Constraining Spiral Galaxy Mass Distributions with the Rss Imaging Spectroscopy Nearby Galaxy Survey

Home , Galaxy rotation curve, NGC 1325, NGC 1964, NGC 2280, NGC 45, NGC 5364

CONSTRAINING SPIRAL GALAXY MASS DISTRIBUTIONS WITH THE RSS IMAGING SPECTROSCOPY NEARBY GALAXY SURVEY

CARL J. MITCHELL

A dissertation submitted to the

Graduate School—New Brunswick

Rutgers, The State University of New Jersey

in partial fulﬁllment of the requirements

for the degree of

Doctor of Philosophy

Graduate Program in Physics and Astronomy

written under the direction of

J. A. Sellwood

and approved by

New Brunswick, New Jersey

October, 2017 ABSTRACT OF THE DISSERTATION

Constraining Spiral Galaxy Mass Distributions with the RSS Imaging Spectroscopy Nearby Galaxy Survey

By CARL J. MITCHELL

Dissertation Director:

J. A. Sellwood

Kinematic measurements of galaxies provide a way to trace their mass distributions. The

RSS Imaging spectroscopy Nearby Galaxy Survey (RINGS) was designed to probe the mass distributions of 19 spiral galaxies on small spatial scales by obtaining a suite of multi-wavelength kinematic and photometric data. In this dissertation, I introduce the high-spatial-resolution, medium-spectral-resolution Hα kinematic portion of the survey, and detail the process which has been used to convert the raw Fabry-P´erotobservations into useful kinematic data and models. These Hα kinematic data were obtained with the Robert

Stobie Spectrograph (RSS) at the Southern African Large Telescope (SALT). I then demonstrate how these Hα kinematic data can be combined with the other types of observations in RINGS, H I radio interferometry and broadband photometric imaging, to probe these galaxies’ mass distributions.

ii Acknowledgments

This work would not have been possible without the contributions of a number of other people. First and foremost, I must thank Jerry Sellwood for providing me with his support and insight over the last several years. I owe considerable gratitude to the other contributors of the RINGS project – Kristine Spekkens and Karen Lee-Waddell, who provided the H I data used in Chapter 4; Rachel Kuzio de Naray and Natasha Urbancic, who provided the photometric data used in Chapter 5; Ted Williams, whose Fabry-Pérotwisdom knows no bounds; and Alex Bixel, who assisted me in the development of my Fabry-Pérotdata reduction code. Conversations with Tad Pryor were especially helpful in understanding the Fabry-Pérot data. Every member of the Rutgers astronomy community has helped me to develop, both as a student and as a person. And of course, this work would not have been possible without the financial support of the NSF, the GAANN program, and the

Department of Physics and Astronomy. Finally, I must thank my countless friends and family who have supported me throughout my time here.

This research made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under con- tract with NASA; Astropy, a community-developed core Python package for Astronomy

(Astropy Collaboration et al. 2013); matplotlib, a Python library for publication quality graphics (Hunter 2007); SciPy (Jones et al. 2001); IRAF, distributed by the National Optical

Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under agreement with the NSF (Tody 1993); and PyRAF, a product of the Space Telescope Science Institute, which is operated by AURA for NASA. Many of the observations described here were obtained with the Southern African Large Telescope.

iii Table of Contents

Abstract ...... ii

Acknowledgments ...... iii

List of Tables ...... vi

List of Figures ...... vii

1. Introduction ...... 1

1.1. Evidence for Cold Dark Matter ...... 1

1.2. Cold Dark Matter’s Successes and Limitations ...... 3

1.3. Probing Spiral Galaxy Mass Distributions ...... 5

1.4. The RSS Imaging-Spectroscopy Nearby Galaxy Survey ...... 13

2. RINGS Medium-Resolution Hα Fabry-P´erotDataset ...... 17

2.1. Introduction ...... 17

2.2. Data Acquisition and Reduction ...... 20

2.3. Velocity and Intensity Maps ...... 35

2.4. Summary ...... 47

3. RINGS Hα Kinematic Modelling ...... 49

3.1. Introduction ...... 49

3.2. Axisymmetric Models and Rotation Curves ...... 50

3.3. Summary ...... 66

iv 4. NGC 2280 H I Kinematic Data and Comparisons ...... 67

4.1. Introduction ...... 67

4.2. NGC 2280: Basic Properties ...... 68

4.3. H I Observations ...... 68

4.4. Velocity Map Comparison ...... 74

4.5. Modelling Comparison ...... 77

4.6. Summary ...... 88

5. NGC 2280 Mass Modeling ...... 90

5.1. Introduction ...... 90

5.2. Photometric Measurements of NGC 2280’s Stellar Mass Distribution . . . . 93

5.3. Determining the Stellar Contribution to the Rotation Curve ...... 95

5.4. NGC 2280’s Dark Matter Halo ...... 100

5.5. Sources of Uncertainty ...... 103

5.6. Summary ...... 107

6. Summary ...... 111

Bibliography ...... 114

v List of Tables

1.1. Galaxies in the RINGS Sample ...... 14

2.1. RINGS Medium-Resolution Fabry-P´erotObservations ...... 21

3.1. Best-Fitting Axisymmetric DiskFit Model Parameters ...... 57

4.1. Galaxies Near NGC 2280 ...... 72

4.2. NGC 2280 H I Observation Parameters ...... 73

4.3. NGC 2280 Model Comparison ...... 78

5.1. Color-Mass-to-Light-Ratio-Relation Model Parameters ...... 96

vi List of Figures

1.1. Galaxies in the RINGS Sample ...... 15

2.1. Fabry-P´erotGhosts ...... 25

2.2. Sample Fabry-Pérotspectra and line profile fits ...... 32

2.3. NGC 337A Fabry-P´erotData ...... 35

2.4. NGC 578 Fabry-P´erotData ...... 36

2.5. NGC 908 Fabry-P´erotData ...... 36

2.6. NGC 1325 Fabry-P´erotData ...... 37

2.7. NGC 1964 Fabry-P´erotData ...... 37

2.8. NGC 2280 Fabry-P´erotData ...... 38

2.9. NGC 3705 Fabry-P´erotData ...... 38

2.10. NGC 4517A Fabry-P´erotData ...... 39

2.11. NGC 4939 Fabry-P´erotData ...... 39

2.12. NGC 5364 Fabry-P´erotData ...... 40

2.13. NGC 6118 Fabry-P´erotData ...... 40

2.14. NGC 6384 Fabry-P´erotData ...... 41

2.15. NGC 7606 Fabry-P´erotData ...... 41

2.16. NGC 7793 Fabry-P´erotData ...... 42

2.17. Radial R-band Surface Brightness Proﬁles ...... 44

2.18. Radial Hα Intensity Proﬁles ...... 45

2.19. Radial N2 Index Proﬁles ...... 46

2.20. Radial Oxygen Abundance Proﬁles ...... 47

vii 3.1. NGC 337A DiskFit Axisymmetric Model ...... 52

3.2. NGC 578 DiskFit Axisymmetric Model ...... 52

3.3. NGC 908 DiskFit Axisymmetric Model ...... 53

3.4. NGC 1325 DiskFit Axisymmetric Model ...... 53

3.5. NGC 1964 DiskFit Axisymmetric Model ...... 53

3.6. NGC 2280 DiskFit Axisymmetric Model ...... 54

3.7. NGC 3705 DiskFit Axisymmetric Model ...... 54

3.8. NGC 4517A DiskFit Axisymmetric Model ...... 54

3.9. NGC 4939 DiskFit Axisymmetric Model ...... 55

3.10. NGC 5364 DiskFit Axisymmetric Model ...... 55

3.11. NGC 6118 DiskFit Axisymmetric Model ...... 55

3.12. NGC 6384 DiskFit Axisymmetric Model ...... 56

3.13. NGC 7606 DiskFit Axisymmetric Model ...... 56

3.14. NGC 7793 DiskFit Axisymmetric Model ...... 56

3.15. Rotation Curve Literature Comparison ...... 59

4.1. R-band, Hα, and H I Intensity Maps of NGC 2280 ...... 69

4.2. NGC 2280 Line Proﬁle Fits ...... 70

4.3. NGC 2280 Hα Fabry-P´erotKinematic Map ...... 71

4.4. NGC 2280 H I Kinematic Map ...... 75

4.5. NGC 2280 Velocity Diﬀerence Map ...... 77

4.6. NGC 2280 Model Comparison ...... 79

4.7. NGC 2280 Model Residuals ...... 80

4.8. NGC 2280 Hα and H I Rotation Curve Comparison ...... 82

4.9. NGC 2280 Rotation Curve Comparison - Approaching/Receding ...... 83

4.10. NGC 2280 Anomalous H I Line Proﬁles ...... 85

4.11. NGC 2280 Beam-Smeared Rotation Curves ...... 86

viii 4.12. NGC 2280 Hα and H I Intensity Proﬁles ...... 87

5.1. NGC 2280 BV Photometry ...... 94

5.2. NGC 2280 Stellar Mass Maps ...... 97

5.3. NGC 2280 Exponential Disk Fits ...... 99

5.4. NGC 2280 Stellar Rotation Curve Contributions ...... 101

5.5. NGC 2280 Halo Density Proﬁles ...... 102

5.6. NGC 2280 Halo Proﬁle Functional Fits ...... 104

5.7. Eﬀects of CMLR Normalization Uncertainty ...... 105

5.8. Eﬀects of Distance Uncertainty ...... 106

5.9. Eﬀects of Vertical Proﬁle Uncertainty ...... 108

ix 1

Chapter 1

Introduction

The formation and evolution of galaxies are well-explained by the so-called ΛCDM paradigm.

In ΛCDM, the energy content of our universe is dominated by a repulsive energy density dubbed “dark energy” and an invisible matter component known as “dark matter.” Only about 5% of the universe is composed of the ordinary matter with which we are most familiar (Komatsu et al. 2009).

ΛCDM has been extremely successful as a theory, explaining a wide range of astronomical phenomena across a wide range of spatial scales (see review by Somerville & Dav´e

2015). Despite this, there remain some open questions, particularly on small scales within the central regions of galaxies.

In this introduction, I provide an overview for the evidence for the “CDM” in ΛCDM, the

“Cold Dark Matter,” and discuss some of its successes and current limitations as a theory, in particular the diﬃculty of testing it on small spatial scales. I then brieﬂy discuss some of the wide range of methods that can be used to probe the mass distributions of galaxies.

Finally, I introduce the RSS Imaging-Spectroscopy Nearby Galaxy Survey (RINGS), which was designed to utilize some of these techniques to probe galaxy mass distributions on small spatial scales.

1.1 Evidence for Cold Dark Matter

Galactic rotation curves were one of the earliest probes of galaxy mass distributions and provide one of the most stark pieces of evidence for the existence of dark matter. In spiral 2 galaxies, stars and gas rotate in a plane. A rotation curve is a measurement of the speed of this rotation as a function of radius, i.e. Vc(R), where Vc is the circular speed and R is the 2-dimensional radius measured in the plane of the disk (e.g. Rubin et al. 1982). In these galaxies, the light coming from stars is known to roughly follow a distribution that declines exponentially with radius, i.e. I(R) e−R/Rs where I is some measure of the light ∝ intensity or surface brightness and Rs is some scale radius (van der Kruit & Freeman 2011).

Assuming this light distribution approximately traces the mass distribution of the stars, a rotation curve can be derived by equating the gravitational force of the stellar disk on a test mass to the centripetal force. When the light distribution of visible stars is used to p predict a rotation curve in this way, it reaches its peak velocity (Vmax = 0.62 GMdisk/Rs)

−1/2 at a radius of about 2.2Rs and slowly declines as V R at large radii. ∝ By contrast, the rotation curves of real galaxies are known to ﬂatten to constant values of velocity at large radii (Bosma 1978). This discrepancy implies one of two things - either the laws of physics used to derive the rotation curve are incorrect or there exists additional non- stellar mass contributing to the gravitational force at large radii. The latter interpretation of this phenomenon has typically been preferred, and the ﬂatness of rotation curves at large radii is now one of the most frequently cited pieces of evidence for dark matter.

Rotation curves illustrate one of the many ways in which the motion of astronomical objects can be used to measure mass distributions. The motions of entire galaxies within galaxy clusters are also too rapid to be explained by visible matter alone. Unlike rotation curves, these motions are not circular and planar; they are 3-dimensional, having both rotational and radial components. By measuring the dispersion in velocity along the line of sight and assuming the cluster is in virial equilibrium, the total mass of the galaxy cluster can be determined. As with the rotation curves of disk galaxies, the luminous matter does not have suﬃcient mass to explain the dispersions of velocities within galaxy clusters.

In fact, dark matter was ﬁrst postulated by Zwicky (1937a) to explain anomalously high velocity dispersions among the galaxies in the Coma cluster. Velocity dispersions remain a 3 common method for determining the masses of galaxy clusters (e.g. Sif´onet al. 2016).

Perhaps the strongest piece of evidence for dark matter comes from observations of galaxy clusters undergoing mergers with each other. Such events are extremely rare, and only a few are currently known. Current examples of such systems include the “Bullet

Cluster” (Clowe et al. 2006) and MACS J0025-1222 (Bradaˇcet al. 2008). Galaxy clusters consist of stars, gas, and dark matter. These clusters are so massive that light from distant objects bends around them in a phenomenon known as gravitational lensing (Zwicky 1937b;

Walsh et al. 1979). When two galaxy clusters undergo a merger, their stars and dark matter pass through one another relatively unaffected by the merger event, while their gas undergoes collisions and loses momentum. X-ray observations of these interacting clusters reveal that the intracluster gas has ceased travelling with the stars and remains concentrated at the spot of the clusters’ collision. But gravitational lensing observations have revealed that the vast majority of the mass in these clusters does not spatially coincide with the gas. This effect is extremely well-illustrated by Figure 1 of Clowe et al. (2006), which demonstrates the spatial offset between the X-ray emission and lensing mass contours in the Bullet Cluster. Because most of the baryonic mass in these clusters is contained in the X-ray emitting gas, this spatial offset indicates that there must be an unseen matter component causing the lensing.

1.2 Cold Dark Matter’s Successes and Limitations

According to the standard ΛCDM paradigm, a period of rapid expansion known as “infla- tion” caused quantum-scale fluctuations to grow in size and become causally disconnected in the first moments of the universe (Guth 1981). As the universe expanded and cooled, overdense clumps of matter began to grow due to their own gravity. Within these overdense regions, galaxies and clusters of galaxies were formed. Observations of the Cosmic

Microwave Background (CMB) such as those by the Wilkinson Microwave Anisotropy Probe

(WMAP) and the Planck telescope reveal the large-scale distribution of matter and energy 4 shortly after this inflationary period, when the universe was 1/1000 its present size (Ko- ∼ matsu et al. 2009; Planck Collaboration et al. 2014). These distributions are then used as the initial conditions for dark matter particles in cosmological computer simulations, which evolve these distributions forward in time, producing predictions for the large-scale distributions of dark matter halos in our universe. Observations of the distributions of galaxies and clusters of galaxies confirm that the large-scale structure of the universe closely matches the distributions of dark matter halos predicted by ΛCDM theory and these cosmological simulations (see review by Somerville & Davé2015). This remarkable matching of theory and observation requires that galaxies inhabit these dense dark matter halos and that the dark matter be non-relativistic in nature, i.e. it is thermally “Cold,” which provides the C in ΛCDM.

The successful predictions of ΛCDM go beyond the spatial distribution of galaxies.

These cosmological simulations also provide predictions of the relative number densities of dark matter halos of diﬀerent masses, the so-called “mass function” of these halos, that qualitatively match the observed number densities of galaxies, though it remains unclear whether discrepancies exist in this relationship at small mass scales (see review by Somerville

& Dav´e2015).

Despite these tremendous successes, ΛCDM has been somewhat limited in its predictions, particularly on small spatial scales and at high matter densities, regimes in which non-linear eﬀects become important. Gravity is the dominant force governing galaxy formation and evolution on large scales, and dark matter is the dominant source of gravity.

The primary method by which astronomers observe galaxies is through the collection of light, which dark matter does not seem to emit. Some of the most signiﬁcant remaining open questions in the ﬁeld of galaxy formation are due to this mismatch.

On small spatial scales within galaxies and at high matter densities, gravity is no longer the only force that must be considered. The interactions of gas and stars with each other and with dark matter play a significant role in shaping galaxies on these scales. While 5 gravitational forces are relatively easy to calculate, the non-gravitational effects of stars and gas are far more complicated to model. Simulations that incorporate the physical effects of gas and stars are computationally very expensive to perform and require empirical prescriptions for how these “baryonic” effects1 alter galaxies on scales smaller than the simulations’ resolution. The comparison between theoretical models and observations is further complicated by the fact that it is difficult to observe galaxies on such small scales.

Thus it remains unclear to what extent ΛCDM is consistent with real galaxies on these scales. Progress towards both simulations and observations of ever-increasing resolution is allowing both theorists and observers to probe galaxies and our theories of cosmology on smaller scales than ever before.

1.3 Probing Spiral Galaxy Mass Distributions

Spiral galaxies are generally thought to be composed of a few separate mass components, the most signiﬁcant of which are an extended halo of dark matter and a much smaller disk of baryonic matter. Cosmological simulations indicate that dark matter halos contain considerable substructure, but that their innermost regions are smooth (Springel et al.

2008). The inner part of the halo is often thought to be spherical in shape, although more generally it can take on a triaxial ellipsoidal shape (Jing & Suto 2000). The baryonic disk is composed of both diﬀuse gas and dense stars, and often includes geometric features such as spiral arms, bars, and rings (van der Kruit & Freeman 2011). Many galaxies also contain a dense spheroidal stellar bulge at their centers (van der Kruit & Freeman 2011).

Most of the light from spiral galaxies comes from the stellar disk, while most of the mass is contained in the dark matter halo. As mentioned above, observations of galaxy kinematics can be used to probe mass distributions. In the case of spiral galaxies, observations of rotation curves can be used to measure the combined eﬀect of these diﬀerent mass

1To astronomers, baryonic matter is any matter that isn’t dark matter - including leptons. Because leptons have very little mass relative to baryons, this linguistic approximation is also a good mathematical approximation. 6 components, but separating the contributions of these components is a more difficult problem. Complications come from many sources. The full 3-dimensional geometry of the mass distributions must be considered – baryonic matter distributed in a flattened plane affects the rotation curve in a different way than does spherically distributed dark matter. The density profiles of dark matter halos are not well-constrained – cosmological simulations have historically favored broken power-law forms such as the Navarro-Frenk-White (NFW) and Einasto profiles, while most indirect measurements of halo profiles from observations of galaxies seem to favor a pseudo-isothermal distribution (Einasto 1965; Navarro et al. 1996;

Gao et al. 2008). These halo density profiles differ most significantly in their central regions, with some having steep inner gradients known as “cusps” and others having shallow

“cores.” The decomposition of galactic rotation curves into the separate contributions of the disk, halo, and bulge is therefore quite a non-trivial problem.

As mentioned above, the light distribution of spiral galaxies roughly follows a function that exponentially declines with radius, which can then be transformed to a stellar rotation curve that peaks at 2.2 exponential scale lengths and slowly declines (van der Kruit &

Freeman 2011). However, transforming from the stellar light distribution to the stellar mass distribution is not so trivial. Such a transformation depends crucially on the stellar mass-to-light ratio, often denoted Υ M/L. Because the luminosities of individual stars ≡ scale non-linearly with their masses (as well as their ages and chemical compositions), the mass-to-light ratio of a stellar population is diﬃcult to determine accurately. While this ratio is often assumed to be constant over the entire stellar disk, it may not be. By varying this ratio, the predicted stellar rotation curve can be scaled up and down at will. If the ratio is allowed to spatially vary, the shape of the stellar contribution to the rotation curve can also be altered. Because the mass distribution of the dark matter halo is essentially a free parameter, it is completely degenerate with the mass-to-light ratio. If the disk mass-to-light ratio is as large as it can be without ever exceeding the measured rotation curve, it is known as a “maximal disk.” Disks that do not provide the bulk of the rotational 7

support (Vdisk/V < 0.85) at 2.2 disk scale lengths in their galaxies are termed “submaximal”

(Sackett 1997). This degeneracy between the mass distributions of the disk and halo, in particular at small radii, has appropriately become known as the “disk-halo degeneracy.”

The degeneracy is well-illustrated by Figures 6-8 of van Albada et al. (1985), which show a series of mass models for the spiral galaxy NGC 3198 ranging from a maximal disk to a massless disk. Note how the halo mass distribution can be tuned to allow for a wide range of disk mass-to-light ratios.

Numerous methods have been employed to try to break this degeneracy and constrain the mass distributions of galaxies at small radii, some of which are discussed below. In general, these methods try to ﬁnd some property of a galaxy that is not dependent on the full 3-dimensional mass distribution, but rather only on the 2-dimensional distribution of the disk.

1.3.1 Stellar Population Modelling

One possible way to separate the mass of the stellar disk from other components of a galaxy is to try to convert its luminosity distribution directly to a mass distribution. As discussed above, the non-linear relationship between a star’s mass and its luminosity makes a direct measurement of a galaxy’s stellar mass diﬃcult. However, if the relative numbers, ages, and chemical compositions of diﬀerent types of stars are well-known for a galaxy’s stellar population, a mass-to-light ratio for the whole population can be reasonably determined.

This is the principle behind stellar population synthesis (SPS) modelling (e.g. Bruzual &

Charlot 2003; Bell & de Jong 2001). An extensive review of this topic is provided by

Conroy (2013). In these models, a sample stellar population is generated and evolved over time, forming new stars and enriching the population’s chemical abundances according to prescriptions. The stellar populations that result from these models can then be used to derive empirical relations between a population’s mass-to-light ratio and other spectral properties. A common relationship derived from these models is that between mass-to-light 8 ratio and “color” (a measure of the ratio of ﬂuxes in two diﬀerent photometric bands).

The SPS models of Bruzual & Charlot (2003) and color-mass-to-light-ratio relations

(CMLRs) of Bell & de Jong (2001) were used by Dutton et al. (2005) to decompose the rotation curves of a sample of six spiral galaxies. Each of these galaxies’ disks was found to be submaximal, providing 33 59% of the rotational support necessary to match their − rotation curves. Using a similar method, Bolatto et al. (2002) concluded that the dwarf spiral galaxy NGC 4605 most likely has a maximal disk. The debate over the reliability of such stellar mass estimates is ongoing. Various updated SPS models and CMLRs have emerged over the years, such as those of Portinari et al. (2004), Zibetti et al. (2009), and Into

& Portinari (2013). For typical values of B V color, these CMLRs diﬀer by multiplicative − factors of up to 2-3 in their predicted mass-to-light ratios (McGaugh & Schombert 2014).

The large scatter among the various SPS and CMLR model predictions comes from a number of factors. A crucial assumption of SPS models is the form of the “initial mass function” (IMF), the probability distribution function for the masses of newly-formed stars.

Some common choices for this function are a simple power-law (Salpeter 1955), a broken power-law (Kroupa 2001), or a log-normal distribution (Chabrier 2003). Each of these functions differs in the relative quantities of low-mass and high-mass stars it predicts will be formed, with the largest differences at the lowest masses. High-mass stars not only produce much more light overall than low-mass stars, but they also produce light that is at much higher frequencies (bluer) than do low-mass stars. The relative abundances of high-mass and low-mass stars will therefore affect both the colors of these stellar populations and their mass-to-light ratios (Conroy 2013; Courteau et al. 2014). Another large source of uncertainty is the assumption of a star formation history for these models. Stellar populations redden and become much dimmer with age as their most massive and luminous stars die, affecting their colors and increasing their mass-to-light ratios. The relative abundances of metals2 to hydrogen, known as metallicity, can mimic the effects of age in a stellar

2To astronomers, all elements beyond helium are considered “metals.” 9 population (Conroy 2013).

Additional sources of uncertainty in these methods are introduced before the CMLR models are even applied to a galaxy. Not only is the transformation from photometric measurements to masses uncertain, but the photometric measurements themselves are uncertain. Color measurements can be heavily affected by dust extinction within a galaxy, where small grain-like particles preferentially absorb photons at shorter wavelengths (Con- roy 2013). The luminosity used in converting light to mass via CMLRs is also affected by dust extinction, but this is not the largest source of uncertainty in measuring galaxy luminosities. The relationship between observed flux and intrinsic luminosity depends on the square of the distance to the galaxy in question. Distances to galaxies are often highly uncertain, leading to very large uncertainties on a disk’s stellar mass when using the methods described above (Bell & de Jong 2001).

1.3.2 Fabry-P´erotObservations and Barred Galaxy Fluid Dynamics

Spiral galaxies that contain a bar oﬀer another potential way to break the degeneracy between the mass components of the disk and the halo. Bars are elongated structures that drive non-circular ﬂows of gas and stars in the centers of galaxies. These streaming motions driven by the bar are highly sensitive to the bar’s gravitational potential but not the halo’s

(Weiner et al. 2001a). If these ﬂows can be measured, they present a way to measure the mass in the bar. Coupled with photometric observations, a mass-to-light ratio for the bar can be derived.

Measuring these bar flows requires 2-dimensional kinematic measurements at spatial resolutions better than 200 pc in the galaxy of interest (Marinova & Jogee 2007; Sellwood ∼ & Sánchez 2010). This requirement makes the use of Fabry-Pérotobservations particularly useful. A Fabry-Pérot etalon consists of two highly (but not perfectly) reflective parallel plates. Successive reflections of light between the plates will destructively interfere unless their phases align. Light that emerges from the etalon must therefore have been in-phase 10 with its successive reflections. Combining an etalon with a narrow-band filter allows a single interference order to be selected, turning the Fabry-Pérotetalon into an effective very-narrow-band filter. By changing the spacing between the reflective plates of the etalon, different wavelengths can be selected. By taking a series of observations of a galaxy with a

Fabry-P´erotsystem at several diﬀerent values of plate spacing, a data cube can be produced with two spatial dimensions (the plane of the sky) and one spectral dimension (wavelength).

If the system is tuned to the wavelength of a bright emission line of known rest wavelength, e.g. Hα, this instrument can be used to produce a two-dimensional map of the line-of-sight velocities in a galaxy (Weiner et al. 2001a; Z´anmarS´anchez et al. 2008).

The non-axisymmetric potential of the bar structure drives non-circular flows of gas in the centers of barred galaxies. The gas in the bar experiences hydrodynamic shocks as con- sequence of these non-circular flows, that must be modelled with hydrodynamic simulations to extract information about the bar potential. Weiner et al. (2001b) and ZánmarSánchez et al. (2008) have used this method in conjunction with optical photometry data to derive mass-to-light ratios for the bars of NGC 4123 and NGC 1365, respectively. Their analyses strongly favored mass-to-light ratios for the bar that, if adopted for the entire stellar disk, imply that these galaxies’ disks are maximal or nearly maximal.

This method requires a very careful selection of target galaxy in order for it to work well. The galaxy must have an intermediate inclination – inclined enough that line-of-sight velocities can be extracted at high signal-to-noise, but not so far inclined that the disk plane is signiﬁcantly compressed along the minor axis (Weiner et al. 2001a). The position angle of the bar relative to the position angle of the galaxy’s projection on the sky is also important

– too far aligned or misaligned and the bar ﬂows become degenerate with circular motions within the galaxy (Sellwood & S´anchez 2010). Finally, the galaxy must exhibit strong Hα emission in the bar region and the regions immediately surrounding it in order to observe the shocks (Weiner et al. 2001a). In many galaxies, Hα emission is sparse near the bar

region, limiting the application of this method to a small subset of galaxies. 11

Another signiﬁcant limitation of this method is that it only measures the mass-to-light ratio of the bar, not the entire stellar disk. Some assumption must be used to infer the mass of the other regions of the disk. The simplest and most common assumption that can be made is that the mass-to-light ratio is constant across the entire disk (Weiner et al. 2001b).

Because galaxies are known to have gradients in color across their disks, this assumption may not be valid. Weiner et al. (2001a) also tested disk models in which the mass-to-light ratio was allowed to vary with radius outside of the bar region and found that it made little diﬀerence in the disk contribution to the rotation curve. Fortunately, much of the scatter among diﬀerent CMLRs, in particular the scatter due to the unknown IMF, corresponds to a simple multiplicative scaling of the mass-to-light ratios at all colors (Courteau et al. 2014).

Combining the bar mass-to-light ratios derived from these types of kinematic observations and modelling with CMLRs can provide more robust constraints on the mass of the disk

(de Jong & Bell 2007).

1.3.3 Other Methods

As mentioned above, gravitational lensing is a general relativistic eﬀect that can be used to probe the masses of galaxies. While a galaxy’s rotation curve depends on the full 3- dimensional density distribution, the angle by which light is deﬂected by a gravitational lens depends on the 2-dimensional column mass density along the line of sight. The combination of these two types of observations can allow the contributions of the spherical halo and the planar disk to be separated (e.g. Trott & Webster 2002). Until recently, very few spiral galaxies suitable for such an analysis were known, and most of these galaxies had extremely large bulge components (Courteau et al. 2014). These bulge-dominated galaxies were found to have submaximal disks, though most of the centripetal attraction was not provided by dark matter, but rather by these galaxies’ bulges (Trott et al. 2010; Dutton et al. 2011).

Barnab`eet al. (2012) performed a similar analysis on the disk-dominated galaxy SDSS

J2141-0001 and found that the baryonic matter components (including the bulge) provide 12

87% of the centripetal attraction at 2.2 disk scale lengths. ∼ Debattista & Sellwood (2000) performed a series of N-body simulations of isolated

barred spiral galaxies to determine the eﬀects of dynamical friction on a galaxy’s bar.

Dynamical friction is an eﬀect ﬁrst described by Chandrasekhar (1943) by which a dense

object moving through a collisionless medium of light particles experiences a drag force.

Because galaxy bars are composed of dense objects (stars) moving through the collisionless

medium of a dark matter halo, Weinberg (1985) predicted that the rotation speed of a

galaxy’s bar would decrease over time due to this eﬀect. Bar rotation speed is typically

parameterized by the dimensionless parameter , with < 1.4 being considered fast and R R > 1.4 slow3. The simulations of Debattista & Sellwood (2000) found that submaximal R disks in dense dark matter halos result in bars slowing to 1.7 within a few tens of R ∼ millions of years, while maximal disks had bars that remained fast. In galaxies with fast bars, this theoretical result places a lower limit on the mass of the disk. Using a method developed by Buta (1986), Pérezet al. (2012) measured values of for 44 barred galaxies in the SDSS R and COSMOS surveys, finding all of these galaxies to have fast-rotating bars. The method of Buta (1986) is based on measuring the radii of ring features in these galaxies. These rings are the result of dynamical resonances induced by the bar’s gravitational potential. While the pattern speed of the bar is not measured directly by this method, the dimensionless parameter can be determined. A different method, proposed by Tremaine & Weinberg R (1984), was used by Aguerri et al. (2015) on measure bar pattern speeds for 15 galaxies in the CALIFA survey, all of which were found to be fast. By contrast with the method of Buta

(1986), the method of Tremaine & Weinberg (1984) measures the bar pattern speed directly by taking a luminosity-weighted average of the kinematic measurements of a galaxy’s bar region. Based on the simulation results of Debattista & Sellwood (2000), these observations of fast-rotating bars imply that these galaxies have disks that are close to maximal.

While the orbital speeds of stars in the disk planes of galaxies are sensitive to the

3The dimensionless parameter is the ratio of the “corotation radius” (the radius at which the galaxy’s R angular rotation speed is equal to the bar’s pattern speed) to the bar’s semi-major axis. 13 full 3-dimensional mass distributions of the disk and halo, motions in-and-out of the disk plane are sensitive primarily to the mass in the disk alone. By measuring the dispersion in velocities of stars or other objects perpendicular to the disk, the disk mass distribution can be determined (Westfall et al. 2011). Coupled with a measurement of a rotation curve, the disk’s contribution to that rotation curve can then be constrained. These two measurements are diﬃcult to conduct simultaneously for a single galaxy, as the circular and out-of-plane velocities are perpendicular. The 3-dimensional shape of the disk and its “velocity ellipsoid” must therefore be assumed or derived from empirical scaling relations (e.g. Kregel et al.

2002). Herrmann & Ciardullo (2009) apply this method to ﬁve galaxies by measuring the out-of-plane velocity dispersions of planetary nebulae. Of their sample, they ﬁnd a mixture of maximal and submaximal disks, noting a correlation between a disk’s contribution to the rotational support and galaxy morphology – galaxies with more tightly bound spirals and larger bulges were more likely to be maximal. Bershady et al. (2011) applied this method to a sample of 30 galaxies, utilizing the kinematics of stars rather than planetary nebulae.

They concluded that all of the disks in their sample were submaximal, typically providing

47% of the rotational support in their galaxies.

1.4 The RSS Imaging-Spectroscopy Nearby Galaxy Survey

The RSS Imaging-Spectroscopy Nearby Galaxy Survey was designed to address this question of how the diﬀerent mass components of galaxies are distributed. The survey consists of

19 nearby spiral galaxies that span a large range of masses, luminosities, and morphologies

(Kuzio de Naray et al. 2017, in prep.). For each of these galaxies, three complementary sets of data are being collected: (1) high-spatial-resolution kinematic maps of the Hα line of excited hydrogen, (2) low-spatial-resolution kinematic maps of the H I 21 cm line of neutral hydrogen, and (3) imaging in the BVRI photometric bands. Most of these data have been collected and processed. The morphology and completion status for each galaxy in the survey are summarized in Table 1.1 and Figure 1.1. 14

Table 1.1. Galaxies in the RINGS Sample

Galaxy Class FP Type FP Complete H I Complete Phot Complete

NGC 45 SA(s)dm HR No Yes Yes NGC 247 SAB(s)d HR No Yes Yes NGC 337A SAB(s)dm MR Yes No Yes NGC 578 SAB(rs)c MR Yes Yes Yes NGC 908 SA(s)c MR Yes Yes Yes NGC 1325 SA(s)bc MR Yes Yes Yes NGC 1744 SB(s)d HR No Yes Yes NGC 1964 SAB(s)b MR Yes Yes Yes NGC 2280 SA(s)cd MR Yes Yes Yes NGC 3621 SA(s)d HR No Yes No NGC 3705 SAB(r)ab MR Yes Yes Yes NGC 4517A SB(rs)dm MR Yes No Yes NGC 4939 SA(s)bc MR Yes No Yes NGC 5364 SA(rs)bc pec MR Yes No Yes NGC 6118 SA(s)cd MR Yes No Yes NGC 6384 SAB(r)bc MR Yes No Yes NGC 7606 SA(s)b MR Yes No Yes NGC 7793 SA(s)d MR Yes Yes Yes UGCA 90 Im HR No Yes Yes

Note. — A summary of the 19 galaxies in the RINGS survey and their observation status as of 6 July 2017. From left to right, columns are: (1) galaxy designation, (2) morphological classification, (3) whether the Hα Fabry-Pérotdata on each galaxy are medium- or high- spectral-resolution, (4) whether the Fabry-Pérotobservations of each galaxy are complete, (5) whether the H I 21 cm observations of each galaxy are complete, and (6) whether the photometric observations of each galaxy are complete. Note that while we have obtained Hα Fabry-Pérotobservations of 14 of the galaxies, H I 21 cm observations of 12 of the galaxies, and photometric observations of 18 of the galaxies, the full suite of observations is available for only 7 galaxies. Of these, only one of the galaxies (NGC 2280) has had its H I 21 cm data reduced to a usable format. 15

Figure 1.1 The 19 galaxies in the RINGS sample span a wide range of masses and luminosities. The points in magenta are the 14 galaxies presented in Chapters 2 and 3.

The purpose of the high-spatial-resolution Hα kinematic data is primarily to determine the kinematics of these galaxies near their central regions, where the eﬀects of baryonic matter are expected to be most pronounced. Fourteen of the 19 RINGS galaxies have been observed with the medium-spectral-resolution Fabry-P´erotinterferometer aboard the

Robert Stobie Spectrograph (RSS) at the Southern African Large Telescope (SALT). Chap- ters 2 and 3 discuss these observations, the processing we have done to obtain useful kinematic data from them, and the modelling we have done of these kinematics. The remaining

5 galaxies are scheduled to be observed with the SALT FP instrument’s high-spectral- resolution mode. The Hα Fabry-Pérotkinematic data were also sought for the purposes of obtaining kinematic observations of bar flows similar to those of Weiner et al. (2001a) and reproduce their fluid dynamics analysis on a larger sample (Weiner et al. 2001b). Unfortu- nately, the sparseness of the RINGS Fabry-Pérotkinematic maps in the innermost regions of these galaxies has rendered such analysis impossible in most cases. The common practice 16 of spatially binning or blurring such data to improve the signal-to-noise ratio would be in- effective in this case, as detection of the non-axisymmetric bar feature requires the data to have spatial resolution (<200 pc) (e.g. Marinova & Jogee 2007; Sellwood & Sánchez 2010;

Barrera-Ballesteros et al. 2014; Holmes et al. 2015). The content of Chapters 2 and 3 is largely reproduced from Mitchell et al. (2017, submitted to A.J.).

The lower-spatial-resolution H I data are intended to complement the Hα Fabry-P´erot

data. These data were primarily obtained with the Karl G. Jansky Very Large Array

(JVLA) radio telescope. Compared to the Hα data, the H I data have better spectral

resolution and worse spatial resolution. The H I data also generally have a larger spatial

ﬁlling factor (i.e. the data have fewer gaps in coverage) and larger spatial extent (i.e. the

kinematics are visible at larger radii). The H I 21 cm emission also comes from a diﬀerent

emission source – while the Hα line comes from excited hydrogen gas, the H I emission

comes from neutral hydrogen. Chapter 4 compares our H I 21 cm observations of the

RINGS galaxy NGC 2280 with our Hα Fabry-P´erotdata for the same galaxy. Much of

the content in that chapter is reproduced from Mitchell et al. (2015a) and the conference

proceedings of Mitchell et al. (2015b).

The multi-band photometric data were obtained with the Kitt Peak National Observa-

tory (KPNO) 2.1 m telescope and the Cerro Tololo Inter-American Observatory (CTIO)

0.9 m telescope (Kuzio de Naray et al. 2017, in prep.). The purpose of the photometric

data is primarily to place constraints on the stellar mass distributions of these galaxies.

In most galaxies, the majority of the stellar mass is contained in the older, redder stellar

population, while the majority of the light is emitted by the young, bluer population. As

mentioned in the above section about stellar population modelling, the total mass contained

in stars can be better constrained by probing the light distribution of a galaxy in several

wavelength bands. Chapter 5 details our attempts to produce stellar mass models of the

galaxy NGC 2280 and thereby constrain its dark matter distribution. 17

Chapter 2

RINGS Medium-Resolution Hα Fabry-P´erotDataset

2.1 Introduction

Much of the content of this chapter is reproduced from the ﬁrst half of Mitchell et al. (2017, submitted to A.J.).

The standard cosmological paradigm of Cold Dark Matter with the addition of a cosmological constant (ΛCDM) has been successful at interpreting astrophysical phenomena on a wide range of scales, from the large scale structure of the Universe to the formation of individual galaxies (see review by Somerville & Dav´e2015). However, it remains somewhat unclear whether the internal structures of simulated galaxies formed in a ΛCDM framework are consistent with observations of real galaxies.

In spiral galaxies, the structure of dark matter halos can be constrained using rotation curves (e.g. Bosma 1978). Typically, the observed rotation curve is decomposed into contributions from stars and gas and any remaining velocity is attributed to dark matter.

In cosmological simulations of dark matter structure growth, dark matter halos have been observed to follow a broken power law form (e.g. Einasto 1965; Navarro et al. 1996, 2004;

Gao et al. 2008). To account for the additional gravitational pull provided by baryons, modifications can be applied to theoretical halo density profiles to increase their densities at small radii (e.g. Gnedin et al. 2004). These modifications typically take the form of ana- lytic functions that are fitted to halo profiles from simulations containing baryonic effects.

Applying these modiﬁed halo models to observed rotation curves produces dark matter halos that are underdense relative to the predictions of ΛCDM simulations. 18

Numerical simulations that incorporate stellar feedback in galaxies have partially eased this tension by showing that feedback from baryonic processes can redistribute dark matter within a galaxy (Governato et al. 2010; Pontzen & Governato 2012; Teyssier et al. 2013).

These eﬀects are stronger in galaxies with lower masses (e.g. Oh et al. 2011; Brook et al.

2011; Pontzen & Governato 2014). Recent simulations have shown that the ability of a galaxy to redistribute dark matter through stellar feedback depends on the ratio of its stellar mass to its halo mass (e.g. Di Cintio et al. 2014; Brook 2015). These M∗/Mhalo-

dependent density proﬁles have been shown by Katz et al. (2017) to be more consistent

with the photometry and rotation curves of real galaxies than traditional NFW proﬁles.

The relationship between dark matter halos and observed rotation curves is not a trivial

one, as measurements of rotation curves can be biased by non-circular motions, projection

eﬀects, and halo triaxiality (e.g. Rhee et al. 2004; Hayashi & Navarro 2006; Valenzuela

et al. 2007). Measurements of one-dimensional rotation curves are therefore insuﬃcient to

constrain the three-dimensional mass distributions. All of these mechanisms for potential

bias in rotation curves leave kinematic signatures in the full three-dimensional velocity

distributions of galaxy disks. For example, gas streaming along bars and spiral arms has

both circular and radial components to its velocity, and therefore will aﬀect the line of sight

velocities along the major and minor axes diﬀerently (Sellwood & S´anchez 2010).

Measurements of the velocity ﬁeld of the entire disk at high spatial resolution are required

to extract these kinematic signatures. For example, to separate bar-like ﬂows in spiral

galaxies from their rotation curves, <200 pc spatial resolution is required (e.g. Marinova &

Jogee 2007; Sellwood & S´anchez 2010; Barrera-Ballesteros et al. 2014; Holmes et al. 2015).

In recent years, the state of the art in numerical simulations has moved to smaller and

smaller spatial scales. However, comparisons of these simulations to observed galaxies have

been lacking, partially due to a lack of velocity ﬁelds of suﬃciently high resolution for

comparison.

We have designed the RSS Imaging spectroscopy Nearby Galaxy Survey (RINGS) to 19 obtain the high-resolution kinematic data necessary to probe these open questions of galaxy structure. Our survey targets 19 nearby, late-type spiral galaxies over a wide range of masses

−1 −1 (67 km s < Vflat < 275 km s ) and luminosities (-17.5 > MV > -21.5). The survey is designed to exploit the large collecting area and large ﬁeld-of-view of the Robert Stobie

Spectrograph (RSS) on the Southern African Large Telescope (SALT). In addition to the high spatial resolution Hα kinematic data from SALT’s RSS, we are obtaining lower spatial resolution H I 21 cm kinematic observations and have obtained BVRI photometric imaging of these galaxies.

A number of previous surveys have obtained two-dimensional Hα velocity ﬁelds of galaxies with similar goals to RINGS, e.g. BHαBAR (Hernandez et al. 2005), GHASP (Epinat et al. 2008), GHαFaS (Hernandez et al. 2008), DiskMass (Bershady et al. 2010a), and

CALIFA (Sánchez et al. 2012). Compared to these surveys, our data are more extended thanks to SALT’s large primary mirror and large angular field-of-view. The typical angular resolution of the RINGS data is similar to that of the DiskMass and CALIFA surveys and somewhat worse than that of GHαFaS. However, the RINGS galaxies are typically more nearby than the galaxies in those surveys, and our physical resolutions are comparable to those of GHαFaS or higher than those of DiskMass and CALIFA. The typical spectral resolution of our data (R 1300)1 is similar to that of CALIFA (R 1000) and lower than that ∼ ∼ of DiskMass (R 8000) and GHαFaS (R 15000). We also had different target selection ∼ ∼ criteria than these surveys, choosing a representative sample of partially inclined galaxies across a wide range of Hubble classifications, masses, and luminosities.

In this chapter, we describe the data reduction process used to produce the RINGS

Fabry-PérotHα kinematic maps for 14 of the 19 RINGS galaxies. The maps are derived from data taken in the medium-resolution mode of SALT’s Fabry-Pérotsystem. The typical angular resolution of our resulting Hα velocity fields is 2.500, corresponding to a typical ∼ 1The spectral resolution of an instrument is often expressed as its “resolving power,” R λ/∆λ, where ≡ ∆λ is the smallest wavelength difference that can be resolved at wavelength λ. For example, R = 1000 at the wavelength of Hα (6562A)˚ corresponds to a spectral resolution of 6.562A.˚ 20 spatial resolution of 250 pc at the source locations. In addition, we present azimuthally- ∼ averaged Hα and [N II] profiles for these galaxies, and use these profiles to derive oxygen

abundance gradients.

2.2 Data Acquisition and Reduction

We obtained data on 14 nearby late-type galaxies with the medium-resolution mode of

the Fabry-P´erotinterferometer on the RSS of SALT. Our data were acquired over a total

exposure time of 19 hours during the period 11 Nov 2011 to 8 Sept 2015. A typical single

observation consists of 25 exposures, each of length 70 seconds. The medium-resolution ∼ ∼ etalon has a spectral full width at half maximum (FWHM) at Hα of 5 A.˚ For each exposure ∼ taken in an observation, we oﬀset the wavelength of the etalon’s peak transmission by 2 A˚ ∼ from the previous exposure. Each observation therefore represents a scan over a 50 A˚ range ∼ in 2 A˚ steps. For each galaxy, we attempted to obtain at least two such observations. A ∼ summary of the properties of these 14 galaxies and our observations is provided in Table

2.1. References for the distances in that table are as follows: a Bottinelli et al. (1985)

using B-band isophotal diameter Tully-Fisher relation, b Willick et al. (1997) using H -band

Tully-Fisher relation, c Theureau et al. (2007) using H -band Tully-Fisher relation, d Parodi

et al. (2000) using SN Ia B- and V -band light curves (SN 1971L), e Willick et al. (1997)

using I -band Tully-Fisher relation, and f Pietrzy´nskiet al. (2010) using 17 Cepheid variable

stars.

Note that NGC 2280, which we have discussed previously in Mitchell et al. (2015a), is

among the galaxies presented in this work. Because several aspects of our data reduction

process have changed somewhat (e.g. ﬂat-ﬁeld correction and ghost subtraction, discussed

below) since that work was published, we have chosen to present an updated velocity ﬁeld

of that galaxy here to ensure homogeneity across the ﬁnal sample. 21

Table 2.1. RINGS Medium-Resolution Fabry-P´erotObservations

Note. — A summary of our observations and resulting kinematic maps for the 14 galaxies presented here. From left to right, columns are: (1) galaxy name, (2) morphological classification, (3) observation date, (4) number of exposures and time per exposure, (5) effective seeing with worst seeing for each galaxy marked in bold, (6) estimated uncertainty in our wavelength solution,g (7) number of pixels in our fitted maps, (8) number of independent resolution elements in our fitted maps, (9) redshift-independent distance and reference, (10) angular scale at the distances in column 9, (11) seeing in physical units at the distances in column 9, and (12) absolute I -band magnitude derived from the photometry of Kuzio de Naray et al. (2017, in prep.) and the distances in column 9. g At the wavelength of Hα, a wavelength shift of 0.1 A˚ corresponds to a velocity shift of 4.6 km s−1 22

2.2.1 Preliminary Data Reduction

We have utilized the PySALT2 (Crawford et al. 2010) software package to perform preliminary reductions of our raw SALT images. The tasks in PySALT apply standard routines for gain variation corrections, bias subtraction, CCD crosstalk corrections, and cosmic ray removal.

2.2.2 Flattening

The unusual design of SALT introduces unique challenges in calibrating the intensity of our images. SALT’s spherical primary mirror3 is composed of a hexagonal grid of 91 1-meter

mirrors. Unlike most telescopes, the primary mirror remains stationary over the course of

an observation and object tracking is accomplished by moving the secondary optics package

in the primary mirror’s focal plane. The full collecting area of the primary mirror is almost

never utilized, as some mirror segments are unable to illuminate the secondary depending

on a target’s position. Overall, the available collecting area of the primary mirror is smaller

by 30% at the beginning and end of an observation relative to the middle. ∼ The individual mirror segments are removed for realuminization and replaced on weekly ∼ timescales in a sequential scheme. This results in the reﬂectivity of the primary mirror vary-

ing as a function of position on the mirror, and these variations change over time as diﬀerent

mirror segments are freshly realuminized.

As a target galaxy passes through SALT’s ﬁeld of view, individual mirror segments

pass in and out of the secondary payload’s ﬁeld of view, changing the fraction of the total

collecting area utilized as a function of time.

Furthermore, diﬀerential vignetting of images occurs within the spherical aberration

corrector (SAC) on the secondary payload. This eﬀect also varies as a function of object

position overhead (as the secondary package moves through the focal plane to track an

2http://pysalt.salt.ac.za/ 3https://www.salt.ac.za/telescope/#telescope-primary-mirror 23 object). This vignetting eﬀect changes image intensities by 5-10% across an image. ∼ The combined eﬀects of these factors result in image intensity variations that are: position-dependent within a single image, pointing-dependent over the course of an observation as the target drifts overhead, and time-dependent over the weekly segment- ∼ replacement timescale.

A traditional approach to ﬂat-ﬁeld calibration (i.e. combining several exposures of the

twilight sky) is insuﬃcient for correcting these eﬀects, as this approach will not account

for the pointing-dependent eﬀects. Theoretical modelling of the sensitivity variations by

ray-tracing software is not feasible due to the frequent replacement of mirror segments with

diﬀerent reﬂective properties.

In a previous paper (Mitchell et al. 2015a), we utilized an approach for NGC 2280 that

compared stellar photometry in our SALT Fabry-P´erotimages to R-band images from the

CTIO 0.9m telescope (Kuzio de Naray et al. 2017, in prep.). For 50 stars present in both ∼ sets of images, we computed an intensity ratio between our SALT images and the R-band

image. For each SALT image, we then ﬁtted a quadratic two-dimensional polynomial to

these intensity ratios. By scaling each of our images by its corresponding polynomial, we

were able to correct for these variations.

Unlike NGC 2280, most of our target galaxies do not overlap with dense star ﬁelds and

we therefore cannot apply this approach. Instead, we have developed a new approach that

utilizes the night sky background to calibrate our photometry. We make the assumption

that the intrinsic continuum night sky background has uniform intensity over the 80 ﬁeld

of view over the course of each individual exposure ( 70 s). We then mask objects in our ∼ fields using a sigma-clipped cutoff for stars and a large elliptical mask for the galaxy. We fit

the remaining pixels with a quadratic two-dimensional polynomial of the same form used

in the stellar photometry approach described above. We then scale the pixel values in each

image by this ﬁtted polynomial. If the assumption of uniform sky brightness is valid, this

method results in a uniformly illuminated ﬁeld. 24

In order to validate the assumption of uniform sky intensity, we have applied this “sky-

fitting” approach to our data on NGC 2280 and compared it to our previous “star-fitting” approach for the same data. Uncertainties in the coefficients of the fitted polynomials in these two methods were estimated as part of the fitting procedure and compared between the two approaches. The polynomial coefficients were found to agree within the estimated

1-σ uncertainties. This suggests that the sky-fitting approach is sufficient for flattening our images. The assumption of a uniform sky background is less likely to be valid if a target galaxy fills a large fraction of the field of view, as is the case with our observations of NGC 7793. We have examined several spectra obtained from overlapping observations of this galaxy, and it appears any errors introduced by a non-uniform sky background are small compared to other sources of uncertainty. This suggests that even in this case, our assumption of a uniform sky background over the 80 field of view is sufficient to flat-field the data.

We utilize this “sky-fitting” approach to flat-field correction for all 14 of the galaxies presented in this work.

2.2.3 Ghost identiﬁcation and subtraction

Reflections between the Fabry-Pérotetalon and the CCD detector result in each object in an image appearing twice - once at its true position and again at a reflected position, known as the “diametric ghost” (Jones et al. 2002). The positions of these reflections are symmetric about a single point in the image, the location at which the instrument’s optical axis intersects the plane of the CCD. The left panel of Figure 2.1 illustrates this effect in one of our observations of NGC 6384.

As will be discussed in Section 2.2.5, the wavelength calibration solutions for our images are symmetric about the same central point. The ghost positions are therefore extremely useful for precisely determining the location of this point. By matching each star in an image to its ghost and averaging their positions, we are able to determine our reﬂection 25

0.07

0.06

0.05

0.04

0.03 Ghost-to-Star Intensity Ratio

0.02

0.01

0.00 0 100 200 300 400 500 Radius [pixels]

Figure 2.1 Left: A median-combined image of our 15 July 2014 observations of NGC 6384 with detected star-ghost pairs marked with blue lines. The large red star marks the location of the point about which the intensity ratios of a ghost to its star are symmetric. The large rectangular feature in the lower-right portion of the left panel is the shadow of SALT’s tracking probe and the affected pixels have been masked from any calculations. Right: The black points with error bars mark the intensity ratios between ghosts and stars as a function of radius from the point marked in the left panel. These star/ghost pairs were selected from all of our SALT Fabry-Pérotobservations. The solid red line shows our linear fit to these intensity ratios. 26 centers to within a small fraction of a pixel.

While useful for determining the location of the symmetry axis, the presence of these ghosts adversely affects our goal of measuring velocities. In particular, the reflected image of a target galaxy often overlaps with the galaxy itself. This effect is extremely undesirable, because it mixes emission from gas at one location and velocity with emission from gas at a different location and velocity.

We perform aperture photometry on each star-ghost pair to determine intensity ratios between the ghosts and their real counterparts. These ratios are typically 5%. In a ∼ previous paper (Mitchell et al. 2015a), we addressed this issue by rotating each image by

180◦ about its symmetry axis and subtracting a small multiple of the rotated image from the original. After examining a much larger quantity of data, it appears that the intensity ratio between an object and its ghost depends linearly on the object’s distance from a central point. This decreasing ghost intensity ratio is caused by vignetting within the camera optics of the non-telecentric reflection from the CCD. This central point’s location is not coincident with the center of reflection (private communication: D. O’Donoghue), but appears to be consistent among all of our observations. The right panel of Figure 2.1 shows the dependence of the ghost intensity ratio on radius from this point. We have fitted a linear function to the flux ratios of star-ghost pairs in several of our observations, that decreases from 6% at the central point to 2% at the edge of the images. We then apply ∼ ∼ the same reflect-and-subtract approach as in (Mitchell et al. 2015a), rescaling the reflected

images by this linear function rather than a constant factor. This process removes most of

the ghost image intensity from our science images without necessitating masking of these

regions.

2.2.4 Alignment and Normalization

Among the images of a single observation, we use the centroid locations of several stars to

align our images to one another. Typically, the image coordinate system drifts by 0.2500 ∼ 27 over the course of an observation.

As mentioned previously, diﬀerent fractions of SALT’s primary mirror are utilized over the course of a single observation. Thus, the photometric sensitivity of each image varies over an observational sequence. To correct for this eﬀect, we perform aperture photometry on the same stars that were used for aligning the images in order to determine a normalization factor for each image. We then scale each image by a multiplicative normalization factor so that each of these stars has the same intensity in all of our images. Typically, between

10 and 50 stars are used in this process, though in some extreme cases (e.g. NGC 578), the number of stars in the images can be as low as 5.

The combined effects of flattening uncertainty (Section 2.2.2), ghost subtraction 2.2.3, and normalization uncertainty result in a typical photometric uncertainty of 10 12%. ∼ − When combining multiple observations that were taken at different telescope pointings, we have utilized the astrometry.net software package (Lang et al. 2010) to register our images’ pixel positions to accurate sky coordinates. We then use the resulting astrometric solutions to align our observations to one another.

Just as we used stellar photometry to normalize images from among a single observation sequence, we use the same photometry to normalize diﬀerent observation sequences to one another. Stars that are visible in only one pointing are not useful for this task, so we use the photometry of stars that are visible in more than one observation sequence.

2.2.5 Wavelength Calibration

Collimated light incident on the Fabry-Pérotetalon arrives at different angles depending on position in our images. Different angles of incidence result in different wavelengths of constructive interference. Thus, the peak wavelength of an image varies across the image itself. The wavelength of peak transmission is given by

λcen λpeak(R) = (2.1) (1 + R2/F 2)1/2 28

where λcen is the peak wavelength at the center of the image, R is the radius of a pixel from the image center, and F is the eﬀective focal length of the camera optics, measured in units of pixels. The image center is the location where the optical axis intersects the image plane, and is notably the same as the center of the star-ghost reﬂections discussed in section 2.2.3.

The peak wavelength at the center is determined by a parameter, z, that controls the spacing of the etalon’s parallel plates. It may also be a function of time, as a slight temporal drift in the etalon spacing has been observed. In general, we ﬁnd that the function

λcen(z, t) = A + Bz + Et (2.2) is suﬃcient to describe the central wavelength’s dependence on the control parameter and time. This equation is equivalent to the one found by Rangwala et al. (2008) with the addition of a term that is linear in time to account for a slight temporal drift. We ﬁnd that their higher-order terms proportional to z2 and z3 are not necessary over our relatively narrow wavelength range.

Across a single image, the wavelength of peak transmission depends only on the radius,

R. Therefore, a monochromatic source that uniformly illuminates the ﬁeld will be imaged

2 2 1/2 as a symmetric ring around the image center, with radius Rring = F (λ /λ 1) . cen ring − Before and after each observation sequence, exposures of Neon lamps were taken for the purposes of wavelength calibrations, that appear as bright rings in the images. Additionally, several atmospheric emission lines of hydrogen, [N II], and OH- are imaged as dim rings in our observations of the RINGS galaxies. By measuring the radii of these rings, we can determine best-fitting values for the constants A, B, E, and F in the above equations using a least-squares minimization fit. We then use these fitted parameters to calibrate the wavelengths in our images. The sixth column of Table 2.1 shows the uncertainty in each observation’s wavelength solution, calculated as the root mean square residual to our wavelength solution divided by the square root of the number of degrees of freedom in the 29

ﬁt. Typically, 20 30 ring features are used in ﬁtting our wavelength solutions. ∼ −

2.2.6 Sky Subtraction

The sky background radiation in our images is composed of two components: a continuum that we treat as constant with wavelength, and emission lines from molecules in the atmosphere.

Once a wavelength solution has been found for our images, we search for ring signatures of known atmospheric emission lines in our images (Osterbrock et al. 1996). We fit for such emission lines and subtract the fitted profiles from our images. Occasionally, additional emission lines are seen (as prominent rings) even after such subtraction. These emission lines fall into two broad categories: adjacent spectral orders and diffuse interstellar bands.

The medium-resolution Fabry-P´erotsystem has a free spectral range (FSR) at Hα of

75 A.˚ Thus, an atmospheric emission line 75 A˚ from an image’s true wavelength may ∼ ± appear in the image due to the non-zero transmission of the order-blocking ﬁlter at 75 ± A.˚ Several such emission lines have been detected in our data and subsequently ﬁtted and

subtracted from our images.

In several of our observations, we have detected emission consistent with the diﬀuse

interstellar band (DIB) wavelength at 6613 A˚ (Williams et al. 2015). DIBs are commonly

seen as absorption lines in stellar spectra, but are not often observed in emission (Herbig

1995). This emission has also been ﬁtted and subtracted from our data in the same fashion

as the known night-sky emission lines. The DIB emission was detected in our observations

of NGC 908, NGC 1325, and NGC 2280.

Once ring features from emission lines have been ﬁtted and subtracted, we have run a

sigma-clipped statistics algorithm to determine the typical value of the night sky continuum

emission. This continuum value is then subtracted from each of our images before we

produce our ﬁnal data cube. 30

2.2.7 Convolution to Uniform Seeing

Because atmospheric turbulence and mirror alignment do not remain constant over the course of an observation, each of our images has a slightly different value for the effective seeing FWHM. In producing a data cube, we artificially smear all of our images to the seeing of the worst image of the observation track. In principle, we could choose to keep only images with better effective seeing and discard images with worse seeing. When our observations were obtained, SALT did not have closed-loop control of the alignment of the primary mirror segments. Thus the image quality tended to degrade over an observational sequence. Discarding poorer images would therefore tend to preferentially eliminate the longer wavelength images, because we usually stepped upward in wavelength over the sequence. Discarding images would also reduce the overall depth of our observations. For these reasons, we choose to not discard any images when producing the final data cubes presented in this work.

The correction to uniform seeing is done by convolution with a Gaussian beam kernel with σ2 = σ2 σ2 . We also shift the position of the convolution kernel’s center beam worst − image by the values of the shifts calculated from stellar centroids described in section 2.2.4. In this way, we shift and convolve our images simultaneously. The “Seeing” column of Table 2.1 lists the worst seeing FWHM from each of our observations. Typical worst seeing values are between 200 and 300. In the cases where we combine multiple observations of the same object, we convolve all observations to the seeing of the worst image from among all observations of that object, then combine the results into a single data cube.

2.2.8 Line Proﬁle Fitting

In addition to observing the Hα line, our wavelength range is wide enough to detect the

[N II] 6583 line as well. We simultaneously fit for both of these lines in our spectra. The 31 transmission profile of the Fabry-Pérotetalon is well-described by a Voigt function,

Z ∞ 0 0 0 V (λ; σg, γl) = G(λ , σg)Γ(λ λ , γl)dλ , (2.3) −∞ −

where G(λ, σg) and Γ(λ, γl) are Gaussian and Lorentzian functions, respectively. Calculating this convolution of functions is computationally expensive, and we therefore make use of the pseudo-Voigt function described by Humlek (1982). At each spatial pixel in our data cubes, we ﬁt a 6-parameter model of the form

I(λ; C,FH ,FN , λH , σg, γl) = C +FH V (λ λH ; σg, γl)+FN V (λ 1.003137λH ; σg, γl), (2.4) − − where I(λ; ...) is the image intensity as a function of wavelength and the 6 model parameters. C represents the continuum surface brightness, FH the integrated surface brightness of the Hα line, FN the integrated surface brightness of the [N II] 6583 line, λH the peak wavelength of Doppler-shifted Hα, and σg and γl the two line widths of the Voigt proﬁle.

We assume that the Hα and [N II] 6583 emission arise from gas at the same velocity, and the factor of 1.003137 in the above equation reﬂects this assumption.

We fit for these 6 parameters simultaneously using a χ2-minimization routine, where the uncertainties in the pixel intensities arise primarily from the photon shot noise. The shot noise uncertainties are propagated through the various image reduction steps (flattening, normalization, sky subtraction, convolution) to arrive at a final uncertainty for the intensity at each pixel. To account for the uncertainty in overall normalization of each image, we also add a small fraction of the original image intensity (typically 3-5%) in quadrature to the uncertainty at each pixel. This source of uncertainty (from normalizing the images relative to each other) is distinct from the uncertainty introduced in the process of flatfielding individual images.

The χ2-minimization routine also returns an estimate of the variances and covariances of our 6 model parameters. We mask all pixels with ∆IH /IH > 1 or ∆σg/σg > 1 to ensure 32

1.00 NGC 337A NGC 337A NGC 337A 0.75 0.50 0.25 0.00 S/N: 3450 S/N: 371 S/N: 17

1.00 NGC 578 NGC 578 NGC 578 0.75 0.50 0.25 0.00 S/N: 2191 S/N: 785 S/N: 22

1.00 NGC 1964 NGC 1964 NGC 1964 0.75 Normalized Flux 0.50 0.25 0.00 S/N: 2012 S/N: 124 S/N: 18

1.00 NGC 6118 NGC 6118 NGC 6118 0.75 0.50 0.25 0.00 S/N: 753 S/N: 120 S/N: 19 6580 6600 6620 6640 6580 6600 6620 6640 6580 6600 6620 6640 Wavelength [A]˚

Figure 2.2 Selected spectra (solid points with error bars) and best-fitting line profiles (solid red lines) from our data cubes. The left panels show pixels with very high signal-to-noise. The middle panels show pixels with much lower signal-to-noise. The right panels show pixels very low signal-to-noise that are just above our detection thresholds. All spectra have been normalized so that the maximum value of each spectrum is 1. Each row’s spectra are different pixels selected from a single galaxy’s data cube. The different colors and shapes of points correspond to observations from different nights. that only pixels with sufficiently well-constrained parameters are retained, where here we are using ∆ to refer to the χ2-estimated uncertainty in a parameter.

Figure 2.2 shows an assortment of spectra and line profile fits from our data cubes ranging from very high signal-to-noise regions (left column) to very low signal-to-noise regions (right column). The line profiles shown are the best fits to all of the data points from multiple observations combined into a single data cube. We estimate the signal-to- noise of these fitted line profiles by comparing the line intensity of the Hα line to the

2 χ -estimated uncertainty in the continuum, i.e. S/N = FH /∆C

In converting wavelengths to velocities, we ﬁrst adjust our wavelengths to the rest frame of the host galaxy by using the systemic velocities in Table 3.1. We then use the relativistic 33

Doppler shift equation: 2 (λ/λ0) 1 v = c 2 − (2.5) (λ/λ0) + 1

2.2.9 Idiosyncrasies of Individual Observations

NGC 7793 Sky Subtraction

The nearest galaxy in our sample, NGC 7793, required us to modify slightly our procedure for subtracting the night sky emission lines from our images. Because it is so close, its systemic velocity is small enough to be comparable to its rotational velocity; i.e. some of its gas has zero line-of-sight velocity relative to Earth. Additionally, it takes up a substantially larger fraction of the RSS ﬁeld of view than do the other galaxies discussed in this work. This means that night sky emission of Hα and [N II] is sometimes both spatially and spectrally coincident with NGC 7793’s Hα and [N II] emission across a large fraction of our images.

Because the night sky emission was contaminated by the emission from NGC 7793, we were unable to use the “fit-and-subtract” technique as described in section 2.2.6. Instead, we temporarily masked regions of our images in which the night sky emission ring overlapped the galaxy and fit only the uncontaminated portion of the images. Visual inspection of the images after this process indicates that the night sky emission was removed effectively without over-subtracting from the galaxy’s emission.

We were unable to obtain all of our requested observations of NGC 7793 before the decommissioning of SALT’s medium-resolution Fabry-P´erotetalon in 2015. Consequently, we have acquired 4 observations of the eastern portion of this galaxy but only 1 observation of the western portion. We are therefore able to detect Hα emission from areas of lower signal on the eastern side of the galaxy. All 5 observations overlap in the central region, which is the area of greatest interest to our survey. 34

Migratory Image Artifacts

In our 28 Dec 2011 observations of NGC 908, NGC 1325, and NGC 2280 and our 29 Dec

2011 observation of NGC 578, we detect a series of bright objects that move coherently across our images. These objects have a diﬀerent point spread function from that of the real objects in our images, and appear to be unfocused. In a time sequence of images, these objects move relative to the real objects of the ﬁeld in a uniform way.

The relative abundance of these objects appears to be roughly proportional to the abundance of stars in each image, though we have been unable to register these objects with real stars. In the case of our 29 Dec 2011 observation of NGC 578, one of these objects is so bright that its diametric ghost (see section 2.2.3) is visible and moves in the opposite direction to the other objects’ coherent movement.

Based on this information, we have arrived at a possible explanation for the appearance of these strange objects. We believe that on these two nights in Dec 2011, a small subset of

SALT’s segmented primary mirror, perhaps only one segment, was misaligned with the rest of the primary mirror. This subset of the primary mirror then reflected out-of-field light into our field. As the secondary optics package moved through the focal plane to track our objects of interest, the stars reflected from outside the field then appear to move across the images due to the misalignment of this subset of mirror segments. New edge sensors have been installed between SALT’s primary mirror segments in the time since these observations were taken, so these types of image artifacts should not be present in future observations.

We have applied a simple mask over our images wherever these objects appear. Any pixels that fall within this mask are excluded from any calculations in the remainder of our data reduction process.

Other Image Artifacts

SALT utilizes a small probe to track a guide star over the course of an observation to maintain alignment with a target object. In some of our observations, the shadow of this 35

NGC 337A

-07◦32’ 1 0 1 2 3 4 0.0 0.5 1.0 1.5 2.0 2.5 1040 1060 1080 1100 1120 32 31 − 10− 10− N × × -07◦33’

E -07◦34’

-07◦35’

-07◦36’

-07◦37’

-07◦38’ 2 2 1 2 2 1 Median Surface Brightness [W m− arcsec− A˚ − ] Integrated H-alpha Surface Brightness [W m− arcsec− ] Line of sight Velocity [km s− ] Beam Size:

-07◦32’ 0 2 4 6 8 0 1 2 3 4 0 2 4 6 8 10 33 32 10− 10− × × -07◦33’

-07◦34’

-07◦35’

Declination-07◦36’ Declination

-07◦37’

-07◦38’ 2 2 1 2 2 1 Continuum Surface Brightness [W m− arcsec− A˚ − ] Integrated [NII] Surface Brightness [W m− arcsec− ] Velocity Uncertainty [km s− ] s s s s s s s s s s s s s s s s s s 48 48 48 42 42 42 36 36 36 30 30 30 24 24 24 18 18 18 m m m m m m m m m m m m m m m m m m 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 h h h h h h h h h h h h h h h h h h 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 Right Ascension

Figure 2.3 Our reduced Hα Fabry-Pérotdata for NGC 337A. Top left: the median flux for each pixel in our combined data cube. Bottom left: the fitted continuum flux. Top center: the fitted integrated Hα line flux. Bottom center: the fitted integrated [N II] line flux. Top right: the fitted line-of-sight velocity. Bottom right: the estimated uncertainty in the fitted line-of-sight velocity. At a distance of 2.57 Mpc, the physical scale is 12.5 pc/00. guide probe overlaps our images (e.g. the lower right of the image in Figure 2.1). Similar to our treatment of the migrating objects above, we apply a mask over pixels that are affected by this shadow. We also apply such a mask in the rare cases in which a satellite trail overlaps our images.

2.3 Velocity and Intensity Maps

Figures 2.3-2.16 show 2D maps of median surface brightness, continuum surface brightness

(i.e. C from equation 2.4), integrated Hα line surface brightness (FH ), integrated [N II] line surface brightness (FN ), line-of-sight velocity, and estimated uncertainty in velocity for each of our 14 galaxies. The total number of ﬁtted pixels and number of independent resolution elements in each galaxy’s maps are summarized in Table 2.1.

Many of these maps (e.g. NGC 1964, NGC 5364, NGC 6384, NGC 7606) show signiﬁcant 36

NGC 578

2 0 2 4 6 8 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 1450 1500 1550 1600 1650 1700 1750 1800 32 30 − 10− 10− N × × -22◦39’

-22◦40’

-22◦41’

2 2 1 2 2 1 Median Surface Brightness [W m− arcsec− A˚ − ] Integrated H-alpha Surface Brightness [W m− arcsec− ] Line of sight Velocity [km s− ] Beam Size:

0 2 4 6 8 0 1 2 3 4 5 0 2 4 6 8 10 32 31 10− 10− × × -22◦39’

-22◦40’ Declination Declination

-22◦41’

2 2 1 2 2 1 Continuum Surface Brightness [W m− arcsec− A˚ − ] Integrated [NII] Surface Brightness [W m− arcsec− ] Velocity Uncertainty [km s− ] s s s s s s s s s 36 36 36 30 30 30 24 24 24 m m m m m m m m m 30 30 30 30 30 30 30 30 30 h h h h h h h h h 01 01 01 01 01 01 01 01 01 Right Ascension

Figure 2.4 Same as Figure 2.3, but for NGC 578. At a distance of 27.1 Mpc, the physical scale is 131 pc/00.

NGC 908

0.0 0.2 0.4 0.6 0.8 1.0 0 1 2 3 4 5 1300 1400 1500 1600 1700 31 31 10− 10− N × × -21◦12’

E -21◦13’

-21◦14’

-21◦15’

-21◦16’

2 2 1 2 2 1 Median Surface Brightness [W m− arcsec− A˚ − ] Integrated H-alpha Surface Brightness [W m− arcsec− ] Line of sight Velocity [km s− ] Beam Size:

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.0 0.5 1.0 1.5 2.0 0 2 4 6 8 10 32 31 10− 10− × × -21◦12’

-21◦13’

-21◦14’ Declination Declination -21◦15’

-21◦16’

2 2 1 2 2 1 Continuum Surface Brightness [W m− arcsec− A˚ − ] Integrated [NII] Surface Brightness [W m− arcsec− ] Velocity Uncertainty [km s− ] s s s s s s s s s s s s s s s 18 18 18 12 12 12 06 06 06 00 00 00 54 54 54 m m m m m m m m m m m m m m m 23 23 23 23 23 23 23 23 23 23 23 23 22 22 22 h h h h h h h h h h h h h h h 02 02 02 02 02 02 02 02 02 02 02 02 02 02 02 Right Ascension

Figure 2.5 Same as Figure 2.3, but for NGC 908. At a distance of 19.4 Mpc, the physical scale is 94.1 pc/00. 37

NGC 1325

-21◦31’ 2 0 2 4 6 8 0 1 2 3 4 5 1400 1500 1600 1700 1800 32 31 − 10− 10− N × ×

E -21◦32’

-21◦33’

-21◦34’ 2 2 1 2 2 1 Median Surface Brightness [W m− arcsec− A˚ − ] Integrated H-alpha Surface Brightness [W m− arcsec− ] Line of sight Velocity [km s− ] Beam Size:

-21◦31’ 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0 2 4 6 8 10 32 31 10− 10− × ×

-21◦32’

Declination-21◦33’ Declination

-21◦34’ 2 2 1 2 2 1 Continuum Surface Brightness [W m− arcsec− A˚ − ] Integrated [NII] Surface Brightness [W m− arcsec− ] Velocity Uncertainty [km s− ] s s s s s s s s s s s s 36 36 36 30 30 30 24 24 24 18 18 18 m m m m m m m m m m m m 24 24 24 24 24 24 24 24 24 24 24 24 h h h h h h h h h h h h 03 03 03 03 03 03 03 03 03 03 03 03 Right Ascension

Figure 2.6 Same as Figure 2.3, but for NGC 1325. At a distance of 23.7 Mpc, the physical scale is 115 pc/00.

NGC 1964

0.5 0.0 0.5 1.0 1.5 2.0 2.5 0 2 4 6 8 1400 1500 1600 1700 1800 1900 31 31 − 10− 10− N × × -21◦55’

-21◦56’

-21◦57’

-21◦58’

2 2 1 2 2 1 -21◦59’ Median Surface Brightness [W m− arcsec− A˚ − ] Integrated H-alpha Surface Brightness [W m− arcsec− ] Line of sight Velocity [km s− ] Beam Size:

0 1 2 3 4 0.0 0.5 1.0 1.5 2.0 2.5 0 2 4 6 8 10 32 31 10− 10− × × -21◦55’

-21◦56’

-21◦57’ Declination Declination

-21◦58’

2 2 1 2 2 1 -21◦59’ Continuum Surface Brightness [W m− arcsec− A˚ − ] Integrated [NII] Surface Brightness [W m− arcsec− ] Velocity Uncertainty [km s− ] s s s s s s s s s s s s s s s 36 36 36 30 30 30 24 24 24 18 18 18 12 12 12 m m m m m m m m m m m m m m m 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 h h h h h h h h h h h h h h h 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 Right Ascension

Figure 2.7 Same as Figure 2.3, but for NGC 1964. At a distance of 20.9 Mpc, the physical scale is 101 pc/00. 38

NGC 2280

0.25 0.00 0.25 0.50 0.75 1.00 1.25 0 2 4 6 8 1600 1700 1800 1900 2000 2100 -27◦35’ 31 31 − 10− 10− N × ×

-27◦36’ E -27◦37’

-27◦38’

-27◦39’

-27◦40’

-27◦41’

2 2 1 2 2 1 Median Surface Brightness [W m− arcsec− A˚ − ] Integrated H-alpha Surface Brightness [W m− arcsec− ] Line of sight Velocity [km s− ] Beam Size: -27◦42’

0 1 2 3 4 0.0 0.5 1.0 1.5 2.0 0 2 4 6 8 10 -27◦35’ 32 31 10− 10− × ×

-27◦36’

-27◦37’

-27◦38’

-27 39’ Declination◦ Declination

-27◦40’

-27◦41’

2 2 1 2 2 1 Continuum Surface Brightness [W m− arcsec− A˚ − ] Integrated [NII] Surface Brightness [W m− arcsec− ] Velocity Uncertainty [km s− ] -27◦42’ s s s s s s s s s s s s s s s s s s s s s 06 06 06 00 00 00 54 54 54 48 48 48 42 42 42 36 36 36 30 30 30 m m m m m m m m m m m m m m m m m m m m m 45 45 45 45 45 45 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 h h h h h h h h h h h h h h h h h h h h h 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 06 Right Ascension

Figure 2.8 Same as Figure 2.3, but for NGC 2280. At a distance of 24.0 Mpc, the physical scale is 116 pc/00.

NGC 3705

1.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 1 2 3 4 5 6 7 800 850 900 950 1000 1050 1100 1150 1200 31 31 − − 10− 10− N × × +09◦18’

+09◦17’

+09◦16’

2 2 1 2 2 1 Median Surface Brightness [W m− arcsec− A˚ − ] Integrated H-alpha Surface Brightness [W m− arcsec− ] Line of sight Velocity [km s− ] Beam Size: +09◦15’

0 1 2 3 4 5 6 7 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 0 2 4 6 8 10 32 31 10− 10− × × +09◦18’

+09◦17’ Declination Declination

+09◦16’

2 2 1 2 2 1 Continuum Surface Brightness [W m− arcsec− A˚ − ] Integrated [NII] Surface Brightness [W m− arcsec− ] Velocity Uncertainty [km s− ] +09◦15’ s s s s s s s s s 12 12 12 06 06 06 00 00 00 m m m m m m m m m 30 30 30 30 30 30 30 30 30 h h h h h h h h h 11 11 11 11 11 11 11 11 11 Right Ascension

Figure 2.9 Same as Figure 2.3, but for NGC 3705. At a distance of 18.5 Mpc, the physical scale is 89.7 pc/00. 39

NGC 4517A

0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 1 2 3 4 1350 1400 1450 1500 1550 1600 +00◦25’ 32 31 − 10− 10− N × ×

+00◦24’

+00◦23’

+00◦22’ 2 2 1 2 2 1 Median Surface Brightness [W m− arcsec− A˚ − ] Integrated H-alpha Surface Brightness [W m− arcsec− ] Line of sight Velocity [km s− ] Beam Size:

0 1 2 3 4 5 6 7 0.0 0.2 0.4 0.6 0.8 1.0 0 2 4 6 8 10 +00◦25’ 33 31 10− 10− × ×

+00◦24’

Declination+00◦23’ Declination

+00◦22’ 2 2 1 2 2 1 Continuum Surface Brightness [W m− arcsec− A˚ − ] Integrated [NII] Surface Brightness [W m− arcsec− ] Velocity Uncertainty [km s− ] s s s s s s s s s 36 36 36 30 30 30 24 24 24 m m m m m m m m m 32 32 32 32 32 32 32 32 32 h h h h h h h h h 12 12 12 12 12 12 12 12 12 Right Ascension

Figure 2.10 Same as Figure 2.3, but for NGC 4517A. At a distance of 26.7 Mpc, the physical scale is 129 pc/00.

NGC 4939

2 0 2 4 6 8 0 1 2 3 4 5 6 2900 3000 3100 3200 3300 3400 32 31 − 10− 10− N × × -10◦18’

-10◦19’ E

-10◦20’

-10◦21’

-10◦22’

-10◦23’ 2 2 1 2 2 1 Median Surface Brightness [W m− arcsec− A˚ − ] Integrated H-alpha Surface Brightness [W m− arcsec− ] Line of sight Velocity [km s− ] Beam Size:

0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0 2 4 6 8 10 32 31 10− 10− × × -10◦18’

-10◦19’

-10◦20’

Declination-10◦21’ Declination

-10◦22’

-10◦23’ 2 2 1 2 2 1 Continuum Surface Brightness [W m− arcsec− A˚ − ] Integrated [NII] Surface Brightness [W m− arcsec− ] Velocity Uncertainty [km s− ] s s s s s s s s s s s s s s s s s s 30 30 30 24 24 24 18 18 18 12 12 12 06 06 06 00 00 00 m m m m m m m m m m m m m m m m m m 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 h h h h h h h h h h h h h h h h h h 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 Right Ascension

Figure 2.11 Same as Figure 2.3, but for NGC 4939. At a distance of 41.6 Mpc, the physical scale is 202 pc/00. 40

NGC 5364

+05◦04’ 0.50 0.25 0.00 0.25 0.50 0.75 1.00 1.25 0 1 2 3 4 5 6 7 8 1100 1200 1300 1400 1500 31 31 − − 10− 10− N × × +05◦03’

E +05◦02’

+05◦01’

+05◦00’

+04◦59’

2 2 1 2 2 1 +04◦58’ Median Surface Brightness [W m− arcsec− A˚ − ] Integrated H-alpha Surface Brightness [W m− arcsec− ] Line of sight Velocity [km s− ] Beam Size:

+05◦04’ 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0 2 4 6 8 10 32 31 10− 10− × × +05◦03’

+05◦02’

+05◦01’ Declination Declination +05◦00’

+04◦59’

2 2 1 2 2 1 +04◦58’ Continuum Surface Brightness [W m− arcsec− A˚ − ] Integrated [NII] Surface Brightness [W m− arcsec− ] Velocity Uncertainty [km s− ] s s s s s s s s s s s s s s s 24 24 24 18 18 18 12 12 12 06 06 06 00 00 00 m m m m m m m m m m m m m m m 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 h h h h h h h h h h h h h h h 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 Right Ascension

Figure 2.12 Same as Figure 2.3, but for NGC 5364. At a distance of 18.1 Mpc, the physical scale is 87.8 pc/00.

NGC 6118

0.2 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 1350 1400 1450 1500 1550 1600 1650 1700 1750 31 30 − 10− 10− N × ×

-02◦16’

-02◦17’

-02◦18’

2 2 1 2 2 1 Median Surface Brightness [W m− arcsec− A˚ − ] Integrated H-alpha Surface Brightness [W m− arcsec− ] Line of sight Velocity [km s− ] Beam Size:

0 1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5 0 2 4 6 8 10 32 31 10− 10− × ×

-02◦16’

-02◦17’ Declination Declination

-02◦18’

2 2 1 2 2 1 Continuum Surface Brightness [W m− arcsec− A˚ − ] Integrated [NII] Surface Brightness [W m− arcsec− ] Velocity Uncertainty [km s− ] s s s s s s s s s 54 54 54 48 48 48 42 42 42 m m m m m m m m m 21 21 21 21 21 21 21 21 21 h h h h h h h h h 16 16 16 16 16 16 16 16 16 Right Ascension

Figure 2.13 Same as Figure 2.3, but for NGC 6118. At a distance of 22.9 Mpc, the physical scale is 111 pc/00. 41

NGC 6384

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0 1 2 3 4 5 6 1400 1500 1600 1700 1800 1900 31 31 +07◦06’ 10− 10− N × ×

+07◦05’ E

+07◦04’

+07◦03’

+07◦02’

2 2 1 2 2 1 +07◦01’ Median Surface Brightness [W m− arcsec− A˚ − ] Integrated H-alpha Surface Brightness [W m− arcsec− ] Line of sight Velocity [km s− ] Beam Size:

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 0 2 4 6 8 10 32 31 +07◦06’ 10− 10− × ×

+07◦05’

+07◦04’

Declination+07◦03’ Declination

+07◦02’

2 2 1 2 2 1 +07◦01’ Continuum Surface Brightness [W m− arcsec− A˚ − ] Integrated [NII] Surface Brightness [W m− arcsec− ] Velocity Uncertainty [km s− ] s s s s s s s s s s s s s s s 36 36 36 30 30 30 24 24 24 18 18 18 12 12 12 m m m m m m m m m m m m m m m 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 h h h h h h h h h h h h h h h 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 Right Ascension

Figure 2.14 Same as Figure 2.3, but for NGC 6384. At a distance of 19.7 Mpc, the physical scale is 95.5 pc/00.

NGC 7606

0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 2000 2100 2200 2300 2400 2500 31 31 − 10− 10− -08◦27’ N × ×

E -08◦28’

-08◦29’

-08◦30’

-08◦31’

2 2 1 2 2 1 Median Surface Brightness [W m− arcsec− A˚ − ] Integrated H-alpha Surface Brightness [W m− arcsec− ] Line of sight Velocity [km s− ] Beam Size:

0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.2 0.4 0.6 0.8 1.0 0 2 4 6 8 10 32 31 10− 10− -08◦27’ × ×

-08◦28’

-08◦29’ Declination Declination -08◦30’

-08◦31’

2 2 1 2 2 1 Continuum Surface Brightness [W m− arcsec− A˚ − ] Integrated [NII] Surface Brightness [W m− arcsec− ] Velocity Uncertainty [km s− ] s s s s s s s s s s s s s s s 18 18 18 12 12 12 06 06 06 00 00 00 54 54 54 m m m m m m m m m m m m m m m 19 19 19 19 19 19 19 19 19 19 19 19 18 18 18 h h h h h h h h h h h h h h h 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 Right Ascension

Figure 2.15 Same as Figure 2.3, but for NGC 7606. At a distance of 34.0 Mpc, the physical scale is 165 pc/00. 42

NGC 7793

1 0 1 2 3 4 5 0.0 0.2 0.4 0.6 0.8 1.0 0 50 100 150 200 250 300 350 -32◦32’ 32 30 − 10− 10− N × ×

-32◦33’ E -32◦34’

-32◦35’

-32◦36’

-32◦37’

-32◦38’

-32◦39’ 2 2 1 2 2 1 Median Surface Brightness [W m− arcsec− A˚ − ] Integrated H-alpha Surface Brightness [W m− arcsec− ] Line of sight Velocity [km s− ] Beam Size:

0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0 2 4 6 8 10 -32◦32’ 32 31 10− 10− × ×

-32◦33’

-32◦34’

-32◦35’

-32◦36’ Declination Declination

-32◦37’

-32◦38’

-32◦39’ 2 2 1 2 2 1 Continuum Surface Brightness [W m− arcsec− A˚ − ] Integrated [NII] Surface Brightness [W m− arcsec− ] Velocity Uncertainty [km s− ] s s s s s s s s s s s s s s s s s s s s s s s s s s s 12 12 12 06 06 06 00 00 00 54 54 54 48 48 48 42 42 42 36 36 36 30 30 30 24 24 24 m m m m m m m m m m m m m m m m m m m m m m m m m m m 58 58 58 58 58 58 58 58 58 57 57 57 57 57 57 57 57 57 57 57 57 57 57 57 57 57 57 h h h h h h h h h h h h h h h h h h h h h h h h h h h 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 Right Ascension

Figure 2.16 Same as Figure 2.3, but for NGC 7793. At a distance of 3.44 Mpc, the physical scale is 16.7 pc/00. Because we obtained 4 observations of the East (approaching) side of this galaxy and only 1 observation of the West (receding) side, our sensitivity is signiﬁcantly higher on the Eastern portion of these maps. All 5 observations overlap in the central region. 43 gaps in Hα emission in the innermost regions of these galaxies. One potential explanation of these central Hα gaps could be stellar absorption of the Hα line (e.g. Pickles 1998).

This effect is most significant in older, redder stellar populations where the Hα emission is weakest. In longslit spectral observations, this absorption effect is sometimes mitigated by the fitting of stellar continuum absorption templates to the data. The spectral resolution and range of our data are insufficient to fit such templates, and we therefore are unable to extract reliable velocities from the Hα line in these regions.

Figure 2.17 shows the azimuthally averaged R-band continuum surface brightness of our galaxies derived from our Hα Fabry-Pérotdata cubes plotted against three different measures of galactocentric radius. These surface brightness profiles assume that the disk projection parameters are those of the best-fitting I -band models of Kuzio de Naray et al.

(2017, in prep.). The surface brightness proﬁles show qualitative and quantitative agreement with the R-band surface brightness proﬁles of Kuzio de Naray et al. (2017, in prep.), but have a smaller radial extent.

Figure 2.18 shows the azimuthally averaged integrated Hα surface brightnesses of our galaxies, i.e. the values of FH in Equation 2.4. These values should be considered as lower limits on the true Hα intensity, as the averages were taken over all pixels in a radial bin, including those that fell below our signal-to-noise threshold.

2.3.1 [N II]-to-Hα Ratio and Oxygen Abundance

Figure 2.19 shows the azimuthally averaged value of the ratio of the integrated [N II] 6583

surface brightness to the integrated Hα surface brightness, commonly known as the “N2

Index,” N2 log(FN2 6583/FHα). It is important to note that the plotted quantity is the ≡ average value of the ratio (i.e. FN /FH ) and not the ratio of the averages (i.e. FN / FH ). h i h i h i We note that all of our galaxies show a similar downward trend in this parameter. The relative intensities of these two lines are complicated functions of metallicity and electron temperature in the emitting gas. This line intensity ratio is also known to be very sensitive 44

25 ] + Offset 2 −

NGC 4939 35 NGC 4517A NGC 337A + 0.5 NGC 908 + 3.5 NGC 6384 + 4 NGC 6118 + 6 NGC 7606 + 8 NGC 2280 + 9.5 40 NGC 1325 + 11 NGC 1964 + 13 NGC 3705 + 14.5 NGC 5364 + 16 Continuum Surface Brightness [R-mags arcsec NGC 578 + 17.5 NGC 7793 + 19 45 0 10 20 30 40 500 1 2 3 0 2 4 6 8 R [kpc] R/R23.5,I R/Ropt,I

Figure 2.17 Left: Azimuthally averaged R-band continuum surface brightness proﬁles plotted as functions of galactocentric radius in kpc. Center: The same values plotted as functions of galactocentric radius rescaled by each galaxy’s R23.5 in the I -band. Right: The same values plotted as functions of galactocentric radius rescaled by each galaxy’s Ropt in the I -band. In each panel, the lines have been vertically oﬀset by a constant to separate them. 45

15.0 − ]) + Offset 2 − 17.5 − arcsec 2 − 20.0 −

22.5 −

25.0 − NGC 4939 + 18 NGC 4517A + 18 NGC 337A + 16.5 27.5 NGC 908 + 14.5 − NGC 6384 + 14 NGC 6118 + 12 NGC 7606 + 10.5 30.0 NGC 2280 + 8.5 − NGC 1325 + 7.5 NGC 1964 + 6 32.5 NGC 3705 + 5 − NGC 5364 + 3

(Integrated H-alpha Surface Brightness) [W m NGC 578 + 1

10 NGC 7793

log 35.0 − 0 20 40 600 1 2 3 0 2 4 6 8 10 R [kpc] R/R23.5,I R/Ropt,I

Figure 2.18 Left: Azimuthally averaged integrated Hα surface brightness proﬁles plotted as functions of galactocentric radius in kpc. Center: The same values plotted as functions of galactocentric radius rescaled by each galaxy’s R23.5 in the I -band. Right: The same values plotted as functions of galactocentric radius rescaled by each galaxy’s Ropt in the I -band. In each panel, the lines have been vertically oﬀset by a constant to separate them. 46

NGC 4939 + 7 NGC 4517A + 7 N2 Index + offset 2 NGC 337A + 6.5 NGC 908 + 5.5 NGC 6384 + 5 NGC 6118 + 4.5 1 NGC 7606 + 4 NGC 2280 + 3.5 NGC 1325 + 2.5 0 NGC 1964 + 2 NGC 3705 + 1.5 NGC 5364 + 1 NGC 578 + 0.5 1 NGC 7793 − 0 20 40 600 1 2 3 0 2 4 6 8 10 R [kpc] R/R23.5,I R/Ropt,I

Figure 2.19 Left: Azimuthally averaged N2 Index (N2 log(FN2 6583/FHα)) plotted as ≡ functions of galactocentric radius in kpc. Center: The same values plotted as functions of galactocentric radius rescaled by each galaxy’s R23.5 in the I -band. Right: The same values plotted as functions of galactocentric radius rescaled by each galaxy’s Ropt in the I -band. In each panel, the lines have been vertically oﬀset by a constant to separate them.

to the degree of ionization of the gas (Shaver et al. 1983).

Because this ratio is very sensitive to the metallicity of a galaxy and does not strongly

depend on absorption, it is known to provide a good proxy for oxygen abundance (e.g.

Pettini & Pagel 2004; P´erez-Montero & Contini 2009; Marino et al. 2013). This relation

arises from a combination of two physical eﬀects: (1) The (O/H) abundance is inversely

correlated to the degree of ionization of the gas, as is the ratio of [N II] to [N III], and

(2) the (N/O) ratio is also inversely correlated to the (O/H) abundance (Pettini & Pagel

2004). Marino et al. (2013) give the following relation between the N2 Index and oxygen

abundance:

12 + log(O/H) = 8.743 + 0.462 N2 (2.6) ×

We have used this N2-oxygen relation to derive oxygen abundance gradients for our galaxies, 47

12.0

11.5

11.0

10.5

10.0 NGC 4939 + 3.5 NGC 4517A + 3.5 NGC 337A + 3.25 12+log(O/H)+Offset NGC 908 + 2.75 9.5 NGC 6384 + 2.5 NGC 6118 + 2.25 NGC 7606 + 2.0 NGC 2280 + 1.75 9.0 NGC 1325 + 1.25 NGC 1964 + 1.0 NGC 3705 + 0.75 8.5 NGC 5364 + 0.5 NGC 578 + 0.25 NGC 7793 0 20 40 600 1 2 3 0 2 4 6 8 10 R [kpc] R/R23.5,I R/Ropt,I

Figure 2.20 Left: Azimuthally averaged oxygen abundances (12 + log(O/H)) plotted as functions of galactocentric radius in kpc. Center: The same values plotted as functions of galactocentric radius rescaled by each galaxy’s R23.5 in the I -band. Right: The same values plotted as functions of galactocentric radius rescaled by each galaxy’s Ropt in the I -band. In each panel, the lines have been vertically oﬀset by a constant to separate them.

displayed in Figure 2.20.

2.4 Summary

We have utilized observations with the medium-spectral-resolution SALT RSS Fabry-P´erot

interferometer to produce line-of-sight velocity maps of the Hα line of excited hydrogen in

14 of the galaxies in the RINGS sample. At the assumed distances to these galaxies, these

kinematic maps typically have a spatial resolution of 100-300 pc. ∼ We have also measured the ratio of the [N II] line intensity to that of the Hα line as a

function of radius. This ratio was then used to predict the oxygen abundance gradients in

these galaxies.

These kinematic data will be modelled in Chapter 3 to extract information about these 48 galaxies’ rotation curves and their projection on the sky. In Chapter 4, we will compare our Hα kinematic map for NGC 2280 with H I 21 cm kinematic data for the same galaxy.

In Chapter 5, the Hα kinematic data for NGC 2280 will be combined with photometric observations to place constraints on this galaxy’s mass distribution. 49

Chapter 3

RINGS Hα Kinematic Modelling

3.1 Introduction

Much of the content of this chapter is reproduced from Mitchell et al. (2017, submitted to

A.J.).

In Chapter 2, we utilized Fabry-P´erotobservations to produce two-dimensional maps of line-of-sight velocities from the Hα line in 14 of the RINGS galaxies. In this chapter, we present models of the Hα kinematic data of Chapter 2 using the DiskFit software package

(Spekkens & Sellwood 2007; Sellwood & S´anchez 2010). For each galaxy, we present the best-ﬁtting projection parameters and rotation curve derived from these models. We then compare these rotation curves to previous measurements from the literature and compare the projection parameters to those found in the photometric DiskFit models of Kuzio de

Naray et al. (2017, in prep.).

The kinematic data and models of NGC 2280 will then be used in Chapter 4 to compare to H I 21 cm data for the same galaxy. In Chapter 5, we will again use the kinematic models of NGC 2280 along with the photometric observations of Kuzio de Naray et al. (2017, in prep.) to place constraints on the mass distribution of this galaxy’s dark matter halo. 50

3.2 Axisymmetric Models and Rotation Curves

We have utilized the DiskFit1 software package (Spekkens & Sellwood 2007; Sellwood &

Sánchez 2010) to fit axisymmetric rotation models to our Hα velocity fields. Unlike tilted- ring codes, e.g. rotcur (Begeman 1987), DiskFit assumes a single projection geometry for the entire galactic disk. In addition to fitting for five parameters that describe the projection geometry, it fits for a circular rotation speed in each of an arbitrary number of user-specified radius bins (i.e. the rotation curve). The five projection parameters are: the position of the galaxy center (xc, yc), the systemic recession velocity of the galaxy (Vsys),

the disk inclination (i), and the position angle of the disk relative to the North-South axis

(φPA).

For N user-speciﬁed radius bins, DiskFit ﬁts for the N + 5 parameters using a χ2-

minimization algorithm. The velocity uncertainties used in calculating the χ2 values arise

from two sources: the uncertainty in ﬁtting a Voigt proﬁle to each pixel’s spectrum (Section

2.2.8) and the intrinsic turbulence within a galaxy. This intrinsic turbulence must be added

to our uncertainty budget because we may observe emission from H II regions that are not

moving at the circular speed for their location in a galaxy, that would not be accounted for

in the uncertainty of the spectral ﬁt. For the Milky Way, this intrinsic turbulence, ∆ISM ,

is of the order 7-12 km s−1 (Gunn et al. 1979). Similar values for this parameter have been

found for other spiral galaxies and dwarf galaxies (e.g. Kamphuis 1993; Tamburro et al.

−1 2009). In ﬁtting these models, we have adopted a value of 12 km s for ∆ISM in each

of our galaxies and add this value in quadrature to the velocity uncertainties from the line

proﬁle ﬁts.

We calculate uncertainties for each of these ﬁtted parameters using the modiﬁed boot-

strap method described in Sellwood & S´anchez (2010). The well-known bootstrap procedure

assumes residual values are randomly distributed and calculates new best-ﬁtting parameters

after shuﬄing these residual values randomly. Due to the fact that these velocity maps can

1DiskFit is publicly available for download at http://www.physics.rutgers.edu/spekkens/diskﬁt/ 51 contain structure not accounted for in our models, residual velocities may be in fact be correlated over much larger regions than a single resolution element, invalidating this common assumption. To account for this, the modiﬁed bootstrap method preserves regions of correlated residual line of sight velocity when resampling the data to estimate the uncertainty values.

DiskFit is also capable of fitting models that include non-axisymmetric kinematic features such as bars, warped disks, and radial flows. These models have a much larger parameter space and are therefore much more computationally expensive to produce. In this work, we consider only flat, axisymmetric disk models. Some of these galaxies exhibit clear bar features in their photometry. These features and other potential asymmetries will be azimuthally averaged in these models. If these kinds of features are present, they should leave signatures in the residual velocity maps for these galaxies on scales much larger than our spatial resolution. In our future work on this sample, we plan to explore more complex kinematic models for these galaxies.

Table 3.1 lists the projection parameters and reduced-χ2 values for our best-ﬁtting ax-

isymmetric models to our 14 Hα velocity ﬁelds. Figures 3.1-3.14 show the model line-of-sight

velocity maps (left panel), residual velocity maps (middle panel), and rotation curves (right

panel) for each of these galaxies. A black cross in the left panels of these ﬁgures marks the

galaxy center and shows the position angle and relative lengths of the major and minor axes

in the best-ﬁtting model. The uncertainty values in Table 3.1 and in the rotation curves

of Figures 3.1-3.14 are the estimated 1-σ uncertainties from 1000 bootstrap iterations. In some cases (e.g. NGC 7793), the inclination of the galaxy is poorly constrained in our axisymmetric models. This leads to a large uncertainty in the overall normalization of the rotation curve even when the shape of the rotation curve is well-constrained. This is why the uncertainties in our rotation curves often appear larger than the point-to-point variation of the velocities.

These projection parameters have also been measured by Kuzio de Naray et al. (2017, 52

NGC 337A Galactocentric Radius [kpc] 0 1 2 3 1025 1050 1075 1100 1125 -20 -15 -10 -5 0 5 10 15 20 Model Line-of-sight Velocity [km/s] Residual Velocity [km/s] 175

200 200 150

125 100 100 100

0 0 75

50 Circular Velocity [km/s]

Y [arcsec North] 100 100 − − 25

200 200 0 − 200 0 200 − 200 0 200 0 50 100 150 200 250 − − X [arcsec East] X [arcsec East] Galactocentric Radius [arcsec]

Figure 3.1 Left: Our best-fitting axisymmetric DiskFit model of NGC 337A’s line-of-sight Hα velocity field. Center: A map of the data-minus-model residual velocities for the best- fitting model in the left panel. Right: A rotation curve extracted from the best-fitting axisymmetric model with 1-σ uncertainties derived from our bootstrapping procedure. The radii were chosen to be approximately 1 beam-width apart. The center, major axis, and minor axis of our best-fitting DiskFit model are marked with a black cross.

NGC 578 Galactocentric Radius [kpc] 0 5 10 15 20 1500 1600 1700 1800 -20 -15 -10 -5 0 5 10 15 20 350 Model Line-of-sight Velocity [km/s] Residual Velocity [km/s] 300

250 50 50 200

0 0 150 100 Circular Velocity [km/s]

Y [arcsec North] 50 50 − − 50

0 100 50 0 50 100 100 50 0 50 100 0 50 100 150 − − − − X [arcsec East] X [arcsec East] Galactocentric Radius [arcsec]

Figure 3.2 Same as Figure 3.1 but for NGC 578. The large uncertainties on the points are due almost entirely to the galaxy’s inclination being poorly constrained. 53

NGC 908 Galactocentric Radius [kpc] 0 5 10 1300 1400 1500 1600 1700 -20 -15 -10 -5 0 5 10 15 20 Model Line-of-sight Velocity [km/s] Residual Velocity [km/s] 250

200 100 100 150

0 0 100 Circular Velocity [km/s] Y [arcsec North] 100 100 50 − − 0 200 100 0 100 200 200 100 0 100 200 0 50 100 150 − − − − X [arcsec East] X [arcsec East] Galactocentric Radius [arcsec]

Figure 3.3 Same as Figure 3.1 but for NGC 908.

NGC 1325 Galactocentric Radius [kpc] 0 5 10 1400 1500 1600 1700 1800 -20 -15 -10 -5 0 5 10 15 20 400 Model Line-of-sight Velocity [km/s] Residual Velocity [km/s]

100 100 300

50 50 200 0 0

100 50 50 Circular Velocity [km/s] Y [arcsec North] − −

100 100 − − 0 100 0 100 100 0 100 0 50 100 − − X [arcsec East] X [arcsec East] Galactocentric Radius [arcsec]

Figure 3.4 Same as Figure 3.1 but for NGC 1325.

NGC 1964 Galactocentric Radius [kpc] 0 5 10 15 500 1400 1500 1600 1700 1800 1900 -20 -15 -10 -5 0 5 10 15 20 Model Line-of-sight Velocity [km/s] Residual Velocity [km/s] 400

100 100 300

200 0 0 100 Circular Velocity [km/s] Y [arcsec North] 100 100 − − 0

200 100 0 100 200 200 100 0 100 200 0 50 100 150 − − − − X [arcsec East] X [arcsec East] Galactocentric Radius [arcsec]

Figure 3.5 Same as Figure 3.1 but for NGC 1964. 54

NGC 2280 Galactocentric Radius [kpc] 0 10 20

1600 1700 1800 1900 2000 2100 -20 -15 -10 -5 0 5 10 15 20 350 Model Line-of-sight Velocity [km/s] Residual Velocity [km/s] 300 200 200 250

100 100 200

0 0 150

100

100 100 Circular Velocity [km/s] Y [arcsec North] − − 50 200 200 − − 0 200 0 200 200 0 200 0 50 100 150 200 − − X [arcsec East] X [arcsec East] Galactocentric Radius [arcsec]

Figure 3.6 Same as Figure 3.1 but for NGC 2280.

NGC 3705 Galactocentric Radius [kpc] 0.0 2.5 5.0 7.5 10.0 800 900 1000 1100 1200 -20 -15 -10 -5 0 5 10 15 20 350 Model Line-of-sight Velocity [km/s] Residual Velocity [km/s] 300 100 100 250

50 50 200

0 0 150 100

50 50 Circular Velocity [km/s] Y [arcsec North] − − 50 100 100 − − 0 100 0 100 100 0 100 0 50 100 − − X [arcsec East] X [arcsec East] Galactocentric Radius [arcsec]

Figure 3.7 Same as Figure 3.1 but for NGC 3705.

NGC 4517A Galactocentric Radius [kpc] 0 5 10 15 1400 1500 1600 -20 -15 -10 -5 0 5 10 15 20 Model Line-of-sight Velocity [km/s] Residual Velocity [km/s] 200

100 100 150

50 50 100 0 0

50 50 Circular Velocity [km/s] 50 Y [arcsec North] − −

100 100 − − 0 100 0 100 100 0 100 0 25 50 75 100 − − X [arcsec East] X [arcsec East] Galactocentric Radius [arcsec]

Figure 3.8 Same as Figure 3.1 but for NGC 4517A. 55

NGC 4939 Galactocentric Radius [kpc] 0 10 20 30 40 350 2900 3000 3100 3200 3300 3400 -20 -15 -10 -5 0 5 10 15 20 Model Line-of-sight Velocity [km/s] Residual Velocity [km/s] 300

250

100 100 200

150 0 0 100 Circular Velocity [km/s]

Y [arcsec North] 100 100 − − 50

0 200 100 0 100 200 200 100 0 100 200 0 50 100 150 − − − − X [arcsec East] X [arcsec East] Galactocentric Radius [arcsec]

Figure 3.9 Same as Figure 3.1 but for NGC 4939.

NGC 5364 Galactocentric Radius [kpc] 0 5 10 15 1100 1200 1300 1400 1500 -20 -15 -10 -5 0 5 10 15 20 Model Line-of-sight Velocity [km/s] Residual Velocity [km/s] 400

300 100 100

200 0 0

Circular Velocity [km/s] 100 Y [arcsec North] 100 100 − −

0 200 100 0 100 200 200 100 0 100 200 0 50 100 150 200 − − − − X [arcsec East] X [arcsec East] Galactocentric Radius [arcsec]

Figure 3.10 Same as Figure 3.1 but for NGC 5364.

NGC 6118 Galactocentric Radius [kpc] 0 5 10 15 1400 1500 1600 1700 -20 -15 -10 -5 0 5 10 15 20 Model Line-of-sight Velocity [km/s] Residual Velocity [km/s] 250

200

50 50 150

0 0 100 Circular Velocity [km/s]

Y [arcsec North] 50 50 50 − −

0 100 50 0 50 100 100 50 0 50 100 0 50 100 − − − − X [arcsec East] X [arcsec East] Galactocentric Radius [arcsec]

Figure 3.11 Same as Figure 3.1 but for NGC 6118. 56

NGC 6384 Galactocentric Radius [kpc] 0 5 10 15 20 1400 1500 1600 1700 1800 1900 -20 -15 -10 -5 0 5 10 15 20 500 Model Line-of-sight Velocity [km/s] Residual Velocity [km/s]

400

100 100 300

0 0 200 Circular Velocity [km/s] Y [arcsec North] 100 100 100 − −

0 200 100 0 100 200 200 100 0 100 200 0 50 100 150 200 − − − − X [arcsec East] X [arcsec East] Galactocentric Radius [arcsec]

Figure 3.12 Same as Figure 3.1 but for NGC 6384.

NGC 7606 Galactocentric Radius [kpc] 0 10 20 30 2000 2100 2200 2300 2400 2500 -20 -15 -10 -5 0 5 10 15 20 Model Line-of-sight Velocity [km/s] Residual Velocity [km/s] 400

100 100 300

200 0 0

Circular Velocity [km/s] 100 Y [arcsec North] 100 100 − − 0 200 100 0 100 200 200 100 0 100 200 0 50 100 150 200 − − − − X [arcsec East] X [arcsec East] Galactocentric Radius [arcsec]

Figure 3.13 Same as Figure 3.1 but for NGC 7606.

NGC 7793 Galactocentric Radius [kpc] 0 2 4 0 100 200 300 -20 -15 -10 -5 0 5 10 15 20 300 Model Line-of-sight Velocity [km/s] Residual Velocity [km/s] 250 200 200 200 100 100 150 0 0 100

100 100 Circular Velocity [km/s] Y [arcsec North] − − 50 200 200 − − 0 200 0 200 200 0 200 0 100 200 300 − − X [arcsec East] X [arcsec East] Galactocentric Radius [arcsec]

Figure 3.14 Same as Figure 3.1 but for NGC 7793. 57

Table 3.1. Best-Fitting Axisymmetric DiskFit Model Parameters

Note. — The parameters of our best-fitting axisymmetric DiskFit models. From left to right, columns are: (1) galaxy name, (2-3) distance and angular scale reproduced from Table 2.1, (4-5) right ascension and declination of the galaxy center, (6) systemic velocity, (7) inclination, (8) position angle, and (9) reduced-χ2 for the best fitting model. 58 in prep.) by using DiskFit to fit multi-band photometric data on these galaxies. In most cases, the two sets of measurements agree within the uncertainties of the kinematic models.

However, there are some signiﬁcant diﬀerences that we discuss in the following subsections about each galaxy. Often, the majority of the projection parameters of these two sets of models will agree for a single galaxy, but a single poorly constrained parameter, e.g. inclination or position angle, will be in tension. At the time of writing, uncertainties on the projection parameters of Kuzio de Naray et al. (2017, in prep.)’s photometric models are not yet available. Because of this, we are able to make qualitative but not quantitative statements about the level of agreement between the two sets of models.

In Figure 3.15, we compare our best-ﬁtting rotation curves to previously measured values from the literature (Mathewson & Ford 1996; Rubin et al. 1982; Sperandio et al. 1995;

Meyssonnier 1984; Dicaire et al. 2008; Davoust & de Vaucouleurs 1980). In most cases, our measurements extend to much larger radii than the previous available measurements.

In several cases (e.g. NGC 578, NGC 6118, and NGC 7606), our rotation curves agree well with the previous measurements. In other cases, discussed in the below sections on individual galaxy, there exist signiﬁcant diﬀerences between our data and the previously measured rotation curves.

3.2.1 Notes on Individual Galaxies

NGC 337A

NGC 337A is one of the most sparsely sampled galaxies in the RINGS medium-resolution

Hα kinematic data, as seen in Figure 2.3. It is also one of the two galaxies in this work

(along with NGC 4517A) that are classiﬁed as Irregular. Despite this, our model is able to sample the rotation curve over a wide range of radii (Figure 3.1) extending out to 18 ∼ kpc. At a few locations (e.g. 2500), the velocity data are too sparse to accurately measure the rotation curve. 59

MF96a R+82a S+95a N+11a M84a D+08 36cm DdV80 MF96r R+82r S+95r N+11r M84r D+08 3.6m This work

300 300 200 200

100 100

NGC 578 NGC 908 0 0 0 50 100 150 0 25 50 75 100 125 150

300 300

200 200

100 100 NGC 1325 NGC 1964 0 0 0 20 40 60 80 100 120 0 50 100 150 200 300 ] ]

1 150 1 − − 200 100 [km s [km s c c V 100 50 V NGC 2280 NGC 4517A 0 0 0 50 100 150 200 0 20 40 60 80 100 120

300 200 200 100 100 NGC 6118 NGC 6384 0 0 0 25 50 75 100 125 0 50 100 150 200

400 200 300

200 100 100 NGC 7606 NGC 7793 0 0 0 50 100 150 200 0 100 200 300 400 Galactocentric Radius [arcsec]

Figure 3.15 A comparison of our best-fitting model rotation curves (black circles with error bars) to previous measurements from the literature. In all cases, squares are from the approaching side of the galaxy, triangles from the receding side, and circles from an azimuthal average. Unless otherwise specified, we have used own own best-fitting values for systemic velocity and inclination (see Table 3.1) to deproject the data. Red points (NGC 578, 908, 1964, 2280, and 7606): Mathewson & Ford (1996) via Hα longslit spectroscopy (Note: We have adopted a systemic velocity of 1960 km s−1 for NGC 1964 rather than our best-fitting value to match the authors’ spectra. The authors also report a rotation curve for NGC 1325, but the wavelength calibration for those data appears to have been incorrect.). Blue points (NGC 1325 and 7606): Rubin et al. (1982) via Hα and [N II] longslit spectroscopy. Green points (NGC 2280 and 6384): Sperandio et al. (1995) via Hα and [N II] longslit spectroscopy. Magenta points (NGC 4517A): Neumayer et al. (2011) via Hα IFU spectroscopy. Cyan points (NGC 6118): Meyssonnier (1984) via optical longslit spectroscopy. Brown and purple points (NGC 7793): Dicaire et al. (2008) via Hα Fabry-Pérotspectrophotom- etry. Orange points (NGC 7793): Davoust & de Vaucouleurs (1980) via Hα Fabry-Pérot spectrophotometry. 60

Our best-fitting projection parameters for this galaxy are significantly different2 than the photometric models of Kuzio de Naray et al. (2017, in prep.). In particular, the axis about which the galaxy is rotating appears to be significantly misaligned to the axis about which the light distribution is symmetric. While the kinematic data are clearly blueshifted on the West side of the galaxy and redshifted on the East, NGC 337A has two prominent, loosely-wound spiral arms that are roughly aligned to the North-South axis over a wide range of radii. These spiral arms dominate the light distribution and may be responsible for this misalignment.

NGC 578

NGC 578 exhibits one of the strongest visible bars among this sample of galaxies. While many rotation curves commonly peak and then decline somewhat, NGC 578’s rotation curve appears to be either ﬂat or continuing to rise at the most distant radii for which we are able to measure velocities. This peak feature in rotation curves is very useful in constraining a galaxy’s inclination. Due to the lack of such a peak in NGC 578, its inclination is quite uncertain (note that it has one of the largest inclination uncertainties in Table 3.1). Because this galaxy’s inclination is poorly constrained, the extracted rotation curve (right panel of

Figure 3.2) has large uncertainties in its overall normalization.

The best-ﬁtting inclination and position angle for our kinematic models of this galaxy disagree signiﬁcantly with the photometric models of Kuzio de Naray et al. (2017, in prep.).

The diﬀerence in position angle appears to be due to a region on the Northern minor axis that is strongly non-axisymmetric.

NGC 908

NGC 908 has a single large spiral arm towards the north-east side of the galaxy (see the top left panel of Figure 2.5) that is unmatched by a corresponding spiral arm on the opposite

2Uncertainties for the photometric models are unknown at the time of writing, so this statement cannot be quantified at present. 61 side. There is a corresponding region of large correlated residual velocity to our best-fitting model in Figure 3.3. This region is also likely responsible for the sudden increase in the extracted rotation curve beyond 12000and could be indicative of a disk that is warped at large radii. Our best-fitting values for NGC 908’s position angle and inclination disagree somewhat with those of Kuzio de Naray et al. (2017, in prep.), though this is not entirely surprising given the asymmetry of this galaxy. As shown in Figure 3.15, our extracted rotation curve for NGC 908 in general agrees well with the previous measurements by

Mathewson & Ford (1996), though we measure systematically slightly higher velocities in the innermost regions and do not cover the inner 1000 of the galaxy. ∼

NGC 1325

NGC 1325 appears to be a relatively normal spiral galaxy. Our extracted rotation curve

(Figure 3.4) is approximately ﬂat over a wide range of radii. Notably, we detect no Hα emission in the innermost 2500 of the map. All of our best-ﬁtting projection parameters for this galaxy agree extremely well with the photometric models of Kuzio de Naray et al.

(2017, in prep.).

At large radii (R > 5000), our extracted rotation curve agrees well with the measurements of Rubin et al. (1982). In the innermost region (R < 2500), we are unable to make a comparison due to the gaps in our data. In the intermediate region between these (2500 <

R < 5000), our measurements have systematically higher velocities than those of Rubin et al.

(1982); our rotation curve has already peaked before reaching these radii, while theirs is still rising (Figure 3.15).

NGC 1964

NGC 1964 appears for the most part to be a normal spiral galaxy, with the exception of a single Hα emission region with a highly discrepant velocity near the galaxy’s center. This region is visible as a bright red spot in the upper right panel of Figure 2.7. Despite being 62 located on the approaching side of this galaxy, the region is receding at a line-of-sight velocity of about 200 km s−1 faster than the systemic velocity of the galaxy. Unsurprisingly, this region has a large eﬀect on our axisymmetric model, causing the extracted rotation curve

(right panel of Figure 3.5) to take on negative values (i.e. counter-rotation). The inclination of our best-ﬁtting model is somewhat diﬀerent (about 1.5-σ) from the photometric models of Kuzio de Naray et al. (2017, in prep.).

Beyond R > 4000, our rotation curve agrees very well with the previous measurements by Mathewson & Ford (1996). Interior to this region, the region with a large anomalous recessional velocity on the approaching side of the galaxy causes are axisymmetric model to take on negative values, as mentioned above. This region causes the large discrepancy in NGC 1964’s rotation curve in Figure 3.15.

NGC 2280

We have previously presented our kinematic data on NGC 2280 in Mitchell et al. (2015a).

The most significant difference between the maps and models presented in that work and those presented here is an increased spatial resolution due to a change in our pixel binning procedure. As mentioned in Sections 2.2.2 and 2.2.3, we have made small refinements to our

ﬂatﬁelding and ghost subtraction routines that have improved the data reduction process.

We have also begun ﬁtting for the [N II] 6583 line in addition to the Hα line, which results in a slightly increased image depth.

Overall, NGC 2280 is a fairly typical spiral galaxy. Unlike many of the other galaxies in our sample, we are able to extract reliable velocities at both very small and very large radii, producing one of the most complete rotation curves in this sample.

The inclination and position angle of this galaxy are very well constrained in our models, with uncertainties of less than 1◦ for both parameters. These values are consistent with our previous work on this galaxy in Mitchell et al. (2015a). However, our values for these parameters diﬀer by several degrees from the photometric models of Kuzio de Naray et al. 63

(2017, in prep.).

Our rotation curve measurements for NGC 2280 lie at systematically slightly larger velocities than the previous measurements by Mathewson & Ford (1996). Our data also extend to much larger radii than these data. Our measured rotation curve also lies at more than double the values measured by Sperandio et al. (1995).

NGC 3705

NGC 3705 is a fairly typical spiral galaxy. We detect no Hα emission in the central 2000 of ∼ the galaxy, however the data appear to be consistent with a rising rotation curve over this region. After this inner rise, it appears to be consistently ﬂat over a large range of radii.

Our values for NGC 3705’s projection parameters agree within the uncertainties with the values from Kuzio de Naray et al. (2017, in prep.).

NGC 4517A

NGC 4517A, like NGC 337A, is both very sparsely sampled by our Hα kinematic data and morphologically classified as Irregular. The rotation curve extracted from our axisymmetric model of this galaxy is sparse and has large uncertainties. These uncertainties are mostly a result of the large uncertainty in its inclination. Because NGC 4517A is nearly face- on, its inclination is difficult to determine from sparse kinematic data, which results in large uncertainties in the normalization of the rotation curve. The projection parameters of our best-fitting model have some of the largest uncertainties in Table 3.1, likely due to the irregularity of the galaxy and the sparse sampling of our maps. Our values for these parameters are in slight disagreement with the values of Kuzio de Naray et al. (2017, in prep.), but this is not surprising given the sparseness of the kinematic maps and the large uncertainties on our values. Our measurements of NGC 4517A’s rotation curve in general agree with the values measured by Neumayer et al. (2011), though both our data and theirs are quite sparse (Figure 3.15). 64

NGC 4939

NGC 4939, the most luminous galaxy in this sample, is a fairly typical spiral galaxy. We detect no Hα emission in the innermost 1000 of the galaxy. Beyond this radius, the rotation ∼ curve appears to be consistent with being ﬂat at a value of 270 km s−1 out to nearly 40 kpc in the disk plane. Our kinematic projection parameters for this galaxy agree well with the photometric projection parameters of Kuzio de Naray et al. (2017, in prep.).

NGC 5364

NGC 5364 is another typical spiral galaxy. Its Hα emission very strongly traces its spiral arms. While we detect no Hα emission within the innermost 1500, we appear to capture ∼ the rise of the rotation curve slightly beyond this region. Because the kinematic data are

somewhat sparse, our axisymmetric models have a relative large uncertainty on the galaxy’s

inclination, leading to large uncertainty in the overall normalization of the rotation curve.

The position angle of our best-ﬁtting model is in tension with the photometric models of

Kuzio de Naray et al. (2017, in prep.).

NGC 6118

NGC 6118 appears to be a typical spiral galaxy. The rotation curve extracted from our

axisymmetric models rises approximately linearly from the center to 2500, then shows a ∼ slight decline and increase before becoming roughly ﬂat beyond 5000. Beyond 12000, the data become quite sparse and the rotation curve therefore has quite large uncertainties. Our best-ﬁtting model’s inclination is in slight tension with the values of Kuzio de Naray et al.

(2017, in prep.).

NGC 6384

NGC 6384 is another regular spiral galaxy. Like NGC 5364, its Hα emission closely traces

its spiral arms. We detect no Hα emission within the innermost 2500. The rotation curve ∼ 65 is roughly ﬂat from this point to the outermost limits of our data. Our best-ﬁtting model’s inclination is in slight tension with the photometric models of Kuzio de Naray et al. (2017, in prep.). As is the case with NGC 2280, our rotation curve measurements of NGC 6384 lie at systematically higher velocities than those of Sperandio et al. (1995).

NGC 7606

NGC 7606 is the fastest-rotating galaxy in this sample and the second most-luminous.

It is another typical spiral galaxy. We detect no Hα emission in the innermost 2000, ∼ though the rotation curve appears to still be rising just outside this radius. The rotation curve appears to decline somewhat from 50-12000 and then begin increasing again in the ∼ outermost regions, possibly indicating a warped disk. The inclination and position angle of this galaxy are very well-constrained by our kinematic models and agree very well with the photometric models of Kuzio de Naray et al. (2017, in prep.).

In general, our rotation curve measurements agree well with the previous measurements by Rubin et al. (1982) and Mathewson & Ford (1996). These previously measured rotation curves both show diﬀerent rotation on the approaching and receding sides of the galaxy, and our axisymmetric model typically lies between these curves.

NGC 7793

NGC 7793’s rotation curve appears to rise over the innermost 3000, then decline, then ∼ continue rising over 50-10000. In the outermost parts of the galaxy, the data are too sparse ∼ to reliably measure the rotation curve. The large uncertainties on individual points in the rotation curve are due largely to the large uncertainty in NGC 7793’s inclination in our model. The projection parameters of our best-ﬁtting model agree with those of Kuzio de

Naray et al. (2017, in prep.) within the uncertainties.

Our measured rotation curve lies systematically above the previously measured rotation curves of Davoust & de Vaucouleurs (1980) and Dicaire et al. (2008). 66

3.3 Summary

We have used the DiskFit software package of Spekkens & Sellwood (2007) and Sellwood &

S´anchez (2010) to model the velocity ﬁelds presented in Chapter 2. From these models, we have extracted rotation curves at very high spatial resolution. In most cases, the projection geometries of these models agree extremely well with the photometric models of Kuzio de

Naray et al. (2017, in prep.).

As of 2015 Sept, the medium-resolution Fabry-Pérotetalon of SALT RSS is no longer available for observations due to deterioration of the reflective coatings. The remaining five galaxies of the RINGS sample are scheduled to be completed in the Fabry-Pérotsystem’s high-resolution mode.

In Chapter 4, we compare our data and models of NGC 2280’s Hα kinematics to H I

21 cm observations and models for the same galaxy. In Chapter 5, we combine the rotation

curve for NGC 2280 from this chapter with the photometric data of Kuzio de Naray et al.

(2017, in prep.) to constrain the mass distributions of this galaxy’s disk and dark matter

halo. 67

Chapter 4

NGC 2280 H I Kinematic Data and Comparisons

4.1 Introduction

Much of the content of this chapter is reproduced from Mitchell et al. (2015a) and the conference proceedings of Mitchell et al. (2015b).

In Chapters 2 and 3, we introduced the medium-spectral-resolution Hα Fabry-P´erot kinematic data of the RINGS survey and our axisymmetric kinematic modelling of those galaxies. In this chapter, we compare these data for one of the RINGS galaxies, NGC 2280, with similar maps and models of the same galaxy obtained using Karl G. Jansky Very

Large Array (VLA) observations of the 21 cm line of H I. We do so both to demonstrate that the FP instrument on SALT can provide reliable velocity maps of the quality needed to accomplish the science goals of RINGS, and to demonstrate the complementary nature of the two sets of kinematic measurements. The spatial and velocity resolutions of these two instruments differ substantially, and they measure different components of the interstellar gas in the galaxy. However, in both cases the radiating gas should be a good tracer of the gravitational potential, and the measured velocities therefore ought to agree within the estimated uncertainties. We find that this is indeed the case over much of the visible disk, though some notable differences are discussed.

Note that the figures and model parameters in this chapter were produced from an older reduction of the Fabry-Pérotdata for this galaxy that predates the data used in the previous chapters. The differences between these data and the data presented in Chapter 2 are discussed in detail in that chapter. The most significant differences are (1) the spatial 68 smoothing procedures that were used – the data in this chapter have somewhat lower spatial resolution and higher signal-to-noise than do the data in Chapter 2, and (2) the data cube presented in this chapter was fitted with only the Hα line, not the [N II] line.

In Figure 4.1, we show intensity maps produced from all three aspects of the RINGS survey for this galaxy – broadband photometric imaging, Hα Fabry-Pérotspectrophotom- etry, and H I interferometry. In Figure 4.2, we show line profiles and spectral fits from our

Hα data similar to those plotted in Figure 2.2. In Figure 4.3, we show the Fabry-P´erot kinematic map and uncertainty map that will be used for the remainder of this chapter.

4.2 NGC 2280: Basic Properties

NGC 2280 is classiﬁed as a SA(s)cd galaxy (de Vaucouleurs et al. 1991). Figure 4.1(a) shows an R-band continuum image taken with the CTIO 0.9m telescope (Kuzio de Naray et al.

00 2017, in prep.). Lauberts & Valentijn (1989) give a value for R25 of 380.19 in the B band.

−1 Koribalski et al. (2004) give a heliocentric systemic velocity of vsys 1899 km s . The ' −1 galactocentric velocity of vgsr 1703 km s , together with an adopted Hubble constant ' −1 −1 of H0 = 73.0 km s Mpc , indicate a distance of 23.3 Mpc, and thus an angular scale ∼ −1 of 0.113 kpc arcsec . At this distance, the apparent V-band magnitude, mV = 9.61 (de

Vaucouleurs et al. 1991), corresponds to an absolute magnitude MV = 22.23. Its radio − ﬂux at 1.49 GHz is 59.7 mJy (Condon et al. 1996).

Arp & Madore (1987) note the existence of ﬁve apparent companion galaxies to NGC 2280.

We list several possible companion galaxies (galaxies within 1◦ of NGC 2280 and with similar systemic velocities) in Table 4.1.

4.3 H I Observations

Our H I observations were taken on 13 Oct 2006 using the VLA in BC configuration during the expansion phase of the array, which at the time contained five retro-fitted EVLA anten- nae. Standard flux calibrators, 3C147 and 3C286, were observed at the beginning and end 69

−

− −

Figure 4.1 Intensity maps of NGC 2280 on the same spatial scale. (a) An R-band continuum image acquired using the CTIO 0.9 m. (b) The stacked intensity of our SALT RSS Fabry- Pérotimages from 11 Nov 2011, which includes both the Hα and continuum emission integrated over the narrow wavelength range of our data. The circular boundary reflects the 80 field of view, and the gaps in the image are between CCD chips. (c) The total Hα ∼ intensity from line profile fits to our SALT Fabry-Pérotdata. (d) The total H I intensity R Idv from the VLA. 70

100 S/N = 50.2 (a) 90 80

[ADU] 70 60

Intensity 50 40

S/N = 19.9 (b) 25

15 Intensity [ADU] Intensity 10

6580 6585 6590 6595 6600 6605 6610 6615 6620 Wavelength [Angstroms]

Figure 4.2 Sample spectra and Voigt profile fits to individual pixels in our Hα velocity map data. The pixels whose profiles are plotted here are marked in Figure 4.3. 71

( (-/s] Velocity Uncertainty [km/s]

1 2 3 4 5 6 7 X [kpc] -11.3 0.0 11.3 -11.3 0.0 11.3

22.6 E

11.3

0.0 Y [kpc] Y

− -11.3

− -22.6

− − X [arcsec]

Figure 4.3 Velocity map (left) and velocity uncertainties (right) produced from the Hα data. The small circle in lower right corner of the velocity map represents the 4.900 eﬀective beam size. Arrows indicate the pixels whose line proﬁles have been plotted in Figure 4.2. 72

Table 4.1. Galaxies Near NGC 2280

0 −1 a Galaxy Angular Separation ( ) Velocity Separation (km s ) mR

ESO 427- G005b 11.910 +136 15.42 ESO 427- G 004b 13.314 -194 15.79 AM 0643-272c 14.358 +304 – ESO 490- G 035b 26.535 +242 13.13 ESO 490- G 036b 29.326 +39 13.63 NGC 2272d 30.299 +231 11.29 AM 0644-280c 31.556 +117 – ESO 490- G 044b 33.400 +269 13.27 ESO 490- G 031b 55.400 +92 14.06 ESO 490- G 042b 56.824 -141 14.58 ESO 490- G 038d 59.278 +75 13.01

Note. — Galaxies with measured systemic velocities near that of NGC 2280 and angular separations from NGC 2280 less than 1◦. The R-band apparent magnitudes are to the R25 isophote and that for NGC 2280 is 10.76. aLauberts & Valentijn (1989) bGarcia et al. (1994) cMatthews et al. (1995) dHuchra et al. (2012) 73

Table 4.2. NGC 2280 H I Observation Parameters

Parameter Value

VLA conﬁguration BC Synthetic beam FWHM 11.4600 9.5400at 74.39◦ × Time on-source 370 minutes Usable total bandwidth 2.5 MHz Band center (helio) 1888 km s−1 Spatial resolution 10.4600 Spatial resolution 1.18 kpc RMS noise, H I line 0.47 mJy/beam

Note. — Parameters for our H I observations of NGC 2280 with the Karl G. Jansky Very Large Array telescope.

of the observing run. A nearby phase calibrator, 0609-157, was observed for 4.5 minutes ∼ for every 30 minutes on the target source for a total of 370 minutes of on-source observing. ∼ Data editing and reduction was completed using the Astronomical Image Processing

System (AIPS) version 31Dec12 (Greisen 2003). Due to technical reports of power aliasing affecting the EVLA-EVLA baselines, all ten potentially affected baselines were flagged and removed from the data. The remaining data were then calibrated using standard AIPS tasks where the flux density for each source was determined relative to that of the flux calibrators and the phase of the data was retrieved from the computed phase closures from the phase calibrator. Bandpass solutions were also derived using the flux calibrators to correct for amplitude variation. The edited cube was imaged with robust weighting and cleaned, producing a synthesized beam FWHM of 11.4600 9.5400 at a position angle of × 74.39◦, a spectral resolution of 10.4 km s−1, and an RMS noise in each spectral channel of

σ = 0.47 mJy. A summary of the observation parameters is provided in Table 4.2.

Figure 4.1(d) shows a map of the total H I intensity R Idv derived from the continuum- subtracted, calibrated data cube. Locations where R Idv < 6.4 1020 atoms cm−2 before × primary beam correction – the 3σ, 3-channel sensitivity limit of the cube – have been masked. We estimate velocities and uncertainties from a Hermite 3 ﬁt (van der Marel & 74

Franx 1993) following a similar approach to that described in Noordermeer et al. (2005)

(see also de Blok et al. 2008). The Hermite 3 fit is known to provide a better estimate of the location of a asymmetric line profile’s peak than the commonly-assumed Gaussian profile

(van der Marel & Franx 1993). We use ﬁts obtained from a smoothed and clipped version of the data cube as initial guesses in our ﬁt to the full-resolution cube. The resulting Hermite

3 velocities are kept only for pixels where (a) the uncertainty on the best ﬁtting velocity is

−1 σV < 25 km s , (b) the peak of the Hermite 3 proﬁle exceeds 3σ, (c) the velocity dispersion

−1 −1 R σd is in the range 5 km s < σd < 100 km s , and (d) Idv > 0 in the intensity map of

Figure 4.1.

Figure 4.4 shows the Hermite 3 velocity ﬁeld and uncertainties for NGC 2280. As with

Figure 4.3, the H I velocity map reveals a similar circular flow pattern, but with some differences. Velocities are determined over a wider region, with more complete coverage in the outer parts, but we were unable to obtain velocities in an elliptical region at the center that is extended roughly along the major axis. Even without data in this region, the inner velocity gradient appears shallower than in the Hα velocity map. The flow pattern is remarkably regular, with no clear twists in the iso-velocity contours, even in the outer parts, suggesting that any possible warp in the disk of NGC 2280 is mild and that the galaxy is undisturbed.

4.4 Velocity Map Comparison

Figure 4.5 shows diﬀerences between the velocities in our Hα and H I velocity maps where both measurements are above our S/N thresholds. The diﬀerences are generally small

−1 (green color), but larger differences of & 40 km s are evident in some places and are not randomly distributed. In some parts, particularly in the north, positive differences (red) persist over regions that are azimuthally extended and there are hints that they could be associated with spiral features, shown by the black lines, although many red areas also lie squarely between arms. There are fewer differences 40 km s−1 (blue) and they show . − 75

−

− −

Figure 4.4 Velocity map (Left) and velocity uncertainties (Right) produced from the H I data. 76 essentially no correlation with spiral locations.

While the loci of large positive diﬀerences do coincide with spiral arms in one or two instances, interpreting them as due to spiral arm streaming makes little dynamical sense, for the following reason.

The NW side of the galaxy is approaching, which means that the NE side is tipped towards us if we assume the spirals trail. The diﬀerence map shows small velocity diﬀerences

(green) that suddenly jump to 40 km s−1 (red) on the NE sides of the spiral arms in one ∼ or two places in the N part of the map. The sign of the velocity diﬀerence (VHI VHa) − implies that the Hα emission is coming from gas that is moving, relative to that producing

the H I line, towards us along our line of sight. Because the NE is the near side of the

galaxy, this excited gas is therefore moving radially outwards from the center of the galaxy.

However, spiral streaming theory suggests that post-shock gas should have a component

of velocity in towards the galaxy center inside corotation for the pattern. So either the

spiral arms are outside corotation wherever this diﬀerence is seen, and the gas acquires its

outward velocity before it passes through the arm, or the spirals are leading. Neither of

these alternatives seem palatable.

Because the velocity diﬀerences are not well correlated with spiral arms, nor do they

have the sign expected from spiral streaming theory where they do coincide with spirals, we

suspect that they have some other origin. We note that similar patchy diﬀerences between

VHI and VHa were reported by Phookun et al. (1993) in the galaxy NGC 4254, for which

they could ﬁnd no convincing explanation.

We use the biweight (Beers et al. 1990) to estimate the Gaussian spread of the velocity

diﬀerences. This estimator is especially designed to determine the spread from the bulk of

the data without being biased by possible heavy tails in the distribution. Using the biweight,

−1 we find the mean velocity difference between our two maps to be VHI VHa = 7.9 km s . − This value appears to be dominated by velocity differences in the NW (approaching) side of the galaxy. The 1-σ scatter in these differences is 14.0 km s−1, which is consistent with 77

X [kpc] -29.38 -22.035 -14.69 -7.345 0.0 7.345 14.69 22.035 29.38 260.0 29.38

40 195.0 22.035

30 130.0 14.69 20

65.0 7.345 10

0.0 0.0 0 Y [kpc] Y

Y [arcsec] Y -10 -65.0 -7.345 V_HI - V_Ha [km/s] V_Ha - V_HI -20 -130.0 -14.69 -30

-195.0 -22.035 -40

-260.0 -29.38 -260.0 -195.0 -130.0 -65.0 0.0 65.0 130.0 195.0 260.0 X [arcsec]

Figure 4.5 Diﬀerences in line-of-sight velocity between individual pixels in our Hα and H I velocity maps. The black lines show visually-estimated locations of the spiral arm features.

the intrinsic 8.0 km s−1 ISM turbulent motions estimated by Gunn et al. (1979) combined

with a diﬀerence of two observed quantities with our estimated uncertainties.

Thus aside from the patchy large diﬀerences shown in Figure 4.5, our two velocity

measurements in NGC 2280 generally diﬀer by an amount that is no more than the usual

expectation for turbulence in the ISM.

4.5 Modelling Comparison

As in Chapter 3, we have used DiskFit to ﬁt our Hα and H I velocity maps of NGC 2280.

For each of our two velocity maps, we ﬁt two separate models: one for which the position 78

Table 4.3. NGC 2280 Model Comparison

Note. — A comparison of the previously measured properties of NGC 2280 to the properties measured from our best ﬁtting Hα and H I velocity map models and our favored values. Ellipticities from previous works were derived from the major and minor axis measurements in those works. aLauberts & Valentijn (1989) from optical photometry

b Jarrett et al. (2003) from 2MASS Ks photometry cHuchra et al. (2012) dSpringob et al. (2005) from H I spectrum eKoribalski et al. (2004) from H I spectrum f Bottinelli et al. (1990) from H I spectrum gSandage (1978) from optical spectrum

angle, ellipticity, and center were free to vary, and the other with these parameters held

ﬁxed at common values so that we can directly compare the ﬁtted rotation curves. Our

ﬁrst ﬁts are of simple disk models without bars or warps.

The measurement uncertainties needed to estimate χ2 for the ﬁt are the ∆V found

when ﬁtting the Hα and H I lines. Because the emission we observe may not be coming

from matter traveling at the circular speed, we add an additional 8 km s−1 in quadrature

to the uncertainties in both velocity maps. This value is typical of turbulent motions in

the interstellar medium of a galaxy (Gunn et al. 1979). We ﬁnd the resulting velocity

uncertainties to be consistent with the biweight-esimated scatter in the diﬀerences between

our two velocity maps in Figure 4.5. 79

−

− −

Figure 4.6 Best ﬁtting models to the Hα (Left) and H I (Right) velocity maps.

4.5.1 Projection parameters

Table 4.3 gives the fitted values, together with our estimated uncertainties, of the projection parameters from the two maps separately. The two estimates of the systemic velocity differ by 1.80 km s−1, which is well within the quoted 1-σ uncertainties. Our values are smaller than those quoted by Koribalski et al. (2004) and by Springob et al. (2005). Because our systemic velocity was derived from 2-D velocity maps and theirs from a single-dish H I measurements, we do not find this difference worrisome.

Our kinematic estimates of the position angle and ellipticity from our two maps are also in excellent agreement with each other, and agree tolerably well with previous apparent ellipticity (e = 1 b/a) estimates from a photometric B-band image (Lauberts & Valentijn − 80

Data-model Residual Velocity [km/s]

-40 -30 -20 -10 0 10 20 30 40 X [kpc] -11.3 0.0 11.3 -11.3 0.0 11.3

22.6

11.3

0.0 Y [kpc] Y

− -11.3

− -22.6

− X [arcsec]

Figure 4.7 Data-model residuals for the best ﬁtting models to the Hα (Left) and H I (Right) velocity map. 81

1989) and from 2MASS near-infrared data (Jarrett et al. 2003). Mild discrepancies between photometric and kinematic estimates of inclination can arise from intrinsic mild ellipticities caused by outer spiral arms, for example. Our favored values for the parameters in Table

4.3 were determined by weighted means of our two best ﬁtting models, with weights given by the inverse variances of these quantities.

4.5.2 Uncertainty Estimates

Figures 4.6 and 4.7 show respectively our best ﬁtting rotation-only models for both the Hα and H I velocity maps and the corresponding residual maps. The values of the reduced χ2

for these models are 2.33 and 1.75 respectively, indicating a poor formal ﬁt to the data given

their estimated uncertainties. The residual velocities are signiﬁcantly larger than our typical

velocity uncertainties, which are usually dominated by our adopted value of 8 km s−1 for

turbulent motions in the ISM, and are generally spatially correlated, indicating that the gas

in NGC 2280 has more complicated motion than is allowed for in our models. For example,

our models do not include non-circular streaming motions associated with spiral arms. A

dynamical origin for the larger residuals is supported by the fact that their general pattern

is similar in the two separate sets of data.

4.5.3 Rotation Curves

Figure 4.8 shows the circular speed derived from our ﬁts to the Hα and H I velocity maps,

with the error bars showing 1σ uncertainties estimated from 1000 bootstrap iterations. ± The abscissae were chosen such that the points are spaced 1 beam FWHM apart.

The individual patches of large velocity difference discussed above are not sufficient to explain the systematic offset in the Hα and H I model rotation curves over the region 4000 <

R < 12000. To investigate this further, we have ﬁtted DiskFit models to the approaching and receding halves of the two velocity ﬁelds independently. We show the resulting rotation curves in Figure 4.9. Note that the approaching (NW) Hα, receding (SE) Hα, and receding 82

Radius in Disk Plane [kpc] 5.65 11.3 16.95 22.6 28.25 33.9 39.55 45.2 300

250

200

150 Circular Speed [km/s] Speed Circular

100

H-alpha HI 50 0 50 100 150 200 250 300 350 400 Radius in Disk Plane [arcsec]

Figure 4.8 Rotation curves for NGC 2280 derived from the model ﬁts to our Hα and H I data. 83

Radius in Disk Plane [kpc] 5.65 11.3 16.95 22.6 28.25 33.9 39.55 45.2 350 H-alpha Approaching H-alpha Receding 300 HI Approaching HI Receding

250

200

150 Circular Speed [km/s] Speed Circular

100

50 0 50 100 150 200 250 300 350 400 Radius in Disk Plane [arcsec]

Figure 4.9 Rotation curves for NGC 2280 produced from independent model ﬁts to the approaching and receding halves of our Hα and H I data. 84

(SE) H I curves all appear to be consistent with each other over the region of interest, while the approaching (NW) H I curve appears to be signiﬁcantly diﬀerent.

Here we note the presence of a large, spatially coherent, positive residual velocity in the H I ﬁeld. This region extends from approximately (X,Y ) = (5000, 10000) to (X,Y ) =

(000, 7500) in the right panel of Figure 4.7 and intersects the region where the rotation curve − discrepancy is most pronounced. We have examined the H I line proﬁles in this region and

have found that many of them have a skewed shape or are multiply peaked. We plot

two such line proﬁles in Figure 4.10. The peaks of these proﬁles lie at higher recessional

velocities than are predicted by our best-ﬁtting DiskFit model. We believe the lower- velocity “shoulders” of these asymmetric line proﬁles correspond to the galaxy’s rotation, while the higher-velocity peak corresponds to a stream of neutral gas external to the galaxy.

Assuming this stream of gas is in the foreground of NGC 2280, it would correspond to an inflow of neutral gas. We believe this stream of gas may be having a significant effect on the DiskFit model circular velocity over this radial region, causing the large difference in rotation curves that we observe.

The combined Hα rotation curve (Figure 4.8) manifests a series of small “bumps” that are less prominent or non-existent in the H I rotation curve. These bumps stand out more clearly on the approaching side (blue circles in Figure 4.9), while the rotation curve is smoother on the receding side. They are almost certainly related to the large velocity diﬀerences visible in Figure 4.5, which revealed patches of excited gas moving more rapidly towards us (red) on the approaching side (north west), while there are fewer anomalous velocities on the receding side.

Aside from these anomalous H I velocities, the rotation curves derived from our two maps appear to be in reasonable agreement with each other beyond R 12000, and most ∼ diﬀerences stem from the diﬀerent spatial coverage and resolutions of the separate maps.

As shown in Figures 4.3 and 4.4, the Hα velocity map is more sparsely sampled at large radii than is the H I velocity map, leading to larger ﬂuctuations and greater residuals in the 85

Figure 4.10 Two sample H I line profiles from the region of large anomalous velocity in our H I velocity field. We believe these skewed profiles may arise from an external stream of gas flowing towards or away from NGC 2280 along the line-of-sight. 86

Radius in Disk Plane [kpc] 1.13 2.26 3.39 4.52 5.65 6.78 250

200

150

100 Circular Speed [km/s] Speed Circular

50 H-alpha HI Smeared H-alpha 0 0 10 20 30 40 50 60 Radius in Disk Plane [arcsec]

Figure 4.11 Inner rise of rotation curves derived from the model ﬁts to our unsmeared Hα, H I, and Hα smeared to the resolution of the H I data. optically estimated circular speed (Figure 4.8).

4.5.4 Inner velocity gradient

The slope of the inner rise of the H I circular speed is also shallower than that found from the

Hα data. One obvious reasons for this diﬀerence is beam smearing of the H I measurements

(Bosma 1981; Swaters et al. 2000), which has the eﬀect of combining velocities of gas away from the major axis with those from gas on the major axis. Because projection causes the line-of-sight velocity to be systematically smaller away from the major axis, beam smearing biases rotational velocity measurements towards lower values.

In order to investigate the eﬀects of spatial resolution on our velocity maps, we have 87

Radius in Disk Plane [kpc] 0.0 5.65 11.3 16.95 22.6 1.0 H-alpha HI

0.8

0.6

0.4

0.2 Azimuthally Averaged Intensity [arbitrary units] [arbitrary Intensity Averaged Azimuthally

0.0 0 50 100 150 200 Radius in Disk Plane [arcsec]

Figure 4.12 Azimuthally averaged intensity profiles of NGC 2280 from our Hα and H I data, in 500 radius bins. Note the central hole in the H I intensity profile that is not present in the Hα profile. 88 convolved our FP data with a Gaussian beam identical to that used for the H I data. This procedure required us first to take out the center-to-edge velocity gradient in the FP frames in order to make a new data cube with single velocity “channels” before blurring. We then modelled the resulting velocity map with the DiskFit software. In Figure 4.11, we plot the

inner rise of rotation curves for our unsmeared Hα (blue circles), smeared Hα (red inverted

triangles), and H I data (green triangles). As expected, the beam smeared Hα rotation curve has a shallower rise inside R = 2000 than that of the unsmeared Hα rotation curve.

However, the beam smeared Hα rotation curve still rises more steeply than does the H I

rotation curve, although the H I data are sparse within 3000 of the galaxy center. We ∼ attribute the yet shallower rise to a deﬁciency of H I emission in the center of NGC 2280.

Figure 4.12 shows the azimuthally averaged intensity proﬁles for the Hα and H I data. The

H I surface density drops toward the center, consistent with the 3000 central hole in the ∼ intensity map (Figure 4.1), a common feature of H I emission near the center of galaxies

(e.g. Wang et al. 2014).

The weak H I line cannot yield reliable velocities, whereas the Hα intensity rises continu- ously into the center enabling reliable velocity measurements at small radii. This difference in the radial distribution is probably responsible for the remaining difference between the rotation curves. Note that there must be some hydrogen in the center to produce the Hα emission, and the neutral gas is probably molecular therefore; however, we have been unable to find any existing CO observations to confirm the presence of molecular gas.

4.6 Summary

We have presented detailed velocity maps of the nearby spiral galaxy NGC 2280 produced from Fabry-Pérotmeasurements of the Hα line of excited gas and from aperture synthesis measurements of the 21cm line of H I. Despite the fact that these two maps were derived from different components of the ISM having different spatial distributions, and were measured with different instruments having widely differing spatial and spectral resolutions, the 89 measured velocities are generally in excellent agreement.

We have obtained estimates of the systemic velocity, disk inclination and position angle using DiskFit. Our derived values from the two maps agree within their estimated uncer-

◦ −1 tainties and we favor φPA =157.66 0.37 , e =0.555 0.012, and vsys =1888.74 1.02 km s . ± ± ± These values are broadly consistent with previous estimates, as shown in Table 4.3. Where significant differences do exist, they are not particularly worrisome. Values derived from different methods (e.g. 2D kinematic modelling vs. longslit spectra or photometry) often disagree.

Additionally, the two datasets yield similar rotation curves. The diﬀerences in spatial extent and resolution between the Hα and H I velocity maps demonstrate the complemen- tarity of the measurements. At small radii, the resolution of the Hα velocity map allows for a more precise measurement of the inner slope of the rotation curve. The better-ﬁlled velocity map from the H I allows us to measure the rotation curve to large radii with greater precision than could be obtained from the Hα velocity map.

We have compared the velocities from the two datasets at overlapping pixels, and find a near Gaussian spread of differences with a dispersion of 14 km s−1, consistent with an ∼ intrinsic velocity dispersion of 8 km s−1 broadened by the combined uncertainties from ∼ measurements by the two instruments. However, a small fraction of the pixels manifest much larger differences 40 km s−1, with the sense that the H I gas on the approaching ∼ ± side of the galaxy is receding at a faster velocity than the Hα gas at the same location. The origin of this difference may be a stream of neutral gas external to NGC 2280.

Precise measurements of the kinematics of spiral galaxies on small spatial scales are imperative for studying these galaxies’ mass distributions in a cosmological context. Velocity maps produced from Hα Fabry-P´erotinterferometry and H I aperture synthesis such as those presented here will be very useful tools for measuring the dynamics of the galaxies in the RINGS sample. 90

Chapter 5

NGC 2280 Mass Modeling

5.1 Introduction

As discussed in Chapter 1, one of the several method of determining the stellar contribution to a galaxy’s rotation curve is to convert its light distribution directly to a mass distribution using stellar population synthesis (SPS) models. In order to place constraints on the stellar mass distributions of the galaxies in the RINGS sample, we have obtained photometric observations of 18 of these galaxies in the BVRI photometric bands at 200 resolution ∼ (Kuzio de Naray et al. 2017, in prep.). The light from galaxies traces its stars, but does not do so trivially (see the recent review by Conroy 2013).

Stars of diﬀerent masses, ages, and chemical compositions emit light diﬀerently. The

Stefan-Boltzmann law gives the luminosity of a star with radius R and temperature T as

L R2T 4 (5.1) ∝

High-mass stars fuse hydrogen in their cores much more rapidly than do lower-mass stars.

These high-mass stars therefore emit much more light than their low-mass counterparts, due to both their larger radii and higher temperatures. Their higher temperatures also cause them to emit more high-frequency (bluer) light. Because of the high reaction rates in their cores, high-mass stars rapidly exhaust their supply of hydrogen, dying young.

Because of these differences in how different stars emit light, a galaxy containing a mix of young and old stellar populations will suffer from a significant degeneracy. Most of the 91 light coming from a galaxy is dominated by its high-mass, younger stellar populations. In particular, they completely dominate the bluer photometric bands because of their large radii and high surface temperatures. Because these massive stars die young, the B photometric band provides a good measurement of recent star formation. Most of the stellar mass of these galaxies is contained in their low-mass stellar populations. Because low-mass stars have long lifetimes, the stars in this population can be much older. They are many orders of magnitude less luminous than their high-mass counterparts and are therefore much more difficult to detect. However, they are much more numerous than high-mass stars. Because their surface temperatures are much lower, their light is mostly emitted at lower frequencies, and redder photometric bands such as the near-infrared I-band or the infrared JHKs bands provide a much better tracer of this population.

As a stellar population ages and higher-mass stars die, its light distribution becomes dimmer and redder, though its mass remains the same. This has the effect of increasing the mass-to-light ratio of the population, leading to a relationship between color and mass- to-light ratio, the so-called CMLR. This relationship is complicated by metallicity, which can mimic the effects of age on a stellar population’s color. Metals in a stellar atmosphere provide more opportunities for free-free absorption of photons, increasing the radii of stars and decreasing their surface temperatures. The combination of these effects leads to high- metallicity stars having redder light distributions than lower-metallicity star of the same mass.

The above discussion applies to stars on the main sequence, but the issue of relating photometric measurements to a stellar population is further complicated by highly evolved stars which have exhausted hydrogen in their cores. These giant stars are much cooler and larger than their main-sequence counterparts, emitting more and redder light despite having the same mass.

There are two common practices when attempting to convert photometric data into a stellar mass model for a galaxy. The ﬁrst is to pick a photometric band and assume a 92 constant ratio between luminosity and stellar mass across the entire galaxy disk. Typically, a low-frequency optical band such as I or even an infrared band is used, as these bands are more sensitive to the low-mass stellar population that contains the bulk of the mass. A more sophisticated approach requires modelling the galaxy’s stellar population as a mixture of multiple populations with diﬀerent ages and chemical compositions. With some assumptions about the history of star formation in a galaxy and how metal-enriched gas from older stellar populations is recycled into newly formed stars, these models can be used to derive a relationship between color and mass-to-light ratio.

Once a map of stellar mass has been derived using one of these approaches, it can be converted to a gravitational potential, which can then be diﬀerentiated along the radial direction to derive the stellar contribution to the rotation curve. Combined with a measurement of the galaxy’s total rotation curve (e.g. Chapters 2 - 4), this approach can be used to separate the stars’ contribution to the rotation curve from the halo’s contribution.

In this chapter, we utilize the photometric measurements of NGC 2280 by Kuzio de

Naray et al. (2017, in prep.) and several color-mass-to-light-ratio-relations (CMLRs) to produce maps of NGC 2280’s stellar mass distribution (Bell et al. 2003; Portinari et al.

2004; Zibetti et al. 2009; Into & Portinari 2013; McGaugh & Schombert 2014). We then ﬁt these mass distributions with axisymmetric models using the photometry-ﬁtting feature of

DiskFit (Spekkens & Sellwood 2007). We utilize the GALAXY code of Sellwood (2014) to determine the gravitational potential of these disk models and their contributions to the rotation curve. We then subtract these disk rotation curves in quadrature from those extracted from our Hα Fabry-Pérotdata in Chapter 3 to determine the contribution of NGC 2280’s dark matter halo to its rotation curve and its density profile. Finally, we explore the effects of different sources of uncertainty on these models, in particular the uncertain normalization of the CMLRs, the uncertain distance to NGC 2280, and the uncertain vertical density distribution of the stellar disk. 93

5.2 Photometric Measurements of NGC 2280’s Stellar Mass Distribution

We have obtained photometric measurements of NGC 2280 at 1.800 seeing in the BVRI ∼ photometric bands with the CTIO 0.9m telescope (Kuzio de Naray et al. 2017, in prep.).

The R band is not particularly useful for estimating stellar mass via this method, as it is contaminated by Hα emission from recent star formation, so we will limit ourselves to the

BVI bands for the purposes of constraining NGC 2280’s stellar mass. As demonstrated by McGaugh & Schombert (2014), the I-band mass-to-light ratios of several authors’ SPS models can be expressed as a function of the B V color, making this set of photometric − bands a convenient choice.

We have performed standard data reduction steps on these images to correct for cosmic ray impacts to the CCD, ﬂat-ﬁeld correct the images, and measure and subtract the contribution of the sky background from the images. Standard stars were used to calibrate the photometry (Kuzio de Naray et al. 2017, in prep.), and then these foreground stars were masked from further analysis so as to not be confused with light from the galaxy.

The images were then convolved with a small Gaussian beam to place them at uniform resolution, with the ﬁnal resolution given by the worst seeing of the set of images (1.800 in the B-band). Figure 5.1 shows the B and V images of NGC 2280, as well as an image of the B V color at every point. In producing the B V color image, the foreground − − extinction values of Schlaﬂy & Finkbeiner (2011) were used to correct for dust reddening.

Note that NGC 2280 exhibits a clear color gradient from B V 1.0 in the central region − ∼ to B V 0 towards the edge of the visible disk, indicating that the light distribution is − ∼ much redder in the central region.

Equation 1 of McGaugh & Schombert (2014) provides the functional form of a CMLR that can be ﬁtted to the results of a stellar population synthesis (SPS) model:

log (ΥI ) = a + b(B V ), (5.2) 10 − 94

Figure 5.1 Our B-band (left) and V -band (center) images of NGC 2280 with foreground stars masked, as well as a map of B V color (right) that has been corrected for foreground − extinction. 95

where ΥI is the I-band mass-to-light ratio in units of M /L , a and b are ﬁtted constants,

and B V is the usual photometric color. For the SPS models of Bell et al. (2003) (using a − Salpeter IMF), Portinari et al. (2004) (using a Kroupa IMF), Zibetti et al. (2009) (using a

Chabrier IMF), and Into & Portinari (2013) (using a Kroupa IMF), the parameters a and

b are summarized in Table 5.1.

McGaugh & Schombert (2014) have noted that for diﬀerent choices of colors and photo-

metric bands, the CMLRs of these various works are not self-consistent – e.g. the best-ﬁtting

relationship for ΥI vs. B V color may result in a diﬀerent stellar mass than the best-ﬁtting −

relationship for ΥB vs. V I color for a given choice of BVI ﬂuxes. These authors have − therefore reformulated these four CMLRs in a way that enforces self-consistency among

diﬀerent bands, and their updated parameters are also summarized in the ﬁnal four rows

of Table 5.1.

We have utilized all eight of the CMLR formulations in Table 5.1 to convert our I-band

photometric image and B V color map (Figure 5.1) into maps of stellar mass surface − density in NGC 2280. Figure 5.2 shows the maps that result from this procedure. Note

that the values in these maps are independent of the distance to NGC 2280 – the distance

will, however, become important when trying to measure the total stellar mass of NGC 2280.

5.3 Determining the Stellar Contribution to the Rotation Curve

The photometry-ﬁtting application of DiskFit can also be applied to maps of surface density

such as those in Figure 5.2. For each of these eight maps of NGC 2280’s stellar mass surface

density, we have produced an axisymmetric model of the mass distribution. As with the

kinematic models of Chapter 3, these models ﬁt for the disk position and projection in the

plane of the sky. Unlike the kinematic models, these models ﬁt for the average surface

density (average ﬂux in the case of true photometric data) in each elliptical bin rather than

the circular speed (Spekkens & Sellwood 2007).

In addition to the proﬁle of the projected disk, we have also allowed for spheroidal 96

Table 5.1. Color-Mass-to-Light-Ratio-Relation Model Parameters

Model Name Citation a b

bell03 (a) -0.399 0.824 port04 (b) -0.537 0.970 zibe09 (c) -1.075 1.475 into13 (d) -0.782 1.294 bell03s (a), (e) -0.259 0.565 port04s (b), (e) -0.302 0.644 zibe09s (c), (e) -0.446 0.915 into13s (d), (e) -0.394 0.820

Note. — Model parameters for the eight I-band CMLR models used in generating our mass models of NGC 2280. From left to right, columns are (1) Model Name used to refer to each model in Figures 5.3-5.6, (2) citation code for the model (see below), (3- 4) model parameters in equation 5.2. The ﬁrst set of four models use the parameters of: (a) Bell et al. (2003), (b) Portinari et al. (2004), (c) Zibetti et al. (2009), and (d) Into & Portinari (2013). The second set of four models uses the “self-consistent” reformula- tions of these models by (e) McGaugh & Schombert (2014). 97

Figure 5.2 Maps of stellar surface mass density in our eight mass models derived from the CMLRs of Table 5.1. 98 bulges with Sérsicprofiles at the centers of the galaxy in these models. These bulges are assumed to have their axis of symmetry aligned with the disk’s rotational axis. While the bulge and disk are partially separable due to the projection of the disk onto ellipses in the plane of the sky, they are still somewhat degenerate and bulges differ substantially among our eight mass models. We have also fitted our BVRI photometric images of

NGC 2280 with similar disk+bulge models. Figure 5.3 shows radial surface-brightness profiles of these 4 photometric models and surface-density profiles of our 8 mass models, as well as a best-fitting exponential disk profile to each. Note that while none of the photometric bands is particularly consistent with an exponential disk (and the disk scale length varies considerably between bands), the combination of the disk’s color gradient and

I-band surface-brightness proﬁle result in mass proﬁles that are very nearly exponential.

In order to convert these disk mass models into disk contributions to the rotation curve, the distance to NGC 2280 and a proﬁle for the vertical mass distribution of the disk must be assumed. As in Chapter 2, we have adopted a distance to NGC 2280 of 24.0 Mpc, as determined by Willick et al. (1997) using the H-band Tully-Fisher relation. Bershady et al.

(2010b) ﬁt an oblateness relation to the data of Kregel et al. (2002), producing a scaling relationship between the exponential scale length of a disk and its vertical distribution. The typical mass model in Figure 5.3 has a scale length of 1.47 kpc, implying an exponential scale height hz = 0.25 kpc using this oblateness relation. We examine the eﬀects of these assumptions about distance and vertical mass distribution in Section 5.5.

We have then utilized the GALAXY code (Sellwood 2014) to numerically solve for the gravitational potential of the disk, assuming the distance and vertical proﬁle above. The resulting disk rotation curves are plotted alongside our Hα Fabry-P´erotmeasurements of

NGC 2280’s rotation curve in Figure 5.4. Note that each of these models peaks at around

3 kpc, and at that radius they typically have Vdisk/VFP 0.71 ( 0.53 in the case of the ∼ ∼ “zibe09” model), implying that each of these disk models is slightly submaximal.

As mentioned above, one of the models, “zibe09,” is signiﬁcantly diﬀerent from the 99

Figure 5.3 Circular points show the axisymmetric disk profile fits to our BVRI photometry of NGC 2280 (left column) and our eight disk mass models of the galaxy derived from the stellar mass maps in Figure 5.2 (center and right columns). Dashed lines show the best- fitting exponentially declining function to each model. These models assume a distance to NGC 2280 of 24.0 Mpc. 100 others. One potential contribution to the much lower degree of maximality in this model is that an unusually large fraction of the galaxy’s mass was assigned to the bulge component

(and therefore an unusually small fraction to the disk). Mass in a ﬂattened disk provides a stronger centripetal attraction than does a spherical distribution, both due to the mass being physically closer to the disk’s midplane, and due to the direction of the centripetal force being more strongly aligned to the radial direction. At large radii, the disk and bulge distributions should asymptotically approach the same rotation curve, which does not appear to be the case in Figure 5.4. This implies that the unusually large bulge contribution in this model cannot be the only cause of this discrepancy, and further investigation is required in order to determine why this model is so diﬀerent from the rest.

To convert the bulge light distributions of our DiskFit models to bulge contributions to the rotation curve, we have numerically integrated Equation 13 of Noordermeer (2008).

Each model’s combined disk+bulge contribution to the rotation curve is presented in the bottom panel of Figure 5.4.

5.4 NGC 2280’s Dark Matter Halo

Assuming that the stellar disk, bulge, and dark matter halo are the dominant mass components of NGC 2280, the total rotation curve can be expressed as a sum of their individual contributions in quadrature as follows:

2 2 2 2 Vtotal(R) = Vdisk(R) + Vbulge(R) + Vhalo(R), (5.3) with the halo contribution given by

GM(< R) V 2 (R) = (5.4) halo R 101

Figure 5.4 Disk (Top) and Disk+Bulge (Bottom) contributions to NGC 2280’s rotation curve (solid lines) derived from each of the axisymmetric mass models in ﬁgure 5.3. Points with error bars show our Hα Fabry-P´erotmeasurements of NGC 2280’s rotation curve extracted from our models in Chapter 3. These models assume a distance to NGC 2280 of 24.0 Mpc. 102

Figure 5.5 The best-fitting halo density profiles in each of our eight mass models. Note that with the exception of the “zibe09” model, all of the halo density profiles agree quite closely.

for a spherical halo. This can then be diﬀerentiated to give the density proﬁle of the halo:

1 1 d ρ (R) = (RV 2 ). (5.5) halo 4πG R2 dR halo

In Figure 5.5, we plot the halo proﬁles derived from our mass models of NGC 2280 using the above equations. With the exception of the “zibe09” model, the models produce very similar halo density proﬁles.

In Figure 5.6, we attempt to ﬁt common functional forms of halos to the proﬁles in Figure

5.5. The profiles we display here are the Navarro-Frenk-White (NFW) profile, the pseudo- isothermal profile, and a simple power-law fit (Navarro et al. 1996). We also attempted to fit 103 an Einasto profile, but in all cases the best-fitting curvature parameter α was either negative

(i.e. the power-law slope became shallower with increasing radius, which is unphysical) or zero (equivalent to a simple power-law) and we therefore do not present those ﬁts here

(Einasto 1965; Gao et al. 2008). Next to each set of curves in Figure 5.6, we also display the reduced-χ2 of the ﬁts. While none of these functional forms provides a particularly good

fit to the data, a power-law profile is favored by six of these models (including all four of the “self-consistent” models) while a pseudo-isothermal profile is favored by the heavy-bulge

“zibe09” model and an NFW proﬁle is favored by the “into13” model.

5.5 Sources of Uncertainty

The uncertainties on individual points in the Fabry-Pérotrotation curve and uncertainties in the photometric data have already been taken into account in producing the halo density profiles of the previous section. However, three additional potential sources of uncertainty have not yet been accounted for, which we discuss below. These are the uncertain normalization of the CMLRs due primarily to the unknown IMF, the uncertain distance to NGC 2280, and the uncertain vertical density profile of the disk. In each case below, we take the “bell03” model from above and produce two additional models that vary the parameter in question.

Changing the mass normalization of the CMLRs has the eﬀect of scaling up the disk and bulge contributions to the rotation curve by a constant factor proportional to M 1/2.

This causes the halo’s contribution to the rotation curve to be reduced, especially in the innermost regions of the galaxy. In Figure 5.7 we demonstrate this eﬀect for mass models with 1.9 times as much mass (“highmass”) and (1/1.9) times as much mass (“lowmass”) as the “bell03” model. The “highmass” model is a fully maximal disk – in fact the combined disk+bulge+halo contributions exceed the Fabry-P´erotrotation curve at a few locations

(within the 1-sigma uncertainties of those data). Note that while a power-law halo proﬁle is preferred for the sub-maximal “bell03” model and the even lighter “lowmass” model, the 104

Figure 5.6 The best-fitting functional forms of NFW (yellow dashed curves), pseudo- isothermal (green dotted curves), and power-law (red dot-dashed curves) halos to each of our halo density profiles (blue solid lines) from 5.5. For each fit, the reduced-χ2 is shown in the legend. 105

Figure 5.7 Top Left: Halo density profile and fitted functional forms for the “bell03” mass model. Top Right: The same but for a model with 1.9 times as much mass, Bottom Left: The same but for a model with (1/1.9) times as much mass. Bottom Right: All three halo profiles on the same scale for comparison. model with a maximal disk prefers a pseudo-isothermal profile.

Changing the distance to NGC 2280 affects this analysis in a slightly more complicated fashion than does the mass normalization. Increasing the distance to the galaxy causes the points of the Fabry-Pérotrotation curve to extend to larger physical radii due to the changing angular scale, but the measured velocities do not change. The points of the disk and bulge contributions will also extend to larger physical radii for the same reason, but the velocities will change because the luminosity (and therefore mass) of the galaxy will have changed. The mass increases as D2 and the radii increase as D1. Because velocity is proportional to (M/R)1/2, this has the net effect of raising each velocity point in the 106

Figure 5.8 Top Left: Halo density profile and fitted functional forms for the “bell03” mass model with NGC 2280 at a distance of 24 Mpc. Top Right: The same but for a model where NGC 2280 at 1.5 times its assumed distance, Bottom Left: The same but for a model where NGC 2280 is at (1/1.5) times its assumed distance. Bottom Right: All three halo profiles on the same scale for comparison. disk and bulge rotation curves by a factor proportional to D1/2. Finally, the factors of R

and derivatives with respect to R in the above equations are also aﬀected. In Figure 5.8,

we show the combined eﬀect of these relationships in models where NGC 2280 is 1.5 times

as distant (“farther”) and (1/1.5) times as distant (“closer”) compared to our assumed distance of 24.0 Mpc. Note that as the distance to NGC 2280 increases, the measurements move farther outward in radii and the halo contributes less to the total rotation curve.

The final source of uncertainty we consider is uncertainty in the vertical mass distribution of the disk in our models. While not mentioned above, the scale height also depends 107 on the distance to NGC 2280 through the scale length and the oblateness relation. The oblateness relation itself is somewhat scattered (Bershady et al. 2010b), leading to some uncertainty in the vertical mass distribution. In Figure 5.9, we show the disk contribution to the rotation curve in models with twice the vertical scale height (“high hz”) and half the vertical scale height (“low hz”). The effect of compressing the disk slightly increases the disk’s contribution to the rotation curve for two reasons – (1) matter in the disk is now closer to a test particle rotating in the disk’s midplane (and the gravitational force is therefore stronger), and (2) the unit vector from a test particle to the matter in the disk has a larger component along the radial direction (and therefore a larger fraction of the gravitational force contributes to the centripetal acceleration). Unlike changing the mass normalization and distance to NGC 2280, the differences between these 3 models produce very little difference between the halo density profiles. In fact, the difference between the disk rotation curves in these “high hz” and “low hz” models is less substantial than the differences between the different CMLR mass models in Figure 5.4.

As demonstrated above, the largest contributions to uncertainty in this analysis are the mass normalization and distance to the galaxy. If either the mass normalization or the distance to NGC 2280 (or some combination of these) are increased by a factor of 1.9, ∼ the disk becomes fully maximal. Because the uncertainty in the CMLR normalization is typically of order 60% (Courteau et al. 2014) and the uncertainty in distances from the ∼ Tully-Fisher relation is typically of order 30%, these mass models of NGC 2280 are still ∼ quite poorly constrained and could be made consistent with a maximal disk with relative ease.

5.6 Summary

Using the photometric observations of Kuzio de Naray et al. (2017, in prep.) and a number of CMLRs available from the literature we have produced maps of NGC 2280’s stellar mass at 1.800 resolution. We have then modelled these maps of stellar mass with the DiskFit ∼ 108

Figure 5.9 Disk contributions to the rotation curve (solid lines) in three mass models based on the “bell03” mass model - one with twice the vertical scale height (bottom curve), one with half the vertical scale height (top curve), and one the same as the “bell03” model (middle curve). Our Hα Fabry-Pérotrotation curve data are provided as circular points with error bars for comparison. 109 software, using the model outputs to predict the stars’ contribution to NGC 2280’s rotation curve. We have then combined these predicted rotation curves with the Hα Fabry-Pérot rotation curve measurements of Mitchell et al. (2017, submitted to A.J.) to determine the contribution of non-stellar matter to the rotation curve. Assuming that this matter is due to NGC 2280’s dark matter halo, we have derived halo density profiles for this galaxy and modelled them with common functional forms. In general, the consistencies of these various functional forms with the derived density profiles are very similar – i.e. these data do not strongly distinguish between the different functions.

We have also explored some of the most important assumptions that were used in producing these mass models and the uncertainties caused by these assumptions. By far the two most dominant effects are the uncertain distance to NGC 2280 and the uncertain normalization of the CMLRs. These two sources of uncertainty affect the stellar rotation curve contributions in similar ways, and their combined effect is to make the overall normalization of the stellar rotation curve highly uncertain. The assumption that all of the non-stellar mass of NGC 2280 belongs to the dark matter halo is also clearly untrue – galaxies also contain gas and we have not modelled the gas contribution to the rotation. Accounting for the gaseous disk of NGC 2280 would have a similar effect to increasing the mass normalization of the CMLRs discussed in Section 5.5.

The procedures of this section may be extended in a number of ways. As mentioned above, measurements of the galaxy’s gas (e.g. by CO and H I 21 cm observations) would allow for a more detailed accounting of the galaxy’s baryonic matter. If the distance to

NGC 2280 can be more precisely determined (e.g. by Type Ia SNe, TRGB, or Cepheids), the overall scaling of the baryonic contributions can be more tightly constrained. If the

Fabry-P´erotrotation curve data were combined with the lower-resolution H I rotation data

(Chapter 4), the density proﬁle of the halo may be constrained at larger radii than presented in this chapter.

Additional constraints on the baryonic matter distribution in NGC 2280 potentially 110 could be provided by dynamical modelling. While the Fabry-Pérotkinematic data on this galaxy do not strongly indicate the presence of a bar flow, the photometric DiskFit models of Kuzio de Naray et al. (2017, in prep.) indicate that this galaxy may have a bar. With an additional constraint on the position angle of the bar from the photometric models, it is possible that the signature of a bar flow may be extracted from the kinematic DiskFit models. We have searched for such a bar feature in the outdated kinematic data used in

Chapter 4 and were unable to detect one, though we have not yet repeated such a search for the updated, higher-spatial-resolution data presented in Chapter 2. If such a feature is found, an analysis similar to that of Weiner et al. (2001b) may be carried out. As mentioned in Chapter 1, these kinds of dynamic models can be used to constrain the mass normalization of the CMLRs by measuring the mass-to-light ratio of the bar. The prominent

(and highly symmetric) spiral arms in NGC 2280 may also make it conducive to another form of dynamical modelling – N-body simulations have shown that the multiplicity of spiral arms in a galaxy is related to the density of the disk (e.g. Sellwood & Carlberg 1984,

2014; D’Onghia et al. 2013). Like the bar kinematic modelling, this could place additional constraints on the mass normalization. 111

Chapter 6

Summary

Two-dimensional velocity ﬁelds of the Hα line of excited hydrogen at high spatial resolution are a useful tool in studying galaxy dynamics. In this document, we have introduced the medium-spectral-resolution Fabry-P´erotHα kinematic sample of the RSS Imaging- spectroscopy Nearby Galaxy Survey (RINGS) and have discussed and demonstrated methods that may be used to study the dynamics of these galaxies. The Hα kinematic data of

RINGS is being complemented by H I 21 cm data at lower spatial resolution and higher spectral resolution, as well as multi-band optical photometric data.

In Chapter 2, we introduced the medium-spectral-resolution Hα kinematic portion of

RINGS and discussed the data reduction procedures we have developed in order to extract line-of-sight velocities from the SALT Fabry-P´erotdata. We presented kinematic maps of the Hα line at spatial resolutions of 100-300 pc in the 14 galaxies that comprise the ∼ sample. We also presented maps of the continuum R-band surface brightness, Hα line intensity, and [N II] line intensity in these galaxies. The R-band surface brightness proﬁles are qualitatively similar to the photometric measurements of Kuzio de Naray et al. (2017, in prep.). We then used the ratio of the [N II] line intensity to that of Hα to derive oxygen

abundance gradients for these galaxies.

In Chapter 3, we presented axisymmetric kinematic models of the 14 Hα velocity ﬁelds

of Chapter 2. These models were used to extract rotation curves from our measurements

of these galaxies at high spatial resolution. In addition, the models place constraints on

the projection of these galaxies in the plane of the sky. The rotation curves were compared

to previous measurements available from the literature, and the projection geometries were 112 compared to those derived from the photometric models of Kuzio de Naray et al. (2017, in prep.). In most cases, we found agreement among the measurements of the different data sets. In some cases, significant differences were found. One potential cause of these differences could be that these galaxies reside in asymmetric dark matter halos, though other explanations are also possible.

In Chapter 4, we compared our Hα kinematic map of NGC 2280 with an H I kinematic map for the same galaxy. We also compared axisymmetric models of these two velocity maps. In general, there is very close agreement between the two sets of measurements.

However, there are also significant regions of correlated difference between the two maps, which we investigated further by modelling the approaching and receding sides of the galaxy separately. This separation makes it clear that the H I velocity field is asymmetric in a way in which the Hα velocity field is not, which could be the signature of a stream of neutral gas flowing in or out of the galaxy.

Finally, in Chapter 5, we combined our Hα measurement of NGC 2280’s rotation curve with the photometric measurements of Kuzio de Naray et al. (2017, in prep.) to produce models of that galaxy’s stellar mass distributions and place constraints on its halo density profile. We found that these sets of data were insufficient to strongly distinguish between multiple common dark matter halo density profiles, primarily due to the large uncertainties in the mass normalization of CMLRs and the distance to NGC 2280.

The analysis performed here may be extended in a number of ways. First, the analysis of Chapters 4 and 5 may be reproduced for the other 18 RINGS galaxies as more data become available. In the case of the ﬁve galaxies that were not observed in the SALT

Fabry-P´erot’smedium-spectral-resolution mode before it was decommissioned, the higher- spectral-resolution data cubes will allow for even more precise measurements of the line-of- sight velocities at each spatial resolution element.

The distances to three of the RINGS galaxies (NGC 45, NGC 247, and NGC 7793) are much more tightly constrained than the distances of the other galaxies. These three galaxies 113 are so nearby that individual stars can be resolved, permitting the determination of much more accurate distances. Furthermore, the close proximity of these galaxies will allow for kinematic measurements to be taken at much higher physical resolution (e.g. < 100 pc) due to the decreased angular scale. The combination of these factors means that the methods of

Chapter 5 may be applied to these galaxies with signiﬁcantly fewer sources of uncertainty, allowing for much more precise constraints to be placed on these galaxies’ dark matter halos.

As mentioned in Chapters 1 and 5, the dynamics of non-axisymmetric structures galaxies such as bars (Weiner et al. 2001b; Sellwood & S´anchez 2010) and spiral arms (Sellwood &

Carlberg 1984, 2014; D’Onghia et al. 2013) may be used to place additional constraints on the mass-to-light ratio of the disk. Many of the RINGS galaxies exhibit such structures to varying degrees. For example, NGC 578 has a very prominent bar, NGC 2280 and

NGC 6384 may have bars, and nearly all of the RINGS galaxies have very regular spiral arm patterns.

In our ongoing work, we plan to produce non-axisymmetric models of the barred galaxies in the RINGS sample. If the data are of suﬃcient quality to extract information about the bar kinematics, the resulting gas ﬂow measurements may be used to directly measure the mass-to-light ratio of the bar. Combined with an analysis of the type performed in

Chapter 5, we may be able to signiﬁcantly improve the constraints on the mass distributions of the galaxies in the RINGS sample. 114

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