LONG PERIOD VARIABLE STARS IN THE GLOBULAR CLUSTER M5 (NGC 5904)

Kyle Pellegrin

A Thesis

Submitted to the Graduate College of Bowling Green State University in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

August 2020

Committee:

Andrew C. Layden, Advisor

John B. Laird

Dale W. Smith c 2020 � Kyle Pellegrin

All Rights Reserved iii

ABSTRACT

Andrew C. Layden, Advisor

Long Period Variable (LPV) stars have been poorly studied in globular clusters due to having long pulsation periods ranging from 30-1000 days. Previous cluster studies have focused mainly on RR Lyrae variables, which only require a few days of observations in order to well quantify their light curves, making these studies of little use to understand LPV behavior. M5 is a prime target for studying LPV stars, and its characteristics have been well studied (such as metallicity, distance, etc.), but little work has been done previously on the LPV populations. Images of M5 were collected by the PROMPT telescopes at Cerro Tololo Inter-American Observatory (CTIO) over 8 months, spanning most of 2011, with additional data provided by the BGSU observatory in 2007, 2009, 2010. This wide time span allows for a thorough char- acterization of LPVs that has not previously been possible. Initial light curve results have been very promising, with successful characterization of W Virginis and RV Tauri type variables. The variability of known LPVs, V50 and V171-V180, were also successfully characterized with un- precedented detail. Updated periods were determined for the eleven known LPVs, four new LPVs were discov- ered, and four additional stars were found to be suspected variable stars. The creation of a Color Magnitude Diagram (CMD) supports the hypothesis that LPV pulsations become more regular, and amplitudes increase, as a star moves up the RGB. Finally, all of the evidence from the PROMPT data set was compiled and each star variability type was determined based upon the observed light curves and the star’s location on the CMD. Suggestions for future observations was also provided to assist in future work improving the characterization of each LPV. iv

To my wife Anna and my family who always believed in me v

ACKNOWLEDGMENTS

This work would not have been possible without the direction and support from Dr. Andrew Layden. Dr. Layden provided a welcoming and nurturing environment to do research in and his endless support, knowledge, and patience are appreciated beyond words. I would also like to thank the members of the thesis committee Dr. John Laird and Dr. Dale Smith, who both provided great feedback that have helped improve this paper to what is seen today. I’d also like to thank my parents, Steve and Cheryl, who always encouraged me to follow my dreams. I cannot thank them enough for their love and support along the way. Finally, I owe a big thanks to my wife Anna who has supported me in this endeavor through thick and thin. This wouldn’t have been possible with out her love, support, and patience. vi

TABLE OF CONTENTS

Page CHAPTER 1. INTRODUCTION ...... 1 CHAPTER 2. OBSERVATIONS ...... 5 2.1 Location ...... 5 2.2 Equipment ...... 5 2.2.1 Telescope and Camera ...... 5 2.2.2 Filters ...... 5

2.3 Observing Procedure ...... 6 2.3.1 Exposure Times ...... 6 2.3.2 Requesting Observations ...... 6 CHAPTER 3. PRELIMINARY IMAGE ANALYSIS ...... 8 3.1 Initial Review of Images ...... 8 3.1.1 Observing Cadence ...... 9 3.1.2 Reference Star Selection ...... 10 3.2 Statistics from Digital Images ...... 11 3.2.1 CCD Cameras and Poisson Statistics ...... 11 3.2.2 Sky Background ...... 13 3.2.3 Full Width at Half Maximum ...... 13

3.2.4 Ellipticity ...... 15

CHAPTER 4. ISIS IMAGE SUBTRACTION ...... 16

4.1 Introduction ...... 16

4.2 Image Preparations before Using the ISIS Process ...... 17

4.2.1 Image Scaling ...... 17 4.2.2 Image Alignment ...... 18 4.2.3 Image Trimming ...... 19 4.2.4 Step 1: Reference Image Creation ...... 21 vii

4.2.5 Step 2: Image Subtraction ...... 21 4.2.6 Step 3: Creating a Composite Image ...... 23 4.3 Identification of Known Variable Stars ...... 25 4.3.1 World Coordinate System ...... 25 4.3.2 Marking Known Variables ...... 27 CHAPTER 5. PERIOD DETERMINATION ...... 30 5.1 Flux Difference Photometry with ISIS ...... 30 5.2 Period Determination ...... 30 5.2.1 Period Aliases and Harmonics ...... 32 5.2.2 Determining Period Uncertainty ...... 32 5.3 Two Test Cases with Known Variables ...... 33 5.3.1 Light Curve Analysis of V42 ...... 33 5.3.2 Light Curve Analysis of V84 ...... 35 5.4 Known Long Period Variables ...... 38 5.4.1 Light Curve Analysis of V50 ...... 38 5.4.2 Light Curve Analysis of V171 ...... 42 5.4.3 Light Curve Analysis of V172 ...... 44 5.4.4 Light Curve Analysis of V173 ...... 48 5.4.5 Light Curve Analysis of V174 ...... 50 5.4.6 Light Curve Analysis of V175 ...... 52

5.4.7 Light Curve Analysis of V176 ...... 54

5.4.8 Light Curve Analysis of V177 ...... 58

5.4.9 Light Curve Analysis of V178 ...... 60

5.4.10 Light Curve Analysis of V179 ...... 62

5.4.11 Light Curve Analysis of V180 ...... 65 5.5 Newly Discovered Variable Stars ...... 68 5.5.1 Light Curve Analysis of V309 ...... 68 viii

5.5.2 Light Curve Analysis of V312 ...... 70 5.5.3 Light Curve Analysis of V313 ...... 72 5.5.4 Light Curve Analysis of V403 ...... 74 5.6 Summary of Results: New Variable Stars ...... 76 5.7 New Suspected Variable Stars ...... 77 5.7.1 Light Curve Analysis of V300 ...... 77 5.7.2 Light Curve Analysis of V307 ...... 80 5.7.3 Light Curve Analysis of V315 ...... 82 5.7.4 Light Curve Analysis of V318 ...... 84 5.8 Summary of Results: Suspected Variable Stars ...... 86 CHAPTER 6. CREATION OF A COLOR MAGNITUDE DIAGRAM ...... 88 6.0.1 Photutils for PSF Photometry ...... 88 6.0.2 Transformation of Instrumental Magnitudes to Standard Magnitudes . 89 CHAPTER 7. DISCUSSION OF RESULTS ...... 93 7.1 Variable Star Type Designations ...... 93 7.2 Known LPVs ...... 93 7.2.1 Summary of Results for V50 ...... 95 7.2.2 Summary of Results for V171 ...... 96 7.2.3 Summary of Results for V172 ...... 97 7.2.4 Summary of Results for V173 ...... 98

7.2.5 Summary of Results for V174 ...... 98

7.2.6 Summary of Results for V175 ...... 99

7.2.7 Summary of Results for V176 ...... 100

7.2.8 Summary of Results for V177 ...... 100

7.2.9 Summary of Results for V178 ...... 101 7.2.10 Summary of Results for V179 ...... 102 7.2.11 Summary of Results for V180 ...... 103 ix

7.3 Newly Discovered Variable Stars ...... 104 7.3.1 Summary of Results for V309 ...... 104 7.3.2 Summary of Results for V312 ...... 105 7.3.3 Summary of Results for V313 ...... 105 7.3.4 Summary of Results for V403 ...... 105 7.4 Summary of Suspected Variable Stars ...... 106 7.4.1 Summary of Results for V300 ...... 106 7.4.2 Summary of Results for V307 ...... 107 7.4.3 Summary of Results for V315 ...... 107

7.4.4 Summary of Results for V318 ...... 108 CHAPTER 8. CONCLUSION ...... 109 8.1 Comparison of Variability along the RGB ...... 109 8.2 Suggested Cadence for Future Observations ...... 111 8.3 Long Secondary Periods in LPVs ...... 113 8.4 Comparison of LPVs to M13 ...... 114 8.5 Final Summary of Results ...... 117

BIBLIOGRAPHY...... 109 x

LIST OF FIGURES

Figure Page 3.1 Examples of unusable images ...... 8 3.2 Observing cadence of PROMPT dataset ...... 9 3.3 Airmass vs. Julian Date ...... 10 3.4 The star inside the orange circle is the reference star for the globular cluster. . . . . 11 3.5 Examples of various color mapping schemes ...... 12 3.6 Distribution of sky background counts from PROMPT data set ...... 13 3.7 Comparison of FWHM values across each image in the data set ...... 14 3.8 Measured ellipticity values across the PROMPT dataset...... 15 4.1 Step 1: Reference image creation ...... 16 4.2 Step 2: Creating subtracted images ...... 17 4.3 Step 3: Creating the composite image ...... 17 4.4 Position of the cluster center across entire data set ...... 19 4.5 Trimmed area of image ...... 20 4.6 Reference image ...... 22 4.7 Examples of subtracted images ...... 22 4.8 Composite image ...... 24 4.9 Composite image with all known variable stars marked ...... 26

4.10 Composite images with various types of variable stars labeled...... 28

4.11 All known LPVs in M5 listed by Clement ...... 29

5.1 V42 light curves ...... 34

5.2 V42 power spectrum ...... 35

5.3 V42 light curve (yellow points) with models (red points) ...... 35 5.4 V84 light curves ...... 36 5.5 V84 power spectrum ...... 37 5.6 V84 light curve (yellow points) with models (red points) ...... 37 xi

5.7 V50 light curves...... 38 5.8 Power spectrum for V50 over the period range 20-200 days ...... 39 5.9 Light curves (yellow data points) with models (red data points) for V50 ...... 40 5.10 Folded light curves used to determine the period uncertainty for V50...... 41 5.11 V171 light curves ...... 42 5.12 V171 power spectrum ...... 42 5.13 Light curve with models ...... 44 5.14 Light curves for V172 ...... 44 5.15 Power spectrum for V172 over the period range 20-200 days ...... 45

5.16 Light curves (yellow data points) with models (red data points) for V172 ...... 45 5.17 V172 folded light curves to determine period uncertainty ...... 47 5.18 V173 light curves ...... 48 5.19 V173 power spectrum ...... 49 5.20 173 light curve (yellow points) with 125+309 day model (red points) ...... 50 5.21 V174 light curves ...... 50 5.22 V174 power spectrum ...... 51 5.23 V174 light curve (yellow points) with 78+50 day model (red points) ...... 52 5.24 V175 light curves ...... 52 5.25 Power spectrum for V175 ...... 53 5.26 Models for V175 ...... 54

5.27 V176 light curves ...... 54

5.28 V176 power spectrum ...... 55

5.29 Models for V176 ...... 57

5.30 V177 light curves ...... 58

5.31 Power spectrum: 20-200 days ...... 59 5.32 V177 light curve (yellow points) with top four period combined model (red points) . 60 5.33 V178 light curves ...... 60 xii

5.34 V178 power spectrum ...... 61 5.35 178 light curve (yellow points) with 145 day model (red points) ...... 62 5.36 V179 light curve ...... 62 5.37 V179 power spectrum ...... 63 5.38 Model applied to V179 light curve and phased light curve...... 64 5.39 V180 light curves ...... 65 5.40 V180 power spectrum ...... 66 5.41 Light curves of V180 with models ...... 67 5.42 V309 light curves ...... 68

5.43 V309 power spectrum ...... 69 5.44 V309 light curve (yellow points) with models (red points) ...... 70 5.45 V312 light curves ...... 70 5.46 V312 power spectrum ...... 71 5.47 V312 light curve (yellow points) with models (red points) ...... 72 5.48 V313 light curves ...... 72 5.49 V313 power spectrum ...... 73 5.50 V313 light curve (yellow points) with 166 day model (red points) ...... 74 5.51 V403 light curves ...... 74 5.52 V403 power spectrum ...... 75 5.53 V403 light curve (yellow points) with models (red points) ...... 76

5.54 V300 light curves ...... 78

5.55 V300 power spectrum ...... 79

5.56 V300 light curve (yellow points) with 98+35 day model (red points) ...... 80

5.57 V307 light curves ...... 80

5.58 V307 power spectrum ...... 81 5.59 V307 light curve (yellow points) with 280 day model (red points) ...... 82 5.60 V315 light curves ...... 83 xiii

5.61 V315 power spectrum ...... 83 5.62 V315 light curve (yellow points) with 303+157 day model (red points) ...... 84 5.63 V318 light curves ...... 85 5.64 V318 power spectrum ...... 86 5.65 V318 light curve (yellow points) with 167+84 day model (red points) ...... 86 6.1 Photutils detection of sources ...... 89 6.2 V and I transform plots ...... 91 6.3 Color magnitude diagrams (CMDs) for M5...... 92 7.1 Published light curves from Arellano Ferro et al...... 94

8.1 Summary of results from Osborne et al. study on LPV in M13...... 115 xiv

LIST OF TABLES

Table Page 5.1 Sample of output from ISIS after performing flux-difference photometry on V50 . . 30 5.2 Period search regions ...... 31 5.3 Top five period values for V171 ...... 43 5.4 Top five period values for V173 ...... 48 5.5 Top five period values for V175 ...... 53 5.6 Top 3 periods for V176 ...... 55

5.7 Top four periods for V177 ...... 59 5.8 Top five period values for V179 ...... 64 5.9 Top three period values for V180 ...... 66 5.10 Top four period values for V309 ...... 69 5.11 Top five period values for V403 ...... 75 5.12 Summary of periods for newly discovered variable stars ...... 77 5.13 Top four period values for V300 ...... 79 5.14 Summary of periods for suspected variable stars ...... 87 7.1 Periods of known LPVs ...... 95 8.1 Summary of characteristics of LPVs going from the tip of the RGB downwards by I magnitude from the PROMPT data set ...... 110 1

CHAPTER 1. INTRODUCTION

There are many different mechanisms that can lead a star to exhibit variability, but all can be divided into two main classes; extrinsic and intrinsic variables. Extrinsic variables are stars whose variability is caused by something external to the star itself. Typical examples of this variable type are eclipsing variables; where another body passes in front of the observed star (such as a planet or even another star), or variability can be due to microlensing events. Intrinsic variables include stars whose variability is caused by something internal to the star itself such as pulsating variables (where the star expands and contracts over time), cataclysmic variables (where a white dwarf will show an outburst due to fusion in the hydrogen or helium layer accreting onto the white dwarf from partner star), eruptive variables (eruptions associated with stellar magnetic activity), and ellipsoidal variables (tidal distortion of a star usually caused by a close neighbor star that is non-eclipsing). [9] Globular clusters (GCs) are collections of hundreds of thousands of Population II stars that are gravitationally interacting with each other. While a wide variety of variable stars exist in a GC, the most common stars in a GC are RR Lyrae stars followed by Cepheids. Both of these stars are classic examples of pulsating variable stars, and have played important roles in understanding stellar evolution and determining distances. A lesser studied variable star also found in GCs are Long Period Variable (LPV) stars. LPVs are red giant stars that exhibit stellar pulsation, with periods ranging from 30-1000 days. This long pulsation period has traditionally been the reason these variables are overlooked, as it can be difficult to gather enough information with an appropriate cadence to adequately cover even one complete pulsation period. LPVs are broken down into two main categories; regular and semi-regular. Regular LPVs (Also known as Mira type variables. Denoted as M type variables) are characterized by having regular, sinusoidal-like, light curves with an amplitude greater than 2.5 magnitudes, while semi-regular LPVs (denoted as SR type variables) have erratic appearing light curves with amplitudes below 2.5 magnitudes. It is understood that the erratic nature of semi-regular LPV light curves is caused by a super- 2 position of multiple modes of stellar pulsation occuring within the star. The International Variable Star Index further subdivides the semi-regular variable star category based upon specific pulsation period ranges and the star’s spectral type. The designations are SRA, SRB, SRC, SRD, and SRS type variable stars. The most likely type of LPV to be found in a globular cluster are SRA and SRB type variable stars. SRA type variable stars are giants that have a small but persistent period- icity (amplitude of less than 2.5 mag in V ) and periods between 35 and 1200 days. SRB variables by comparison are giants with poorly defined periodicity, with mean cycles between 20 and 2300 days. [19] Of the remaining designations, SRC type variables are supergiants with an amplitude of ap- proximately 1 mag and periods of at least 30 days. SRD variables are giants or supergiants of F, G, or K spectral types that have amplitudes of 0.1 to 4 magnitude, with periods between 30 to 1100 days. Finally SRS type variables are red giants with short periods (on the order of a few days to a month).[19] SRA and SRB are the most likely semi-regular designations to be seen in a globular cluster because they are the most inclusive designations in the SR catagory. If a strong primary period is detected for a relatively well behaved red giant, but the star still behaves to erratically for an M type designation, then it would best meet the designation of SRA. Conversely, if multiple periods are detected, this will disqualify the star for the SRA designation, but would qualify the star for an SRB designation. Currently, LPV stars are poorly studied in globular clusters due to their long pulsation periods.

Globular clusters (GCs) provide a unique environment to study LPVs, as it is understood that all member stars formed at the same time, from the same gas cloud. This means that characteristics such as distance, age, and metallicity (amount of elements heavier than helium contained in the GC compared to the sun) are the same across GC member stars. Furthermore, since GCs are comprised of hundreds of thousands of Population II type stars, there is inevitably a subset of these stars that will be LPVs, allowing multiple LPVs to be studied at once. Unfortunately cluster studies have typically focused on the short period RR Lyrae and Cepheid 3 stars, which only take a few nights of observations to fully characterize. These short term observa- tions are of little use to understand the behavior of LPV stars, since only a fraction of one pulsation cycle is covered. Therefore, long term observations of GC are needed in order to effectively un- derstand long term LPV behavior. The unique GC environment allows for testing a prediction of LPV stellar pulsation theory; that higher metallicity red giants will undergo more regular, higher amplitude pulsations, compared to red giants with low metallicity. By studying a variety of GCs with a range of metallicities, LPV behavior can be connected to the changing metallicity values across the various GCs. Metallicity is the measurement of the ratio of elements present in a star that are heavier than hydrogen compared to our own sun. The value is usually given as a ratio, [Fe/H], with [Fe/H]=0 signalling that the star has the same metallicity as the sun. The range of globular cluster metallic- ities is from approximately [Fe/H]=-2.3 to [Fe/H]=0. M5 has a metallicity of [Fe/H]=-1.29 [12], thus placing it in the middle of the range of GC metallicities. The first LPV in M5 (NGC 5904) was discovered by Bailey in 1917, who suggested a pe- riod of 106 days [6]. The most comprehensive study of M5 for LPVs to date was accomplished in a 2015 paper by Arellano Ferro et al. [5] Arellano Ferro’s team identified eleven LPVs. Un- fortunately, their study only had data from 11 nights between Feburary 29, 2012 and April 9th, 2014. While their long time base allowed for the detection of LPV variability, but the low sam- pling density (approximately 5.3 observations per year) did not allow enough temporal resolution to determine the periods for all of these LPVs. By contrast, the PROMPT data set has a sampling density of approximately 489.4 observations per year.

Out of the 11 LPVs found by Arellano Ferro et al. five of the LPVs light curves were of sufficient resolution to allow for an estimation of their periods, along with the LPV discovered by

Bailey. The results of the Arellano Ferro et al. group’s 2015 paper is summarized in the ’Catalog

Period’ column in Table 7.1 located in Chapter 7. Considering typical LPV pulsation periods can span from 30-1000 days, it is possible that the there are undetected LPVs in M5. The goals of this project are to first identify the LPVs discovered 4 by Ferro et al. and provide updated photometry for these stars, allowing for better determination of each LPV’s period as well as allowing for the determination of the variability type of each LVP. By utilizing this more comprehensive set of observations, it is possible to determine if undiscovered LPVs are present in M5. If new LPVs are discovered, period values and VSX designations will be determined from the available data. 5

CHAPTER 2. OBSERVATIONS

2.1 Location

Images of M5 were taken with the Panchromatic Robotic Optical Monitoring and Polarimetry Telescopes (PROMPT) at the Cerro Tololo Inter-American Observatory, located in the Chilean Andes 500 km north of Santiago at an elevation of 2200 m. This remote location high in the mountains not only provides minimal light pollution, but also decreases the effects atmospheric distortion compared to an observatory at sea level. [17]

2.2 Equipment

2.2.1 Telescope and Camera

The observatory runs six 0.41m Ritchey-Chretien telescopes, each equiped with an Apogee Alta F47 CCD camera [14] with an array size of 1024x1024 pixels [4]. This setup gives a field of view of 10x10 arcminutes, and a resolution of 0.59 arcseconds per pixel. Each of these telescopes is out fitted with different filters and the collection of telescopes can either be used independently from each other, or in unison studying one target. The PROMPT array’s primary use is in studying the visible afterglow from gamma ray bursts, as well as following up on supernova events. When not being utilized for their primary purpose, the PROMPT array is available for use by researchers worldwide via the Skynet Robotic Telescope Network. [20] For this research, the PROMPT 4 telescope was utilized.

2.2.2 Filters

Johnson-Cousins V and I photometric filters were used when capturing images of M5. The choice of these two particular standard photometric filters are twofold; Firstly, LPV stars are known to be cool by stellar standards, which puts the peak of their blackbody radiation curve into the infrared region, therefore the most signal would be gathered by looking at the infrared portion of the spectrum. Secondly, the V filter was utilized so that a color-magnitude diagram of the cluster could be produced, which will allow for the analysis of the overall stellar population M5. V filters are also historically used in variable star work; therefore by utilizing this filter, these observations 6 of M5 have a wide basis of comparison with previous studies.

2.3 Observing Procedure

2.3.1 Exposure Times

I filter images were taken in a series of both long (30 s) and short (10 s) exposure times while V filter data was taken with a 40 s exposure time. A typical set of observations from one night would be to take 4 long exposure I filter images, 4 short exposure I filter images, and 4 V filter images. Long and short exposures were taken to protect against stars becoming unusable due to being overexposed in the long exposure image. The long exposures are very useful for ensuring a high signal to noise ratio (S/N), as well as detecting fainter stars. A problem can arise if a star is bright enough to overexpose the CCD camera during this longer exposure. If the star becomes overexposed, the star will enter the nonlinear region of the CCD camera response and become unusable for the analysis. Futhermore, if enough light hits the CCD camera, the CCD could also hit the maximum photon count of 65,535, thus completely saturating the pixel. If this occurs, at best the pixel would be unusable and worse, additional photo electrons could spill over from the saturated pixel to the surrounding pixels influencing their count values as well. If any of these situations occur in the long exposure images, the shorter exposure images can be used to allow those bright stars to be accurately studied. Different exposure times were not taken in the V filter because there is a very low probability that LPVs would overexpose in the V filter region. As described in section 2.2.2, LPVs are cool, red giant type stars that emit primarily in the infrared range of the spectrum. There is less risk of overexposure in the V filter during any portion of the star’s variability because the variability may be seen most strongly in the wavelengths where the star has peak output, the infrared region.

2.3.2 Requesting Observations

Observations are requested via the Skynet website and queued in the observatory’s control soft- ware based on their priority. Gamma-ray burst events classify as the highest priority, while educa- tional outreach activities (such as observations submitted by K-12 schools) classify as the lowest priority. Observations relating to this research were usually prioritized in the middle of this range. 7

[15] Once the requested image set was finished, Skynet automatically calibrated the data by taking and applying the required calibration images automatically for dark subtraction, bias subtraction, flat fielding. The images were then uploaded to a secure site where it was then downloaded to a storage hardrive at BGSU for later analysis. [15] 8

CHAPTER 3. PRELIMINARY IMAGE ANALYSIS

3.1 Initial Review of Images

Each image in the PROMPT data set was reviewed visually to determine if it was of sufficient quality for use in later analysis. During this initial step, images were considered ‘usable’ if the cluster was visible in the image without obvious signs of issues such as smearing due to tracking issues, clouds, etc. Figure 3.1 showcases several examples of images that were rejected.

(c) Due to poor tracking, or (a) Due to Clouds (b) Due to Clouds slewing the telescope during an exposure

Figure 3.1: Examples of unusable images 9

Any images deemed unusable were subsequently removed from the data set, while the re- maining images were retained. Initially, the data set included a total of 547 images, and after visually reviewing them, 469 were considered usable. After each step in the analysis process (see Chapter 4 for details on the analysis process), the quality of the output was evaluated to determine if all the images were still of sufficient quality to use. Statistical measures, such as FWHM, were combined with qualitative observations, such as the presence of artifacts or residual signals on an image, to make a conclusion on the quality of an image. This process of image evaluation was chosen over setting hard threshold values for various image quality measures (such as sky background level, Full Width at Half Maximum, etc.) before analysis began in order to remain as inclusive as possible with the data set. A disadvantage to this approach is that it requires the researcher to have familiarity with each step of the analysis in order to effectively determine the quality of the output.

3.1.1 Observing Cadence

Figure 3.2 shows the observing cadence of the PROMPT data set. Each blue box corresponds to a night of observations, where each night has on average 12 total images (4 I filter long exposures, 4 I filter short exposures, and 4 V filter images). The large gap in the timeline from mid-August 2010 to December 2010 corresponds to months where the GC is below the horizon all night at the observatory.

Figure 3.2: Observing cadence of PROMPT data set. Images taken on April 11 2011 were used as reference images. Yellow X’s correspond to a night chosen for use in the ISIS residual image. See section 4.1 for more information.

A more detailed view of the observing cadence is given by looking at the airmass of the GC over time. Airmass is a measure of how much atmosphere light must travel through in order to 10 reach the telescope. When airmass is minimized, there will be less distortion of the image due to atmospheric effects. At the zenith airmass is at a minimum, and is defined as being equal to one. As the observer begins looking at objects that are located further away from the zenith, the amount of atmosphere the observer is looking through increases. As seen in Figure 3.3, observations were not taken once airmass reached 2.5 or above, which corresponds to a zenith angle (the angle between the zenith position and the object of interest from the observer’s perspective) of roughly 67◦.

Figure 3.3: Airmass vs. Julian Date

The gap seen in Figure 3.3 corresponds to the same gap in Figure 3.2, where the GC is below the horizon and no longer observable. It can also be seen in Figure 3.3 that airmass increases as the cluster is reaching the time of year where it is below the horizon at the observatory. This is due to the earth’s revolution around the sun, which causes the GC to appear lower in the sky each night until it is below the horizon. Since the GC does not rise as high in the sky, the observer is looking through more atmosphere, thus leading to an increase in airmass.

3.1.2 Reference Star Selection

To determine the overall quality of the data set, a single star was chosen to act as a reference star for the cluster. The reference star was identified in each image and image statistics for this 11

reference star can be generalized to the image as a whole, thus allowing for a comparison of image quality across the data set. The criterion used to determine if a star is suitable to be a reference star is to verify that the star is reasonably bright, easy to identify in each cluster image, and sufficiently isolated from neighboring stars in the image so that there is no signal contamination. Once these qualifications are met, the final choice of reference star is up to the personal preference of the researcher. The orange circle in Figure 3.4 denotes position of the reference star in M5.

Figure 3.4: The star inside the orange circle is the reference star for the globular cluster.

3.2 Statistics from Digital Images

3.2.1 CCD Cameras and Poisson Statistics

A CCD chip is a semiconductor device that is able to count incident photons. The semiconductor material is divided up in to many small, electrically isolated bins known as pixels. As a photon strikes a pixel, the photon is converted into an electron via the photoelectric effect, and this resultant electron will be temporarily stored by the pixel during the exposure. Once the exposure is over, a computer will read out how many electrons are in each pixel and store that information in a FITS formatted image. These counts in the FITS image can then be used to apply a color mapping scheme 1 where lower counts (where fewer photons were detected) correspond to one color and

1The term ’color’ used here refers to the color displayed on the computer screen and not the star’s intrinsic V-I color 12 higher counts (where more photons were detected) correspond to another color. Values in between the two extremes are then assigned various shades of the two colors. Usually black and white are chosen for the job, but any two colors can be chosen in practice. The actual color mapping is an arbitrary choice left to the researcher, as the color mapping will only determine how the image is displayed visually on the computer screen, and doesn’t have any influence on any quantitative aspects of the stored FITS image. When choosing a color mapping scheme (also known as screen stretch), care must be given to understand what values are being included in the displayed image. It is very common to set threshold limits such that all pixels that fall below a certain count are black, and all pixels that rise above a certain count are white, thus potentially visually obscuring features that may be of interest.

(a) Favoring low pixel values (b) favoring mid-range values (c) Favoring high pixel values

Figure 3.5: Examples of various color mapping schemes

As seen in 3.5, favoring high pixel values allows for detail of the inner core of the GC to become visible, but many dimmer stars around the rest of the GC become ignored. Conversely, if low pixel values are favored, then dimmer stars become much easier to see in the image, but any core structure is seemingly lost as well as the background noise in the image becoming more apparent. Therefore, when visually looking at images, it is important to consider the choice of color map as various features in the image are searched for. Again, what is important in this process are the counts that the computer read from each pixel, as this information is what is used in any data analysis process. The act of individual photons hitting each pixel on the CCD chip is a random process that 13 is described by Poisson statistics. The Poisson distribution is the discrete version of the Gaussian distribution, therefore there is a wide variety of statistical tools that can be used to understand the signals in each image.

3.2.2 Sky Background

The sky background of the image measures how much signal is being contributed from the empty sky. The most common sources of sky background signal is from light pollution and moonlight. Light pollution has been minimized due to the telescope being located in the remote Chilean Andes, and while moonlight will increase the background signal of the observations, it is typically far less detrimental to LPV observations compared to the contribution of light pollution at a less remote site. Figure 3.6 shows the distribution of average sky background counts from each image across the data set. Most background counts for this data set are below 200 counts, making the background level very low considering that dim variable stars in the images were found to have a signal of a few thousand counts.

Figure 3.6: Distribution of sky background counts from PROMPT data set

3.2.3 Full Width at Half Maximum

The Full Width at Half Maximum (FWHM) is a statistical measure that determines how point- like the stars are in an image. It is defined as the width of the Gaussian curve at half of its maximum value. Atmospheric turbulence will cause distortion in the signal from the star as its light passes 14 through the atmosphere, thus increasing the FWHM of the star on the image. In general, the smaller the FWHM value, the lesser the effects of atmospheric turbulence on the image. Figure 3.7 shows the FWHM values of the reference star in each image across the data set. It is important to understand the effects of the FWHM on the images used for analysis. For instance, as FWHM increases, signals from stars become more spread out, thus making the stars appear larger in an image. As signal becomes spread out over more pixels, stars can sometimes have their signals ’bleed over’ into each other thus contaminating their true signal in the affected image.

Figure 3.7: Comparison of FWHM values across each image in the data set 15

3.2.4 Ellipticity

Ellipticity of a star is a measure of how circular the star appears in an image. Stars that have an ellipticiy of zero are perfectly circular, while stars that have non-zero ellipticity have some amount of ‘oval-ness’ to them. Figure 3.8 showcases the distribution of measured ellipticity across the data set. Stars with ellipticity values close to zero will appear round in the image, and are desirable to achieve. The most common cause of non-zero ellipticity can be attributed to imperfect tracking by the telescope, which tended to be larger for images with longer exposure times taken at higher airmass.

Figure 3.8: Measured ellipticity values across the PROMPT dataset. 16

CHAPTER 4. ISIS IMAGE SUBTRACTION

4.1 Introduction

The ISIS image subtraction package, developed by Christophe Alard [2], was utilized to find the locations of variable stars in M5. The end result of this process is creating a single composite image from the image set that contains only variable stars, and utilizing this image to obtain time-series flux-difference photometry for each variable. By utilizing an image subtraction procedure, ISIS can remove all of the stars whose brightness is constant, thus leaving only variable stars behind. The composite image is only utilized to identify the locations of variable stars in M5, and cannot directly be used for photometry. Considering that M5 contain hundreds of thousands of stars, this procedure saves a very large amount of work when searching for new LPV stars. Figures 4.1, 4.2, and 4.3 show a pictorial representation of how the ISIS process works in order to ultimately create the composite image. In Figure 4.1, a reference image is created that will be utilized in Figure 4.2 to create subtracted images. Finally in Figure 4.3, a subset of the subtracted images are utilized to create the desired composite image. Details of each step can be found in Sections 4.2.4, 4.2.5, and 4.2.6.

Figure 4.1: Step 1: Reference image creation 17

Figure 4.2: Step 2: Creating subtracted images

Figure 4.3: Step 3: Creating the composite image

4.2 Image Preparations before Using the ISIS Process

Before the images can be used in the ISIS process, some preparation of the images must first be done. Recall that the calibration (flat field, bias subtraction, dark subtraction) of the images was done automatically at the observatory (see Chapter 2 for more info). The remaining preparation steps are to scale the images, then align and trim them, to focus on the more central region of the cluster.

4.2.1 Image Scaling

The ISIS software works well with FITS integer-format data with counts ranging from -32,767 to 32,767 counts, while the PROMPT CCD reports counts from 0 to 65,535 counts. From previous work done by Dr. Layden, there is evidence that the CCD camera used at the observatory (see section 2.2.1 for more info) has a non-linear response above 50,000 counts. To avoid this issue, the images are first linearly scaled by multiplying each pixel by 0.65536, which allows all pixel counts 18 from within the CCD’s linear region to be below the maximum value that ISIS can work with. Next, any pixel value above 32,767 is set to be equal to 32,767, thus causing the ISIS software to treat these pixels as saturated. By treating these pixels as saturated, they will be largely ignored by ISIS during the analysis of the image set.

4.2.2 Image Alignment

The ISIS image subtraction process requires that the stars in each image have the same pixel coordinates across the data set in order to perform each step of the ISIS process effectively, thus requiring each image to be aligned. While there exists a routine in ISIS to astrometrically align the images automatically, if the images are not roughly aligned before running this process, the ISIS software typically has great difficulty aligning the images. This difficulty stems from the large number of overlapping stars found near the center of M5. The goal then is to have the images aligned manually as closely as possible, then allow ISIS to take the final steps to fine tune the image alignment by making x and y axis shifts, image rotation, and image scaling. The images are not all perfectly aligned to begin with due to significant pointing errors at the telescope, as the telescope moves across the sky to locate M5 each night. Looking at Figure 4.4, the large-scale shifts seen on the plot correspond to the pointing errors at the telescope that occur each time an observation has begun. The small clusters of data points seen throughout the plot are indicative of small tracking errors at the telescope when an image set is being acquired each night. These pointing and tracking errors will unfortunately require that the image alignment be corrected by the researcher, but there is a benefit to this phenomenon. Since the image of a star will show up in a slightly different location in each image, different pixels on the CCD chip will be utilized to capture the star’s signal each time. This works as a sort of dithering, which helps to protect against defects in the CCD chip affecting the star in the image. With this dithering occurring, if a CCD defect affects the star in one image, it is very possible that in subsequent images the star moved far enough away from the defect to then be unaffected by it. If there was no difference in the position of the star between images, this defect would cause all information from that star to be untrustworthy, instead of only a subset of images being unusable for that particular 19

Figure 4.4: Position of the cluster center (in pixel coordinates) in each un-aligned image across the entire data set. An un-trimmed image is 1024x1024 pixels in size.

star. In order to align the images, there must be a reference point in each image to compare across the entire data set. This reference point has already been chosen, and its location recorded in each image. It is the reference star discussed in section 3.1.2. The information on the location of the reference star in each image, along with the distance from the reference star to the center of M5 (in pixel coordinates) is fed into a FORTRAN program, written by Dr. Layden, that will align the images in the image set.

4.2.3 Image Trimming

The ISIS process was designed for the moderately crowded, uniformly dense star fields of the

galactic bulge. The center region of M5 is very dense and has many overlapping stars, which can

cause trouble when having ISIS do a photometric alignment of the images. This is exacerbated

when the outer periphery of M5 is included in the analysis as well, as the extreme stellar density gradient from the center of M5 to the image borders causes ISIS to find invalid solutions. The cause of this behavior stems from having less bright stars available in the outer region of the GC to constrain the fit of the image alignment compared to the center of the cluster. The ISIS 20 software takes a selection of the brightest stars in the image, and uses those stars to determine the quality of the image alignment. Previous students of Dr. Layden’s have found that if the alignment is significantly mismatched, ISIS’s solutions will diverge into spurious solutions. The solution to this problem is to trim the images so that ISIS can work with the more crowded regions of M5, where traditional photometry procedures are often inadequate, and study the outer regions with more traditional methods such as using DAOPHOT. By allowing ISIS to work on just the central region of M5, with the images being roughly aligned, the ISIS software is able to do a good job with the image subtraction and photometry process. The size of the trimmed area was determined qualitatively with consideration given to the density of stars within the the trimmed region along with how many stars would be cut off, or otherwise excluded, by the new borders. Figure 4.5 shows what region of the image was utilized for the ISIS process.

Figure 4.5: The yellow box denotes the where the image was trimmed. The inside of this box is the image that was utilized by the ISIS software.

Now that the trimmed area is defined, the position of the borders, with respect to M5’s center (in pixel coordinates) can be fed into a FORTRAN program written by Dr. Layden which will trim the aligned images. The images from the PROMPT telescopes are 1024x1024 pixels, covering 10x10 arcmins on the sky, and after trimming, the images became 700x700 pixels in size, covering 21

6.8x6.8 arcmins. In the resulting images, M5’s center is purposefully not centered in the image frame. This is due to a discovery by Moe AlJassim while completing his 2017 thesis on LPVs in NGC 6388. He discovered that the image alignment routine in ISIS had difficulty aligning the images if the GC was centered in the image frame. By offsetting the GC center by >75 pixels in the X and Y directions, ISIS was able to accomplish the image alignment much more easily. [3]

4.2.4 Step 1: Reference Image Creation

The first step in the ISIS image subtraction process is to create a quality reference image. A good reference image is comprised of enough high-quality images such that a high S/N ratio is achieved. High-quality images must be used in this step because any poor quality images (determined by high FWHM, large ellipticities, etc.) will affect the final reference image, which will be utilized for the next step of the process. Images used to create the reference image were chosen from the same night, with all images from that night appearing cloudless. It was found that by using images from the same night, the alignment between images was very close, and it was also found that the images were almost uniformly affected by the same degree of atmospheric dimming, with very similar airmass values. For the analysis of the M5 data, it was determined that five images from April 6, 2011 created a good quality reference image (as evidenced by low FWHM values compared to the values found across the data set), and ellipticity near 12. As seen in Figure 4.1, these five images were averaged together to create the reference image. The result of this process can be seen in Figure 4.6.

4.2.5 Step 2: Image Subtraction

The second step in the ISIS image subtraction process is to subtract the reference image from each image in the data set. This will produce a subtracted image for each image of the data set (see

Figure 4.2). This step is important for removing the non-variable stars. As stated in Section 4.2.4, the reference image acts as a ’zero point’ when determining the flux changes of each star. If a star’s brightness is more or less constant, then when the reference image is subtracted, the star’s signal will be removed in the subtracted image. On the other hand, if a star is a variable star, its flux will be different in each image in the data set. When the reference image is subtracted, any difference 22

Figure 4.6: Reference image

in flux between the two images will cause some residual signal to remain on the subtracted image. It is these residual signals in the subtracted images that are utilized in step 3 to create the composite image.

(a) April 6, 2011 (b) February 16, 2011

Figure 4.7: Examples of subtracted images

Figures 4.7 are subtracted images from two different nights. The first one is from April 6, 2011 while the second is from February 16, 2011. Recall from Section 4.2.4 that the night chosen to create the reference image was April 6, 2011. Therefore, the reference image will be very similar 23 to each image from that night and cause the signal from all stars to be almost completely removed since the star’s brightness would not have changed drastically between two exposures. Note that the subtraction will never be perfect between the reference image and each image that comprises it because the reference image is five images averaged together, and each individual image will contain small random variations due to randomly positioned cosmics in the image, atmosphere fluctuations, and the Poisson noise in each image. The image from February shows a much wider variety of residual signals on the image. Stars that are dimmer compared to the reference image show up as black regions while stars that are brighter than the reference image show up as white regions. These signals are what will be utilized in step 3 of the ISIS image subtraction process to create the composite image.

4.2.6 Step 3: Creating a Composite Image

The final step in the ISIS image subtraction process is the creation of the composite image. As seen in figure 4.2, step 2 created a subtracted image for each image in the image set. The goal is to now combine enough of these subtracted images to make the residual signals of the variable stars in the image high enough above the background noise to be visually detectable in the composite image. To achieve this, 10-15 dates are randomly chosen in the data set, and one subtracted image from each date is utilized to create the composite image. The reason these dates are chosen randomly is to try to avoid creating a periodicity in the images. If there was an obvious periodicity to selecting these images, it is possible that a variable may be observed at the same brightness over and over, thus making it appear it is not a variable star. This strategy of randomly selecting dates was determined to work best during this ISIS step by previous students of Dr.

Layden’s doing similar research on other GC’s.

Since each date of observations has 4 images of each filter and exposure (I filter long, I filter short, V filter), the best subtracted image from this group of four can be chosen to create the composite image. For the analysis of M5, 15 images were utilized to create a composite image. The nights used in this process for the I filter long exposure data can be seen in Figure 3.2 as yellow X’s 24

on the timeline. These 15 subtracted images were then combined by using the mean of absolute normalized deviations, thus producing the composite image. The most important aspect of using the mean of absolute normalized deviations is to use absolute values from the subtracted images. This allows for any instances when the star is dimmer than the reference image, thus a negative flux difference, to be used to increase the S/N of the residual signal of the variable star instead of allowing the negative flux difference work to decrease the overall signal on the composite image. The normalization process merely scales the pixel values such that all values are between zero and one.

Figure 4.8: Composite image

Figure 4.8 is the composite image created from the I filter, long exposure PROMPT data.

Variable stars show up as white regions in the image, while non-variable stars have been removed.

It is important to remember at this point that the composite image is not utilized for photometry, only to visually see the locations of the variable stars in M5 and record their locations in pixel coordinates. 25

4.3 Identification of Known Variable Stars

The Clement catalog, maintained by Christine Clement at the University of Toronto [10], con- tains a list of all known variable stars in a variety of globular clusters, including M5. In any globular cluster, most catalog entries correspond to RR Lyrae-type variables and only a few known LPVs. In M5 specifically, the Clement catalog contains 127 stars classified as RR Lyrae and 12 LPVs, only 5 of which were able to have their periods determined. In order to use the catalog information to its fullest, stars must be identified in the images from their celestial coordinates. The easiest way to do this is to insert a world coordinate system (WCS) into an image to identify each star. Figure 4.9 shows an example of what can be done once a WCS is added to an image. This figure uses the information from the Clement catalog to mark the known variables on the composite image created from the ISIS process. Any stars not marked on the composite image are potentially new variable stars. Note that it is not necessary to have every image in the image set contain a WCS, as the ISIS process relies on pixel coordinates to run, not celestial coordinates. Also, since the images are already aligned prior to using the ISIS software, photometry on the images is easier and doesn’t require WCS information to work well.

4.3.1 World Coordinate System

FITS images can contain information in their header that allows each pixel in the image to be related to a position in the sky, given in celestial coordinates (right ascension and declination).

When this header information exists, the image is said to contain a world coordinate system (WCS).

Having this ability available in a FITS image makes it very easy to identify specific targets in an image, and has the additional benefit of being accessible by a wide variety of astronomy software and Python libraries which can make analysis of the data easier.

Images from the PROMPT telescopes did not come with a WCS predefined in the image headers. Luckily the software IRAF (Image Reduction Analysis Facility) contains routines that allow a WCS to be inserted into an image. This process works by manually creating a text file that contains a variety of stars listed in both celestial coordinates and pixel coordinates. After selecting 26

Figure 4.9: Composite image with all known variable stars marked a variety of stars from all around the image, IRAF calculates how the WCS must be applied in order to match the given information about stellar positions, and maps out the full coordinate system to the image. To determine what the celestial coordinates of each chosen star is, the 2MASS catalog was utilized with the SAOImage ds9 (ds9) software. The process begins with pulling an image of M5 from the 2MASS archive that contains a WCS, and then manually matching stars in the 2MASS image to stars in the PROMPT image using visual pattern matching. Once at least 20 stars have been identified, IRAF can then be used to begin mapping the WCS to an image.

The IRAF documentation provides additional details on the fitting procedure. [13] It states that the IRAF task ’ccmap’ computes the plate solution for an image using the aforementioned list of pixel and celestial coordinates, and will then work to place the plate solution in the form:

ξ = f(x, y) and η = g(x, y) 27 where ξ and η are RA and DEC, in units of seconds/pixel, and the functions f(x, y) and g(x, y) are second-order polynomial fitting functions. Once the error in the fit is deemed low enough by the user (usually when the magnitude of the error of the fit is less than one second/pixel), ‘ccmap’ outputs a database file that contains all of the necessary information to insert the WCS into the image. The IRAF process ‘ccsetwcs’ is then used to take the database file and perform the insertion of the WCS. This process brings an interesting question: how can a WCS be inserted into the composite image when many of the stars have been removed by the ISIS image subtraction process? Recall that back in section 4.2 it was stated that the images used by the ISIS software have been aligned and trimmed before using. This means that the location of the stars in each image do not change their pixel location from image to image. Therefore, a high-quality image from the data set, or the reference image created by ISIS, can be used to work out the WCS mapping and the calculated mapping parameters can be directly applied to the composite image.

4.3.2 Marking Known Variables

A Python program was created by Pellegrin using available Python libraries (such as astropy, matplotlib, PyAstronomy, etc.) that would allow the composite image to be manipulated in both celestial and pixel coordinates. The celestial coordinates, catalog numbers, and variable star type of all variable stars identified in M5 were summarized from the Clement catalog in a text file. This text file was then read by the Python program, and a small blue circle was plotted on the image for each entry in the text file. The results of this process can be see in Figure 4.9.

This Python program also has the flexibility to mark variables of specific types and print the catalog numbers on the image, allowing for objects of interest to be looked at independently of the other variables in the cluster. Examples of this can be seen in Figure 4.10. Of particular interest is

Figure 4.11, which shows the location of the twelve known LPVs in M5. It was found that most of the known LPVs in M5 appeared quite strongly in the M5 composite image. Notable exceptions are V177, V179, and V179 which appeared weakly in the composite image while V181 was not included as it was located outside of the trimmed image’s area. 28

. (a) Known RR0/ RRAB type stars (b) Known RR1/ RRC type stars

(c) Other known variables (d) Stars incorrectly identified as variable stars

Figure 4.10: Composite images with various types of variable stars marked and labeled. Yellow tags on the image (where presented) denote catalog ID’s of each star. 29

Figure 4.11: All known LPVs in M5 listed by Clement 30

CHAPTER 5. PERIOD DETERMINATION

5.1 Flux Difference Photometry with ISIS

The ISIS software has the ability to perform photometry on all of the aligned images in the image set. Once the locations (in pixel coordinates) of all desired objects are known, a text file is created and used as input that allows the ISIS software to perform time-series flux-difference photometry. ISIS then creates a file for each star that was listed in the input textfile, and outputs information on the date of each image, the flux of the star in each image, and the uncertainty of the flux measurement in each image. See Table 5.1 for a sample of data from the ISIS output file.

Date [HJD] Flux [ADU] Uncertainty [ADU] 5754.478800 6313.0404 477.0128 5665.701800 3756.2366 557.8087 5608.791400 33591.0237 513.0616 ...... 5651.707100 -4982.8236 565.2300

Table 5.1: Sample of output from ISIS after performing flux-difference photometry on V50

Flux difference photometry was performed on all 12 known LPV stars [10], 14 candidate LPV stars, and two other objects of interest (V42 and V84). RR Lyrae stars, and other rapidly changing variables, were not studied in this research. The observing cadence of the image set is optimized for LPV detection, and while it is possible to gain some information about RR Lyraes in the GC with this image set, there are many studies designed for these objects in the GC. Therefore, the analysis of M5 has been largely constrained to studying LPV type stars only.

5.2 Period Determination

LPV variability is often comprised of multiple pulsation modes blended together, and the asso- ciated periods can even change from cycle to cycle, as LPVs are less regular than stars like RR

Lyraes. These phenomena seldom allow for just a visual interpretation to yield the correct period for an LPV. Fourier analysis is one way to determine what the primary period is of the star, along with the other main pulsational periods that interact with each other to produce the observed light curve. 31

To find the pulsational periods of the LPVs in M5, period determination was accomplished by utilizing the American Association of Variable Star Observers period finding software, VStar. VStar utilizes Date Compensated Discrete Fourier Transform (DCDFT) algorithms in order to determine the various harmonics that are present in the light curve and produces a power spectrum of probable period values. [7] ‘Date compensated’ refers to the ability of the software to apply Fourier analysis to the light curves while taking gaps in the data into account, usually caused by the observing cadence. Table 5.2 summarizes the four different regions of possible periods that were searched. While VStar can search for periods across a spectrum automatically, it has been found that searching in these four distinct regions provides additional constraint to the process which allows VStar to produce more accurate results.

Shortest Period [Days] Longest Period [Days] Step Size [Days] 0.2 2.0 0.0001 2.0 20.0 0.001 20.0 200.0 0.01 200.0 999.0 0.1

Table 5.2: Period search regions

These four regions were chosen in Table 5.2 because they cover the typical periods of common objects in GCs. Going from the top of the table to the bottom, the periods are typical for RR Lyraes, Cepheids, LPV, and LPV with a long secondary period. The resolution of the period search is directly proportional to the period being searched for therefore, as the potential period values increase,

the resolution that can be achieved during a DCDFT analysis decreases. Computational time is also saved by reducing the resolution at higher periods, as it is typically necessary to have more than a few significant figures of precision. LPV’s with a Long Secondary Period (LSP) are rare, but there is a possibility that such variables could be found, as previous studies on M5 would not be able to detect this behavior if it is present due to their short span of observations. By looking for large peaks in the power spectrum for each region, VStar provides evidence 32

for what type of variable has been detected. See Section 5.4.1 for details on how the power spectra from each region in Table 5.2 helps to determine variable type.

5.2.1 Period Aliases and Harmonics

Once a primary period has been determined for a variable star, it is important to determine what the aliases and harmonics of that period are in order to determine what peaks in the power spectra are not real signs of variability. An alias is caused by the periodicity of the observing cadence interacting with the true period- icities in the data set. The most common aliases that are observed are N-day or N-year periodicites (where N is an integer). The N alias (A) of a true period (P ) can be determined by the following equation (keeping all units in days or years):

1 A = 1 P +N

The most common aliases that are observed are N-day or N-year periodicites (where N is an integer). Dr. Layden’s prior experience with LPV period determination has found that when N | | is small (typically N 3), the corresponding alias is more likely to be present in the power | | ≤ spectrum, while aliases corresponding to larger values of N (typically N > 3)are less likely to | | | | occur. Harmonics, on the other hand, are simply multiples or fractions of the primary period. Dr. Layden has produced an Excel widget that takes the primary period value found from VStar and calculates 5-day and 5-year aliases as well as the following N-harmonics: ± ± 8 4 P NP and N N=1 N=1 � � Where P is the primary period and N is the integer harmonic. Previous work by Dr. Layden has

show that high N values are typically less likely to appear in the power spectra, while low N | | | | values are much more likely.

5.2.2 Determining Period Uncertainty

To determine the uncertainty in the primary period found by VStar, the star’s light curve is first folded by the primary period value. Additional folded light curves are produced by changing 33 the period in appropriate increments (usually 1 or 2 days), and visually deciding when the ± ± coherence of the folded light curve becomes dramatically altered. For an example of this process, see Section 5.4.1. This process works well for stars whose light curve is fairly regular, but can be problematic for stars which very erratic appearing light curves (such as V179). Typically as the detect period increases, the uncertainty in the period increases as well in a linear fashion. By studying the light curves of relatively regular LPVs, it was found that the uncertainty was 4% of the measured period value. Therefore, any period detected in the PROMPT data has a corresponding uncertainty of 4% of its value.

5.3 Two Test Cases with Known Variables

Before analyzing the image set for LPVs, two variable stars were chosen to test the data set. V42 is a W Virginis type star, and V84 is a RV Tauri type star. Both of these stars have long enough periods to be adequately resolved by our data set, but are short enough to allow for multiple cycles of the period to be observed. Furthermore, these stars are well studied, and their periods are well defined in the Clement catalog [10].

5.3.1 Light Curve Analysis of V42

V42 is a W Virginis star first discovered by Bailey in 1917 [6], with an update to its period in 2010 by Rabidoux et al. [10] The Variable Star Index (VSX) denotes W Virginis type variables as pulsating variables with periods from 0.8 to 35 days, and with ampitudes ranging from 0.3 to 1.2 mag in V. [19]

The light curves for V42, seen in Figure 5.1, appear to show very erratic, and quickly chang- ing behavior in both the I and V filters. This is due to the observing cadence of the data set acting on the relatively short period of this W Virginis type star. By folding the light curve by the primary period, where rotational phase is plotted on the X axis instead of time, the data will then be dis- played in a manner that allows for better visualization of the star’s periodicity. Folded light curves can be seen in Figure 5.3 as the yellow data points. 34

(a) I filter light curve (b) V filter light curve

Figure 5.1: Light curves for V42. Error bars are smaller than the data point in most cases. The orange line is the median value for each date and is displayed to guide the eye through the data trend

The power spectrum for V42, Figure 5.2, shows that there is a very strong primary period located at 25.72 days, and a second weaker period located at 9.58 days which was found to not be an alias of the 25.72 day period. Upon first constructing a model for V42, Figure 5.3a, the 25.72 day period seems to do a great job matching the overall trend of the light curve, but struggles to explain the more extreme features seen near the light curve’s peak. Creating a 25.72+9.58 day model, led to the introduction of more scatter into the model and provided a worse fit, suggesting that the 9.58 day period does not play a major role in V42’s overall pulsation. It is typical for W Virginis type stars to display ’ringing’ in their light curves, where their period excites the pulsations causing harmonics of that period to interact. The most successful model took this into account (Figure 5.3b) by introducing seven harmonics (seven harmonics was settled on after trial and error) to the 25.72 day period, which led to the model fitting the shape of the light curve almost perfectly. Adding in the 9.58 day period to this new model caused very little change in the model, further providing evidence that the 9.58 day period does not contribute to the overall trend of the light curve. The analysis leads to the conclusion that the period for V42 is 25.75 days, which is in good agreement to the accepted value in the Clement catalog of 25.735 days. 35

Figure 5.2: V42 power spectrum

(b) V42 light curve with 25.72 day, 7 harmonics, (a) V42 light curve with 25.72 day model model

Figure 5.3: V42 light curve (yellow points) with models (red points)

5.3.2 Light Curve Analysis of V84

V84 is a RV Tauri star that was first discovered by Bailey in 1917 [6], with an update to its period in 2010 by Rabidoux et al. [10]. The Variable Star Index (VSX) denotes RV Tauri variables as pulsating supergiants with characteristic light curves displaying alternating shallow and deep minima, reaching 3-4 magnitudes in V in amplitude. [19] 36

The light curve for V84, seen in Figure 5.4, appears very similar to the V42 light curve. Again, RV Tauri stars are known to have short periods compared to the targeted LPV stars, there- fore folding the light curve is a necessary step in order to have a better visualization of the star’s periodicity. Examples of the V84 folded light curve can be seen in Figure 5.6.

(a) I filter light curve (b) V filter light curve

Figure 5.4: Light curves for V84. Error bars are smaller than the data point in most cases. The orange line is the median value for each date and is displayed to guide the eye through the data trend

The power spectrum for V84, Figure 5.5, shows that the 26.83 day period is very dominant. Upon making a model of the 26.83 day period, Figure 5.6a, it is seen that the model does a good job matching the general trend of the folded light curve, but it misses the depth of the light curve at the minima. Since RV Tauri stars are known to exhibit alternating shallow and deep minima in their light curves [19], RV Tauri period is defined from one minima to the next minima like it. For instance, a deep minimum to the next deep minimum, which leads the DCDFT analysis to find a period that is half of the actual value since only half of the full period of variability has been detected.

Taking this into account, Figure 5.6b shows the same model fitted to a light curve that is folded by twice the primary period determined by DCDFT (53.66 days). While the fit of the model appears to remain unchanged, it is important to note that this folded light curve exhibits the alternating shallow and deep minima that can be expected from a RV Tauri star, suggesting that 53.66 days 37 may be a more appropriate period for this star. In conclusion, due to the period found by DCDFT analysis, combined with finding the al- ternating minima by folding the light curve by twice the DCDFT period value, it is reasonable to conclude that the period of V84 is 53.66 days, which is in agreement with the period stated in the Clement catalog of 53.95 days. [10]

Figure 5.5: V84 power spectrum

(a) V84 folded light curve (folded by 26.83 days) (b) V84 folded light curve (folded by 53.66 with 26.83 day model days) with 26.83 day model

Figure 5.6: V84 light curve (yellow points) with models (red points) 38

5.4 Known Long Period Variables

5.4.1 Light Curve Analysis of V50

V50 is a known, relatively well behaved LPV star. As seen in the light curves in Figure 5.7, V50’s pulsations are very clean, with high signal-to-noise, and large amplitude variations (approx- imately 83,000 ADU in I and 17,000 ADU in V ). Furthermore, looking at Figure 5.7, the maxima and minima in the I and V filters match in time, which is evidence that the observations were able to capture the LPVs true luminosity variations.

(a) I filter light curve (b) V filter light curve

Figure 5.7: Light curves for V50. Error bars are smaller than the data point in most cases. The orange line is the median value for each date and is displayed to guide the eye through the data trend 39

Taking the I filter data and running a DCDFT analysis through VStar on the data yields the power spectrum seen in Figure 5.8. It is clearly seen that the primary period is 102 days, and is very dominant over other pulsational periods. All period ranges outlined in Table 5.2 were searched for V50, but the other peaks found in each range were quite small compared to the 102 day peak. Furthermore, after analyzing all stars summarized in this thesis, it was found that a 1 day period showed up strongly, as well as its harmonics at 1/2, 1/3, and 1/4 of a day, along with a 7 day period, along with its 1/2 harmonic of 3.5 days, which is suggestive that the observing cadence has inserted this one day period, and one-week periodicity, as an alias.

Figure 5.8: Power spectrum for V50 over the period range 20-200 days

Using the primary period of 102 days, a model (red plotted points) was created and plotted with the data which is seen in Figure 5.9a. This model fits the observed data (yellow data points) very well, and suggests that this is the primary period for V50. A second model was created in

Figure 5.9b to explore the effect of including the next most dominant period, 61 days, into the model. Referencing Dr. Layden’s alias widget, it is seen that 61 days is not an alias or harmonic of the primary 102 day period, thus providing some evidence that the 61 day period may be part of the star’s periodicity. 40

Looking at this model, it is seen that the addition of the 61 day period to the model helps the model match the observed data near the local maxima and minima points on the plot, but does not cause a dramatic improvement in the visual fit of the model. This suggests that 102 day period is the primary period of pulsation for V50, and the 61 day is interacting to cause the more extreme features in the plot (such as the minima at 5,800 HJD), therefore V50 is most likely multi-periodic.

(a) 102 day period model (b) 102 & 61 day period interacting model

Figure 5.9: Light curves (yellow data points) with models (red data points) for V50

The final step in the analysis is to determine the uncertainty in the determined period. To do this, the light curve of V50 is folded by the 102 day primary period. Additional folded light curves, with varying periods, are then produced and visually inspected. When the coherence of the folded light curve changes noticeably, that is considered the limit for the potential range of primary period values. Figure 5.10 shows an example of creating multiple folded light curves with different primary periods for V50. After reviewing the range of folded light curves, it was concluded that the primary period for V50 is 102 3 days. ± 41

Figure 5.10: Variety of folded light curves for V50 used to determine the period uncertainty. The blue and orange data points are the same data, but denote where the cycle repeats itself. 42

5.4.2 Light Curve Analysis of V171

(a) I filter light curve (b) V filter light curve

Figure 5.11: Light curves for V171. The symbols are as in Figure 5.7

Figure 5.13 shows the I and V filter light curves for V171. Both light curves show very low nightly scatter and the star exhibits large amplitude flux variations (approximately 29,000 ADU in I and 9,500 ADU in V ). The power spectrum for V171, Figure 5.12, shows the most dominant periods for V171, which fall into the 100 day and greater range. An 11 day period was discovered that had comparable power to the 114 day period, but it was found that the 11 day period was an alias of the 183 day period, and therefore was not considered further.

Figure 5.12: V171 power spectrum 43

Period [Days] Power 361 53.4 183 46.4 11 (Alias) 11.38 114 9.3

Table 5.3: Top five period values for V171

The model displayed in Figure 5.13a was constructed using the 361 day, 183 day, and 114 day periods combined, while the model in Figure 5.13b was constructed with just the 183 day and 114 day periods. Both models fit the majority of the V171 light curve, with the greatest difference between the models at 5700 HJD. The three period model (Figure 5.13a) shows a sharper minimum at 5700 HJD compared to the two period model (Figure 5.13b), which shows a flat-bottomed minimum at 5700 HJD. If it can be shown that the spike downwards at 5700 HJD is real, and not just observational or photometric scatter in the data set, then the three period model would be considered to fit the light curve well as it dips down more into that feature than the two period model does. It is also important to note that the 361 day period is very close to being a year (365 days), therefore the detected 361 day period could be an alias due to the observation cadence. More data are needed to determine if the sharp minimum at 5700 HJD is real, as well as to determine if the 361 day period is an alias from the observing cadence, or if it is a real pulastional period. 44

(a) V171 light curve (yellow points) with (b) V171 light curve (yellow points) with 361+183+114 day model (red points) 183+114 day model (red points)

Figure 5.13: Light curve with models

5.4.3 Light Curve Analysis of V172

(a) I filter light curve (b) V filter light curve

Figure 5.14: Light curves for V172 45

Figure 5.15: Power spectrum for V172 over the period range 20-200 days

The V172 light curves in Figure 5.16 show more nightly scatter in the data than the previ- ous light curves, but still retain modest flux amplitudes (9,000 ADU in I and 9,700 ADU in V ). Exploring the four period ranges summarized in Table 5.2, it was found that the most dominant period was at 195 days, as seen in Figure 5.15, with the peaks in the other period ranges were much weaker than those seen in the 20-200 day region.

(a) 195 day model (b) 195 and 53 day model interacting

Figure 5.16: Light curves (yellow data points) with models (red data points) for V172 46

Using the information from Figure 5.15, a model of the primary period, 195 days, was con- structed and is shown in Figure 5.16a. The primary period of 195 days does an adequate job matching the overall variations of the light curve, but it does not explain the shorter term periodic behavior. The next most dominant period, 53 days, was included into Figure 5.16b, and does a much better job matching the more subtle features of the V172 light curve, suggesting that this star is multi-periodic. 47

Figure 5.17: Folded light curves for V172 used to determine period uncertainty. The blue and orange data points are the same data, but denote where the light curve repeats itself. 48

Looking at the folded lightcurves in Figure 5.17, it is seen that the coherence of the folded light curve begins breaking down at around 10 days. Given the results of the analysis, the primary period of V172 appears to be 195 10 days. ± 5.4.4 Light Curve Analysis of V173

(a) I filter light curve (b) V filter light curve

Figure 5.18: Light curves for V173. The symbols are as in Figure 5.7

The light curves for V173, seen in Figure 5.18, appear very erratic with a moderate amount of nightly scatter in the I filter, and very little nightly scatter in the V filter. The largest amplitude of the flux variations is approximately 10,700 ADU in I and 6,200 ADU in V . Looking at Figure 5.19, there appears to be three periods above 100 days that appear to domi- nate the power spectrum, as well as two shorter periods that are weaker but still reasonably strong. The top five periods for V173 appear in Table 5.4, and were found to not be an alias or harmonic of each other, therefore each period will be explored in the creation of a model to fit V173’s light curve.

Period [Days] Power 124 21.5 309 20.3 210 13.3 41 9.1 28.9 7.6

Table 5.4: Top five period values for V173 49

Figure 5.19: V173 power spectrum

Working with various models, it was found that the combination of the 125 day and 309 day periods was able to very effectively match the overall trend of V173’s light curve as seen in Figure 5.20. Adding in the 210 day period to the model caused only a very minor change in the model that did not offer an improvement to the models fit of the light curve. This behavior, combined with the difficulty resolving a peak for the 210 day period in the power spectrum (Figure 5.19), suggests that additional observations of M5 need to be taken in order to increase the resolution of the data set at these periods in order to confirm the presence of a 210 day period. Exploring the effect of including the 41 day and 29 day periods in the model, found that in- cluding either, or both, of these periods with the 125 and 309 day periods, did not offer a substantial improvement in the fit of the model to the light curve. The conclusion from this analysis is that the

125 day and 309 day periods serve as the primary periods for V173 and more data are required to determine if the shorter periods would still remain as a potential component of V173’s variability. 50

Figure 5.20: 173 light curve (yellow points) with 125+309 day model (red points)

5.4.5 Light Curve Analysis of V174

(a) I filter light curve (b) V filter light curve

Figure 5.21: Light curves for V174. The symbols are as in Figure 5.7 51

Figure 5.21a shows the I filter light curve for V174. Interestingly, the light curve is very well defined (low scatter and large amplitudes), but appears non-sinusoidal. These features in the light curve are evidence that V174 has multiple periods interacting with each other causing this behavior. The power spectrum for V174, seen in Figure 5.22, supports the idea of multiple periods interacting as two very dominant peaks, corresponding to 50 days and 78 days, were detected. This feature is evidence that V174 is multi-periodic, making it unreasonable to discuss this star having a primary period, as both periods are important to the star’s overall pulsation behavior. Another interesting feature of this power spectrum is the shoulder on the left side of the 78 day peak. This suggests that there may be another strong period that our data were unable to resolve. In order to determine if this shoulder could be a third period, and to what extent this would interact with the 50 and 78 day periods, more observations of M5 are necessary in order to capture multiple cycles of V174’s pulsation to achieve better resolution in V174’s power spectrum.

Figure 5.22: V174 power spectrum 52

Figure 5.23: V174 light curve (yellow points) with 78+50 day model (red points)

5.4.6 Light Curve Analysis of V175

(a) I filter light curve (b) V filter light curve

Figure 5.24: Light curves for V175. The symbols are as in Figure 5.7 53

Figure 5.25: Power spectrum for V175

Light curves for V175 are seen in Figure 5.24 and show low pulsation amplitudes (2,700 ADU in I and 1,100 ADU in V ). There is a moderate amount of nightly scatter found in both light curves, which may have a more pronounced impact on the overall trend of the light curve given the low amplitude of flux variations in each filter. The power spectrum for V175, seen in Figure 5.25, shows the strongest period occurring at 290 days. The remaining peaks are quite weak by comparison, and a summary of the top 4 peaks can be found in Table 5.5. The peaks listed in the table were not found to be aliases or harmonics of each other.

Period [Days] Power 290 29.9 24.2 7.5 40.5 7.4 118.67 6.7

Table 5.5: Top five period values for V175

When constructing the model, it was found that the 290 day period reasonably described the overall trend of the light curve (Figure 5.26a). Adding in the additional shorter periods provided no clear evidence of improving the model’s fit (Figure 5.26b provided as an example). Considering 54

this behavior combined with the relatively low power of the sorter periods in the power spectrum (Figure 5.25), it is clear that this data set is not sufficient to make a statement about the effect of the shorter periods on the light curve, but is sufficient to confirm the presence of a 290 day peak.

(a) V175 light curve (yellow points) with 290 (b) V175 light curve (yellow points) with day model (red points) 290+24.2 day model (red points)

Figure 5.26: Models for V175

5.4.7 Light Curve Analysis of V176

(a) I filter light curve (b) V filter light curve

Figure 5.27: Light curves for V176. The symbols are as in Figure 5.7

Figure 5.27 shows the I and V light curves of V176 from the PROMPT data set. Overall, V176’s light curve shows a moderately large amplitude (13,600 ADU in I and 2,800 ADU in V ) 55 and a non-sinusoidal behavior that is most clearly seen in the I filter light curve (Figure 5.27a) suggesting that V176 may be multi-periodic. Figure 5.28 is the power spectrum for V176, with the most dominant periods listed in Table 5.6. 85 days is an alias of the 159 day period, while the 35 day period is not an alias. Given that the 85 day period is an alias, it would typically not be considered to be a real period of the star, but it is interesting that 85 days has the second highest power of all the periods found during the DCDFT analysis. It is a possibility that while 85 days is an alias, the star could still be pulsating with this 85 day periodicity, but until more data is available to better resolve this region of the power spectrum, it is uncertain if this is the case. The proceeding models will explore the effect of the 85 day and the 35 day period combined with the primary period of 159 days, but the model including the 85 day period should be met with some skepticism until more data is available.

Figure 5.28: V176 power spectrum

Period [Days] Power

159 24.6

85 9.8

35 8.7

Table 5.6: Top 3 periods for V176 56

As seen in Figure 5.29a, the 159 day period does a reasonable job describing the overall periodicity of V176. This period appears to deviate from the light curve around the second maxima, 5750 HJD, suggesting another period may be necessary to better match the observed light curve. Figure 5.29b adds in the 85 day period to the model, which appears to do a better job fitting the light curve prior to 5750 HJD, and offers some improvement on the remainder of the fit to the light curve. Again, with 85 days being an alias of the 159 day period, it is uncertain if this model is an accurate representation of the star’s periodicity. Finally Figure 5.29c combines the primary 159 day period with the 35 day period, which adds scatter to the model which is comparable to the scatter in the light curve. This phenomena suggests that the 35 day period could be a true period of this LPV. Ultimately, more data is needed in order to determine if the 85 day period is an alias, or an actual period of this LPV, as well as to gain a better understanding of the 35 day periods effect on V176. 57

(b) V176 model: 159 day and 85 day periods (a) V176 model: 159 day period combined

(c) V176 model: 159 day and 35 day periods combined

Figure 5.29: Models for V176 58

5.4.8 Light Curve Analysis of V177

(a) I filter light curve (b) V filter light curve

Figure 5.30: Light curves for V177. The symbols are as in Figure 5.7

The light curves for V177, seen in Figure 5.30, show a weak periodicity, which is expected to appear in the power spectrum as low powered peaks with low amplitudes. Furthermore, the amplitude of the light curve is very low with an amplitude of approximately 1,500 ADU in I and 450 ADU in V which suggests that the noise in the image will play a large role in the overall light curve of V177. Looking at Figure 5.31, four periods appear to dominate the power spectrum; which can be found in Table 5.7. Furthermore, when exploring the range of periods typically associated with LSPs (200-999 days), the power spectrum showed that there was power in that range of period values, but the analysis could not resolve a particular period. A longer time span of data is required to be able to better resolve this period region, and to determine if V177 exhibits an LSP. 59

Period [Days] Power 40 6.7 164 6.6 89 5.9 113 5.5

Table 5.7: Top four periods for V177

Figure 5.31: Power spectrum: 20-200 days

Fitting a model to the V177 light curve was difficult. The top four periods determined by DCDFT analysis all have low power compared to other LPVs observed. The model that best fits the light curve combines the top four periods together, as seen in Figure 5.32, but still does not adequately describe all features of the light curve. The low amplitudes found in V177’s light curves makes it difficult to determine period values with certainty, and given this combined with the lack of a clearly defined periodic trend in the light curves, it may be that V177 is not an LPV. 60

Figure 5.32: V177 light curve (yellow points) with top four period combined model (red points)

5.4.9 Light Curve Analysis of V178

(a) I filter light curve (b) V filter light curve

Figure 5.33: Light curves for V178. The symbols are as in Figure 5.7

Figure 5.33 shows the light curves for V178. Both light curves have moderate amplitudes (8,500 ADU in I and 2,200 ADU in V ) along iwth moderate nightly scatter. The power spectrum for 61

V178, Figure 5.34, shows that there is one dominant period at 145 days and a much weaker period at 82 days, which was found to be an alias of the 145 day period. When building the model for V178, Figure 5.35, it was found that the 145 day period described the trend of the light curve very well, confirming that the primary period of V178 is 145 days.

Figure 5.34: V178 power spectrum 62

Figure 5.35: 178 light curve (yellow points) with 145 day model (red points)

5.4.10 Light Curve Analysis of V179

(a) I filter light curve (b) V filter light curve

Figure 5.36: Light curves for V179. The symbols are as in Figure 5.7 63

V179’s light curves are seen in Figure 5.36. The I light curve have a large amplitude of 14,000 ADU while the V light curve has a moderate amplitude of 3,300 ADU. Thus suggests that the nightly scatter in the data will affect the V filter data more than the I filter data. The power spectrum for V179 is shown in Figure 5.37, and the top periods found are sum- marized in Table 5.8. While none of the periods in Table 5.8 are aliases, it was found during the creation of a model that the 50 day and 158 day periods combined fit the light curve adequately (Figure 5.38), and adding in additional periods did not substantially improve the fit of the model. A phased light curve of V179 (phase= 50 days) is also displayed as Figure 5.38c to assist in de- termining the overall fit of the model to the data. As pulsation periods of a star become shorter compared to the time span of the observations, often a phased light curve can become a useful tool in understanding the variations of the star. Considering that the strongest period detected is 50 days, it is possible that the other periods detected may play a role in the periodicity of V179, but a final conclusion cannot be made until more data, with better resolution, becomes available to further explore both the short (38 day) and long (205 day) periods detected by the DCDFT analysis.

Figure 5.37: V179 power spectrum 64

Period [Days] Power 50 18.6 158 12.8 38 12.5 205 11.4

Table 5.8: Top five period values for V179

(a) V179 light curve (yellow points) with 50 day (b) V179 light curve (yellow points) with model (red points) 50+158 day model (red points)

(c) V179 phased light curve (yellow points, phase=50 days) with 50+158 day model (red points)

Figure 5.38: Model applied to V179 light curve and phased light curve. 65

5.4.11 Light Curve Analysis of V180

(a) I filter light curve (b) V filter light curve

Figure 5.39: Light curves for V180. The symbols are as in Figure 5.7

Figure 5.39 shows the light curves for V180. Both filters show large amplitudes (20,000 ADU in I and 10,000 ADU in V ) with relatively low scatter (not including the outlying points in the V light curve). The erratic appearing, well defined light curve in the I filter suggests that V180 is a multi-periodic star. The power spectrum of V180, Figure 5.40, shows three strong periods, summarized in Table 5.9, but it was found that the 98 day period is an alias of the 213 day period. Furthermore, 444 days is almost twice the value of 213 days, creating suspicion that one of these periods is a harmonic of the other, although if this is true it is very unusual that a harmonic and its base period would have very similar power in the power spectrum. This could also just be coincidence, and the 213 day and 444 day period could both be real periods of V180.

Multiple models of V180’s light curve were made in an attempt to understand the relationship between the detected periods, and upon creating models of V180’s light curve (Figure 5.41) it was found that the 213 day period adequately described the overall trend of V180’s light curve. The

444 day period did a reasonable job by itself, but it appears to miss the general trend for the data earlier than 5700 HJD. When making a model comprised of the 213+444 day model, the largest difference is at the minimum near 5600 HJD, where the 214+444 day model appears to fit the few present data points left of the minima more poorly than the 213 day period on its own. 66

Interestingly, the model comprised of the 444+213+98 day periods is very similar to the 213+98 day period model. It is difficult to say that one of these models is better than the other, although it is important to note that the 444 day period is not needed in order to provide a good model fit to the observed light curve, suggesting that the 444 day period may not be a real compo- nent of V180’s pulsations. While the 98 day period is an alias of the 213 day period, its ability to greatly improve the fit of the model suggests that it may actually be a real component of V180’s pulsation, and that it is just a coincidence that it is also an alias of the 213 day period.

Figure 5.40: V180 power spectrum

Period [Days] Power 444 29.9 213 27.5 98 12.1

Table 5.9: Top three period values for V180 67

(a) V180 light curve (yellow points) with 213 (b) V180 light curve (yellow points) with 444 day model (red points) day model (red points)

(c) V180 light curve (yellow points) with (d) V180 light curve (yellow points) with 444+213 day model (red points) 444+213+98 day model (red points)

(e) V180 light curve (yellow points) with 213+98 day model (red points)

Figure 5.41: Light curves of V180 with models 68

5.5 Newly Discovered Variable Stars

The following four stars were newly found to be variable during the analysis of M5. The ID numbers listed below were chosen by Pellegrin during image analysis, and are somewhat arbitrary identifiers. Once the analysis of these stars has been completed, the results will be offered to the Clement catalog [10] where their ID numbers will be changed to reflect the ID system of the catalog.

5.5.1 Light Curve Analysis of V309

(a) I filter light curve (b) V filter light curve

Figure 5.42: Light curves for V309. The symbols are as in Figure 5.7

The light curves for V309 (Figure 5.42) suggests that V309 is a semi-regular, multi-periodic LPV. The amplitude of V309 is moderate (approximately 8,000 ADU in the I filter and 1,500 ADU in the V filter) with moderate scatter.

The power spectrum for V309 (Figure 5.43) shows two strong peaks, one at 265 days and another at 23 days. When creating models for V309, the most successful model used just the 265 day period, although the addition of the 23 day period introduced scatter that is on the order of what is seen in the V309 light curve, suggesting the 23 day period may play a role in the star’s overall periodicity. Additional data are required to see what extent these weaker short periods play a role in V309’s pulsations. 69

Figure 5.43: V309 power spectrum

Period [Days] Power

265 13.13

23 12.3

56 7.1

114 3.9

Table 5.10: Top four period values for V309 70

(a) V309 light curve with 265 day model. (b) V309 light curve with 265+23 day model.

Figure 5.44: V309 light curve (yellow points) with models (red points)

5.5.2 Light Curve Analysis of V312

(a) I filter light curve (b) V filter light curve

Figure 5.45: Light curves for V312. The symbols are as in Figure 5.7

Upon examining the light curves for V312, it was concluded that the data point at (5623.76, -

1131.29) in the I filter light curve is an outlier and was removed from the data set prior to analysis.

This data point is still retained in Figure 5.45a in order to show the entirety of the data set prior to analysis. Looking at the overall trend of V312, it is seen that V312 exhibits a moderate amplitude in each filter (2,500 ADU in I and 2,300 ADU in V ), with a substantial amount of nightly scatter 71 in the light curve. Given V312’s moderate amplitudes, it is likely that some of the variation seen in the light curve is due to scatter inherent in the data. Figure 5.46 is the power spectrum for V312, and suggests there are two periods in V312: 370 days and 117 days. It was found that a model of 370+117 days (Figure 5.47b) was able to fit V312’s light curve better than a model that only included the 370 day period (Figure 5.47a), thus adding support to the existence of multiperiodic behavior in V312.

Figure 5.46: V312 power spectrum 72

(a) V312 light curve with 370 day model. (b) V312 light curve with 270+117 day model.

Figure 5.47: V312 light curve (yellow points) with models (red points)

5.5.3 Light Curve Analysis of V313

(a) I filter light curve (b) V filter light curve

Figure 5.48: Light curves for V313. The symbols are as in Figure 5.7

The light curves seen in Figure 5.48 suggests that V313 is exhibiting periodic behavior, but the details of this periodicity will be difficult to determine with certainty due to the low amplitude of the light curve (approximately 2,000 ADU in I and V ) as well as the scatter found in the light curve. The power spectrum for V313 (Figure 5.49) suggests that the primary period is 166 days. Building a model of V313’s light curve (Figure 5.50), it was found that 166 days adequately de- 73 scribes the overall trend of the light curve and upon adding in the shorter period peaks (69 days and 91 days), it is unclear if the addition of these periods improves the fit of the model due to the low amplitude of the flux variations and the low amplitude of the resultant Fourier sine curves. The lower the amplitude of the light curve is, the lower the S/N of the data set becomes, which makes it difficult to be certain that the identified periodicity is real. Therefore, in order to make a conclusion about the influence of these shorter periods, a better temporally resolved data set is required.

Figure 5.49: V313 power spectrum 74

Figure 5.50: V313 light curve (yellow points) with 166 day model (red points)

5.5.4 Light Curve Analysis of V403

(a) I filter light curve (b) V filter light curve

Figure 5.51: Light curves for V403. The symbols are as in Figure 5.7

Figure 5.51 shows the light curves for V403. Both light curves have relatively large amplitudes (17,000 ADU in I and 5,300 ADU in V ) with only a small amount of nightly scatter. The V403 power spectrum (Figure 5.52), shows potentially three dominant periods, which are summarized in Table 5.11. The broad peaks seen in the power spectrum for each period suggests that more 75 data are required in order to resolve this period region, but the detection points still represent local maxima which correspond to potential periods of the star. When creating models (figure 5.53), the 172 day period model was able to adequately describe the overall trend of the V403 light curve. The addition of the 336 day period allows the model to fit the extremes of the data better, such as the minimum found near 5575 HJD.. The conclusion of the analysis is that V403 is likely a multi-periodic star that is pulsating with 172 day and 336 day periods interacting with each other.

Figure 5.52: V403 power spectrum

Period [Days] Power

172 38.5

336 16.3

94 7.2

Table 5.11: Top five period values for V403 76

(a) V403 light curve with 172 day model (b) V403 light curve with 172+336 day model

(c) V403 light curve with 172+94+336 day model

Figure 5.53: V403 light curve (yellow points) with models (red points)

5.6 Summary of Results: New Variable Stars

After analyzing the composite image produced by ISIS, and following up with DCDFT anal- ysis, four new variable stars were discovered in M5, summarized in Table 5.12. 77

Table 5.12: Summary of periods for newly discovered variable stars. Parenthesis denote a sus- pected period.

Temporary ID DCDFT Period [Days]

V309 265

V312 370+117

V313 166

V403 172+336

5.7 New Suspected Variable Stars

The following four stars are suspected to be newly discovered variable stars, due to the evi- dence found during the analysis of the data set, but the characterization of their behavior was not conclusive. Additional observations of M5 are needed in order to determine if these stars are truly variable, and to further characterize their behavior.

5.7.1 Light Curve Analysis of V300

V300 appears strongly in the composite image created by ISIS. Unfortunately, the star is near the edge of the trimmed image, which may have some influence on the quality of the photometry. Figure 5.54 shows that the observed light curves have relatively low amplitude (3,000 ADU in I and 1,000 ADU in V ) with significant scatter due to errors in the photometry. Furthermore, reviewing the reference image shows that V300 is close to another bright star (which is not a variable star), suggesting that V300’s neighbor may have had an influence on the light curve. The results shared in this section correspond to the photometry that was acquired by ISIS and further study of this star is planned using PSF photometry via DAOPHOT on the untrimmed images, which may allow for an improved light curve to be produced. 78

(a) I filter light curve (b) V filter light curve

Figure 5.54: Light curves for V300. The symbols are as in Figure 5.7

The power spectrum for V300, Figure 5.55, suggests that there are multiple periods interacting with each other to create the observed light curve, which would help to explain the erratic nature of the V300 light curves seen in Figure 5.54. Table 5.13 summarizes the top four periods found by DCDFT analysis. The strongest period found was 5.18 days, which is doubtful as this would suggest the star could be a Cepheid, which is not the case when viewing the light curve. Cepheid stars have very regular patterns of pulsation that is not seen in the V300 light curve, even when the light curve is folded by the 5.18 day period. All of the periods detected by DCDFT analysis have relatively low power, especially when comparing the power values to other LPV stars discussed earlier, suggesting the need for a longer time span of observations in order to better capture the star’s variability. The scatter seen in the light curves appears to take place on short time scales (less than 25 days), suggesting the short periods detected in the power spectrum are not real signals, but due to the noise in the data. The

98 day period appears long enough compared to the typical noise in the data that it is most likely a real part of the star’s periodicity.

When creating a model for V300 (Figure 5.56), it was found that a 98+35 day model seemed to fit the light curve reasonably well, and adding additional periods, including testing the 5.18 day period, did not show an improvement in fitting the light curve. The conclusion of this analysis is that there is evidence that V300 may be an LPV with 98-day and 35-day periods interacting 79 together, but it is possible that the 35 day period may be caused by the noise in the data set. More data are needed in order to verify that V300 is in fact a variable star, as well as to provide a more thorough characterization of the star’s behavior.

Figure 5.55: V300 power spectrum

Period [Days] Power

5.18 13.2

98 9.98

35 7.41

27 6.01

Table 5.13: Top four period values for V300 80

Figure 5.56: V300 light curve (yellow points) with 98+35 day model (red points)

5.7.2 Light Curve Analysis of V307

V307 appeared weakly in the composite image created by ISIS, and is a suspected variable star due to the overall trend of the light curve in the I filter. Unfortunately, the data have a large amount of scatter, and relatively low amplitudes (2,000 ADU in I and 700 in V ) which makes it difficult to verify the periodicity of the signal from the star.

(a) I filter light curve (b) V filter light curve

Figure 5.57: Light curves for V307. The symbols are as in Figure 5.7

The resulting power spectrum for V307 (Figure 5.58), found the primary period to be 280 81 days, along with a two other shorter periods that have reasonable power. When fitting a model to V307’s light curve, it was found that using just the 280 day period provided the best fit (Figure 5.59). Due to the scatter in the light curve, it is difficult to conclude if adding the subsequent shorter periods to the 280 day model improves the model’s fit. More data are required in order to verify that V307 is truly a variable star, and to refine the measurement of its primary period.

Figure 5.58: V307 power spectrum 82

Figure 5.59: V307 light curve (yellow points) with 280 day model (red points)

5.7.3 Light Curve Analysis of V315

V315 appears weakly in the composite image produced by ISIS, and its signal in the composite image appeared ’splotchy’ compared to other weakly appearing variable stars. Reviewing V315’s light curves (Figure 5.60), it is difficult to say if it is truly variable due to the relatively low ampli- tude of the light curve (2,000 ADU in I and 1,600 ADU in V ), and due to the scatter in the light curve. Upon completion of the Color Magnitude Diagram (CMD); see Section 6, it was found that

V315 lay next to other LPV stars in the CMD, which caused its status to be upgraded to suspected variable. 83

(a) I filter light curve (b) V filter light curve

Figure 5.60: Light curves for V315. The symbols are as in Figure 5.7

When looking at the power spectrum for V315, Figure 5.61, two periods appear relatively strongly, 303 days and 157 days. When creating a model, it was found that these two period together produced a good fit to the light curve data (Figure 5.62.

Figure 5.61: V315 power spectrum 84

Figure 5.62: V315 light curve (yellow points) with 303+157 day model (red points)

5.7.4 Light Curve Analysis of V318

V318 appears strongly in the ISIS composite image, but it appears very close to a grouping of RR Lyrae stars and LPV V180. Furthermore, the small group of data points near 5800 HJD, seen in both filters, suggests that the photometry on this star may have been influenced by its close neighbors. When comparing V318’s light curve to its close LPV neighbor, V180, it is seen that the trends in each light curve do deviate from each other at various dates. Seeing V318 brighten as V180 dims give some evidence that the photometry was able to detect V318 as a separate star, although the light curve may still be influenced by V180. Overall, the light curves for V318 seen in Figure 5.63 have moderate amplitudes (15,000 ADU in I and 5,000 ADU in V ) with relatively low scatter. 85

(a) I filter light curve (b) V filter light curve

Figure 5.63: Light curves for V318. The symbols are as in Figure 5.7

The power spectrum of V318, Figure 5.64, suggests that the primary period for V318 is 167 days, with a secondary period of 84 days. It was found that a model of the 172+84 day period was able to fit the light curve well (Figure 5.65). Looking at Figure 5.63a (I light curve), if the group of four points near 5800 HJD that are much higher value than anything else in the light curve are considered outliers, DCDFT analysis then determines that a 173 day and 88 day period are dominant in the power spectrum. Interestingly, 88 days is an alias of the 173 day period, which casts doubt on the existence of the shorter period. Furthermore, in both cases, there is a lot of power at periods greater than 350 days, suggesting there may be a longer period present in V318, but the data set does not allow for this region to be resolved enough to find a longer period. In conclusion, there is enough evidence to suggest that V318 is a variable star separate from V180. V180 was found to have a primary pulsation period of 213 days with evidence of a second period of 98 days, while V318 has been shown to have a primary period of 173 days. Additional observations, with better spatial resolution, that are similar to the PROMPT data cadence spanning at least a year (preferably two years) are needed in order to improve the characterization of V318.

Given the evidence for V381’s periodicity, a designation of SRB would be appropriate. 86

Figure 5.64: V318 power spectrum

Figure 5.65: V318 light curve (yellow points) with 167+84 day model (red points)

5.8 Summary of Results: Suspected Variable Stars

Table 5.14 summarizes the periods found for the four suggested variable stars, see each stars respective section for details on why the variability for these stars was not conclusive. 87

Table 5.14: Summary of periods for suspected variable stars. Parenthesis denotes a suspected period.

Temporary ID DCDFT Period [Days]

V300 98+35

V307 280

V315 303+157

V318 166+84 88

CHAPTER 6. CREATION OF A COLOR MAGNITUDE DIAGRAM

6.0.1 Photutils for PSF Photometry

Photutils is an Astropy package used for photometry based on the Python programming language [8]. Photutils contains many of the same algorithms deployed by DAOPHOT, originally written by Peter Stetson [21], but with additional parameters available to use if desired. Photutils was used to perform Point Spread Function (PSF) photometry on the ISIS reference images in order to construct a Color Magnitude Diagram (CMD). By constructing a CMD, a deeper understanding of the overall stellar population of M5 can be achieved, and the location of LPVs on the CMD will offer additional information about what should be expected from their light curves. Stellar evolution and pulsation theories state that stars high up on the RGB are expected to have relatively regular pulsations with large amplitudes, while stars lower on the RGB will have more irregular pulsations of lower amplitude. PSF photometry works by fitting a Point Spread Function, which looks like a 3D Gaussian curve, to the signal of a star in an image, allowing for the measurement of the flux from the star. The Point Spread Function describes the response of the telescope, camera, and atmosphere to the signal from a point source, which is a star in this case. The first step in this process is to identify the stars in an image, and create a list of their positions for use by the PSF fitting function. Figure 6.1b shows the I filter reference image with the sources detected by the IRAFStarFinder function marked. 579 sources were found when setting the detection threshold to 3.5 standard deviations above the background level. 89

(a) I filter reference image. (b) Same image with detected sources marked.

Figure 6.1: Photutils detection of sources. 579 sources were detected with a threshold detection value of 3.5 standard deviations above the background.

After detecting the sources, IRAFStarFinder automatically creates a table that includes the XY pixel position of each source detected, with a simple aperture magnitude. This XY position list of the sources is then fed into the photometry function (BasicPSFPhotometry), which then completed the process of fitting the PSF models to each identified source and creating a table of results listing the flux value for each identified source. These flux values were then converted to instrumental magnitudes for use in creating the CMD.

6.0.2 Transformation of Instrumental Magnitudes to Standard Magnitudes

After determining the instrumental magnitudes of the detected stars, the next task is to transform

these values to the standard magnitude system. This will allow direct comparison of magnitude

values of any included star with the results from other researcher’s work. To accomplish this, it

must be determined how the instrumental magnitude and standard magnitude of the stars compare

against the star’s standard V I color. This is accomplished by selecting a subset of bright, well − isolated stars (usually 15-20) in the data set and finding their standard magnitudes in a catalog to compare against each other. The difference between the standard star’s magnitude and the instrumental magnitude in a single filter (such as the I filter) is plotted vs. the V-I color of the 90 star on a scatter plot. Once all of the pairs of stars have been plotted, a best fit linear trend line is applied to the data, and the slope and y-intercept of this trendline are used as transformation coefficients. These transformation coefficients allow any instrumental magnitude in the data set to be transformed into a standard magnitude. Standard magnitudes for the stars in M5 were found in a database compiled by Peter Stetson1. From this database, 15 relatively bright stars were selected to use in this process. Figure 6.2 shows the V and I transform plots used to calculate the coefficients (provided by the equation of the trend line) needed to transform instrumental magnitudes to standard magnitudes. The transformation equations are shown below.

V = v C C (V I) − v,b − v,m × − I = i C C (V I) − i,b − i,m × − v C i+C (V I) = − v,b− i,b 1+Cv,m C − − i,m

Where V is the standard magnitude of the star in the V filter, v is the instrumental magnitude of the star in the V filter, CV,b is the y-intercept of the trend line in the V transform plot, and Cv,m is the slope of the trend line in the V transform plot. The equation for the I filter is of the same form, just replacing the quantities referred to from the V filter and V transform plot with the quantities from the I filter and I transform plot.

1This catalog can be found at https://www.canfar.net/storage/list/STETSON/Standards 91

(a) I magnitude transform plot (b) V magnitude transform plot

Figure 6.2: Transformation plots. Squares denote data points and the equation of the trend line is displayed.

After completing the transformation to standard magnitudes, the color magnitude diagrams were produced by plotting the color of the star (V I magnitudes) against the standard I magnitude − of each corresponding star, thus producing a CMD. Figures 6.3 show the resultant CMD diagrams, including showing the locations of the 11 known LPVs from Arellano Ferro et al. as well as the four new and four suspected LPVs found in this study (see Chapter 5) in Figures 6.3b and 6.3c. The W Virginis type variable star (V42) is seen in the upper left of the diagram, well above the horizontal branch where RR Lyrae stars are found. The RV Tauri type star (V84) is seen above the RGB, suggesting the location of the Asymptotic Giant Branch (AGB), and the LPVs are seen along the RGB/AGB. 92

(b) V I CMD with LPVs in yellow with ID la- − (a) V I CMD bels. −

(c) V I CMD, zoomed in on the red giant branch, − with LPVs in yellow with ID labels.

Figure 6.3: Color magnitude diagrams (CMDs) for M5. 93

CHAPTER 7. DISCUSSION OF RESULTS

7.1 Variable Star Type Designations

In summarizing the information obtained from each LPV in M5, each star will be assigned a type designation following the criteria set by the International Variable Star Index (VSX). [19] While many designations exist for variable stars, it was found that most of the LPVs in M5 qualify for an SRA, SRB, or L type designations. For a star to qualify as an SRA type variable, it must be a semi-regular giant star (such as a red giant star) exhibiting persistent periodicity and an amplitude less than 2.5 mag in the V filter. The period of the star can be anywhere between 35-1200 days. [19] An SRB designation is used for a semi-regular giant (such as a red giant star) that displays poorly defined periodicity in its light curve. The average period can be in the range of 20 to 2300 days, or with alternating periodic and slow irregular changes. [19] Finally, an L type designation is used for any potential variable star that has very poorly defined periodicity, or periodicity that only appears occasionally. The VSX definition also states that stars are often given an L type designation due to being insufficiently studied, and that many L type variables are actually other semi-regular variable stars. If a star qualifies for an L designation, but it has an amplitude of 1 mag in the V filter, then it is designated as an LB type star instead of an L type. [19]

7.2 Known LPVs

The most comprehensive and up to date study of LPVs in M5 was accomplished in 2015 by

Arellano Ferro et al. [5]. In their paper, 11 nights of observations were acquired between February

29th 2012 and April 9th 2014 using the 2.0m telescope at the Hanle Observatory in India. During their study of M5, they provided an update to the period of LPV V50, which was originally dis- covered in 1917 by Bailey [6], and discovered 11 new LPV variables, five of which were able to have their periods determined. A summary of their LPV period results is given in Table 7.1, and their published light curves are shown in Figure 7.1. 94

Figure 7.1: Published light curves from Arellano Ferro et al 2015. Note that some light curves are phased based upon their estimated period. LPVs shown are V50 and V171-181.

While the Arellano Ferro et al. study provided a large leap in understanding the LPV popu- lation in M5, their analysis was constrained by having only 11 nights of data collected over two years. The PROMPT data reported here was collected over nine months in 2011, with an additional two months in 2010. It is this observing cadence, along with large number of images overall, that allows the PROMPT data set to provide a much better characterization of the LPVs in M5. Fur- thermore, new variable stars were found that were not detected by the low temporal resolution of 95

the Arellano Ferro et al. data set. Table 7.1: Periods of known LPVs. Catalog Periods are from the Clement catalog [10], determined by Arellano Ferro et al [5]. Periods in parenthesis denote a suspected period (see Section 5.4 for more information.

Catalog ID Catalog Period [Days] DCDFT Period [Days]

V50 107.6 103

V171 28.8 (361)+183+114

V172 —- 196+53

V173 43.1 125+309

V174 80.6 78+50

V175 —- 290+(24.2)

V176 133.3 159+(35)

V177 —- (40)+(164)+(89)+(113)

V178 141.6 145

V179 —- 50+158

V180 —- 443+213+(98)

V181 —- N/A

7.2.1 Summary of Results for V50

V50 is a known, relatively well behaved LPV star. V50 was first discovered in 1917 by Bailey

[6], who determined its period was 106 days. V50 remained the only discovered LPV in M5 until

a 2015 study by Arellano Ferro et al. [5] which discovered eleven additional LPVs in M5. In that

2015 paper, the period of V50 was estimated to be 107.6 days. The precision that is presented in

the Arellano Ferro et al. paper is over-estimated, as it was found with the higher time resolution

PROMPT data set that long periods had uncertainties on the order of days (see Section 5.4.1 for an example of how uncertainties were determined). V50 appears very strongly in the composite image (see Figure 4.11) in both the I and V filter and is well isolated from other variable stars. V50 is located at the very tip of the RGB in the CMD 96

(see Figure 6.3c) with an V I magnitude of 1.65 mag, suggesting that it is a highly evolved − red giant star that should exhibit relatively regular pulsations with a large amplitude. Our DCDFT analysis found a primary period of 102 3 days, with evidence suggesting a shorter 61 day period ± could be interacting with the primary period, thus producing the more extreme features seen in the observed light curve. Given the higher time resolution of the PROMPT data set compared to previous studies of M5, the period of 102 3 days is an improvement on the currently accepted period of 107.6 days. In ± the Arellano Ferro et al. paper, V50 had an amplitude of approximately 0.2 mag in the I filter and 1 mag in the V filter. Amplitudes for the known variable stars are determined from the Arellano

Ferro et al. paper due to their use of a larger telescope, thus giving their light curves a better spatial resolution than the PROMPT data, allowing Arellano Ferro et al. to reduce the chance of blending among stars appearing close in their reference image. This allows for a truer estimate of the star’s magnitude. Referencing the Variable Star Index (VSX) variable star type designations [19], it is likely that V50 is a SRA type LPV given that it possesses relatively regular pulsations with a visual amplitude of around 1 mag. Arellano Ferro et al. also designated V50 as an SRA type variable star in their 2015 study.

7.2.2 Summary of Results for V171

V171 was first detected by Arellano Ferro et al. in their 2015 paper. The team found V171 to have an amplitude of 0.1 mag in I and 0.2 mag in V , with an estimated period of 28.8 days. Their analysis led to the conclusion that V171 should be classified as an SRA type variable star.

V171 appears in the PROMPT composite image relatively strongly, near the central region of M5. While V171 is in a more densely population region than V50, it appears to be isolated well enough from other variable stars that its light curve should not influenced by neighboring variable stars. In the CMD, V171 is in the top portion of the RGB, with a V I magnitude of 1.57 − mag, suggesting that V171 should have relatively regular pulsations that have large amplitudes, but being a bit less regular than V50. It was found that V171 had an amplitude of 29,000 ADU in I and 9,500 ADU in V . DCDFT 97 analysis suggested that V171 has a primary period of 183 6 days, with a possible secondary ± period of 114 days. The period estimated by Arellano Ferro et al. of 28.8 days is very close to the 4th harmonic of the 114 day period. The DCDFT analysis confirms the existence of this harmonic as it was detected as a 28.3 day period with a corresponding weak power, but given these characteristics it is concluded that the 23.8 day period is not a true period of V171. In conclusion, the analysis of the PROMPT data found that V171 is a multi-periodic star with strong reliance on 183 day and 114 day periods, with the potential of a 361 day period also playing an important role in the star’s overall pulsation. This analysis found that V171 should be classified as an SRA type variable, which is in agreement with the designation determined by Arellano Ferro et al. More observations of a similar cadence are required, spanning at least another year, in order to capture another cycle of V171 in order to determine if the 361 day period is a real component of V171’s pulsations.

7.2.3 Summary of Results for V172

V172 appears strongly in the composite image, and appears well isolated from other variable stars in the composite image. In the 2015 Arellano Ferro et al. paper [5], V172 was unable to have a period estimated, but was found to have an amplitude of 0.1 mag in I and 0.2 mag in V . In the CMD, V172 appears near V171, in the upper portion of the RGB with a V I magnitude − of 1.56 mag. This leads to the expectation that V172 would have similar characteristics as V171; somewhat regular pulsation with large amplitudes with a weak secondary period present. DCDFT analysis suggests that V172 has a primary period of 195 10 days, and a secondary period of 53 ± days.

The PROMPT light curves found amplitudes of 9,000 ADU in I and 9,700 ADU in V , which is in agreement with the small amplitude variations found by Arellano Ferro et al. These small amplitude variations in the light curve, coupled with the presence of multiple periods suggests that V172 should be designated an SRB type variable star instead of an SRA type as was concluded in the Arellano Ferro et al. study. 98

7.2.4 Summary of Results for V173

Arellano Ferro et al. [5] estimated that V173 had a period of 43.1 days, and found amplitudes of 0.1 mag in both the I and V light curves. V173 appears very strongly in the PROMPT I composite image and moderately strong in the V composite image. In the CMD, V173 appears very close to V175 midway up the RGB, with a V I magnitude of 1.38 mag, suggesting that − V173 and V175 will display similar behavior in their light curves, such as an erratic light curve suggesting multi-periodic behavior. DCDFT analysis concluded that V173 is multi-periodic, with a 125 day and a 309 day period being the strongest periods. Additional weaker periods were detected, but were determined to not offer substantial improvement to the fit of the model (See Section 5.4.4 for additional information). Interestingly, the 41.1 day period found by Arellano Ferro et al. was detected with a power of 9.1. Given that this period is quite weak in the power spectrum, and appears to not improve the fit of the light curve over the 125+309 day model, it seems that the detection of this period is merely coincidental. The PROMPT light curves also found relatively moderate amplitudes of 10,700 ADU in I and 6,200 ADU in V . The multi-periodic behavior of V173 coupled with observed pulsation amplitudes suggest that V173 should be classified as an SRB type variable star instead of its current classification of SRA.

7.2.5 Summary of Results for V174

V174 appears very strongly in both the I and V composite images, and is well isolated from other variable stars. Arellano Ferro et al. [5] estimated V174’s period to be 80.6 days, and found amplitudes of 0.15 mag in I and 0.3 mag in V .

The PROMPT light curves show V174 has a large amplitude of 35,200 ADU in I and 8,900

ADU in V , with very well defined pulsations with minimal scatter. V174 appears very high up on the RGB in the CMD with a V I magnitude of 1.67 mag, making this star redder than − V50. The position of V174 on the CMD suggests that the light curve from this star should have a large amplitude and have relatively regular pulsations. DCDFT analysis found that V174 is 99 multi-periodic with a 78+50 day model fitting the observed light curve very well. Given that V174 is located near V50 on the CMD, the two stars should show similar behavior all else being equal. While the longer period of V50 causes fewer pulsations to have been captured by the PROMPT data set, the more regular behavior of V50 compared to V174, along with V50 having a brighter I magnitude, suggests that V50 has more mass than V174 which allows it to pulsate more regularly than V174 even though the two stars have similar colors. The strong multi-periodic behavior of V174 along with the very clear pulsations seen in the light curve confirms the variable star designation of SRA that was given to V174 by Arellano Ferro et al.

7.2.6 Summary of Results for V175

V175 appears strongly in the PROMPT I and V composite images but is near an RRC type star. The composite image does show the two stars as separate sources (appearing as two separate, complete circles in the image) suggesting that there is not direct cross contamination of V175’s light curve by the RRC type star, but there may be some influence of the background level of V175 due to the proximity of the RRC star. V175 is located midway up the RGB in the CMD with a V I magnitude of 1.39 mag, very − close to the color of V173. The PROMPT light curves shown V175 having an amplitude of 2,700 ADU in I and 1,142 ADU in V . The DCDFT analysis found that the overall trend of the light curve is well explained by a 290 day period. The next strongest period was a relatively weak 24.2 day period, which suggests that the 290 day period could be an LSP if the 24.2 day period is found to be real and representative of the star’s pulsation period. The general rule of thumb for a period to be a potential LSP is that the LSP must be about ten times longer than the next strongest period.

[16]

In the 2015 Arellano Ferro et al. paper V175 was found to have a V and I amplitude of approximately 0.1 mag. Given the strong presence of the 290 day period, the small amplitude variations found in the PROMPT and Arellano Ferro et al. ligth curves, and the moderate scatter seen in the PROMPT light curves, V175 should be classified as an SRB type variable star instead 100 of its current designation of SRA.

7.2.7 Summary of Results for V176

V176 was discovered by Arellano Ferro et al. [5] in 2015 and was estimated to have a pe- riod of 133.3 days. The light curves shown in that study show that V176 has an amplitude of approximately 0.15 mag in I and 0.2 mag in V . V176 shows up strongly in the PROMPT I composite image and weakly in the V composite image, and is well isolated from other variable stars in both images. V176 appears in the lower third of the RGB, with a V I magnitude of 1.28 mag, suggesting that its pulsations should be − lower amplitude and less regular than the other known LPVs previously discussed (V50 and V171- 175). The PROMPT light curves show V176 having an amplitude of 13,600 ADU in I and 2,850 ADU in V . The DCDFT analysis found the strongest period to be 159 days and found two much weaker periods, 85 days and 35 days, as well. The 85 day period was found to be an alias of the strong 159 day period, although a model comprised of the 159+85 day periods fit the observed light curve better than a 159+35 day model, and the 159+85 day model was able to describe more of the extreme features of the light curve than the 159 day model could on its own, which suggests that the 85 day period could be a real component of V176’s pulsations even though it is an alias of the 159 day period. More data are needed in order to confirm this idea. The Arellano Ferro et al. light curves suggest a larger amplitude in the V filter than the I filter for V176, but interestingly the opposite was found in the PROMPT data. Furthermore, the DCDFT analysis did not find evidence for the 133 day period that was suggested by Arellano Ferro et al. although additional observations of similar cadence are needed to better resolve the period peaks in that region of the power spectrum. Given V176’s strong 159 day period and very clearly visible pulsations in the PROMPT light curves, the designation of SRA type variable appears to be appropriate for this star.

7.2.8 Summary of Results for V177

In the 2015 Arellano Ferro et al. paper, V177 was unable to have its period estimated, but was found to have an amplitude of 0.1 mag in the I and V filters. V177 appears moderately strong in 101 the PROMPT I composite image, but is very weak in the V composite image. In each composite image the star is well isolated from other variable stars. V177 appears in the lower third of the RGB in the CMD, with a V I magnitude of 1.31 mag, − which is near the color of V176. The light curve for V177 appears very irregular in both filters, but with relatively low scatter in the I filter. The amplitude of the light curve is approximately 1,500 ADU in I and 450 ADU in V , which refutes the stated amplitudes of 0.1 mag in both filters found by Arellano Ferro et al. The DCDFT analysis found four weak periods (40 days, 164 days, 89 days, and 113 days), with a model comprised of all four of these periods describing the light curve best, but was still inadequate in describing the light curve overall. It was concluded that due to the low power of the detected periods the overall shape of the light curve, and the inadequacy of the fit of the model, it is likely that the actual period of V177 is longer than what could be captured during the observing timespan of the PROMPT data. This suggests that the periods detected by the DCDFT analysis may be indicative of the noise in the data, therefore more data are required in order to provide a true estimate of V177’s period if it is a variable star at all. Given the lack of strong periodic behavior in the PROMPT V177 light curves, as well as the low amplitudes seen in each filter, it is suggested that V177 be classified as an L type variable star instead of its current SRA type designation. To determine if V177 is an SRB or SRA type variable star, additional night of observation are needed with a cadence similar to what is seen with the PROMPT data.

7.2.9 Summary of Results for V178

V178 was discovered in the 2015 study by Arellano Ferro et al. [5], where its period was estimated to be 141.6 days. The light curves included in that study show that V178 has an ampli- tude of 0.1 mag in the I and V filters. V178 appears strongly in the PROMPT I and V composite image, located near the center of M5 placing it among many other variable stars. It appears very close to V179 in the image, and is surrounded by RR Lyrae type variables, which suggest that there will be some contamination of the V178 light curve. V178 appears low on the RGB in the CMD, it is the lowest of all the known LPVs in M5, with 102 a V I magnitude of 1.12 mag. This suggests that V178’s amplitude should be relatively small − compared to the other known LPVs, especially those near the tip of the RGB such as V50. The PROMPT light curves found an amplitude of 8,500 ADU in I and 2,200 ADU in V . The DCDFT analysis found one strong period, 145 days, which was found to adequately describe the trend of the observed light curve. This result is surprising, given its low position on the CMD. There is a moderate amount of scatter in the V178 light curve, suggesting that the PROMPT data set was not able to capture more nuanced behavior of V178 if it is present. The power spectrum for V178 does have wide peaks and a shoulder feature around 115 days in the power spectrum suggesting that with additional data, it may be found that V178 is multi- periodic, although a 145 day model does fit the observed light curve quite well. The results from the analysis of the PROMPT data confirms the period found by Arellano Ferro et al. to within the uncertainty of the data set, and the clear pulsation behavior seen in the PROMPT light curves supports the star’s designation as an SRA type variable.

7.2.10 Summary of Results for V179

The period of V179 was not able to be estimated in the 2015 Arellano Ferro et al. study, but was found to have an amplitude of less than 0.1 mag in I and 0.1 mag in V [5]. V179 appears strongly in the PROMPT I and V composite images, but appears very close to V178 and is surrounded by RR Lyrae type variables, suggesting that the V179 light curve is contaminated with signal from the neighboring variable stars. In the CMD V179 appears near the upper third of the RGB with a V I magnitude of 1.38. Interestingly, V179 resides above the bulk − of known LPV stars in the CMD with a I magnitude of 10.5, suggesting that during PSF fitting the signal from V179 was blended with the light from one of it’s close variable star neighbors. The light curves show V179 to have a large amplitude of 14,000 ADU in the I filter and 3,300 ADU in the V filter suggesting that the small amplitude of the I filter found by Arellano Ferro et al. was negatively impacted by the sampling rate of their data set leading to an under-estimation of the light curve’s amplitude. DCDFT analysis found the strongest period to be 50 days with three additional periods (158 103 days, 38 days, and 205 days). Applying a 50+158 day model is able to adequately describe the observed light curve, but is not able to explain the more extreme features of the light curve. The moderate amount of scatter, combined with the relatively weak power of the other detected periods, make it difficult to assess the fit of the model as additional periods are added to the model. More data are required in order to determine if these weaker periods that were detected play a role in the pulsations of V179. V179 does exhibit strong pulsations in the PROMPT light curves, but the erratic nature of the light curve and the multiple relatively strong periods found in the DCDFT analysis suggest that V179 is not an SRA type star, but instead should be designated an SRB type star.

7.2.11 Summary of Results for V180

In the 2015 study by Arellano Ferro et al. V180 was not able to have its period estimated, but was found to have an amplitude of 0.2 mag in I and 0.3 mag in V [5] V180 appears very strongly in the PROMPT I and V composite images, but appears very close to RR Lyrae type variable stars and the potentially new LPV V318, suggesting that the V180 light curve may be contaminated with signal from the surrounding variable stars. Due to the close proximity of these other variable stars, PSF analysis was not able to adequately identify V180 so it was not able to be included in the CMD. The PROMPT light curves show that V180 has a large amplitude of 20,000 ADU in I and 10,000 ADU in V , which appears to be opposite of the stronger V amplitude found by Arellano Ferro et al. The DCDFT analysis suggests that V180 is multi-periodic and found strong 444 day and 213 day periods with a weaker 98 day period. Interestinly, the 444 day period is roughly twice the value of the 213 day period, suggesting that one period may be a harmonic of the other, but given that both of these periods have similar power, it seems unlikely that one is a harmonic. The

98 day period is an alias of the 213 day period, but during the creation of various models fitted to the light curve, it was found that the 98 day period played a greater role in improving the fit of the model compared to the 444 day period. It is clear that the 213 day period is a main component of the over pulsations of V180, and the evidence found when fitting models to the light curve suggest 104 that the 98 day period is a real component as well and that it is just coincidence that it is also an alias of the 213 day period. The clear variability and large amplitudes seen in the light curves supports the designation as an SRA type variable star. More data are required in order to confirm which periods are the true nature of the V180 periods that were detected. An additional two years of data collected at the same cadence of the PROMPT data set should be able to provide enough cycles of V180’s pulsations to provide better resolution of the peaks in the power spectrum allowing for the longer detected period values to be confirmed as true pulsation periods. Even with the uncertainty surrounding the 444 day and 98 day periods in V180, enough evidence has been found in the PROMPT data to support the designation of SRA type variable star that was determined by Arellano Ferro et al.

7.3 Newly Discovered Variable Stars

The following stars were identified as variable stars during the analysis of the V and I com- posite images. Additional information on the period determination for each of these variables can be found in Chapter 5.

7.3.1 Summary of Results for V309

V309 appears strongly in the I composite image and only moderately strong in the V com- posite image. Both images show V309 being well isolated from other variable stars in M5. The light curves shown a moderate amplitude of 8,000 ADU in I and 1,500 ADU in V . The DCDFT analysis strongly suggested that V309 is multi-periodic, with a 265+23 day period, but when ap- plying models to fit the light curve, the large amount of scatter in the observed light curve makes it difficult to determine the extent the 23 day period plays a role in the overall pulsations of V309.

The V309 power spectrum does show a shoulder feature around an 180 day period, so it is possible with additional data, the resolution of the power spectrum at long periods (greater than 100 days) will be improved enough to determine if a strong period exists around 180 days. Currently it can be concluded that V309 exhibits pulsations that are relatively well described with a 265 day period. In the CMD V309 is within the upper third portion of the RGB with a V I magnitude of 1.52 − 105 mag, placing it just behind V172 and V171. This suggests that as V309 begins to move up the RGB, its pulsations should begin to become more pronounced in the V filter as well as becoming more regular. Putting all of the information gathered on V309 suggests that V309 should be classified as a SRB type variable star.

7.3.2 Summary of Results for V312

V312 appears strongly in the I filter composite image and weakly in the V filter composite image. V312 appears near an RRAB type variable star, but the two have enough separation between them that their signals on the image do not contaminate each other. The light curves show a relatively small amplitude of 2,500 ADU in I and 2,300 ADU in V . The DCDFT analysis suggests that V312 is multi-periodic with a 270 day and 117 day period interacting with each other, leading to V312 being designated as an SRB type variable star.

7.3.3 Summary of Results for V313

V313’s light curve is relatively low amplitude (2,000 ADU in I and V ) with a moderate amount of scatter. V313 appears weakly in the I composite image, and is almost indiscernible in the V composite image. The DCDFT analysis and subsequent fitting of a model to the light curve suggests that V313 has a period of 166 days. The moderate amount of scatter in the observed light curve makes it difficult to make a determination whether the inclusion of the weakly detected shorter periods of V313 play a main role in the overall pulsation of the star. In the CMD V313 is very low on the RGB, with a V I magnitude of 1.21 mag, suggesting − that this star has begun pulsating relatively recently. This explains the erratic and low amplitude nature of the V313 light curves, as pulsations becoome more regular and larger in amplitude as the star moves up the RGB. The low amplitude pulsations of V313, along with the detection of a long period via DCDFT analysis, suggests that V313 is a SRA type variable star.

7.3.4 Summary of Results for V403

The V403 light curve contains relatively little scatter and has large amplitudes (17,000 ADU in I and 5,300 ADU in V ) compared to the other newly discovered variable stars. V403 shows up strongly in both the I and V composite image, but it appears in the image close to RRC and 106

RRAB type variable stars. The low scatter of the observed light curve, along with the detection of periods greater than that of RR Lyrae’s, suggests that any contamination of V403’s light curve has been minimal. Three models were created in response to the periods found by the DCDFT analysis (See Section 5.53) and it was concluded that it is likely that V403 is multi-periodic with 172 day and 336 day periods. The data suggests that there may also be a 94 day period as well, but additional data are required in order to determine the validity of a 94 day period. In the CMD, V403 is in the upper third of the RGB with a V I magnitude of 1.57 mag, − which places it in close proximity to V171 on the CMD. The observed V403 light curve supports the idea that V403 is a more evolved star as large amplitude, relatively regular, pulsations were observed. The behavior seen in the V403 light curves along with its position on the CMD suggest that V403 is a SRA type variable star.

7.4 Summary of Suspected Variable Stars

The following stars are suspected of being variable due to their presence in the composite images. The exact nature of their variability is difficult to conclude from the PROMPT data set, as these stars show low amplitude variations and moderate amount of scatter in their light curves.

7.4.1 Summary of Results for V300

V300 appears weakly in the V composite image, but strongly in the I composite image. In the I composite image its signal is ’splotchy’ compared to the other similarly strong stars in the composite image to the signal. This irregularity in the appearance of the star in the composite image may be due to an issue during the subtraction step in the ISIS process, or due to the star residing near the edge of the trimmed image.

The light curves show low amplitudes of 3,000 ADU in I and 1,000 ADU in V . The DCDFT analysis suggested four relatively weak periods after analyzing the light curve, and it was deter- mined that a model comprised of the 98+35 day periods offered the best fit to the observed light curve. The CMD shows V300 is located in the upper third of the RGB population, with a V-I mag- 107 nitude of 1.56 mag. This suggests that V300 should exhibit more regular pulsations as was seen in V171 and V403, but instead the pulsations of V300 are much more erratic and of low amplitude, which suggests that V300 is less massive than V171 and similar stars. The I magnitude of V300 on the CMD is 10.7 mag while V171 is 10.6 mag (for comparison V172 and V403 are both ap- proximately 10.5 mag), supporting the idea that V300 is less massive than the other stars of similar color. Given the low amplitude pulsations and the moderate scatter found in the PROMPT data, V300 is should be classified as an L type variable star until more data has been acquired.

7.4.2 Summary of Results for V307

V307 appears moderately strong in the I composite image but weakly in the V composite im- age. While other variable stars are nearby to V307, it appears that V307 is sufficiently isolated that these other variable star are not contaminating V307’s light curve. V307 has rather low amplitudes of 2,000 ADU in I and 700 ADU in V . The DCDFT analysis suggests that V307 exhibits a 280 day period. Data with better resolution can help to decrease the amount of scatter seen in the V307 light curve, and additional data will also help to resolve the long period region of the V307 power spectra which will provide a better characterization of V307. In the CMD V307 appears low on the RGB with a V I magnitude of 1.24 mag, suggesting − this star is just beginning its pulsations. Due to the large amount of scatter in V307’s light curves, only the long 280 day period was detected, but its position on the CMD suggests that a data set with better resolution would find more erratic pulsational behavior. Due to this V307 should be currently classified as a L type variable star until more data are available.

7.4.3 Summary of Results for V315

The V315 light curves have low amplitude and a moderate amount of scatter. In the I com- posite image V315 appears moderately strong and in the V image it appears strongly. The DCDFT analysis suggests that V315 is multi-periodic, and a model comprised of a 303+157 day period appeared to fit the observed light curve relatively well. The low amplitude of the V315 light curves suggests that the noise inherent to the data plays a significant role in the observed light curve, mak- ing it possible that the 303+157 day model is fitting the noise in the data and not any pulsations 108 inherent to the star itself. Until more data is available, it is difficult to fully characterize V315 with certainty. Collecting an additional two to three years of data, at the same cadence of the PROMPT data set, should be sufficient to observe multiple periods of V315 in ordet to determine if it is indeed a variable star. With the current evidence provided by the PROMPT data set, V318 should be designated as an L type variable star.

7.4.4 Summary of Results for V318

V315 appears strongly in the I and V composite images, but it appears close to V180 and an RRAB type variable star in the image, suggesting V318’s light curve may be influenced by its neighbors. The light curves show large amplitdues of 10,0000 ADU in I and 5,000 ADU in V . DCDFT analysis suggests V318 is multi-periodic, as a model comprised of a 167+84 day period fit the overall light curve well. More data is required to fully characterize V318, but currently enough is known about this star to classify it as a potential SRA type variable star. On the CMD V318 is located just above V300 on the RGB with a V I magnitude of 1.58 − mag. The I magnitude of V318 on the CMD is 10.6 mag which is slightly brighter than the 10.7 mag of V300. With this brighter magnitude, it is suspected that V318 would be more massive than V300, thus leading to more regular pulsations with a higher amplitude than V300. Given this, V318 could be classified as a SRB type variable, but until more data is available V318 should be classified as an L type variable. 109

CHAPTER 8. CONCLUSION

8.1 Comparison of Variability along the RGB

Stellar pulsation and evolution theory suggests that at a given metallicity, red giant pulsation will become more regular, and larger in amplitude, as the star moves up the RGB. Table 8.1 lists each LPV found in M5 by its position on the RGB beginning at the top right of the RGB and moving downwards toward the left ordered by I magnitude. The remaining columns show the V I magnitude of each star, the period of the star, the I and V flux amplitues, as well as the − designation that was given to each star after the analysis of the PROMPT data. 110

Table 8.1: Summary of characteristics of LPVs going from the tip of the RGB downwards by I magnitude from the PROMPT data set. Star IDs marked with ’*’ denote a suspected variable star, and periods in parenthesis are suspected periods. V180 is not included due to being insufficiently resolved photometrically (see Section 7.2.11).

ID I [mag] V I [mag] Period [d] I Amp. [ADU] V Amp. [ADU] Type − V50 10.3 1.65 103 83,100 17,000 SRA

V174 10.3 1.67 78+50 35,200 8,900 SRA

V172 10.5 1.56 196+53 9,000 9,700 SRB

V179 10.5 1.38 50+158 14,000 3,300 SRB

V403 10.5 1.57 172+336 17,000 5,300 SRA

V171 10.6 1.57 (361)+183+114 29,000 9,500 SRA

V309 10.6 1.52 265 8,000 1,500 SRB

*V318 10.6 1.58 167+84 15,000 5,000 L

*V300 10.7 1.56 98+35 3,000 1,000 L

V312 10.8 1.51 270+117 2,500 2,300 SRB

*V315 10.8 1.52 303+157 2,000 1,600 L

V173 10.9 1.38 125+309 10,700 6,200 SRB

V175 11.0 1.39 290+(24.2) 2,700 1,100 SRB

V176 11.2 1.28 159+(35) 13,600 2,800 SRA

V177 11.2 1.31 (40)+(164)+(89)+(113) 1,500 460 L

V178 11.5 1.12 145 8,500 2,200 SRA

*V307 11.6 1.24 280 2,000 700 L

V313 11.8 1.21 166 2,000 2,000 SRA

Reviewing the data in Table 8.1 shows that stars near the tip of the RGB tend to have much larger pulsations and tend to be brighter than stars lower on the RGB. This general trend is not perfect, as some stars appear to be outliers, such as V178 (Section 7.2.9) which has a large I amplitude in particular. These differences in the overall trend may come from each star having 111

slightly different initial mass, as lower mass stars would evolve up the RGB differently than higher mass stars. Taking this into account, the information in Table 8.1 supports the hypothesis that red giants pulsate more regularly, with increasing amplitudes, as they move up the RGB.

8.2 Suggested Cadence for Future Observations

When selecting an observing cadence to study variable stars, it is important to select a rate that allows for the expected period of the variable star to be captured. If the observing cadence is too infrequent, there is a risk of aliasing the period(s) that are being searched for, or missing them all together. For example the W Virginis type star in M5 (V42) was found to have a period of 25.72 days. If an observing cadence was chosen such that one observation was taken every 25.72 days, V42 would appear to have constant brightness in the resulting data set, as the brightness of the star was measured at the same point in the stars cycle each time. If instead a cadence was chosen that caused poor sampling of the light curve, but sampled a different portion of the light curve each time (such as a cadence of 23 days), then V42 would appear to be very slightly variable, if the amount of variability in the data set was even large enough to be detectable over the noise level in the data. Conversely the observing cadence shouldn’t be too frequent, as this would cost extra time and resources that are difficult to acquire. Arellano Ferro et al. took a large number of images (385 V images and 384 I images), but their observing cadence was to infrequent in order to characterize the LPVs variability in detail as was done with the PROMPT data set. If the problem of selecting an observing cadence is thought of as a signal sampling rate prob-

lem, the Nyquist theorem provides a solution to how often the star should be observed. The Nyquist

frequency (fN ) is the highest frequency that can be completely reconstructed by a given sampling

1 rate frequency (ν). The relationship between these parameters is fN = 2 ν [11]. Utilizing this rela- tionship on the 24 day period detected in V175’s light curve (Section 5.4.6), in order to accurately detect a 24 day period in a light curve, the Nyquist theorem states that an observing cadence of at least one set of observations every 12 days is required. The problem with this approach is that the Nyquist theorem was developed for use in elec- 112 tronic signal processing and it assumes that the signal is continuous, sampled at a constant rate, and sampled over many cycles. The nature of astronomical observations, especially ground based observations, leads to inevitable irregularities in the sampling rate due to factors such as weather conditions. Furthermore, the long period nature of LPV pulsation makes detecting multiple cycles of the star difficult, as it can take over a year to even detect a single cycle. The American Association of Variable Star Observers (AAVSO) provides suggestions on planning observations to study variable stars. In their CCD Photometry Guide, the AAVSO rec- ommends acquiring 20 to 50 equally spaced observations throughout the period of the star. [22] Utilizing this rule, the minimum cadence required to accurately detect the presence of V175’s 24 day period would be one set of observations every 1.2 days and the highest suggested cadence would be one set of observations every 0.48 days. The results from these two sources suggest a range of cadences that would be effective at detecting the presence of the 24 day period (if it is indeed present in the star). When deciding on a final observing cadence, it is wise to lean towards the suggested cadence from the AAVSO as their suggestion incorporates the irregularities found when gathering astronomical data. Therefore, to search for the existence of the 24 day period in V175, it is suggested that a set of observations should be taken at least every 3 days for a duration of at least 72 days. This would allow for three of the 24 day cycles to be included in the resultant light curve, which would allow for easier detection by the DCDFT algorithms. The shortest period detected by the DCDFT analysis is on the order of 24 days, and was found in multiple stars (V175, V173, V309, V300). This suggests that observations of M5 with a cadence of one set of images every 3 days would be adequate to provide evidence on the existence of these shorter periods. Other stars exhibited periods on the order of 100 days, which should be able to be well detected with a cadence of 3 days, if the observations are taken for at least a year. Given that it would be quite difficult to obtain observations every three days for a year, a better option may be to attempt two separate observing runs where one run acquires short term data (one observation every three days for 72 days), while the other observing run continues the PROMPT cadence of 113 one observation a week for at least two years in order to provide more complete cycles for the DCDFT analysis to constrain its results.

8.3 Long Secondary Periods in LPVs

Approximately 25-30% of LPVs have been found to exhibit a Long Secondary Period (LSP) component to their pulsations. An LSP is typically denoted by the presence of a strong period that is roughly ten times longer than the primary period of the star. The mechanism behind LSPs is cur- rently not understood, but a 2009 study by Nicholls et al. sought to identify potential mechanisms that lead to LSP behavior. Unfortunately, they were not able to find definitive evidence supporting one model over another, but they were able to provide a list of known characteristics of LSPs. [16] Some of the charactersistics listed by Nicholls et al. [16] are useful when attempting to iden- tify an LSP via light curve analysis. The most important characteristics of LSPs, as they apply to photometric studies, are:

1. stars exhibiting LSPs have a clearly defined period-luminosity sequence.

2. LSPs have lengths of 250-1400 days

3. LSP variation is not regular and minima are seen to vary in depth from one cycle to the next

4. The primary pulsation period is visible in the light curve at all times.

5. The primary period does not change significantly with LSP phase.

6. LSPs are approximately 8-10 times longer than the primary pulsation period.

The DCDFT analysis for V175 (Section 5.4.6) suggests that an LSP may be present for this star. The strongest period detected was 290 days (power of 29.9), with the next strongest period being 24.2 days (power of 7.5). It was found that the 290 day period model fit the V175 light curve well, and given the low power associated with the 24.2 day period, it was uncertain if the 24.2 day period played a role in the overall pulsations of V175. 114

Looking at the list of LSP characteristics provided by Nicholls et al. the 290 day period does have the proper length (between 250-1400 days), and this long period is about twelve times longer than the 24.2 day period. The ratio is close to the suggested 8-10 times longer than the primary period suggested by Nicholls et al. but it is not conclusive that the 290 day period is an LSP. If additional data are collected as suggested in Section 8.2, the presence of the shorter periods can be verified in the short term data while the additional two years of data, at the same cadence of the PROMPT data set, would allow for multiple cycles of the 290 day period to be detected. With additional long term data not only will the long period peaks in the power spectrum be able to be better resolved, but the additional data would be able to show additional LSP characteristics if they are present in V175 (particularly items 3, 5, and 6 in the above list of known characteristics).

8.4 Comparison of LPVs to M13

M13 is a globular cluster with a metallicity of [Fe/H]=-1.53, which is similar to the metallicity of M5 where [Fe/H]=-1.12. This provides a point of comparison of the LPV populations between globular clusters. A 2016 study was conducted by Osborn et al. that aimed to characterize the LPVs in M13 by utilizing full UBVI CCD photometry data from multiple observatories over many different observing seasons (up to 5 consecutive years) combined with available photography that allowed coverage of M13 from 1962-2014 in B, 1976-2014 in V , and 1991-2014 in I. Their results table is seen in Figure 8.1 [18] 115

Figure 8.1: Summary of results from Osborne et al. study on LPV in M13.

Interestingly, Osborn et al. state that in M13 all red giants with a V I magnitude greater − than 1.38 mag were able to be confirmed as variabl stars, and that amplitudes of 0.08-0.35 mag in V and 0.06-0.21 mag in I were found. [18] This suggests that there are more LPVs in M5 that were not detected by the PROMPT data set, further evidenced by the blue data points found among the identified (yellow) data points in the M5 CMD along the RGB (Figure 6.3c).

Another important comparison between the two globular clusters is their metallicity. M13 has slightly lower metallicity than M5 does; [Fe/H]=-1.53 for M13 compared to [Fe/H]=-1.12 for M5. Stellar evolution and pulsation theory suggests that higher metallicities lead to more regular LPV pulsations with larger amplitudes. Therefore, M5 should exhibit a higher number of SRA/SRB type variables along with the LPVs generally having longer periods with larger amplitudes. Of 116 the currently identified LPVs in M13 (17 identified LPVs in total), only 3 are designated as SRB type (with one additional star begin designated as intermediate SRB/L type) while the rest are designated as L type. In M5 (20 identified LPVs in total including suspsected variables) all LPVs were designated as SRA/SRB except for 5 stars. While detection of new LPVs may shift the ratio of SRA/SRB type to L type stars in M5, it is still clear that there are a greater proportion of SRA/SRB type LPVs in M5, suggesting that M5’s slightly greater metallicity is affecting the LPV population as expected. Figure 8.1 shows that the range of periods found for M13 spans from 30-92 days, with LSPs found for some stars ranging from 168-320 days, while in M5 the general span of periods is 50-443 days with no definitive evidence for LSPs being present. As stated above, it is likely that there are still undetected LPVs in M5, and while these undiscovered LPVs may have shorter periods similar to those in M13, the larger time span of periods found, as well as the preponderance of non-LSP long periods, combined with the lack of stars exhibiting only a short period suggests that there is a fundamental difference between the two LPV populations that can be attributed to the difference in metallicity between the globular clusters. As expected, M5’s LPVs have periods that are generally longer than those in M13. Comparing amplitudes between the globular clusters leads to the expected results. The PROMPT data suggests that the amplitudes found by Arellano Ferro et al. are generally smaller than they should be due to undersampling the star’s light curve. Comparing I magnitudes across the glob- ular clusters, it is seen that in M13 most amplitudes are below one mag, with a few variables exhibiting amplitudes up to 0.17 mag. In M5, referencing the magnitudes provided by Arellano

Ferro et al. it is seen that all but one star has an I amplitude of at least 0.1 mag. M13 V amplitudes well dispersed across 0.08-0.35 mag, while the M5 data has most LPVs around 0.1 mag. Its also interesting to note that the LPVs in M5 are found to have much larger amplitudes in I than in M13, but M13 LPVs gnerally have a larger V amplitude than in M5. 117

8.5 Final Summary of Results

In conclusion, the PROMPT data set was able to provide updated periods to all of the previously known LPVs in M5, except for V181 which fell outside of the trimmed image area. Four new LPVs were found in M5, with an additional four stars being identified as suspected variables. A summary of the period results, with variable type designations, is shown in Table 8.1. Additional observations are required in order to fully characterize the pulsations of many of the LPVs in M5, and to determine if the L type variable stars have some recognizable periodicity that would cause them to become SRA/SRB type stars. Additional data would also be able to determine if there is an LSP present in V175, as the current PROMPT data suggests that this is a possibility but cannot confirm the presence of an LSP. Section 8.2, outlines a suggested observing cadence in order to provide data sets with appropriate temporal resolutions to study the shorter detected periods, as well as suggesting a long term observing campaign to provide additional insight into the long term behavior of the LPVs. 118

BIBLIOGRAPHY

[1] Mohamad A. Abbas. “A Search for Long-Period Variable Stars in the Globular Cluster NGC 6496”. MA thesis. Bowling Green State University, 2011.

[2] Christophe Alard. “Image subtraction using a space-varying kernel”. In: Astronomy and Astrophysics (2000).

[3] Mohammad A. Aljassim. “A 6-Year Study of Long Period Variable Stars in the Globular Cluster NGC 6388”. MA thesis. Bowling Green State University, 2017.

[4] Andor. Apogee Alta. Oxford Instruments Group. URL: https : / / andor . oxinst . com/products/apogee-ccd-camera-series/apogee-alta.

[5] A. Arellano Ferro et al. “New Variables in M5 (NGC 5904) and some Identification Correc- tions”. In: Commissions 27 and 42 of the IAU Information Bulletin on Variable Stars 6137

(2015). URL: https://konkoly.hu/pub/ibvs/6101/6137.pdf.

[6] S.I. Bailey. In: Ann. Astron. Obs. Harvard Coll. (1917).

[7] Dave Benn. Algorithms + Observations = VStar. May 2012. URL: https : / / www . aavso.org/media/jaavso/2881.pdf.

[8] Larry Bradley et al. astropy/photutils: v0.6. Jan. 2019. DOI: 10.5281/zenodo.2533376.

URL: https://doi.org/10.5281/zenodo.2533376.

[9] Marcio Catelan and Horace A. Smith. Pulsating Stars. Wiley-VCH Verlag GmbH & Co.

KGaA, 2015. Chap. 3.

[10] Christine M. Clement et al. “Variable Stars in Galactic Globular Clusters”. In: The Astro-

nomical Journal 122.5 (Nov. 2001), pp. 2587–2599. ISSN: 0004-6256. DOI: 10.1086/

323719. URL: http://dx.doi.org/10.1086/323719.

[11] Weisstein Eric W. Nyquist Frequency. MathWorld-A Wolfram Web Resource. URL: https: //mathworld.wolfram.com/NyquistFrequency.html. 119

[12] William E. Harris. “A Catalog of Parameters for Globular CLusters in the Milkey Way”.

In: The Astronomical Journal 112.4 (1996 (2010 edition)). URL: http://physwww.

mcmaster.ca/˜harris/mwgc.dat.

[13] iraf.net. ccmap (Jan01). Documentation on the IRAF task ’ccmap’. 2001. URL: https: //iraf.net/irafhelp.php?val=ccmap&help=Help+Page.

[14] Paul W. Husband Jr. “Identification and Characterization of Long Period Variable Stars in the Globular Cluster M69”. MA thesis. Bowling Green State University, 2017.

[15] Skynet Robotic Telescope Network. Cerro Tololo Inter-American Observatory. URL: https: //skynet.unc.edu/sites/view?id=2.

[16] C. P. Nicholls et al. “Long Secondary Periods in variable red giants”. In: Monthly Notices of

the Royal Astronomical Society 399.4 (Nov. 2009), pp. 2063–2078. ISSN: 0035-8711. DOI: 10.1111/j.1365-2966.2009.15401.x. eprint: https://academic.oup. com/mnras/article-pdf/399/4/2063/17323335/mnras0399-2063.pdf.

URL: https://doi.org/10.1111/j.1365-2966.2009.15401.x.

[17] Cerro Tololo Inter-American Observatory. Site Description. URL: http://www.ctio. noao.edu/noao/content/Site-Description.

[18] W. Osborn et al. “Variable Stars in M13. II.The Red Variables and the Globular Cluster

Period-Luminosity Relation”. In: 67.2 (June 2017), pp. 131–158. DOI: 10.32023/0001- 5237/67.2.3.

[19] Sebastian Otero, Christopher Watson, and Patrick Wils. Variable Star Type Designations in

VSX. The International Variable Star Index. URL: https://www.aavso.org/vsx/ index.php?view=about.vartypes.

[20] D. Reichart et al. PROMPT: Panchromatic Robotic Optical Monitoring and Polarimetry Telescopes. 2005. arXiv: astro-ph/0502429 [astro-ph].

[21] Peter Stetson. “DAOPHOT: A Computer Program for Crowded-Field Stellar Photometry”. In: Publications of the Astronomical Society of the Pacific 99 (1987), p. 191. 120

[22] American Association of Variable Star Observers. The AAVSO Guide to CCD Photome-

try. Version 1.1. URL: https://www.aavso.org/sites/default/files/ publications_files/ccd_photometry_guide/CCDPhotometryGuide.

pdf.