E+A Galaxy and Spiral E+A Galaxy Candidates in the Hercules Supercluster

Home , Abell 2152, Charles Liu, Hercules Cluster

E+A galaxy and spiral E+A galaxy candidates in the Hercules supercluster

by Rosemary Williams

A THESIS

submitted to

Oregon State University

Honors College

in partial fulfillment of the requirements for the degree of

Honors Baccalaureate of Science in Geophysics (Honors Scholar)

Presented March 5, 2021 Commencement June 2021

AN ABSTRACT OF THE THESIS OF

Rosemary Williams for the degree of Honors Baccalaureate of Science in Geophysics presented on March 5, 2021. Title: E+A galaxy and spiral E+A galaxy candidates in the Hercules supercluster.

Abstract approved:______Charles Liu

E+A galaxies represent an important niche in galaxy evolution as a subset of post- starburst galaxies. Set apart from other post-starburst galaxies by their rapid quenching of star formation, E+As are thought to have started their formation outside a galaxy cluster's center and have fallen inward due to gravity; the star forming gas is ram-pressure stripped from the galaxy, quenching star formation and leaving behind a post-starburst galaxy. This galaxy has a high population of older, redder stars from the pre-starburst galaxy, and also contains new, blue, A-type stars that formed during the merger. This paper investigates E+As within the Hercules supercluster, and pays particular attention to Khutulun (SDSS 2MASX J16015198+1547326), a perfect example of a barred spiral (SBb type) E+A galaxy, and the inspiration for investigating spiral E+As. Spiral E+As represent an even smaller subgroup of galaxies as they have retained their arms through starburst, and thus were most likely formed without a major galaxy merger. This research presents theories on how spiral E+As formed and supports current theories that E+As tend to be in low/medium density regions within clusters and provides evidence that perhaps the gas density region is correlated to how the galaxy underwent starburst.

Key Words: galaxies, evolution, post-starburst, E+A, spiral E+A, Hercules

Corresponding e-mail address: [email protected]

©Copyright by Rosemary Williams March 5, 2021

E+A galaxy and spiral E+A galaxy candidates in the Hercules supercluster

by Rosemary Williams

A THESIS

submitted to

Oregon State University

Honors College

in partial fulfillment of the requirements for the degree of

Honors Baccalaureate of Science in Geophysics (Honors Scholar)

Presented March 5, 2021 Commencement June 2021

Honors Baccalaureate of Science in Geophysics project of E+A galaxy and spiral E+A galaxy candidates in the Hercules supercluster presented on March 5, 2021.

APPROVED:

______Charles Liu, Mentor, representing the American Museum of Natural History

______Randall Milstein, Committee Member, representing Physics

______Xavier Siemens, Committee Member, representing Physics

______Toni Doolen, Dean, Oregon State University Honors College

I understand that my project will become part of the permanent collection of Oregon State University, Honors College. My signature below authorizes release of my project to any reader upon request.

______Rosemary Williams, Author

I would like to thank Dr. Charles Liu for mentoring me through the research process and being one of the most understanding and caring mentors I have ever met. You supported me through the largest research project I have ever tackled, and your constant enthusiasm and encouragement was delightful. Thank you to Dr. Randall Milstein for being a mentor to me since my freshman year and pushing me to apply to so many different opportunities that I never thought I could actually get. Thank you for all your letters of recommendation and for being a member on my thesis committee and providing insightful, critical feedback. Thank you to Dr. Siemens for graciously agreeing to be on my committee without having ever even met me before, I appreciate all of the time you dedicated to this thesis especially given all of your amazing research projects you are currently juggling. I would also like to thank the Y/Dim Collaboration for being such an amazing and supportive research group. I have had such an amazing time getting to know you all and I have learned so much from you. I would also like to acknowledge the NSF

REU program at the American Museum of Natural History for funding this research, and to everyone at the museum who worked tirelessly so the program could go on virtually during a pandemic. This work was supported by the Alfred P. Sloan Foundation via the

SDSS-IV Faculty and Student Team (FaST) initiative, ARC Agreement SSP483, and by

NSF grants AST-1852355, 1852360, 1460939, and 1460860 to the American Museum of

Natural History and CUNY College of Staten Island.

Table of Contents

Table of Contents ...... 8

Chapter 1: Introduction ...... 9 Section 1.1 Background and history ...... 9 Section 1.2 The science behind E+A galaxies ...... 12

Chapter 2: Data acquisition ...... 16

Chapter 3: Results and Analysis ...... 22 Section 3.1 E+A Results and Analysis ...... 23 Section 3.2 Spiral E+A Results and Analysis ...... 26 Section 3.3 Cold and hot ICM regions within Hercules ...... 28

Chapter 4: Discussion ...... 30 Section 4.1 How do spiral E+As form? ...... 30 Section 4.2 ICM hot and cold gas analysis ...... 33

Chapter 5: Considerations ...... 35

Chapter 6: Conclusion ...... 37

Chapter 7: Works Cited ...... 38

Chapter 8: Appendix ...... 41 Section 8.1 Equivalent width code ...... 41 Section 8.2 NN code ...... 42 Section 8.3 3D visualizations of elliptical and spiral E+A galaxies ...... 43 Section 8.4 Example of SDSS classified E+A that is not fully E+A ...... 44

Chapter 1: Introduction

Section 1.1 Background and history

In 1983, Dressler and Gunn identified what would become the first known 'E+A' galaxies while studying the shape of galaxy spectra in the 3C 295 cluster [1]. The spectra that caught their attention lacked star formation and seemed to contain two contradictory star populations: old, red, K-type stars and a considerable population of new, blue, A- type stars. This unlikely combination of stellar populations forced the galaxies’ apparent color into a “green valley” (see Figure 1): bluer than a typical elliptical galaxy and redder than a typical spiral galaxy. They were called “E+A” (or “K+A”) because their galaxy spectra could be modelled using typical “E”-lliptical galaxies (which contain high populations of “K”-type stars) and “A”-type stars.

Figure 1: Color-mass diagram illustrating the location of the green valley from Kevin Schawinski et al [2].

One explanation for how these galaxies formed is a past event triggered a starburst (a period of star formation ~10 times higher than in the average star-forming galaxy) within the galaxy that led to the formation of young, blue stars among the red stars of the host galaxy. Overtime star formation ended, most likely due to star-forming gas being blown out of the galaxy as it moved through its galaxy cluster in a process called ram-pressure stripping (RPS), leaving the galaxy quiescent and E+A. But what triggered these starbursts? In 1988, Lavery and Henry presented spectrographic and photographic evidence of galaxy-galaxy interactions at around redshift -.2 that had triggered starbursts within galaxies [3]. In 1991, Oegerle, Hill, and Hoessel identified the irregular galaxy “G515” (pictured in Figure 2), the first low-redshift E+A galaxy discovered (z = 0.0875), and an important discovery because its high luminosity (rare for elliptical galaxies) and distinct morphology suggested evidence for a recent merger [4].

Figure 2: G515 (left) was one of the first E+A galaxies studied in detail and Khutulun (right) is the spiral E+A galaxy that inspired this research. Note the faint trail of material swinging beneath G515 and the irregular shape of the center alluding to a past merger or harassment event. Images taken from SDSS.

While mergers had been a possibility for how E+A galaxies formed, Dressler and

Gunn believed the high velocity dispersion of E+As made mergers unlikely. But the distinct morphology of Lavery and Henry galaxies and G515’s tidal tail provide evidence that mergers are not only possible, but a likely cause for starbursts in E+A galaxies. My thesis includes a catalogue of newly identified E+A galaxy candidates within the

Hercules supercluster (henceforth Hercules), and pays particular attention to some newly discovered spiral E+A galaxy candidates. Spiral E+A galaxies are a type of quiescent red spiral galaxy, however the archetypal red spirals identified by Masters et al. (2010) in

Galaxy Zoo does not require galaxies to lack H훼 emission or have a negative slope after

~5000 Å which are both qualifications set forth by Greene et al. (submitted January

2021) in classifying E+A galaxies [5] [6]. In 2016, Fraser-McKelvie et al. analyzed six red spirals using integrated field spectroscopy (IFU) to determine if the red spirals are completely passive and confirmed passive red spirals do exist [7]. However none of the galaxies in their sample have significant (≥2 Å) H훿 equivalent widths and thus none of their sample are E+A galaxy candidates. In the same way that all squares are rectangles but not all rectangles are squares, spiral E+As are red spirals but not all red spirals are

E+As. My thesis identifies 220 E+A candidates and 8 spiral E+A candidates, maps their locations over hot and cold gas density regions of the intra-cluster medium (ICM), quantifies the locations of E+A candidates in relation to nearest neighbor galaxies within

Hercules, and discusses how the gas density surrounding E+A galaxies can impact morphology and provide insight to how the galaxy formed. Note all of the E+A candidates listed in this paper are not confirmed E+A as the spectra I analyze are only

12 from the centers of the galaxies. However, I refer to E+A candidates and spiral E+A candidates as E+As and spiral E+As for simplicity in my thesis.

Section 1.2 The science behind E+A galaxies

In order to determine if a galaxy is still star forming, astronomers look at a galaxy’s spectrum. A spectrum is a graph mapping the prevalence (or flux) of light wavelengths within the galaxy, usually between 400nm (ultraviolet light) and 900nm

(infrared light). Because wavelength determines the color of emitted light, spectra can be used to determine the color of a galaxy. And since light is a quantum of energy, different processes emitting or absorbing energy within a galaxy — like hydrogen electrons changing energy levels — leave “footprints” on the actual galaxy spectrum. In the case of star formation, astronomers use hydrogen Balmer lines (denoted by H훼, H훽, H훾, and

H훿) to determine whether a galaxy is star forming because new (and typically blue) stars emit high-energy photons ionizing surrounding gas upon absorption. As the protons and electrons within the gas surrounding high-luminosity stars begin to recombine in a process called hydrogen recombination, the electrons de-excite and fall from high energy levels to low energy levels, emitting discrete quanta of energy that can be seen as specific wavelengths of light on a galaxy spectrum. These wavelengths correspond to the hydrogen Balmer lines (see Figure 3) with each line corresponding to a specific change in energy level. If these emission lines are present on a spectrum, I can confidently say there is still star formation happening within the galaxy and it is not E+A. Unlike emission lines, absorption lines indicate the energy coming from the star is not high enough to ionize the surrounding gas, but the photons can still be absorbed by atoms and excite

13 electrons from low energy levels to high energy levels. This process leaves absorption lines in the spectra where specific wavelengths of light (determined by the energy level jump) are absorbed by gas surrounding the star before they reach our telescopes.

Figure 3: Electron energy level jumps in the Balmer sequence. Hα, Hβ, Hγ, and Hδ correlate to an emitted wavelength of 656 nm, 486 nm, 434 nm, and 410 nm respectively. Diagram made by Rosemary Williams, 2020.

While searching for E+As, I made sure that along with no H훼 emission, the galaxies also had strong H훽, H훾, and H훿 absorption lines. In addition to strong absorption lines, E+A spectra must indicate the presence of K and A-type stars. Figure 4 shows the spectra of an elliptical galaxy overlaid with the spectra of an A-type star to give the basis for what I look for while searching for E+A galaxies. This superposition produces the unique 'E+A' shapes shown in Table 1. But why A-type stars specifically?

Dressler and Gunn (1983) note the observed spectra are "characteristic of an old population in which a large burst of star formation has recently (within 1-2 x 109 years) occurred" [1]. Of every spectral type of star (O, B, A, F, G, K, and M listed from hot and blue to cold and red on the HR diagram, see Figure 5), A-type stars are the bluest stars

14 whose lifespan is greater than 109 years. While O and B stars could have formed within the starburst, the amount of time it takes a galaxy to quench star formation is longer than the lifespan of O- and B-type stars, leaving only A-type to contribute to the blue light being emitted from the galaxy.

Figure 4: The superposition of an A-type star spectrum with a classic elliptical galaxy spectrum. Since E+As are elliptical galaxies filled with A-type stars, and E+A spectrum will look similar to the average superposition of two such spectra. Data taken from SDSS.

The last key feature of an E+A galaxy is the presence of a Dn4000, a steep jump in flux around 4000 Å indicating an old stellar population. If a spectrum has a strong

Dn4000 and a blue slope, I can confidently state both old and new stellar populations are present in the galaxy. The existence of E+A galaxies could explain the “Butcher-Oemler effect,” the hypothesis that galaxy clusters at higher redshifts contain higher populations of blue galaxies in comparison to closer redshifts. My research provides evidence to support the Butcher-Oemler effect and also may kickstart future research into E+As in

Hercules and into spiral E+A galaxy candidates which have not yet been charted.

Figure 5: Hertzsprung-Russell diagram [8]. E+As are typically made of K- and A-type stars which can be found on the main sequence of the HR diagram.

Chapter 2: Data acquisition

Six color-constrained queries from the Sloan Digital Sky Survey (SDSS) Data

Release 16 (DR16) formed the set of galaxies I investigate in this paper with two queries for each of the sub-clusters within Hercules: Abell 2151, Abell 2152, and Abell 2147

(henceforth A2151, A2152, and A2147). Each sub-cluster has one query focused on blue objects with magnitudes between u-r=1.40-2.20, g-r=0.20-0.65, and r-i=0.10-0.30, and one query focused on green objects between u-r=1.35, g-r=0.38-0.83, and r-i=0.18-0.42, each 3 degrees from their sub-cluster's center. Focusing on specific color ranges in queries where

E+As are known to sit allows for fewer extraneous, non-E+As to sort through. There were duplicates within the green and blue sheets and between the clusters, but the extras have been removed. These constraints were chosen based off of analyzing data collected from E+A candidates sorted between 2015-2019 by the Y/Dim Collaboration. The final dataset consists of 2,301 galaxies of which only 1,197 are included in the 0.025 < z < 0.05 redshift range for the cluster. Each galaxy was sorted, paying particular attention to four key E+A attributes described in the introduction and set forth by Greene et al. (2021) [6].

1. A blue slope (negative slope) between ~5000-8000 Å

2. Hydrogen Balmer absorption lines with H훽 equivalent widths ≤2 Å for green and

blue candidates

3. Lack of Hα and [O II] emission

4. Discernable Dn4000

The strength of each of these attributes determines whether E+A candidates were sorted into the blue, green, or ambiguous category (see Table 2). Blue E+A galaxies are theorized to be newer E+As as they still have a substantial blue-star population, whereas green E+As most likely formed earlier. Once the queries are completely sorted, I bring it before at least three other members from the Y/Dim Collaboration to be voted on and verified. If there is any uncertainty surrounding whether the candidate fits all necessary requirements the galaxy is sorted into an ambiguous category.

Blue Green Ambiguous

Table 1: Defining E+A galaxy candidates into three categories based on their spectra. Note that the spectroscopic labels are wrong on the blue E+A example. This was a fairly common problem throughout this research as SDSS did not know how to classify E+As and often mistook them for high-redshift objects.

Notice how a threshold value for slope between categories is not given; this is

because our team does not feel we have the mathematical or scientific reasoning

necessary to give a threshold slope that could be supported by scientific evidence. The

second most common reason galaxies are placed into the ambiguous category is the noise

level, or the "messiness", of a spectrum. Even if a galaxy spectrum has the exact shape

we are looking for, high levels of noise within the data make identifying the equivalent

widths of absorption and emission lines difficult. Measuring equivalent widths is the only

E+A qualification that cannot be done by eye, so Serena Wurmser (a member of Y/Dim)

wrote a Python script allowing users to import a spectrum from SDSS, input the starting

and ending wavelengths of the absorption line, and calculate the equivalent width by

finding the area of the absorption line and dividing by the height of the surrounding

continuum (see Figure 2). This Python script can be found in the appendix.

Equivalent width

Continuum height

Flux Area of absorption line Equivalent area

Wavelength

Figure 6: Measuring equivalent widths in theory versus in practice. The Python program measures the area under the continuum line and above the absorption line (as shown in the figure on the right), then takes that area (simplified as the “area of the absorption line” on the left) and shapes it into a rectangle (“equivalent area” on the left): the width of the rectangle is called the equivalent width. Graphic designed by Rosemary Williams, 2021.

After classifying the galaxies, I developed a code to determine the average nearest

neighbor (NN) distance within Hercules, and then input varying types of E+As to help

quantify the environment surrounding each archetypal E+A. The key assumption made in

19 writing the NN code was that all the galaxies were at close enough redshifts (z < 0.1) that

Hubble’s law could be applied (Equation 1). Note that 퐻0 (the Hubble Constant)

푘푚 ≈ 67.4 , D is the proper distance to an object given its recessional velocity, v, 푠∙푀푝푐

푘푚 which can be determined by multiplying an object’s redshift by 300,000 . 푠

푣 = 퐻0퐷 Eq. 1

The NN code utilizes the law of cosines to determine distances (d in Figure 7) between galaxies, where the right ascension and declination coordinates are used to determine the angle (휃 in Figure 7) between two side lengths corresponding to the

Hubble distance (Eq. 1) of each galaxies’ redshifts (z(a) and z(b) in Figure 7).

galaxy a

z (a)

d = ?

z (b) galaxy b

Figure 7: Diagram of the math used to determine a NN distance between two galaxies. My NN code found the distance “d” using the law of cosines.

There were a few instances where SDSS miscalculated an E+A’s redshift (usually because the database misclassified the galaxy as a quasi-stellar object), so the redshifts have been recalculated using Equation 2. Out of all the recalculated redshifts, only one was changed enough to place it in the cluster redshift range and it has been identified

with a ‘*’ in the table of galaxies. Note the H훼 absorption line (휆푟푒푠푡 =

656 푛푚, 휆표푏푠푒푟푣푒푑 taken from spectrum) is used for the calculations.

휆 − 휆 Eq. 2 푧 = 표푏푠푒푟푣푒푑 푟푒푠푡 휆푟푒푠푡

In order to find 휃, I follow Equation 3 to convert the RA (훼) and Dec (훿) in radians of two objects into their angular displacement, and then convert to degrees for use in the law of cosines.

휋 휋 휋 휋 휃 = 푐표푠−1( 푐표푠 ( − 훿 ) 푐표푠( − 훿 ) + 푠푖푛 ( − 훿 ) 푠푖푛 ( − 훿 ) cos (훼 − 훼 ) ) Eq. 3 2 1 2 1 2 1 2 1 1 2

Although the curvature of the universe does not need to be taken into account at low redshifts, distances based on redshift are difficult to work with in superclusters because the cluster dynamics are more complicated in superclusters compared to smaller, more uniform clusters. Remember that redshift is a velocity, not a distance, but I am making an assumption based on the expansion rate of the universe to determine distances.

This method of determining NN distance will give the correct ranking of density regions, but the wrong values. I devised a shortcut to calculate more accurate values based off of general data available on galaxy clusters. The average distance between two galaxies in a is between 1-10 million lightyears or 0.31-3.1 Mpc [9], although the low-end estimate corresponds to high density regions (like clusters) and the high-end estimate corresponds more to control fields. I have included both values in my calculations but because these are cluster galaxies, the low-end estimates are more accurate. I relate this range of values

21 to my NN value of 5.87 Mpc to find the ratio between published and NN code-calculated, and then multiply this ratio by my measured NN distances for each of the E+A types.

This assumption is likely just as accurate as calculating orbital velocities because I do not have to assume a point mass for the cluster, and I do not have to ignore the effects of three cluster centers on a galaxy’s dynamics. The average diameter of a galaxy (0.03

Mpc) is the estimated error in right ascension and declination, while the error in redshift is determined by dividing the average velocity dispersion of the cluster (~1000 km/s [10]) to the overall redshift of the cluster (~11,000 km/s [10]). The three error estimates are added in quadrature and applied to each NN distance.

Chapter 3: Results and Analysis

Out of 1,197 galaxies sorted in the survey, I categorized 4 blue, 54 green, and 156 ambiguous E+A galaxy candidates in Hercules, out of which 2 green E+A candidates and

6 ambiguous E+A candidates exhibit spiral morphologies.

Figure 8: Depicts the location of a few theoretical evolutionary checkpoints in an E+A galaxy's formation. ★ indicates ongoing mergers.

Figure 8 depicts the location of on-going mergers, starbursts, E+As, and non-E+As in the Hercules supercluster. Note starbursts were classified by the Sloan Digital Sky

Survey Database (SDSS), which I double-checked, and all appear to be starbursts. Figure

8 is important to my research because it tracks select, key evolutionary stages of E+As throughout their formations. While not all starbursts are kicked off by mergers, they certainly play a role in the formation of many E+As. The mergers located in the Hercules supercluster tend to be within filaments leading to and around the cluster center. On first glance it would seem mergers occur in denser regions of clusters, but due to high velocity dispersions in denser regions of clusters, incidents of harassment (as opposed to mergers)

23 are far more likely to occur. The relative number of starbursts to non-starbursts increases in less dense regions, most likely explained by major mergers occurring more frequently outside the cluster center. The high number of starburst galaxies suggest they are a relatively common occurrence in a galaxy's lifespan, and thus E+As could be a key evolutionary checkpoint.

Section 3.1 E+A Results and Analysis

The locations of each distinct type of E+A, qualified in Table 1, are plotted in

Hercules in Figure 8. By using the NN Python code, I quantify the regions that E+As resided in compared to any other kind of galaxy and estimate the density of intra-cluster medium surrounding each galaxy which is important when considering RPS as a quenching mechanism. The average NN distances are presented in Table 2.

NN distances (Mpc) Adjusted NN distances (Mpc)

(pre-adjustment) lower-bound upper-bound

Blue E+A 38.66 2.02 20.2

Green E+A 13.47 0.70 7.0

Ambiguous E+A 16.67 0.87 8.7

All galaxies 5.87 0.31 3.1

Table 2: NN distances from my code compared to their recalculated distance values. The lower bound is based on a NN distance of 10x a galaxy diameter (~0.31 Mpc) and the upper bound is based on a NN distance of 100x a galaxy diameter (~3.1 Mpc). All adjusted NN distances have an estimated error +/-0.1 Mpc.

For reference, the distance between the Milky Way and its closest companion,

Andromeda, is ≈ 0.765 Mpc. The NN code corroborates theories that blue E+As tend to reside in low density regions of clusters; many E+As are thought to form from a merger, and mergers are more likely to happen at low velocities which occur in low density regions of galaxy clusters. In addition, it is thought that over time blue E+As evolve into green E+As into ambiguous E+As and eventually passive ellipticals. If RPS is the driving force behind quenching starburst galaxies, logically new post-starburst galaxies would be farther from cluster centers than more evolved E+As, as galaxies would continue to in- fall even after star formation stops in the galaxy. While we might expect green E+As to be in less dense regions than ambiguous E+As, note that the line between green and ambiguous in uncertain, and the Y/Dim Collaboration has yet to develop a concrete, measurable way to distinguish between the two subsets of galaxies. The evolution of an

E+A is fluid, blue E+As likely become green E+As as their A-type stars leave the main sequence and evolve into red-giants, causing the overall color of the galaxy to become redder overtime. As the A-type star population diminishes over time, the Balmer absorption line equivalent widths shrink over time. See Table 3 for a summary of E+A equivalent widths. Note the equivalent widths for ambiguous E+As are not measured because all of them have very weak hydrogen Balmer absorption lines, far below the 5 Å threshold set by Goto et al. (2007) and the ~2 Å threshold set by Greene et al. (submitted

2021) [11] [6]. E+A galaxies comprised about 4.8% of all the galaxies in the cluster (not including ambiguous E+As).

H훼 (Å) H훽 (Å) H훾 (Å) H훿 (Å) Haverage (Å)

Blue 2.5 6.4 5.1 6.1 6.0

Green 2.0 3.8 2.0 2.3 2.7

Table 3: Equivalent width measurements for all of the E+A candidates within Hercules. Note that Havg does not include H훼. Two significant figures are included somewhat arbitrarily, the beginning and ending wavelengths of each absorption line were estimated by eye, and thus have large sources of error.

Figures 9 and 10 highlight the structure of Hercules in relation to archetypal

E+As. Note the subcluster marker coordinates are taken from the SDSS NASA/IPAC

Extragalactic Database (NED).

Figure 9: 2D representation of the locations of blue, green, and ambiguous E+A galaxies within z +/-0.01 of the subcluster center.

Figure 10: 2D representation of the locations of E+As in reference to their declination and redshift.

Section 3.2 Spiral E+A Results and Analysis

Spiral E+As are in even less dense regions of clusters relative to their elliptical E+A counterparts (see Table 3).

NN distances (Mpc) Adjusted NN distances (Mpc)

(pre-adjustment) lower-bound upper-bound

Green Spiral E+A 35.49 1.87 18.7

Ambiguous Spiral E+A 20.48 1.08 10.8

Table 3: NN distances from my code compared to their recalculated distance values. The lower bound is based on an average NN distance of 10x a galaxy diameter (~0.31 Mpc) and the upper bound is based on a NN distance of 100x a galaxy diameter (~3.1 Mpc). All adjusted NN distances have an estimated error +/-0.1 Mpc.

The equivalent widths of green spiral E+As are very comparable to green elliptical

E+As, see Table 4. Note Khutulun is the only spiral E+A candidate with an average equivalent width greater than 3 Å. Spiral E+As are also rarer than E+As and comprise only 0.17% of the complete Hercules dataset (not including ambiguous E+As).

H훼 (Å) H훽 (Å) H훾 (Å) H훿 (Å) Haverage (Å)

Green 1.2 3.9 2.3 2.3 2.8

Ambiguous 1.7 2.8 1.6 1.9 2.1

Table 4: Equivalent width measurements for all spiral E+A candidates within Hercules. Note Havg does not include H훼. All of the H훽, H훾, and H훿 have equivalent widths larger than 1.4 Å. The H훿 equivalent widths for green spiral E+As were all ≥2 Å. Two significant figures are included somewhat arbitrarily, the beginning and ending wavelengths of each absorption line were estimated by eye, and thus have large sources of error.

Figure 11: Plot of spiral E+As within Hercules in relation to regular E+As and non-E+As.

Figure 12: Plot of spiral E+As within Hercules in relation to regular E+As and non-E+As.

Section 3.3 Cold and hot ICM regions within Hercules

Besides studying how the location of E+As varies, I studied how the ICM varied between E+As and non-E+As to see if there was any correlation. In order to study the environment surrounding E+A candidates, I used data from ROSAT (Figure 13) and

Dickey 1997 (Figure 14) to chart hot and cold gas densities [12] [13]. In order to measure hot ICM, projects like XMM-Newton look at the 4 -7 Å range on a galaxy spectrum, the range that hot gas emits energy. Unfortunately, these wavelengths are not within our

SDSS spectra ranges, so I rely on other surveys and papers to help me complete this analysis. In order to properly plot galaxies over the images, I aligned markers on the original images to match markers on my Python graph since they are in different measurement systems. From these graphs it appears E+As are generally in hot gas regions rather than cold, and there does not appear to be any distinguishable preference of

ICM between spiral and non-spiral E+As.

Figure 13: Map of hot gas densities in A2151 and A2147, data taken from ROSAT [12].

Note ICM clusters toward denser regions of galaxy clusters due to gravity, and thus I assume these X-ray and HI gas maps are from the cluster and not at a different redshift.

These are meant to generalize E+A locations and ICM locations. Until ICM maps have published redshifts, this is my best conclusion. Note no data is available for A2152.

Figure 14: Map of cold gas densities in A2151 and A2147, data taken from Dickey 1997 [13].

Chapter 4: Discussion

Section 4.1 How do spiral E+As form?

In order for a galaxy to maintain a spiral morphology and become E+A, there must be some other mechanisms besides major mergers triggering starbursts. In 2018,

Wilkinson et al. analyzed 196 starburst galaxies at z=0.15 and found that over half the galaxies had not been in a merger in the last 2 Gyr, so there must be other methods to starburst that do not affect morphology [14]. Potentially the accretion of ICM could trigger a starburst, although in most of these spiral E+A cases the galaxies are in very low

ICM density regions. Based on my research I find four other possible explanations, each of which would result in a slightly different type of spiral.

Ruiz-Lara et al. (2020) study the star formation history in our neighborhood (≈2+ kpc from the solar system) and its relationship to dwarf galaxy interactions with the

Large Magellanic Cloud (LMC) and Sagittarius (Sgr). They correlate interactions between the Milky Way and dwarf galaxy Sagittarius at pericenter with periods of rapid star formation [15]. While it is unclear if such dynamics could actually trigger a starburst, they might be able to trigger a small round of star formation that leaves Balmer absorption lines resembling a green E+A.

In 2011, Purcell et al. modelled a dwarf galaxy’s interaction with an S0-type galaxy and found that loose arms formed in the process (see Figure 15) [16]. This could be the driving force behind loosely spiraled ambiguous E+A candidates. Unfortunately, there is little data available on known dwarf galaxies in Hercules, and without the redshifts of objects that look like they could be interacting with the spiral E+As, I cannot state with

31 certainty that dwarf galaxy mergers aid in forming any spiral E+As identified in this thesis.

Figure 15: (Left) Taken from Purcell et al, this graphic is comprised of screenshots from their dwarf galaxy interaction simulation [16]. Compare the Purcell et al loose spiral arms to the loose spiral arms in spiral E+A candidate SDSS J160110.37+164708.1 (Right).

The next possible theory on how spiral E+As maintain their morphology post- starburst, is that RPS can actually impact the morphology of the E+A as it quenches the starburst. In 2016, Steinhauser, Schindler, and Springel model an arbitrary disk galaxy undergoing RPS through different densities of ICM over 1.6 Gyr (Figure 17). This timescale is comparable to the time it takes to form an E+A galaxy. To identify E+A galaxies, I searched through other datasheets from the Leo, Virgo, and Coma clusters and two control fields (RA = 250.45, Dec = 36.47 and RA = 223 Dec = 16) that the Y/Dim

Collaboration has analyzed, and I identified 9 other spiral E+A candidates. Both of the spiral E+As in Figure 16 were taken from control region RA = 250.45, Dec = 36.47, a low ICM density region. The low-density models from Steinhauser, Schindler, and

Springel (row S4(C) in Figure 17) closely match the morphologies in Figure 16, and thus these galaxies could have been S0-type galaxies undergoing starburst and developed arms through RPS, evolving them from E+A to spiral E+A.

Figure 16: IC 4614 and 2MASX J16545550+3728352, notice morphological similarities between these two candidates from low density regions and the galaxies in S4 (c) in Figure 12.

The final method for a galaxy like Khutulun to maintain a strong spiral morphology while undergoing starburst, is the galaxy’s bar funneling star-forming gas to the center of the galaxy to kickstart a starburst. This would suggest that only the central region of Khutulun is E+A and that it could be common for barred spirals to appear E+A at some point in their lifespan. On further inspection of the 8 spiral E+A candidates, 5 have a distinct bar.

Figure 17: Image taken from simulations that Steinhauser, Schindler, and Springel (2016) provide modeling for how ram-pressure stripping affects morphology and star formation over time [17]. G1a iso is a galaxy in an isolated field. S1 experiences the highest density ICM, S4 the middle density ICM, and S3 the low density ICM.

Section 4.2 ICM hot and cold gas analysis

Ram pressure stripping in regions of hot gas ICM could be a trigger for a starburst.

Bekki and Couch (2003) simulate star formation in spiral galaxies over time and theorize that in low density cold ICM regions and high density hot ICM regions starburst could be triggered via compression of hot gas during RPS [18]. In this way RPS can act as both a mechanism to start and end starburst. HI (cold) gas can inhibit RPS from compressing hot gas in a galaxy to kickstart a starburst, so any spiral E+As formed via compression in

RPS would need to form in low density cold ICM regions and higher density hot ICM

34 regions. Based on the data presented in Figures 13 and 14, green spiral E+As are in medium-low density hot ICM and low density cold ICM. The two green spirals within the hot gas mapping of A2147 are Khutulun and SDSS J160202.91+160510. I am not certain the hot gas regions are dense enough for this to be a trigger, and since both these galaxies are barred spirals, a more likely explanation is the bar funneling star forming gas to the central parts of the galaxy (see Section 4.1), as that process is not dependent on location within a galaxy cluster. Ambiguous spiral E+As are in lower density hot ICM regions than green ones, which seems counterintuitive since our understanding of E+As is they fall inward over time. This reversal could indicate hot gas density is related to green spiral E+A formation, but more data should be collected before I draw any conclusions.

Chapter 5: Considerations

My research is constrained by a small sample size. Fortunately, other members of the

Y/Dim Collaboration are studying other galaxy clusters and control fields to learn more about the E+A galaxy population. My thesis does not include their work, but all of our data is being combined and synthesized into a paper for submittal to the Astrophysical

Journal in 2021. The second constraint, briefly outlined earlier in my thesis, is based on how SDSS collects its spectrographs. SDSS uses a single fiber spectroscopy which only focuses on the center of a galaxy and thus we have to assume any galaxy with an E+A central spectrum and uniform golden color throughout the galaxy is completely E+A, but

I cannot know for certain. An example of SDSS producing an E+A-like spectrum for a galaxy that is obviously not quiescent is shown in Figure 18.

Figure 18: This galaxy could be classified as E+A from its central spectrum, but the spiral arms' blue colors suggest star formation is likely still occurring in the galaxy.

In order to determine if a galaxy is fully quiescent, spectral data must be taken from every part of the galaxy (see Figure 14). Mapping Nearby Galaxies at APO (MaNGA) is a new project within SDSS and uses integral field unit spectroscopy to take hundreds of

36 spectra across the target galaxy and would be able to determine if the spiral E+As are fully quenched or not. There was only one spiral E+A candidate with MaNGA data available, but even without MaNGA data the photo taken by SDSS seems non-uniform in color and the full galaxy spectrum confirms there is H훼 emission in the arms (see

Appendix 8.4 for photo and spectrum).

Figure 19: Points on a galaxy where MaNGA takes spectra from. Image taken from SDSS.

Chapter 6: Conclusion

After analyzing the locations of E+As, and in particular spiral E+As, I have been able to conclude that while starburst galaxies typically occur in the outer regions of the

Hercules supercluster, E+As are more commonly found in the mid-range regions around the cluster center (~10 Mpc NN distance). This is most likely due to starburst galaxies forming in the outer regions of the cluster and infalling as they become RPS and quiescent, forming E+A galaxies closer to the cluster center. Spiral galaxies probably achieve E+A status in a variety of ways, ranging from dwarf galaxy interactions, RPS impacting spirality, ICM accretion fueling starburst, or the structure of a barred spiral initiating starburst on its own. Khutulun most likely underwent starburst by its bar pulling star forming gas from its arms to the center and thus leaving its morphology intact.

2MASX J16545550+3728352 (Figure 16), could have formed via a dwarf galaxy merger and thus undergone starburst in a lower density region, causing the final spiral E+A to end up in a low ICG density region. The NN distance is greatest for blue E+As and similar for ambiguous and green E+As, and spiral E+As have even larger NN distances compared to their elliptical E+A counterparts. This is likely due to spiral morphologies having a less likely chance of disruption to morphology in outer cluster regions. Both spiral and non-spiral E+As appear in hot gas density regions as opposed to cold gas regions, although the data on cold gas regions is harder to interpret. At this time, I do not know why E+As are present in hot gas regions, although it could have to do with E+As infalling over time into hot gas as they move toward cluster centers.

Chapter 7: Works Cited

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Chapter 8: Appendix

Section 8.1 Equivalent width code #Code developed by Serena Wurmser (Harvard University) of the Y/Dim research group %pylab inline from astropy.io import fits from astropy import units as u import numpy as np from matplotlib import pyplot as plt from astropy.visualization import quantity_support from specutils import Spectrum1D from specutils.fitting import fit_generic_continuum quantity_support() f = fits.open('http://dr15.sdss.org/optical/spectrum/view/data/format=fits?plateid=2521&m jd=54538&fiberid=293&reduction2d=v5_7_0') specdata = f[1].data f.close() lamb=10**specdata['loglam']*u.AA flux=specdata['flux']*u.Unit('1e-17 erg cm-2 s-1 AA-1') spec=Spectrum1D(spectral_axis=lamb, flux=flux) f, ax=plt.subplots() ax.step(spec.spectral_axis, spec.flux,linewidth=.2) plt.savefig("eqwd.pdf") left_zoom_to = 4300*u.AA #what range do you want to view the spectra?right_zoom_to = 5400 *u.AA right_zoom_to =4700*u.AA continuum=54#estimate the continuum, shown in yellow left_bound=4515# where to start eqw measurement? right_bound=4545#where to end eqw measurement? plt.plot(spec.spectral_axis, spec.flux) plt.xlim(left_zoom_to, right_zoom_to) plt.axhline(y=continuum, color="orange", linestyle="--", linewidth="1") li = np.where((spec.spectral_axis>left_bound*u.AA) & (spec.spectral_axis

Section 8.2 NN code import numpy as np import math

#### ROSEMARY WILLIAMS 2021 ####

#our imported files allea = np.genfromtxt("all.csv", delimiter = ",", names = ["x","y","z"]) #all the galaxies ambig = np.genfromtxt("ambigall.csv", delimiter = ",", names = ["x","y","z"]) #ambiguous e+as green = np.genfromtxt("greenall.csv", delimiter = ",", names = ["x","y","z"]) #green e+as blue = np.genfromtxt("blueall.csv", delimiter = ",", names = ["x","y","z"]) #blue e+as gsp = np.genfromtxt("yesspiral.csv", delimiter = ",", names = ["x","y","z"]) #green spirals asp = np.genfromtxt("ambigspiral.csv", delimiter = ",", names = ["x","y","z"]) #ambiguous spirals alldist=[1000] #where the distance between galaxy[n] and all the other galaxies gets input, 1000 just helps kickstart if/else distances=[] #where all the shortest distances are input x,y,z=blue["x"],blue["y"],blue["z"] #the one we change z = 300000 * z / 67.4 #Mpc, using hubbles law x1,y1,z1=allea["x"],allea["y"],allea["z"] #complete dataset z1=300000*z1/67.4 #Mpc, using hubble's law n=0 while n<1139: #controls what our point is that we are finding distances to, this is all dataset xp,yp,zp=x1[n],y1[n],z1[n] m=0 while m

if ra1==ra2 and dec1==dec2: m=m+1 else: degree=180/math.pi*math.acos(math.cos(math.pi/2-dec1)*math.cos(math.pi/2- dec2)+math.sin(math.pi/2-dec1)*math.sin(math.pi/2-dec2)*math.cos(ra1-ra2)) distance=np.sqrt(z[m]**2+zp**2+2*z[m]*zp*math.cos(degree)) #using law of cosines to find length of edge between galaxies check=distance-alldist[0] #checks to see if this distance is shorter than all the distance currently in alldist[0] if check<0: #if it is smaller it replaces alldist[0] alldist[0]=distance m=m+1 alldist.sort() #sorts all of the nn distances from low to high and then takes the smallest nn distance and puts it in "distances" distances.append(alldist[0]) n=n+1 distances.sort()# we can print this and look at all distances to delete duplicates distances=list(set(distances)) mean=np.mean(distances) print(mean) print(distances)

Section 8.3 3D visualizations of elliptical and spiral E+A galaxies

Section 8.4 Example of SDSS classified E+A that is not fully E+A

The only spiral E+A with MaNGA data, appears E+A in the center but MaNGA confirms that the blue in the arms indicate star forming.

Data files have been appended to the end of this thesis.

Spiral E+A Sheet Key Information Equivalent Widths Discussion link ObjID ra dec z Ha Hb Hg Hd avg (-Ha) E+A? data from link 1237668337934074279 240.47 15.79 0.04115 0.66190407 3.2696959 2.3673764 2.3357091 2.6575938 G Hercules Link 1237665567691833651 240.51 16.09 0.04163 1.6987735 4.5392814 2.203476 2.3051503 3.015969233 G Hercules link 1237665441534181658 239.49 18.21 0.04714 1.4210482 1.7933998 1.5774284 1.9861997 1.785675967 A Hercules Link 1237665567155028265 240.50 15.49 0.03496 1.3051172 2.7102016 1.2245723 1.7936523 1.9094754 A Hercules Link 1237665531723448684 240.79 16.26 0.03682 2.2470449 2.9773546 1.5852449 1.448506 2.003701833 A Hercules Link 1237665532259992030 240.29 16.79 0.03569 1.6086316 3.6110682 1.7186877 2.5359969 2.6219176 A Hercules Link 1237665567692227004 241.42 15.77 0.04038 2.0224438 3.5464371 1.6354073 2.0546026 2.412149 A Hercules Link 1237665532260647216 241.68 16.29 0.03647 1.806623 2.2259741 1.9884338 1.6817316 1.965379833 A Hercules not Hercules: Link 1237668294449496344 175.84 20.26 0.02264 2.0465325 2.0798605 1.9825578 2.0888294 2.0504159 G Leo link 1237658493355884588 186.46 10.46 0.00363 1.1398936 2.4056224 3.4046671 4.198 3.3360965 G Virgo Link 1237667915953668254 176.28 20.16 0.02049 2.7629581 4.9335347 2.7664621 4.1548086 3.9516018 G Leo link 1237662268612215204 230.89 5.92 0.04253 1.9021626 2.7327796 1.9424099 1.8654982 2.180229233 G G515 region Link 1237655129305776346 253.73 37.48 0.06060 1.3238763 2.5832621 0.951537 N/A 1.76739955 G RA = 250.45, Dec = 36.47 Link 1237661387081449571 248.29 34.93 0.03491 1.661155 3.1540465 1.444504 1.5521689 2.0502398 A RA = 250.45, Dec = 36.47 Link 1237659329780121629 249.45 36.11 0.03288 1.4577459 1.5754693 1.3740974 2.2562803 1.735282333 A RA = 250.45, Dec = 36.47 Link 1237667781239964000 223.08 16.96 0.05739 1.72175 2.083428 1.7881165 1.7603505 1.877298333 A RA=223, Dec=15 Blue E+A Sheet Link ra dec redshift u g r i ha hb hg hd have averages: 18.5274 17.0667 16.5851 16.3344 2.45 6.38 5.10 6.11 6.02 link 240.9014 15.7674 0.029 19.5633 18.1890 17.6275 17.3441 1.74 4.47 4.30 4.79 4.52 link 240.2146 15.1513 0.034 16.5017 14.9287 14.3461 14.0246 2.27 8.60 5.58 6.57 6.92 link 241.6255 18.5877 0.038 19.0238 17.4228 16.9134 16.6549 1.89 6.76 4.93 5.57 6.38 Link 240.4759 16.0047 0.039* 19.0209 17.7263 17.4535 17.3141 3.88 5.70 5.58 7.52 6.27 Green E+A Sheet Link ra dec redshift u g r i ha hb hg hd have averages: 18.8653 17.2219 16.5025 16.1604 2.03 3.73 1.97 2.27 2.64 LINK 238.5641 18.2408 0.050 18.8730 17.1104 16.2826 15.9071 1.82 3.49 1.88 1.80 2.39 link 240.6992 13.4990 0.048 19.5554 17.9259 17.2447 16.9272 1.26 4.39 2.12 2.12 2.87 link 239.5616 18.0564 0.047 19.8988 18.1113 17.3082 16.9318 1.66 2.25 1.45 2.54 2.08 LINK 240.2860 20.0999 0.047 19.4773 17.8028 17.0526 16.6903 1.14 1.62 1.82 2.88 2.11 LINK 240.7579 19.0676 0.047 19.2058 17.3916 16.5827 16.2458 1.68 3.25 1.56 1.29 2.03 link 242.1935 16.1905 0.045 20.1369 18.4648 17.7319 17.3891 1.72 4.32 1.68 2.62 2.87 link 239.7994 15.1540 0.043 18.4461 16.7997 16.0824 15.7365 2.34 3.89 1.74 2.21 2.61 link 239.8547 15.2012 0.043 19.3234 17.7663 17.0816 16.7524 1.98 3.09 1.61 3.04 2.58 link 240.5121 16.0863 0.042 19.1728 17.5851 16.8964 16.5929 1.70 4.54 2.20 2.31 3.02 link 240.3787 15.9693 0.041 19.1108 17.3940 16.6367 16.2841 2.19 3.47 1.77 1.48 2.24 link 240.4665 15.7923 0.041 17.1890 15.5096 14.7433 14.3550 0.66 3.27 2.37 2.34 2.66 link 240.7396 16.3407 0.041 19.4951 17.9433 17.2471 16.9206 1.60 2.48 2.48 3.02 2.66 link 240.9227 16.5246 0.041 19.8071 18.2202 17.6234 17.3325 2.28 3.55 2.81 3.66 3.34 link 242.1194 14.6428 0.040 19.3948 17.8486 17.1618 16.8313 2.31 3.77 1.87 3.11 2.92 link 241.5367 15.7863 0.040 17.9241 16.2430 15.4808 15.1350 2.48 3.81 1.53 1.89 2.41 link 241.5145 15.6494 0.040 18.8085 17.3433 16.6066 16.2574 2.19 2.52 1.59 1.95 2.02 link 240.4920 16.3919 0.040 18.7318 17.2742 16.6104 16.3023 2.16 4.99 3.93 1.99 3.63 link 241.6238 18.2679 0.040 18.5476 16.7947 16.0818 15.7288 1.66 3.97 2.41 3.07 3.15 link 240.7081 16.2368 0.039 19.8658 18.4481 17.7754 17.4611 2.22 4.67 3.72 3.17 3.85 link 241.3324 18.3154 0.039 17.6655 15.9287 15.1978 14.8555 2.18 5.94 2.36 3.19 3.83 link 241.9423 18.5256 0.039 18.7818 17.0777 16.3414 16.0036 2.43 2.76 1.38 2.12 2.09 link 240.4452 15.8222 0.039 17.4638 15.7239 14.9773 14.6158 1.87 3.37 1.82 1.98 2.39 link 241.4436 18.5315 0.038 18.2552 16.5117 15.7682 15.4199 2.40 5.10 1.50 2.51 3.04 link 241.6202 18.2703 0.038 19.4349 17.5229 17.0101 16.6888 n/a 4.84 2.60 3.41 3.62 link 241.7993 18.6101 0.038 17.6906 15.9395 15.1878 14.8257 2.64 5.08 2.11 1.78 2.99 link 240.7808 15.8965 0.038 19.4449 17.7889 17.0046 16.6418 1.62 2.90 1.89 2.01 2.27 link 241.8840 15.6482 0.038 19.7042 17.9750 17.2913 16.9795 1.71 4.43 1.64 1.84 2.64 link 240.8155 16.3189 0.038 18.5980 16.9335 16.2541 15.9207 2.58 3.57 2.53 3.72 3.27 link 240.3663 16.4921 0.038 18.7308 17.0231 16.2843 15.9286 2.11 3.20 2.03 2.31 2.51 link 240.7602 16.0332 0.037 18.3301 16.6477 15.9084 15.5572 1.84 3.58 2.26 1.83 2.56 link 240.1693 16.0076 0.037 19.5769 17.9220 17.1757 16.8339 1.60 4.15 1.62 1.92 2.56 link 241.9296 18.4540 0.037 19.5707 17.9251 17.1942 16.8363 2.17 4.51 1.70 1.71 2.64 link 240.5323 16.5938 0.037 19.9097 18.0821 17.3820 17.0479 1.57 3.33 1.80 1.39 2.17 link 239.9811 16.6293 0.037 19.2722 17.8315 17.1143 16.7512 1.94 3.65 1.81 2.58 2.68 link 240.3033 16.4720 0.036 19.1635 17.5065 16.8096 16.4799 2.50 3.48 1.80 2.08 2.45 link 239.5788 16.2004 0.036 19.1802 17.7088 17.0106 16.6788 2.66 2.06 2.25 N/A 2.16 link 240.6968 15.1582 0.036 18.1049 16.4003 15.6351 15.2711 2.63 3.41 1.71 1.78 2.30 LINK 238.7058 18.9171 0.036 16.7245 14.9898 14.2208 13.8457 1.78 3.23 1.69 1.96 2.29 link 240.8660 16.0357 0.036 19.5699 18.1564 17.4240 17.0749 1.59 2.33 1.94 N/A 2.13 link 240.9707 16.3469 0.035 19.1916 17.4894 16.7318 16.3794 2.03 2.83 1.11 2.31 2.08 link 241.3338 17.7467 0.035 19.2157 17.5968 16.8780 16.5211 1.96 2.32 2.68 1.72 2.24 link 240.5914 16.0613 0.035 18.4798 16.9464 16.2320 15.9047 1.86 3.34 1.73 N/A 2.54 link 240.3605 16.0587 0.035 18.6203 16.9729 16.2347 15.8747 2.26 2.77 1.69 N/A 2.23 link 240.3927 15.6660 0.035 19.8243 18.3613 17.6683 17.3308 2.52 6.83 1.67 N/A 2.84 link 241.5126 17.7017 0.034 18.3072 16.8217 16.0501 15.6812 2.08 3.19 1.50 1.40 2.03 LINK 242.2356 19.9000 0.034 18.4440 16.7212 15.9731 15.6234 1.72 4.38 1.78 1.45 2.54 link 241.3447 16.1982 0.034 16.5416 14.8559 14.1003 13.7532 2.09 5.69 1.41 1.75 2.95 link 241.1780 17.4985 0.033 18.8122 17.0603 16.3104 15.9500 1.62 3.82 0.93 1.78 2.18 link 240.6227 15.9406 0.033 19.4465 17.8437 17.1632 16.8326 2.53 4.03 1.65 1.28 2.32 LINK 238.3618 18.2228 0.033 18.4025 16.9203 16.2409 15.9224 2.69 3.66 2.47 2.83 2.98 link 241.1607 17.6097 0.032 19.2107 17.4951 16.9127 16.6260 2.82 5.08 3.20 3.69 3.99 link 241.0836 15.7777 0.031 18.3643 16.8805 16.2140 15.9039 2.28 3.90 1.48 1.82 2.40 link 240.9014 15.7674 0.029 19.5633 18.1890 17.6275 17.3441 1.74 4.47 4.30 4.79 4.52 link 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