QUANTITATIVE ANALYSIS of 3-ARM SPIRAL GALAXIES By

QUANTITATIVE ANALYSIS OF 3-ARM SPIRAL GALAXIES

by COLIN HANCOCK WILLIAM KEEL PREETHI NAIR JEREMY BAILIN BROOKE SIMMONS

A THESIS

Submitted in partial fulﬁllment of the requirements for the degree of Master of Science in the Department of Physics and Astronomy in the Graduate School of The University of Alabama

TUSCALOOSA, ALABAMA

A relatively small fraction of spiral galaxies has three spiral arms. It has been theorized that these “3-arm spirals” are relatively unstable and prone to decaying into even numbered patterns due to tidal interactions. We present a series of quantitative analyses on a large sample of 3-arm spiral galaxies selected by the Galaxy Zoo 2 group. Much of this analysis used the image processing interface known as the Spiral Arc Finder and Reporter (SpArcFiRe). This program traced spiral arms on submitted images of galaxies and provided information that allowed us to replicate the arms in another program like MS Excel. Most of our work involved images taken from the Sloan Digital Sky Survey (SDSS), supplemented with high-resolution Hubble Space Telescope (HST) observations. This allowed us to study the morphological demographics of our sample, for both the internal structure and arm symmetry. The HST images provided special insight into spiral structure and star formation for these galaxies. We analyzed the star formation in particular using the MIRA AL software for photometry. We also attempted in improve the signal-to-noise of our images using data from the Stripe 82 region of SDSS. Unexpectedly, 3-arm patterns coexist with strong central bars roughly as often as other spiral patterns. We also found that 3-arm spirals do not preferentially exist in low-density regions and may be triggered by interactions.

ii DEDICATION

For my family who kept me grounded, and my friends who kept me sane.

iii LIST OF ABBREVIATIONS AND SYMBOLS

ACS Advenceed Camera for Surveys DECaLS Dark Energy Camera Legacy Survey DR7/12 Data Release 7/12 ESA European Space Agency FITS Flexible Image Transport System GZ2 Galaxy Zoo 2 HST Hubble Space Telescope IC Index Catalogue NASA National Aeronautics and Space Administration NGC New General Catalogue PC1 Planetary Camera 1 SDSS Sloan Digital Sky Survey SFR Star Forming Region SpArcFiRe Spiral Arc Finder and Reporter SSPSF Stochastic Self-Propagating Star Formation WFPC2 The Wide Field Planetary Camera 2

iv ACKNOWLEDGMENTS

Firstly, I would like to express my gratitude to my advisor Dr. Bill Keel for his endless support of my research, as well as the myriad advice and discussions throughout my time here. I would also like to thank the rest of my thesis committee: Dr. Jeremy Bailin, Dr. Preethi Nair, and Dr. Brooke Simmons. Especially Drs. Bailin and Nair, for their teaching and advising over the course of my graduate school career. I extend my thanks to Drs. Bruce and Debbie Elmegreen for their contributions, both for their work before our research and their input in the midst of it. I am also grateful to the creators and participants of the Galaxy Zoo 2 project, without whom none of this would have been possible. I would also like to thank Dr. Amy Jones, for taking the time to proofread this work (among other things).

v CONTENTS

ABSTRACT...... ii DEDICATION...... iii LIST OF ABBREVIATIONS AND SYMBOLS...... iv ACKNOWLEDGMENTS...... v LIST OF TABLES...... vii LIST OF FIGURES...... viii 1 INTRODUCTION...... 1 2 METHODS...... 4 3 ANALYSIS...... 12 3.1 Morphological Types ...... 12 3.2 SpArcFiRe and Excel ...... 14 3.3 HST Data ...... 17 3.4 Stripe 82 ...... 23 4 CONCLUSION...... 26 5 REFERENCES...... 46

vi LIST OF TABLES

2.1 Table explaining each step in Figure 2.6...... 11

3.1 Sorting of galaxies according to internal morphology and arm symmetry, with corresponding percentages across from each label...... 12

3.2 Data for each HST image from Figure 3, primarily from the FITS Headers. 18

3.3 Coordinates and brightness of each SFR labelled in Figure 3.7...... 23

4.1 Candidate 3-arm spirals examined...... 29

vii LIST OF FIGURES

1.1 A comparison of a grand design galaxy with a ﬂocculent spiral galaxy . . . 2

2.1 Decision tree for Galaxy Zoo 2, taken from Willett et al. [20]...... 5

2.2 Histogram showing the distribution of neighbor density for galaxies from the 3-arm GZ2 sample...... 6

2.3 Histogram showing the distribution of redshifts for galaxies from the 3-arm GZ2 sample...... 7

2.4 Chart displaying the pitch angles taken from Kennicutt [14] alongside the corresponding average angles reported by SpArcFiRe for the 40 galaxies that were observed by SDSS...... 8

2.5 Chart describing the correlation of pitch angles described by Kennicutt [14] with the average angles reported by SpArcFiRe for the 40 galaxies that were observed by SDSS...... 9

2.6 Example of the processing undertaken by SpArcFiRe...... 10

3.1 A visual display of the galaxies from our sample sorted according to internal morphology and arm symmetry...... 13

3.2 Example of galaxy arcs from SpArcFiRe replicated in MS Excel...... 16

3.3 Example of a galaxy whose arms have very little overlap in radius...... 17

3.4 Cropped images of the two spiral galaxies that we obtained HST data for. . 18

3.5 Comparison of SDSS 1704 images taken with SDSS and HST...... 19

3.6 Zoomed-out and rotated image of SDSS 1704 with an interacting companion. 20

3.7 Side-by-side comparison of IC 3528 with and without photometric regions. 22

viii 3.8 Side-by-side comparison of SpArcFiRe analysis from SDSS DR12 and Stripe 82...... 25

4.1 Montage of 3-arm spiral candidates paired with their corresponding ﬁnal SpAr- cFiRe outputs, showing the overlaid logarithmic spiral arcs...... 34

4.2 Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued)...... 35

4.3 Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued)...... 36

4.4 Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued)...... 37

4.5 Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued)...... 38

4.6 Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued)...... 39

4.7 Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued)...... 40

4.8 Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued)...... 41

4.9 Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued)...... 42

4.10 Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued)...... 43

4.11 Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued)...... 44

4.12 Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued)...... 45

ix 1 INTRODUCTION

A large fraction of galaxies in our local universe are what we refer to as “Spirals.” These possess features such as a flat disk profile, a dense central bulge, and the epony- mous spiral arms that extend from the center. In addition, they may also have a bar- shaped mass distribution across their center, as well as diffuse spherical halos containing star clusters and dark matter. Ever since their spiral nature was first observed in the 1800’s by William Parsons, 3rd Earl of Rosse, they have been captivating astronomers with their vibrant colors and elegant structure. While they are some of the most visually striking objects in the universe, it is still somewhat unclear how exactly the spiral structure is formed. One of the fundamental problems of spiral arms is why they do not “wind up.” That is, given that these galaxies are differential rotators, their arms should wind more and more tightly after only a few galactic rotations. The universe is roughly 14 billion years old, while galactic rotation periods are on the order of several hundred million years. Since we still see plenty of spirals, there must be some mechanism stabilizing the spiral arms (D’Onghia [10],Masters et al. [17]). The two prevailing (but not mutually exclusive) theories regarding this are: the density wave theory and the stochastic self- propagating star formation (SSPSF) model. Under density wave theory (or Lin-Shu theory after Lin & Shu [15]), the spiral arms are comprised of a long-lasting and self-propagating density pattern with a particular speed that is independent of the stars and gas in the disk. This results in the leading edge of the density waves compressing the matter as they pass through, causing a wave of star formation as well as enhancing its own density. By contrast, in the SSPSF model from Seiden & Gerola [19] shock waves from supernovae perturb the interstellar medium,

1 triggering more star formation. With the differential motion of stars in the disk this cre- ates the spiral pattern. While both theories are valid, SSPSF is more generally applica- ble (and works for irregular galaxies as well). Conversely, density wave theory is strictly relevant to spirals. These two methods of arm formation also apply to the different variations of spiral arms. Two broad categories of spirals are known as “grand design” and “flocculent.” Grand design spirals possess well-defined and easily distinguishable arms, while flocculent spirals are “fluffy” with arms that are broken-up and fuzzy (defined in optical). A comparison of the two types can be found in Figure 1.1. Broadly speaking, density wave theory is better for explaining grand design galaxies, while SSPSF is better for flocculent spirals. The majority of spiral galaxies fall somewhere between these two ends of the spectrum, with 10% classified as grand design and 30% considered flocculent (Elmegreen & Elmegreen [12]). As the nature of our work requires being able to clearly see individual spiral arms and it is extremely difficult (if not impossible) to count flocculent arms, the majority of galaxies in our sample lean more towards the grand design type.

Fig. 1.1.: A comparison of a grand design galaxy (M81, ESA/Hubble, left) with a ﬂoccu- lent spiral galaxy (NGC 4414, NASA/ESA/Hubble/SDSS, right).

Spiral arms contain the majority of the cold gas and star-forming regions (SFR’s) in the galaxy. Of the multi-arm spiral galaxies that are observed in the local universe, a majority of them have either two or four spiral arms. More rare are spirals with three

2 spiral arms, as seen in Willett et al. [20]. The reason for this scarcity of odd-numbered spiral modes has been a source of speculation for some time now. One theory for why 3-arm spiral galaxies are relatively rare is that they are potentially unstable. Accord- ing to Elmegreen et al. [11] 3-arm spirals may be susceptible to being dynamically re- settled into an even-numbered mode by major interactions. The idea is that a twofold symmetrical tidal stress on a threefold symmetry pattern would result in the relatively unstable threefold symmetry decaying into an even symmetry. This implies that these galaxies should be isolated (i.e. not in a cluster). We seek to investigate the properties and characteristics of the 3-arm spiral galaxies identiﬁed by the Galaxy Zoo collabora- tion (Lintott et al. [16]), to broaden our understanding of these objects, including testing this particular hypothesis.

3 2 METHODS

The sample of potential 3-arm spiral galaxies that we had to analyze was selected by the Galaxy Zoo group. Galaxy Zoo1 is a citizen science program meant to invite large numbers of people to assist in classifying galaxies. Volunteers are directed to classify galaxies according to their morphology. The sample of galaxies used for this study came from the Galaxy Zoo 2 (GZ2) project, which focused on the brightest 250,000 Sloan Digital Sky Survey2 (SDSS) galaxies. It also offered participants a much wider range of classification options than the original Galaxy Zoo, in particular the number of spiral arms (following the decision tree shown in Figure 2.1). SDSS is a large-scale imaging and spectral survey covering roughly 35% of the sky (Abazajian et al. [1]). The median redshift of galaxies in SDSS is about 0.1, corresponding to a lookback time of roughly 1.3 Gyr (Willett et al. [20]). The galaxies for the list were selected via a plurality of vis- itors designating them as having three arms. The list contained the SDSS Data Release 7 (DR7) ID number, equatorial coordinates, redshift, and logarithmic neighbor density for each galaxy. A table showing these values for the galaxies examined for this study is shown in Table 4.1 at the end of this paper. The total number of potential 3-arm spirals was 1392. Since the list was sorted in order of increasing SDSS ID (effectively random in position), we simply went down the list sequentially. Currently we have analyzed 240 of these galaxies, of which 121 were resolved enough to merit further analysis after visual inspection. We used the SDSS Data Release 12 (DR12) Image List Tool3 to accelerate the process, as it allowed us to view multiple galaxies at once and permitted quick viewing of each one (Alam et al. [3]).

1URL: data.galaxyzoo.org 2URL: http://skyserver.sdss.org/dr12/en/tools/chart/navi.aspx 3URL: http://skyserver.sdss.org/dr12/en/tools/chart/listinfo.aspx

4 Fig. 2.1.: Decision tree for Galaxy Zoo 2, taken from Willett et al. [20].

To examine the environment of the galaxies that we looked at, we made histograms of the neighbor density (Figure 2.2) and redshift (Figure 2.3) for the 240 galaxies that we visually inspected. The neighbor density is given in units of log(Σ), where Σ is de- ﬁned by Baldry et al. [6] as the projected number density with units of Mpc−2. Based on that same paper; we consider a void-like environment to be ≈ −1.5 log(σ), while a cluster environment would be ≈ 1.5 log(σ). Based upon our graph, it appears that a large majority of galaxies in our visually inspected sample are in a “ﬁeld” distribution that does not lean strongly towards a void or cluster. With regards to redshift, the main thing worth mentioning is that our inspected sample starts being biased towards increas- ingly brighter galaxies with redshift. This is a manifestation of the Malmquist bias, and is fairly standard when analyzing galaxy morphology.

5 Fig. 2.2.: Histogram showing the distribution of neighbor density for galaxies from the 3-arm GZ2 sample. The x-axis values mark the upper limits of each bin. A void-like distribution is ≈ −1.5, while a cluster-like distribution would be ≈ 1.5 (Baldry et al. [6]). This implies a majority of galaxies in our sample are in a “ﬁeld” distribution.

The main method we used to analyse these candidates was by taking the best- resolved galaxies from the list and running them through an online software program called SpArcFiRe (Spiral Arc Finder and Reporter; Davis & Hayes [9]). This software operates by fitting logarithmic spirals over the brightest areas of the submitted galaxy to trace the path of the spiral arms. The online interface takes a submitted image (either a JPEG, PNG, or FITS file) and processes it by cropping, centering, deprojecting, and enhancing the contrast of the galaxy. It uses an iterative 2D Gaussian fit to locate the center of the galaxy and rotates the image so the major axis is vertical. Assuming the galaxy is circular when viewed face-on, it then linearly deprojects the image to recre- ate that face-on view. It then outputs a number of images highlighting the processing steps taken (Figure 2.6, Table 2.1), along with several data files outlining the quantita-

6 Fig. 2.3.: Histogram showing the distribution of redshifts for galaxies from the 3-arm GZ2 sample. The x-axis values mark the upper limits of each bin. Above redshifts of ≈ 1.0 we start biasing towards progressively brighter galaxies, as a manifestation of the Malmquist Bias. This results in the extended tail on the higher end. tive properties of each spiral arc. The most useful properties from the numerical data outputs are the pitch angle and curvature constants, which allow for further quantitative analysis. To test the robustness of SpArcFiRe, we compared the pitch angles reported by Robert Kennicutt of 106 bright, nearby NGC galaxies (40 of which were also in SDSS) with the average angle derived from SpArcFiRe (Kennicutt [14]). We also looked up the morphological type for each galaxy to investigate if SpArcFiRe had any sort of system- atic bias. Speciﬁcally, we used the scheme devised by de Vaucouleurs, which divided spiral galaxies mostly by arm tightness. These galaxies ranged from Sa to Sc, corresponding to numerical Hubble stage T 1-5. We compared the average pitch angle of the arms reported by SpArcFiRe to the value reported in Kennicutt [14] for each of the 40 galaxies

7 Fig. 2.4.: Chart displaying the pitch angles taken from Kennicutt [14] alongside the corresponding average angles reported by SpArcFiRe for the 40 galaxies that were observed by SDSS. X-axis values correspond to Hubble stage T 1-5, Y-axis is deﬁned as the absolute pitch angles for both samples. that were observed by SDSS (Figure 2.4, Figure 2.5) . All of the morphological types showed a wider spread of angles from SpArcFiRe than the Kennicutt results. In addition, the pitch angles from SpArcFiRe tend to be higher than those reported in Kenni- cutt [14], especially the early-type Sa galaxies. However, in spite of these issues SpArc- FiRe yields reasonably good results for pitch angle, so we proceeded with using it for the more in-depth parts of our research. One of the main features of these spirals that we used to categorize them was their level of symmetry. This is a particular issue for the odd-numbered spiral modes. We deﬁne spirals with an evenly spaced threefold symmetry as “symmetric” (i.e. with

8 Fig. 2.5.: Chart describing the correlation of pitch angles described by Kennicutt [14] with the average angles reported by SpArcFiRe for the 40 galaxies that were observed by SDSS. X-axis values correspond to Hubble stage T 1-5, Y-axis is defined as SpArcFiRe - Kennicutt pitch angles, as seen in Figure 2.4. equal angular separations around 120◦ each). The other extreme of this resembles a grand design spiral with a third arm halfway between them, where the angular separations are close to 90◦-90◦-180◦. We refer to those types of galaxies as “offset.” While none of these galaxies line up perfectly with these idealized criteria, quite a few lean more towards one over the other. A third category of “unclear” covers everything that doesn’t lean strongly towards one side or the other. In addition to sorting galaxies by symmetry, we also divide them according to their apparent internal structure. Specifically, we made note of whether the galaxies had a central bar structure, a bar and ring, or neither via visual inspection. We note that while SpArcFiRe does conduct some deprojection on submitted images, there are limits

9 Fig. 2.6.: Example of the processing undertaken by SpArcFiRe. Explanations of each step are shown in Table 2.1. The diagonal dark line is a chip gap from the original SDSS image.

10 1. Input image from SDSS. 2. Image cropped, centered, zoomed in, and deprojected.

3. Enhanced the image con- 4. Bright pixel clusters used trast. to outline arms.

5. Initial arm segments over- 6. Initial arcs superimposed laid with the associated on deprojected image. Arc logarithmic spiral arcs ﬁtted color indicates chirality. to these clusters.

7.Final clusters and associ- 8. Final arcs superimposed on ated arcs found by merging the image. compatible arcs Table 2.1.: Table explaining each step in Figure 2.6. Positions of descriptions correspond to those in 2.6. For more detailed explanation see Davis & Hayes [9]. to what it can feasibly do. For strongly inclined galaxies, SpArcFiRe can noticeably dis- tort them and reduce their usefulness for analysis. This resulted in a bias towards face- on galaxies, though that may be present from the original selection from Galaxy Zoo (i.e. it is easier to count arms with galaxies that are face-on).

11 3 ANALYSIS

3.1 Morphological Types

Contrasting the various combinations of internal morphology and symmetry together allows us to analyze broad trends in the entire sample (Figure 3.1). From these results we see some interesting patterns emerge. In terms of symmetry, galaxies designated as offset outweighed both symmetric and unclear galaxies. This is not entirely un- expected, since uneven symmetry is relatively difficult to maintain in nature. Looking at morphology, we see fairly even distributions between the three designated categories. However, this belies an important point; roughly two thirds of the analyzed galaxies had some sort of bar structure. This is somewhat surprising, as one would intuitively think that a twofold interior symmetry would suppress an exterior threefold symmetry. How- ever, these data imply that having a bar structure has no negative effect on forming a three-arm spiral (and may even encourage it). The percentages listed in Table 1 were roughly the same after increasing the sample size (from 180 to 240 galaxies), implying that it’s a fairly consistent pattern.

Unbarred Barred Bar + Ring Symmetric 19 5 8 26.4 % Offset 16 28 23 55.4 % Unclear 10 8 4 18.2 % 37.2 % 33.9 % 28.9 % Table 3.1.: Sorting of galaxies according to internal morphology and arm symmetry, with corresponding percentages across from each label. There are 121 classified galaxies in total. The classification bins are organized the same way as Figure 3.1.

It is worth comparing the results from our symmetry sorting to general results for spirals at similar redshifts. According to Nair & Abraham [18], strong bars occurred

12 Fig. 3.1.: A visual display of the galaxies from our sample sorted according to internal morphology and arm symmetry. Examples of each type (taken from SDSS Data Release 7) presented with the total numbers of each type overlaid. The classification bins are organized the same way as Table 3.1. in 28±3% of galaxies in redshift ranges similar to our sample. The “strong” qualifier is important as Galaxy Zoo 2 can only detect easily seen bars. We are most likely biased towards strong bars, since this was done by visual inspection of the SDSS images. Ad- ditionally, Willett et al. [20] reports that Galaxy Zoo 2 showed galactic bar fractions of about 35% over a wide redshift range. Looking at Table 3.1 and using binomial statis- tics as appropriate for a binary property, we classified a combined 62.8±4.4% of galax-

13 ies in our sample with having bars (with a corresponding 37.2±4.4% unbarred fraction). Our bar fractions display a statistically significant difference from these previous studies, with barred spirals occurring at nearly twice the rate of unbarred ones. This is very un- expected, given our initial hypothesis that interior twofold symmetric structures would suppress threefold exterior patterns. When we look at just the symmetric galaxies, we find a barred fraction of 40.6±8.7%. Conversely, offset spirals display a bar fraction of 76.1±5.2%. Spirals with unclear symmetry fall in-between with 54.5±10.6%. What this tells us is that symmetric spirals have a bar fraction within 1-σ of the typical results, while offset ones show major discrepan- cies beyond 4-σ of previous studies. Given how dominant offset galaxies are (comprising over half of our sample), it is odd that they are the least like typical spiral galaxies. We also see a possible trend of spirals leaning more towards higher bar fractions with more offset symmetry. This could indicate anything from an evolutionary process to a difference in formation. While we can’t make many major conclusions based upon this, it is still interesting to note. We should also discuss those galaxies identified as having ring structures. In both Figure 3.1 and Table 3.1 they are labeled as “Bar + Ring” galaxies. While there are cer- tainly galaxies with rings and not bars, we found it rather difficult to identify them at these redshifts. The result is that bars make it easier to see the rings in the first place. We identified a significant fraction of galaxies as having bars and rings (28.9%). How- ever, it can be difficult to distinguish true rings from “pseudorings” (Buta & Combes [7]) - which are tightly wound spiral arms that nearly overlap - given the resolution limits of images from SDSS. An example of this is shown in Figure 3.5.

3.2 SpArcFiRe and Excel

As part of our eﬀorts to conduct qualitative analysis of these galaxies, we attempted to replicate the arcs drawn by SpArcFiRe in Microsoft Excel. This was made

14 possible by using the values from the output files for each SpArcFiRe analysis. The particular values used were: the pitch angle (ψ), initial theta (θi), starting radius (Ri), and some constants of curvature (a, b). The equation used for plotting a logarithmic spiral was R = aebθ. a is derived from the initial radius, while b is defined as the cotangent of the pitch angle ψ. In this context, radius (R) is defined as pixels from the center of the galaxy. These values were unique for each arm drawn on the galaxy, which are listed in the out put files in descending order of arc length. The advantage of plotting in Excel was that it was relatively easy to plot discrete points. In order to unwind the spiral arcs, 10 points along each arm were calculated in polar coordinates from the initial to final radii (in units of pixels). Plotting these positions on overlapping scatter plots allows us to replicate the arcs overlaid on the inputted galaxies. In addition to replicating the drawn arcs, the Excel plots also provide a quantitative method of organizing galaxies by the symmetry of their arms. Specifically, if we have the angular coordinates of each arm over the same radial range, we can evaluate their angular separations at the same radius. Not only can this give us a general idea of a galaxy’s symmetry, it also allows us to investigate whether the angular separations change as a factor of radius. To be done properly, this would require taking the angular separations at discrete radii along the arms. We also observed that there can be significant variation of pitch angles between individual arms in the same galaxy. This can be seen by comparing the slopes of the curves drawn in angular space. Often there would be two arms with similar pitch angles and a third with a significantly different one. Un- fortunately there are severe limitations to this technique. In addition to the fact that it requires having a galaxy with three well-resolved arms (i.e. identified by SpArcFiRe), there is also no guarantee that those arms overlap significantly in radius (Figure 3.3). The result is that this technique is very limited in terms of how many galaxies it can be applied to, making it often simpler to judge a galaxy’s symmetry by eye instead.

15 Fig. 3.2.: Example of galaxy arcs from SpArcFiRe replicated in MS Excel. Shown are the original SpArcFiRe output (upper left), the primary arms recreated in Excel using values from the SpArcFiRe data ﬁle in units of pixels (upper right), the arms redrawn in Cartesian space of pixels vs angle (lower left), and the Cartesian arms truncated for overlap in radius with discrete data points at equal radii (lower right). For the last panel, the Y-axis has been zoomed in to better present the overlapping radii of the arms.

16 Fig. 3.3.: Example of a galaxy whose arms have very little overlap in radius.

3.3 HST Data

While a major portion of our work focused on images taken from SDSS, we supplemented our sample with other sources. The primary reason for this was to acquire higher-resolution views of individual galaxies. Being able to view galaxies in greater de- tail enables us to conduct more in-depth analysis than would be feasible with just SDSS. Of particular use to us were images taken by the Hubble Space Telescope (HST), which provides some of the best-resolved optical images. There are some major limitations to the number of galaxies that we can obtain Hubble images for. In addition to there being extreme competition for active observing on HST, it can be difficult to find three-arm galaxies in the archive without knowing specifically that they are there. We searched the archive for the coordinates of a large number of galaxies from our sample, but were unable to find any additional centered galaxies. As a result, there are only two galaxies in our research that we were able to acquire HST images for (Figure 3.4; Table 3.2). The first galaxy that we obtained HST data for was SDSS J170414.33+620234.0 (SDSS 1704). We gathered the data thanks to the Galaxy Zoo gap-filler program called Zoo Gems (HST Proposal 15445). The Zoo Gems program is meant to provide lists of

17 Fig. 3.4.: Cropped images of the two spiral galaxies that we obtained HST data for. (Left: SDSS 1704, 2600x2600; Right: IC 3528, 2200x2200)

SDSS 1704 IC 3528 Camera ACS WFPC2 (PC1) Filter F475W F814W Exposure Time [s] 674 464 Date Observed 2018-07-06 2009-11-06 Right Ascension 17:04:14.36 12:34:55.9 Declination +62:02:33 +15:33:56 Hubble Type Sc SBa Redshift Distance (Mpc) 377 185 Arcsec per Pixel 0.049 0.0455 Table 3.2.: Data for each HST image from Figure 3, primarily from the FITS Headers. potential targets for short HST observations in-between major projects. These exposures are generally only 10-12 minutes long, though that is more than enough for our purposes given that the galaxies in our sample have relatively high surface brightness and resolution already. Galaxy Zoo participants were given a list of objects to choose from, and we presented three of the best-resolved spirals from our sample for their consideration. Of those, the one that was ﬁrst observed was SDSS 1704 (Figure 3.5). The second galaxy with HST data was IC 3528. This galaxy was not taken from our original sample list; rather, it was coincidentally noticed on the edge of an unrelated observation as part of another project of Dr. Keel’s research. A follow-up search of the

18 Fig. 3.5.: Comparison of SDSS 1704 images taken with SDSS (left, 4000x4000) and HST (right,2600x2600). Note the dramatic improvement in resolution and the absence of the chip gap, with ring/pseudoring structure that is not visible in the SDSS image.

Hubble Legacy Archive turned up a centered image for it, allowing us to use it in our work. Unfortunately, we were unable to find any more images from the Legacy Archives by searching their coordinates. HST observations are especially useful for analyzing internal structure and star- forming regions (SFR’s). Both subjects are relevant to our broader interest in the evolutionary history of 3-arm spirals. These examples we obtained are no exception. While SDSS 1704 does not possess a bar structure, it still contains a surprising internal pattern. Going by the directions in Figure 3.4, the right-side arm seems to curl all the way to the bulge with the other two arms extending off at closer points. Plus, there is an asymmetric arm opposite the larger and longer one that joins back in on the other side. This results in a twofold symmetric spiral inside a threefold pattern. Another way of looking at it is viewing the three outer arms as attached to a triangular, off-center ring. This ring then has one small arm inside it. In addition, the outer portion of the long arm is distinguishable by having greater amounts of star formation than the other two.

19 Fig. 3.6.: Zoomed-out and rotated image of SDSS 1704 (left) with an interacting companion (right). Their angular separation is roughly 41.500, corresponding to a physical distance of ≈ 65 kpc.

So not only does this galaxy possess multiple concentric spiral patterns, the outer 3-arm pattern is itself asymmetric. These strange patterns appear indicative of galactic interaction, i.e. the gravity from a nearby galaxy is warping and distorting it. As it turns out, there is in fact a nearby galaxy at a comparable redshift (as seen in Figure 3.6). Speciﬁcally, while SDSS 1704’s redshift places it at 377 Mpc, the photometric redshift of the companion lies around 350 Mpc. All things considered, it is a great stroke of luck to have a face-on companion observed in the same ﬁeld of view. It should be noted that the long and most active outer arm is oriented towards the companion, which is a source of long debate in interacting spirals (Arp [5],Hodge [13]). Conversely, the companion is highly asymmetric, with all of its arms on the same side pointing towards SDSS 1704. Of course the reason that this is all relevant is that one of our initial assumptions was that 3-arm spirals form and exist in isolation, as the tidal stress from interactions would result in it decaying into an even-numbered spiral mode. Yet here we see a well-

20 defined 3-arm structure in the middle of a major interaction. This appears to provide strong evidence against the isolated formation hypothesis. In fact, it is possible that the tidal forces from the interaction is what caused the 3-arm structure in the first place (B.G. Elmegreen, Private Communication) When it comes to star formation, SDSS 1704 is a mixed bag. On the one hand, it displays significant amounts of star formation in its inner region (which we define as distinct bright regions in the disk). However, these SFR’s are very densely packed, making it difficult to isolate individual ones for photometric analysis. Even so, we can still make some general observations about the distribution of SFR’s in the disk. Other than the small inner arm on the east side of the bulge, most of the inner disk is covered with SFR’s. At a certain radius though, this star formation cuts off. In particular, the two eastern arms have distinct “kinks” where the pitch angle changes and star formation halts. Tellingly, the western arm (oriented towards the interacting partner) has SFR’s along the length of it. This indicates a significant difference between the arms, and gives weight to the idea that the western arm was either formed or distorted by the interaction. Moving on to IC 3528, this galaxy appears to have a fairly standard appearance. It contains a very distinct bar structure, with either a ring or arms so tight that they appear ring-like. This galaxy is a very good representation of an offset galaxy, with two clearly “primary” arms extending from the ends of the bars and one roughly halfway between them. Oddly, the third arm (on the left side of the figure) seems to fork off from the primary one shortly after where it joins the bar. While the overall structure of this galaxy is perhaps unimpressive, it is extremely useful for performing photometry on its SFR’s. The reason for this is that the individual regions are very distinct and contrast well with the rest of the disk. This makes it a straightforward task to place individual regions on each patch without much of an issue with overlapping. This is in contrast to SDSS 1704, where the SFR’s are plentiful

21 but very tightly packed together. With regards to the positions of the SFR’s, they seem strongly biased to the outer half of IC 3528’s disk. However, this is typical for an “early- type” barred spiral. The bar and the arms to a certain radius appear devoid of star formation. Oddly, there is no accompanying change in pitch angle where the star formation begins.

Fig. 3.7.: Side-by-side comparison of IC 3528 with and without photometric regions.

In order to conduct photometry on these SFR’s, we used a software program called Mira AL x641. This program has similar uses to the ubiquitous astronomy software, ds9. Speciﬁcally, both programs allow us to manipulate the contrast and brightness of the images. The major capability of Mira is that one can place photometry zones on individual SFR’s and use them to automatically calculate the photon counts and apparent magnitude within the source region. An example of the region placement on IC 3528 is shown in Figure 3.7, with the values for each region shown in Table 3.3. This allows us to analyse the amounts of star formation in these galaxies quantitatively. Each photometric region is composed of a circular source region and a concentric background annulus. Mira will also automatically place the centroid of the source region

1URL: www.mirametrics.com/mira al x64.php

22 RA Dec Net Counts/Second m814 M814 12h34m56.242s 15◦33050.38600 5.73879 24.89 -11.45 12h34m55.861s 15◦33051.80600 8.3061 24.49 -11.85 12h34m56.112s 15◦33050.07800 2.1956 25.93 -10.41 12h34m56.034s 15◦33050.47800 3.94953 25.29 -11.05 12h34m55.989s 15◦33050.23500 1.80985 26.14 -10.2 12h34m56.307s 15◦33050.27300 1.74743 26.18 -10.16 12h34m55.873s 15◦34001.56700 2.02152 26.02 -10.32 12h34m55.749s 15◦34001.50100 2.8805 25.64 -10.7 12h34m55.618s 15◦34001.02300 2.3678 25.85 -10.49 12h34m56.173s 15◦34001.78100 8.24995 24.49 -11.85 12h34m56.190s 15◦34000.95500 3.3672 25.47 -10.87 12h34m56.139s 15◦33059.84200 2.58011 25.75 -10.59 12h34m56.235s 15◦34000.04800 3.35646 25.47 -10.87 12h34m56.249s 15◦33059.31700 2.28286 25.89 -10.45 12h34m56.295s 15◦33059.28400 1.56301 26.3 -10.04 Table 3.3.: Coordinates and brightness of each SFR labelled in Figure 3.7. Magnitudes found using the STMAG offset of 26.784 for the F814W filter, and using a distance of 185.1 Mpc (Hubble flow). on where it thinks the center of the SFR is. This can be handy if the regions are distinct, but it can lead to problems when attempting to distinguish between nearby SFR’s where it will default to one over the other. This means that Mira is much more useful for galaxies like IC 3528 with spread-out and distinct SFR’s, as opposed to SDSS 1704 where they are more tightly packed. The radii of the source and background regions can be individually adjusted, though this will change the bounds for all regions in the field. This means one must be careful to keep sources out of the background annuli of other regions.

3.4 Stripe 82

While it is always nice to have high-quality data from HST on hand, it is also difficult to acquire large amounts of it. Therefore, if we want to do photometry on large numbers of galaxies, we need to find ways to supplement our sample with galaxies from the Galaxy Zoo list. Specifically, we pick from the best-resolved galaxies that we have analyzed and use images of them from the SDSS archive for photometry. To that end, we selected FITS files from the SDSS r-filter since that one generally had the highest

23 photon counts of the five filters available. While the regions from Mira presented their own estimations of apparent magnitude, we still wanted to calibrate their accuracy by comparing the magnitudes reported in Mira to those from SDSS Data Release 12 (DR12). While we couldn’t directly compare magnitudes for SFR’s in DR12 directly, we could compare individual stars in Mira and DR12. The method for calculating magnitudes from the photon counts listed in Mira followed the formula: mapp = −2.5 ∗ log(counts) + mbase where mbase = 22.29 for the r-filter. The fractional errors for the stars we used were all under 1%, though the difference increased with the magnitude due to photon noise. Since the stellar magnitudes lined up very well between DR12 and Mira, we decided that we could safely use Mira for SFR’s in galaxies taken directly from SDSS. This means that we could feasibly use well-resolved images from SDSS to supplement our photometric measurements. On the subject of obtaining higher-quality SDSS images, we also looked into an additional survey that might provide better-resolved images of galaxies that we already have. That survey is known as Stripe 82 (Annis et al. [4]). The logic behind the Stripe 82 survey was to repeatedly observe a narrow portion of the SDSS footprint in order to look for supernovae. This would allow astronomers to both identify new events and track their dimming. The survey covers a 300 deg2 field of sky, from declination -1.26◦ to +1.26◦ and right ascension 20:00h to 4:00h. Having 25 observations of the same area of sky would also increase the signal-to-noise ratio of galaxies observed there. This in turn might improve the ability of SpArcFiRe to detect the spiral arms in those galaxies. To test whether it was worth using Stripe 82 data as a superior source to ordi- nary SDSS data releases, we needed to compare curves drawn by SpArcFiRe between both surveys. Of the full list of ≈ 1400 3-arm spiral candidates, 51 fell under the Stripe 82 field. That much of a reduction is to be expected given how small the area of Stripe 82 is compared to the full SDSS field. From that sample of 51, we had previously analyzed 16 of them using SpArcFiRe. We divided up those 16 according to whether their

24 original SpArcFiRe output was good, bad, or mediocre. We did this in order to deter- mine which were the best options for redoing using Stripe 82 data.

Fig. 3.8.: Side-by-side comparison of SpArcFiRe analysis from SDSS DR12 (left) and Stripe 82 (right). Note that the Stripe 82 image is more zoomed in than the original.

We initially tested the worst examples to see if they could be made acceptable. We considered it more eﬃcient to make unusable results better than improving already acceptable ones. The results were unfortunately rather mixed, occasionally even return- ing worse results. That said, roughly half of the galaxies redone with Stripe 82 data did return better-drawn curves than what was generated previously. An example of an im- proved SpArcFiRe output is shown in Figure 3.8. Considering that the likelihood of improving upon previously drawn arcs appears to be a 50%; we decided that using Stripe 82 data for old samples is worth attempting, but not a priority.

25 4 CONCLUSION

Over the course of this study, we selected 3-armed spiral galaxies selected by the Galaxy Zoo 2 project. Out of the total sample of ≈ 1400 galaxies, we looked at 240 of them and analysed 121 of those using the online resource SpArcFiRe. This program identified individual spiral arms and traced their paths based upon logarithmic spirals. SpArcFiRe returned acceptable results for pitch angles based upon previous classification work. Once we had generated SpArcFiRe results for a significant sample of these galaxies, we replicated the drawn arms in Excel. This was done in order for quantitative ex- amination of the pitch angles of the galaxies. We found that 3-armed spirals often demon- strated significant variation between pitch angles for individual arms. This could either be seen visually or by comparing in Excel. While Excel is difficult to apply to large numbers of galaxies, it still provided us with numbers that could be used in the future for potentially automated work. As part of our study, we analyzed the morphological demographics of the galaxies that we analyzed. We found that strongly asymmetric or “offset” spiral patterns were far more common than threefold symmetric ones. This is not especially surprising given the difficulty in maintaining strict symmetry in a differential rotator. It may even provide hints as to the formation and maintenance of these spiral structures. In addition to the symmetry of the spiral arms, we also evaluated the distribution of internal structures for the galaxies. We found that 3-arm spirals were more likely to have bar structures than other spiral galaxies. This was rather surprising, as we expected the presence of an interior twofold symmetry to depress the creation of an exterior threefold pattern. This does not appear to be the case. While symmetric spirals had

26 bar fractions similar to those of other spirals, offset spirals had much higher ones at a 4- σ significance level. Given the prevalence of offset 3-arm spirals, this strongly sways the overall bar fraction. When observing 3-arm spirals with bars, two arms often began from the same end of the bar or forked apart near the base of it. The ring structures were also often strange-looking and distorted, possibly a clue to how they formed. An ongoing issue with this study was distinguishing between proper arms and “spurs” that merely sprout off primary arms. We were unable to find a quantitative method beyond comparing relative lengths and making subjective appraisals. This is especially tricky for poorly resolved galaxies where it can be difficult to differentiate dust lanes from pattern gaps. That said, a future study may find a lot of use in analyzing these galaxies in near-infrared to sort through the dust. When we examined the environments of these spirals, we were surprised that they were not strongly biased towards being isolated. Rather they are quite likely to be interacting with other galaxies. We inferred this both by studying the neighbor density of the galaxies we analyzed and by directly observing several instances of 3-arm spirals with nearby interacting partners (like SDSS 1704). This directly contradicted our previous hypothesis about how these galaxies formed and persisted, where interactions would desta- bilize their pattern and decay to an even-numbered mode. It is still unclear whether there is a difference between 3-arm spirals that formed in situ and those that were possibly generated via distortions from strong interactions. This would be an area where having more high-resolution images and comparison with n-body simulations could help shed light. Star formation was another area where the spirals showed strange features. Specif- ically, our 3-arm spirals often showed distinct variation in SFR distribution between individual arms. SDSS 1704 was our prime example of this, if only because of the limited number of high-quality images. The differences of star formation also hint at the formation of the spiral structure, If one arm displays dramatic differences from the other two,

27 it may indicate that the odd arm out is the one formed via strong tidal disruption. When we began this study, we had referred to earlier analysis suggesting that 3- arm spirals were inherently unstable. However, a variety of evidence that we found has caused us to rethink that presumption. Further study with higher-quality information may provide greater insight into the formation and longevity of 3-arm spirals. Conduct- ing in-depth infrared analysis and using higher resolution images from projects like the Dark Energy Camera Legacy Survey (DECaLS) are particular avenues for further study that we identiﬁed (Abbott et al. [2]). Even continuing to study the list of galaxies from Galaxy Zoo 2 may prove useful, as expanding the sample size is often useful. Regardless, 3-arm spirals clearly have more to them than meets the eye.

28 Table 4.1.: Candidate 3-arm spirals examined.

SDSS Label Right Ascension Declination Redshift Density [log Mpc−2] SpArcFiRe? 587722982284722392 197.7658081 -0.788017809 0.0802477 -0.071742654 Y 587722982292062358 214.5877075 -0.745183349 0.095454998 -0.65035381 Y 587722982824214723 203.7689514 -0.306397468 0.086193599 -0.103088135 Y 587722982834504037 227.2090759 -0.396825612 0.093556799 0.182112818 Y 587722982835749172 230.0630493 -0.317829728 0.120099999 0.116405823 Y 587722983365279858 213.2606506 0.146375731 0.054621201 -0.449093852 Y 587722983365869710 214.6477509 0.15771696 0.053109299 0.624445399 Y 587722983369998691 224.1641388 0.049910601 0.082601704 0.401728365 Y 587722983898349836 204.6655579 0.545839131 0.0228932 0.111841469 Y 587722983899660407 207.5823364 0.54810077 0.0480172 0.016379562 Y 587722983904969020 219.7797699 0.508633018 0.033412199 -0.166352707 N 587722983909228843 229.4519501 0.45905441 0.057499401 0.234788794 N 587722984434565297 203.1618958 0.870477021 0.034478098 -0.315661247 Y 587722984436990089 208.6342926 0.885213554 0.070350297 -0.280623404 Y 587724648190181499 195.7788391 -3.313031673 0.085510701 0.372660151 Y 587724648718139563 175.3409882 -3.053736448 0.108027004 0.644351071 N 587724648719515782 178.461853 -2.971254587 0.13335 -0.051152227 N 587724648720040138 179.7900085 -2.928776503 0.108248003 0.095179572 Y 587724649255993538 177.6334991 -2.61960578 0.092191398 0.37366244 N 587724649261301846 189.7216034 -2.690071583 0.084110796 -0.422885263 N 587725040099328093 196.901474 -2.820178986 0.0816167 0.749572252 N 587725040628662374 179.6791382 -2.394698858 0.103101999 -0.10757338 N 587725040634364147 192.8403931 -2.379525185 0.095700398 -0.29062161 N 587725041700634635 175.6488342 -1.544173956 0.073465303 0.387730111 N 587725041700831400 176.2102966 -1.601321936 0.028433699 0.290724502 Y 587725075530580154 142.9281769 0.59356308 0.072361797 1.138772825 N 587725075530645639 143.0706787 0.544185936 0.107582003 0.577987706 N 587725469063184628 143.5851593 57.14612198 0.086283296 0.004975827 N 587725470127685799 119.943718 42.2574234 0.043697301 0.63901168 N 587725470130045191 124.4992294 46.570755 0.040545698 -0.009786186 N 587725470134960268 136.1876221 54.92919922 0.082172297 0.250256765 N 587725471203328190 122.5228577 46.1930275 0.031549901 -0.165730965 Y 587725474419834948 160.5532074 62.98358154 0.0423191 -0.277014743 Y 587725475493445809 159.0375824 63.68346405 0.117977001 0.343117018 N 587725491063554340 259.7537231 55.89523315 0.0729381 0.331431761 N 587725504482574464 256.0597229 62.04279709 0.082270697 0.562978321 Y 587725505022263551 260.9705811 56.04008865 0.113860004 0.357590874 N 587725550138032206 180.94104 66.34793854 0.062879898 -0.139512255 Y 587725550138359911 182.7640533 66.41734314 0.0589187 -0.304975348 Y 587725550657929473 119.8990402 44.30673218 0.049739599 0.495277886 Y 587725550663696565 132.438797 54.73901749 0.107384004 0.426373539 N 587725550678638758 201.9768524 65.8419342 0.066401199 -0.235357219 Y 587725551199322256 128.6299744 52.8401947 0.0571233 0.353438398 N 587725551731671285 119.0606003 44.75413895 0.107484996 -0.257950727 N 587725552264675555 112.5957031 37.37518692 0.0613106 0.512214526 Y 587725552827629763 211.4616394 66.21304321 0.078613497 0.146216687 N 587725576423342340 257.9342957 64.11213684 0.083350703 1.326597267 Y 587725576425177104 260.7187805 60.12957382 0.027566601 0.437517115 Y 587725576964145486 263.8632813 55.49725342 0.082125902 0.940666879 Y 587725590381396134 258.5144653 65.52737427 0.103276998 -0.045928378 N 587725773991903607 113.9229507 37.09578705 0.084903598 0.53636917 Y 587725774529888536 115.0769043 39.43403625 0.100988999 0.349062361 N 587725774532182269 118.8537827 43.97829437 0.143901005 -0.027599232 N 587725816419713145 216.9904633 62.93592072 0.036302101 -0.127961298 Y 587725816951210192 189.3149109 66.89466858 0.169762999 0.041955672 Y Continued on next page

29 SDSS Label Right Ascension Declination Redshift Density [logMpc−2] SpArcFiRe? 587725816952914079 199.0391388 66.37322998 0.122654997 0.287439246 N 587725816956715153 217.8444366 63.1843605 0.0922774 -0.270990816 N 587725817494110314 220.6885834 62.95259094 0.111272 -0.01208274 Y 587725817501384763 243.3387451 51.4276123 0.060775001 0.173831697 Y 587725818037731481 242.8550415 52.75748062 0.063313298 0.270209529 Y 587725818557825112 165.3217163 67.10636902 0.032922901 -0.240566631 Y 587725818568835091 225.6984406 62.33860779 0.044604901 0.523091146 N 587725980690415749 130.8067474 54.67644882 0.119549997 0.489378556 N 587725981227548754 131.0110168 55.23169327 0.045190401 0.412521929 Y 587725994377085200 245.9456177 50.01944351 0.084718198 -0.1204743 N 587726013995942036 181.7415771 1.480673313 0.082528599 0.348309437 N 587726014011015340 216.1382141 1.177318931 0.038805701 -0.658508857 Y 587726014540415067 199.1515198 1.989209414 0.136796996 0.430630864 Y 587726014541201612 200.9649658 1.884766936 0.082330801 -0.236548499 N 587726014547296416 214.8506622 1.656603336 0.171321005 0.511910188 Y 587726014553194757 228.3454895 1.395302415 0.095231697 1.272423485 N 587726015077875822 200.3880157 2.404493093 0.082568102 0.267984719 N 587726015081480350 208.6761322 2.268020868 0.093928702 0.084128722 Y 587726015619268767 210.8658752 2.528819323 0.072697103 0.495113668 Y 587726015627854156 230.4289703 2.163754702 0.081189603 0.336412294 N 587726016157188298 213.1379852 2.99220562 0.074001603 -0.182992977 N 587726016157384898 213.6126099 3.028626442 0.055740401 0.181053516 N 587726016683245662 188.415329 3.606847286 0.079276502 0.347446359 Y 587726031173517459 177.0756226 1.309355974 0.093886897 -0.35230483 N 587726031708422303 172.626236 1.666331053 0.063508198 0.057454937 Y 587726031712485491 181.8007965 1.750618458 0.078605197 -0.552279381 N 587726031713992776 185.2673492 1.744616866 0.079373904 -0.239590031 Y 587726031714255038 185.8961639 1.827400684 0.100679003 -0.23466945 N 587726031722774723 205.4261627 1.508881211 0.079613499 -0.247439815 Y 587726032242868344 166.9805756 2.013258696 0.042176399 0.931578493 Y 587726032268361917 225.3381042 1.637075424 0.035179898 0.94798066 Y 587726032771481685 148.123642 2.15444994 0.016669299 0.783473354 Y 587726032773447847 152.6161041 2.2282269 0.021674501 -0.421767932 Y 587726033337123057 213.9950867 2.710298777 0.075615801 0.701000772 Y 587726033854922898 170.3623199 3.444915295 0.023043901 -0.103510746 N 587726100411056249 216.6615143 3.504994631 0.071658596 -0.069854768 Y 587726100948648077 218.2941284 3.942550659 0.030048201 -0.24289088 Y 587726100956840037 237.0992584 2.805406332 0.118304998 -0.007999126 N 587726102561620183 223.8881836 4.775010109 0.086743101 -0.045134911 N 587727865643073835 116.7539444 34.30030441 0.061595801 -0.294874791 Y 587727865645302039 120.5533676 38.32532883 0.097926997 0.495576672 N 587727866179617126 115.9665146 33.85608292 0.121211 0.747994171 N 587727866182959120 121.4501266 40.04997253 0.093200199 0.38545151 Y 587727866718454105 118.6927948 37.8286705 0.106784001 0.836065216 N 587727867256701059 120.7575684 40.58369446 0.041628901 0.590522732 N 587727867260305533 127.8945465 46.89668655 0.052127998 -0.213400226 Y 587727942422560973 148.2052612 1.056140304 0.048159201 0.030129437 N 587727944029962495 140.9500885 2.112748384 0.023978701 0.236705168 Y 587727944032780481 147.3014679 2.269948959 0.051281098 2.72117746 N 587727944570962108 150.3757782 2.861286402 0.091746502 -0.135669664 N 587728307490062439 164.7347107 1.430537462 0.040311299 0.294688703 N 587728308022673555 154.9216614 1.690256119 0.076103903 0.579201495 N 587728308026998899 164.8796997 1.740462184 0.0378731 0.111413458 Y 587728308028178584 167.6088715 1.80864656 0.103690997 0.394418629 N 587728309099954319 163.0780182 2.625276804 0.056109399 -0.716343514 Y 587728309103165501 170.3613892 2.746704817 0.0486454 0.169099448 Y 587728309103362162 170.7946472 2.650775194 0.048333 -0.014202361 N 587728309103427628 170.9760284 2.778106689 0.062635198 0.433686992 Y Continued on next page

30 SDSS Label Right Ascension Declination Redshift Density [logMpc−2] SpArcFiRe? 587728309104803983 174.1296844 2.750039816 0.0474892 -0.248559698 Y 587728309637021822 163.5683136 3.139790297 0.111859001 -0.228433393 N 587728310176907418 170.3654175 3.470111847 0.0580488 0.710290686 N 587728668269871147 125.4637756 42.86737061 0.054691698 -0.132534573 Y 587728668806611190 124.7455215 42.90010071 0.154241994 0.434140087 N 587728669338829063 116.1056519 34.62742996 0.084243402 -0.019997756 Y 587728676855414883 174.4056549 63.54940414 0.062813297 -0.386414645 Y 587728676860854290 201.9326477 62.76657486 0.0219815 -0.357505084 Y 587728678465503338 171.1065979 64.35518646 0.0695135 -0.053471956 N 587728678466093256 174.3145294 64.74617767 0.063070901 0.054798287 Y 587728878735458482 167.3995056 3.61271596 0.051714499 0.301005413 N 587728879256600830 131.4159546 2.289460659 0.076618798 0.209001802 N 587728879268528221 158.6273041 3.746047974 0.062852196 0.106126379 Y 587728879794782218 134.335434 2.921313524 0.0130209 1.159887285 Y 587728880345743406 166.6282806 4.858850956 0.075331397 -0.544438459 N 587728880882483370 166.2893219 5.359972 0.127664998 0.53280272 N 587728905027715323 121.2661209 36.25244904 0.095023602 0.029958716 N 587728906100670782 119.0484772 35.40910339 0.112181999 0.233483527 N 587728919520083986 210.4974365 63.29201508 0.035425302 -0.709672927 Y 587728930270019685 137.5379486 48.37560654 0.140976995 0.277221396 N 587728930798043436 118.7441406 33.88451004 0.074334897 0.078771978 N 587728930800861374 123.7002869 38.86044693 0.126076996 0.187274505 Y 587728931333799975 116.4311066 32.10297012 0.0271885 -0.275283432 Y 587728931879911602 134.4768066 48.27788162 0.143379003 0.412524507 N 587728932407803939 116.0138779 33.07738876 0.0554487 0.123751899 Y 587728932421435491 147.8412781 54.96788025 0.060097799 0.151743549 N 587728948512227466 153.4732056 -0.318913698 0.071107902 0.977411561 Y 587728948512555177 154.242691 -0.248007655 0.063059397 -0.203743693 N 587728948514848920 159.5409393 -0.220787764 0.094861299 0.125332608 N 587728949586952357 155.816925 0.624022663 0.099195696 0.088768052 N 587729153599144041 188.0627747 64.12020111 0.100631997 0.653990691 N 587729158433734726 204.3723602 4.104443073 0.023141701 -0.093461189 Y 587729158436028561 209.5634308 3.998300552 0.030011799 -0.688006764 N 587729158442123439 223.4636688 3.484672785 0.0271926 0.157724938 Y 587729158444023993 227.7564392 3.057124853 0.042172499 0.203819307 N 587729158967918716 198.1639557 4.838263512 0.0485279 0.653756608 N 587729158981746829 229.7740784 3.367158413 0.053121001 -0.476923042 Y 587729158983974974 234.9143524 3.199033737 0.033758901 0.560919205 Y 587729159508852867 207.4718323 4.891469479 0.078536101 -0.031688195 Y 587729159510622432 211.5864716 4.703730106 0.025099101 -0.031688195 N 587729159512784935 216.4740295 4.642709732 0.026118901 -0.057643707 Y 587729159768506488 187.3533783 5.343995571 0.066238403 -0.446386812 N 587729227684577303 226.4248962 60.7976532 0.044287901 -0.096744997 Y 587729227690934493 244.3958435 50.24456787 0.041404702 0.133785199 N 587729229298139326 237.7488556 57.16194916 0.105152003 0.455933308 N 587729229299974303 242.3789215 53.86332321 0.062371898 0.55672039 N 587729231980986447 252.9237061 41.66837692 0.042763401 -0.424453991 Y 587729231981248788 253.2739105 41.07405853 0.0605256 -0.369370658 N 587729232514056378 246.6319885 49.18135452 0.0379772 0.291432629 N 587729385534980105 154.2714081 54.82050705 0.038359601 0.267171625 Y 587729386061234378 125.2887421 40.16100311 0.0612689 0.970506772 N 587729386068181126 142.1356964 50.79362488 0.0251687 -0.275230973 Y 587729386069098664 144.8814697 52.05555725 0.0492188 0.328178739 Y 587729386070409386 148.9835815 53.69358826 0.043351602 -0.259032484 Y 587729386602168352 133.931427 46.95993805 0.090065703 -0.132791553 N 587729386608787500 153.9260559 55.66748428 0.0243908 -0.919063965 Y 587729387154571400 191.9852448 59.95717239 0.064157702 -0.469529199 N 587729387157455017 204.6096497 58.55672455 0.070586599 0.537057511 Y Continued on next page

31 SDSS Label Right Ascension Declination Redshift Density [logMpc−2] SpArcFiRe? 587729387687968982 176.0211792 60.21272659 0.059309799 0.451174804 Y 587729388208455933 123.2452316 40.66564941 0.038671602 0.520087182 N 587729408612827251 245.3553925 46.88467407 0.0546753 0.325242704 N 587729408617611639 253.7339172 37.88514709 0.109412998 0.301636764 N 587729409147076767 239.9514923 51.70828629 0.064369902 1.026658442 N 587729652354777743 257.9490967 28.32424355 0.042277399 -0.355445627 Y 587729653425242367 253.847168 35.13617706 0.124159999 0.149992093 N 587729653426094241 255.267807 33.47524261 0.029722599 -0.046822192 Y 587729653962047799 254.3582458 35.49922562 0.111294001 0.504821636 N 587729751674192403 255.8486786 31.6996727 0.077609196 0.036642719 N 587729752206606624 249.0396423 40.36585617 0.137702003 0.530182508 N 587729752211391105 256.6719055 31.28914642 0.0312325 -0.133497892 N 587729752742953164 248.4656525 41.59173965 0.0574327 0.056277544 Y 587729772607045935 203.2357483 -3.027673006 0.046688899 -0.127436572 Y 587729774759313429 214.0213165 -1.259689212 0.050128601 -0.431836495 N 587729776903192708 204.8399506 -2.828279257 0.098030798 0.754283085 N 587729777445503222 217.2727356 -2.168871403 0.053892799 0.313222526 Y 587729777452843431 234.0159607 -1.824975371 0.146682993 0.391934574 Y 587729777986633759 226.9545288 -1.481904387 0.054598201 -0.374197737 Y 587729778524094683 228.284317 -1.111790776 0.121353999 0.048760214 Y 587729782275637591 259.8525696 29.77890968 0.046980299 0.077462024 N 587729782810083559 256.9925842 34.81855392 0.0370772 0.331902335 Y 587729782810280193 257.383667 34.4270401 0.0239603 -0.154937384 Y 587729970180587867 227.0661621 -2.505218267 0.0767885 0.134742739 Y 587729970715623662 222.9046326 -2.390767574 0.100117996 0.368197831 N 587729971256820219 232.7758942 -1.669061184 0.080528103 0.57530257 Y 587729971786809575 216.9318848 -1.587020159 0.0239804 -0.535218522 N 587730021720260745 224.9946747 5.017527103 0.080008097 0.014654055 Y 587730021720457340 225.4548187 4.932230473 0.0354628 -0.682666743 Y 587730022263488871 239.5991058 3.982978821 0.102774002 0.14792142 Y 587730022794592466 226.3898163 5.715410709 0.084894799 0.739863887 Y 587730022795182367 227.7714081 5.520205975 0.035080802 -0.047677305 N 587730023336378628 237.6880035 5.039999962 0.076141 -0.192342731 Y 587730023338541469 242.6575928 4.640855312 0.0741475 -0.175135773 N 587730845819273489 325.8245544 -1.155842185 0.066109203 -0.370514014 N 587730847424315402 313.0932312 0.075727001 0.030282401 -0.550418473 Y 587730847424512345 313.6351013 0.041969541 0.0298643 -0.081801175 Y 587731172767498868 310.0448303 -0.568855882 0.056398202 -0.401703538 N 587731172769465209 314.5380859 -0.449708074 0.087352201 0.048659858 Y 587731185124900959 347.9021912 -1.005213976 0.110841997 0.312250489 N 587731185652138423 325.9941406 -0.554143786 0.061457001 -0.154958487 N 587731185664786507 354.7759705 -0.437527955 0.071611501 0.729479628 Y 587731185665638560 356.8056946 -0.480182022 0.037992399 -0.35016549 N 587731186200674529 352.6361389 -0.137183294 0.0579996 -0.001589817 Y 587731186742788238 4.587526798 0.404853106 0.088382803 0.190133402 N 587731187272122392 347.3344421 0.756495059 0.032299701 -0.172039693 Y 587731187275464902 355.0402527 0.756777585 0.119009003 -0.067775966 N 587731187281494216 8.810570717 0.695979476 0.0412196 0.129647429 Y 587731498650239116 160.6430817 53.79399872 0.163093999 -0.247342473 N 587731498652139646 167.6263885 55.16985703 0.057755999 0.299422255 Y 587731501336494207 166.7773132 57.07055664 0.0478171 0.423491716 N 587731512071880866 25.52885056 -0.607471049 0.100323997 0.236927895 N 587731512076599466 36.37085342 -0.474710166 0.106334999 0.343762759 N 587731512604426317 15.6358633 -0.162156552 0.109851003 0.084235617 N 587731512605016208 17.11448097 -0.087685749 0.061437301 -0.025118179 Y 587731512608227474 24.39802551 -0.135212615 0.072332002 -0.260988576 Y 587731512610914367 30.54935837 -0.130435079 0.019891899 1.170886375 Y 587731512619237386 49.48779678 -0.169074476 0.022861 0.733202916 Y Continued on next page

32 SDSS Label Right Ascension Declination Redshift Density [logMpc−2] SpArcFiRe? 587731513141624938 16.45911598 0.242286861 0.048110701 -0.442573018 N 587731513145884796 26.19384193 0.272287756 0.059688602 0.268028395 Y 587731513152766115 41.93704605 0.414155632 0.0278832 -0.25803312 Y 587731513154666691 46.28573608 0.34342581 0.043621302 -0.609604429 Y 587731513679413352 18.56579399 0.765332222 0.0424411 -0.346614253 Y 587731513680658477 21.36793709 0.736574292 0.089313902 0.029566207 N 587731513685377197 32.22089767 0.786836326 0.042185102 -0.013850237 Y 587731520661225592 118.5432892 28.62351036 0.058866099 0.065812805 Y 587731522273214545 119.7990265 31.80788231 0.059207302 0.404343993 Y 587731679043846285 131.9457855 39.49404907 0.122785002 0.066695203 N 587731679578685688 127.2214737 36.61074448 0.128931999 -0.116274971 N 587735043613720731 131.8312683 31.18174934 0.052076701 0.440052163 Y 587735347487572145 152.4928894 11.94181919 0.108949997 0.014922804 Y 587735348036960323 181.8027191 14.72873592 0.083258599 0.387638826 Y

33 Fig. 4.1.: Montage of 3-arm spiral candidates paired with their corresponding ﬁnal SpAr- cFiRe outputs, showing the overlaid logarithmic spiral arcs. Images proceed in order of SDSS number as seen in Table 4.1 (left to right, top to bottom). First entry has Objec- tID: 587722982284722392

34 Fig. 4.2.: Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued). First entry has ObjectID: 587722984434565297

35 Fig. 4.3.: Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued). First entry has ObjectID: 587725550657929473

36 Fig. 4.4.: Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued). First entry has ObjectID: 587725817501384763

37 Fig. 4.5.: Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued). First entry has ObjectID: 587726031708422303

38 Fig. 4.6.: Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued). First entry has ObjectID: 587727865643073835

39 Fig. 4.7.: Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued). First entry has ObjectID: 587728676860854290

40 Fig. 4.8.: Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued). First entry has ObjectID: 587729158981746829

41 Fig. 4.9.: Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued). First entry has ObjectID: 587729386608787500

42 Fig. 4.10.: Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued). First entry has ObjectID: 587729782810083559

43 Fig. 4.11.: Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued). First entry has ObjectID: 587730847424512345

44 Fig. 4.12.: Montage of galaxies analyzed by SpArcFiRe, as described by Figure 4.1 (continued). First entry has ObjectID: 587731512619237386

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