryonic Matter Correlations

Integrated magnitudes, Hubble T-types, R25’s, and bulge-disk parameters that are used to describe the galaxies are tabulated in Tables 2.1 and 3.1. To further characterize the galaxies, the following physical quantities were derived from their baryonic and observed rotation curves: (1) Vtot,max the maximum observed rotation curve velocity, (2) V∗,max the maximum baryonic mass velocity, (3) R(V∗,max) the radius at which V = V∗,max, and (4) M∗ the baryonic mass within R25 calculated from the B −R colors and the K-band luminosity (LK ). In addition, the dark matter rotation curves calculated in §4.2.2 are described by two quantities: R10, the radius where dark matter contributes 10% to the observed rotation curve (“radius of dark matter onset”), and RX, is the radius where the dark matter contribution equals that of the baryons (the “cross-over radius”). These quantities are listed in Table 5; note that some galaxies do not have a R10 or a RX present in their data. Also note that R10 is similar to Salucci (2001)’s RIBD, or Persic, Salucci, & Stel (1996)’s Rt.

In Figure 5.1, basic physical parameters of galaxies, as derived from their baryonic and observed rotation curves, are plotted versus Hubble T-type. All of the parameters: LB(< R25), B − R color integrated for R ≤ R25, Vtot,max, M∗(< R25), and R25 in units of the K-band scale-length are found to correlate with Hubble

T-type to varying degrees. Our results are in good agreement with Roberts &

Haynes (1994).

70 In Figure 5.2, relations are plotted for Vtot,max and V∗,max, both of which trace the total dynamical and baryonic mass components of the galactic potential, respectively. In Figure 5.2a, following Roberts & Haynes (1994), I plot Vtot,max versus log10, LB(< R25) and find good agreement with their results. Figure 5.2d shows that

Vtot,max is correlated with V∗,max. Due to the flat and usually noisier nature of the observed rotation curves, the measurement of V∗,max is more straightforward than that of Vtot,max. Therefore, V∗,max is used instead of Vtot,max in the other relations in

Figure 5.2. The quantity V∗,max is seen to correlate well with Hubble T-type and size

(R25/hK ) such that the faster rotating galaxies have earlier T-types and are larger.

R(V∗,max), is not found to correlate with any galaxy parameters.

In Figure 5.3a–d RX/hK is plotted versus log10LB(< R25), V∗,max, Hubble

T-type, and R10/hK . This quantity is found to correlate well with these four galactic parameters. The correlations are such that galaxies with greater luminosity, faster

V∗,max’s, later T-types, and larger R10/hK ’s all have RX’s that occur further out in their disks. That there is such a tight relation between RX/hK and R10/hK tells us that the dark matter contribution to the observed rotation curves must increase in a characteristic way between these two radii for all galaxies. This is likely to be the combined effect of a fall-off in the exponential baryonic mass distribution combined with an observed rotation curve that is approximately flat in the region of the fall-off. If this idea is correct, then R10 should have more scatter in its relations with galaxy properties than RX because the observed rotation curves should not

71 be quite flat yet in the region where R10 is measured. The radius RX is measured further out in the observed rotation curve (i.e., where it is practically flat) and therefore should have less scatter in its relations. It is found that R10 indeed has more scatter in its relations with galaxy properties than RX, thus strengthening the simple idea for the cause of the tight relation between the two dark matter radii.

Furthermore, in Figure 5.2d, galaxies are plotted with different symbols according

−1 to their V∗,max: those with V∗,max ≤ 100 km s are plotted as open circles, those

−1 −1 with 100 km s < V∗,max ≤ 200 km s are plotted as filled circles, and those with

−1 200 km s < V∗,max are plotted as open triangles. As V∗,max increases, these two radii move further out in the disk in tandem.

5.3. Radial Behavior of Dark Matter

2 2 In Figure 5.4a, the dimensionless parameter β(r) ≡ V∗ (r)/Vtot(r) is plotted for galaxies with an appreciable dark matter contribution. It measures the fractional contribution of baryons to the gravitational potential as a function of radius. This is similar to the β parameter defined by Salucci (2001), but here it is evaluated at all radii, and not just at Ropt. When β(r) = 1, the baryonic matter of a galaxy accounts for all of its observed rotation curve, β(r) = 0.5 at r = RX, and β(r) = 0 where the dark matter accounts for all of its observed rotation curve. If the baryonic model over-predicts the observed rotation curve, then β(r) > 1. From Figure 5.4a, it

72 is observed that many galaxies have maximal disks: their observed rotation curves are entirely accounted for by baryonic matter in the inner parts. Beyond this inner region, baryonic mass falls off as dark matter begins to dominate. However, some galaxies are dark matter dominated throughout (i.e., those at the bottom of Figure

5.4a). The β(r) curves are plotted in Figure 5.4a according to their V∗,max. They generally increase in V∗,max from the bottom to the top of the plot with the least massive galaxies being dark matter dominated throughout. However, there is clearly scatter about this trend. For most of the galaxies, as their V∗,max increases, so does their proportion of dark to baryonic matter at all radii such that the fastest rotators

(at the top of the plot) are observed to be dominated by baryons until quite far out into their disks. This can also be inferred from Figures 4.12d and 4.14c.

In Figure 5.4b, β(r) is plotted versus radius in units of RX for those galaxies for which an RX is observed. This choice of radial coordinate causes the curves to overlap at r = RX (β(r) = 0.05), and thus allows for a better comparison of their radial behavior. On this plot, the area where β ≥ 0.9 (i.e., where r ≤ R10) denotes the region in which a galaxy is dominated by baryons. The area in the figure where

β ≥ 0.5 denotes the radii beyond which the potential of a galaxy is dark matter dominated. It is observed in Figure 5.4b that the radius where the dark matter onsets varies from galaxy to galaxy with an intrinsic scatter. An examination of the region in Figure 5.4b where β < 0.5 (or, equivalently where r/RX > 1) shows the manner in which the galaxies become increasingly dark matter dominated. The

73 curves in Figure 5.4b are also plotted according to V∗,max with the same coding as in Figure 5.4a. There is systematic scatter among the curves, such that a galaxy’s behavior cannot be predicted based on its V∗,max.

74 Fig. 5.1.— Relations are plotted between basic physical parameters of galaxies and Hubble T-type. Open circles represent galaxies from SDSS DR2 that only have partial imaging.

75 Fig. 5.2.— Relations are plotted for Vtot,max and V∗,max, which trace the total dynamical and baryonic mas components of the galactic potential, respectively. Open circles represent galaxies from SDSS DR2 that only have partial imaging.

76 Fig. 5.3.— Relations are plotted for RX/hK . Open circles represent galaxies from SDSS DR2 that only have partial imaging. In panel d, galaxies are plotted with −1 different symbols according to their V∗,max: those with V∗,max ≤ 100 km s are −1 −1 plotted as open circles, those with 100 km s < V∗,max ≤ 200 km s are plotted as −1 filled circles, and those with 200 km s < V∗,max are plotted as open triangles.

77 2 2 Fig. 5.4.— β(r) ≡ V∗ (r)/Vtot(r) is plotted for galaxies with an appreciable dark −1 matter contribution according to the galaxy’s V∗,max: V∗,max > 250 km s thin solid 201 < V∗,max ≤ 250 dotted line, 120 < V∗,max ≤ 201 dashed line, V∗,max ≤ 120 thick solid line.

78 Table 5.1. Parameters Derived From Observed, Baryonic Matter, and Dark Matter Rotation Curves

Observed Baryonic Matter Dark Matter

Vtot,max V∗,max R(V∗,max) M∗ R10 RX Galaxy (km/s) (km/s) (kpc) (M¯) (kpc) (kpc)

NGC 0157 215 205.6 6.2 7.01e+10 · · · 24.0 NGC 0289 180 169.6 4.1 4.03e+10 · · · 11.7 NGC 0488 350 296.0 10.1 2.87e+11 · · · · · · NGC 0908 200 201.2 7.3 7.07e+10 · · · · · · NGC 1087 135 141.0 5.9 2.78e+10 · · · · · · NGC 1090 165 165.0 7.3 1.97e+10 12.1 20.4 NGC 1241 280 250.1 8.0 1.84e+11 12.4 · · · NGC 1385 140 139.9 2.5 2.48e+10 · · · · · · NGC 1559 150 135.9 4.5 2.28e+10 · · · · · · NGC 1832 180 209.0 3.9 5.26e+10 · · · · · · NGC 2090 160 153.6 2.8 1.72e+10 · · · · · · NGC 2139 140 121.3 4.5 1.86e+10 5.6 · · · NGC 2280 220 177.0 4.4 6.43e+10b 8.7 · · · NGC 2841 325 284.3 4.7 2.87e+11 8.1 12.6 NGC 3198 157 120.1 5.5 1.72e+10 6.7 10.0 NGC 3223 310 305.9 5.7 2.98e+11 · · · · · · NGC 3319 130 50.4 8.9 5.66e+9a 2.6 3.4 NGC 3521 210 259.1 1.5 3.22e+10 10.4 13.3 NGC 3726 165 148.4 10.6 5.80e+10 19.1 · · · NGC 3893 190 186.5 5.3 6.23e+10 13.4 19.3 NGC 3949 170 156.3 3.8 4.03e+10 6.6 · · · NGC 3953 225 227.4 7.7 3.33e+11 17.8 · · · NGC 3992 270 187.4 12.4 1.25e+11 · · · · · · NGC 4051 165 154.1 0.5 1.97e+10 5.8 · · · NGC 4062 160 110.0 3.4 1.10e+10 · · · · · · NGC 4138 190 215.0 2.7 6.23e+10 · · · 17.8 NGC 4580 135 121.1 3.3 4.28e+10 · · · · · ·

(cont’d)

79 Table 5.1—Continued

Observed Baryonic Matter Dark Matter

Vtot,max V∗,max R(V∗,max) M∗ R10 RX Galaxy (km/s) (km/s) (kpc) (M¯) (kpc) (kpc)

NGC 4651 210 200.3 2.7 3.22e+10 3.6 · · · NGC 4698 220 211.6 4.3 6.36e+10 · · · · · · NGC 5371 240 276.2 15.2 3.33e+11 49.1 · · · NGC 5806 180 190.3 1.1 4.03e+10 · · · · · · NGC 6300 205 207.4 5.1 6.66e+10 13.7 20.4 NGC 7083 205 244.7 6.5 9.03e+10a 14.7 · · · NGC 7217 270 282.8 2.0 7.43e+10 · · · · · · NGC 7606 280 228.3 9.8 1.25e+11 8.7 · · ·

a Calculated from (M/L)∗,H instead of (M/L)∗,K

bCalculated from B − V instead of B − R

80 Chapter 6

Conclusions

Photometrically calibrated surface brightness profiles, magnitudes, and physical parameters are presented for a sample of 31 nearby bright (B < 12.5) spiral galaxies for which rotation curves are available in the literature. I have derived baryonic matter rotation curves for 35 galaxies, four of which have photometry already present in the literature. All but 7 of the 35 galaxies have observed rotation curves that can be entirely accounted for by baryonic matter in their inner 5 scale-lengths. Aside from these outliers, I confirm the general trend that has been emerging from the literature (e.g., Persic, Salucci, & Stel (1996)) that more massive galaxy disks have radii of dark matter onset (R10) and dark matter dominance (RX) that occur further out in their disks. In addition, the radii R10 and RX are correlated with each other; they both increase in proportion to M∗. These two radii are found to correlate with

Hubble T-Type, V∗,max, and other parameters that vary along the Hubble Sequence to a lesser extent.

In a similar vein, I compared the behavior of the baryonic contributions to the observed rotation curves by plotting the ratio of their respective potentials.

81 Although enough systematic scatter is found among the resulting curves as to be evidence against a universal rotation curve (Persic et al. 1996), they do convey information by comparing their behavior. Galaxies that rotate faster generally have a baryonic matter contribution that extends further out in their disks. The radius to which it extends is correlated with V∗,max, which is in turn correlated with M∗ and

Hubble T-type. It is demonstrated that there is scatter present both at the radius of dark matter onset and in the manner in which dark matter increases its presence in the disks. The radial form of the onset of dark matter is consistent with what is expected from the fall-off of an exponential baryonic disk in the region where an observed rotation curve is approximately flat.

The data presented here can be used in other investigations into galaxy formation and dark matter. In particular, for a future study, I plan to derive the specific and total angular momenta of these galaxies from the data presented here.

I also plan to derive spin parameters for the galaxies. These quantities will inform models of galaxy formation (both semi-analytic and numerical) that derive many galactic properties from them.

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