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Home , Astrometry, Double star, Variable star

ASTROMETRIC STUDY OF BINARY SYSTEMS

AND PHOTOMETRIC STUDY OF A VARIABLE

by

Tyce Olaveson

A senior thesis submitted to the faculty of

Brigham Young University - Idaho

in partial fulfillment of the requirements for the degree of

Bachelor of Science

Department of

Brigham Young University - Idaho

April 2021 Copyright c 2021 Tyce Olaveson

All Rights Reserved BRIGHAM YOUNG UNIVERSITY - IDAHO

DEPARTMENT APPROVAL

of a senior thesis submitted by

Tyce Olaveson

This thesis has been reviewed by the research advisor, research coordinator, and department chair and has been found to be satisfactory.

Date Stephen McNeil, Advisor

Date Lance Nelson, Committee Member

Date Brian Tonks, Committee Member

Date R. Todd Lines, Chair ABSTRACT

ASTROMETRIC STUDY OF BINARY SYSTEMS

AND PHOTOMETRIC STUDY OF A

Tyce Olaveson

Department of Physics and

Bachelor of Science

My senior research gave me opportunities to complete two astronomy based projects. During each of these I proposed an object of study and presented my

findings. The first of these projects is focused on binary and studies the separation distance and position angle of two star systems. The system with a primary star at RA 11 : 06 : 30.6 DEC −46 : 10 : 28.97 is determined to have position angle of 154o and separation distance of 7.00 arcsec. This system is possibly a and a minimum is calculated. The second system has primary star at RA 11 : 06 : 34.7 DEC −46 : 11 : 55.3, its position angle is measured as 72.67o and separation distance is 11.08 arcsec. data suggests that this system is likely not a physical binary.

The second project is devoted to the variable star V0893 Her. The star is observed in the B, v i and z filters and curves are generated for each

filter. From these curves, we calculate period information and used these to determine the theoretical absolute in each filter. The period is calculated as 0.495 ± 0.036 days. The distance to the star is calculated as

501 ± 24 , which is significantly different from the GAIA spacecraft mission. We conclude that our data was not as clean as we would have hoped, possibly due to the binary nature of the system or some other factors at play. ACKNOWLEDGMENTS

I would like to thank Dr. McNeil for giving me direction and helping me complete this research. I would also like to thank Rachel Freed at InStAR for providing the resources and opportunity to complete the binary star project as well as Michael Fitzgerald at Our Solar Siblings for help working through the variable star project. I would also like to acknowledge my group members:

Roberta Bonnell, Jakob Bergstedt and Dallin Fisher all made considerate con- tributions to the binary star project. My group members for the variable star project were Amber Mistry, Dr. McNeil and Rachel Freed and they helped complete the project. Lastly I would like to thank my wife Rebecca for sup- porting and encouraging me through this entire processes. Contents

Table of Contents vii

List of Figures viii

1 An Overview1 1.1 Binary Stars...... 1 1.2 Variable Stars...... 3

2 Binary Stars5 2.1 Introduction...... 5 2.2 Methods and Procedure...... 6 2.3 Results and Analysis...... 9 2.4 Discussion...... 14

3 Variable Stars 15 3.1 Introduction...... 15 3.2 Methods and Procedures...... 17 3.3 Results and Analysis...... 20 3.4 Discussion...... 22

4 Conclusion 25 4.1 Challenges is all things...... 25 4.2 Future Rewards...... 26

Bibliography 27

vii List of Figures

2.1 Image of Double 1 taken from the Siding Spring Observatory on May 28 2020, boxed in red. The Siding Spring Observatory is located in Australia and is part of the LCO global network...... 8 2.2 Image of Double 2 taken from the Siding Spring Observatory on May 28 2020, boxed in red...... 9 2.3 An example of using AstroImageJ to take measurements of Double 1. 10 2.4 The HR diagram we plotted on. We can see that the stars in Double 1 are both , whereas those of Double 2 are more likely on the giant branch...... 10

3.1 An example of a for an RRab vairable star [1]...... 16 3.2 An image of V0893 Her taken from the Aladin stargazing software.. 18 3.3 An image of V0893 Her taken in the z filter from our cadence..... 18 3.4 Light curve in the i filter using the String Test to calculate the period and sex ...... 22 3.5 Light curve in the V filter using String Test to calculate the period and apt photometry...... 22 3.6 Light curve in the z filter using String Test to calculate the period and apt photometry...... 22 3.7 Light curve generated with information from data collected by Hipparcos 23 3.8 An image of the V0893 Her system exhibiting its binary nature.... 23

viii Chapter 1

An Overview

During the summer of 2020 and amid the swing of Covid-19, I participated in two research projects. In each of these projects I experienced the entire research process, from proposing a project to writing a paper and presenting my results at a conference.

This thesis will go through the details of each project including the conclusions and future prospects for each.

1.1 Binary Stars

The first project is devoted to Binary Stars and is part of the larger effort designed to provide research opportunities for undergraduate students. This program is provided through InStAR [2] and was overseen by Rachel Freed who currently runs the orga- nization. A Binary consists of two or more stars that are gravitationally bound together into an orbit and have long been of interest to . Because we cannot go visit these stars personally (for obvious reasons) we must observe them through our earthly and make due with what light can tell us. We can learn a lot from light; however, our two dimensional images can lead to some incorrect

1 1.1 Binary Stars 2 conclusions at times.

As astronomers, we are only able to see stars in a two dimensional plane. The fact that not all stars have the same can make it challenging to determine dis- tance just by looking at an image of a star field. To compensate for this, astronomers define two categories of binary stars: optical doubles and physical binaries. Optical doubles are binary stars that appear to be in close proximity, but are not in reality.

We often see optical doubles within , where stars appear to be next to each other but are in fact separated by millions of light years of empty space. Quick identification of these types of stars are done through angles. The parallax angle of a star is determined by its change in angular position when seen from differ- ent positions and can be used to calculate the distances to nearby stars. When the parallax angle of stars are similar, it is indicative of stars in close proximity, when the parallax angles are significantly different we can know that the stars are not near each other. Systems without similar parallax angles are not true binary stars since they are not in close physical proximity.

Of the two, physical binaries are the most interesting. These are stars that are gravitationally bound together and what is most commonly known as a binary star.

From these stars, astronomers can use Keplers equations of to determine masses of stars. Sometimes, there are binary stars that fall into neither category and are thus, undetermined. In these cases we begin to calculate potential orbits of the two stars by measuring their positions over hundreds of years.

To keep track of all of these stars, the Washington Catalog (WDS) keeps a database of millions of documented double stars as well as relevant information about their positions. In my research, I find two double star systems that are not included in the WDS and take observations of them to find their classification. The

first of these systems is likely an optical double since the of the two stars 1.2 Variable Stars 3 do not show significant overlap. The second of these systems shows more promise. I measure the positions of these stars and calculate a minimum orbit for the star using

Keplers laws.

In the end, this research will most likely benefit future generations of astronomers.

Since we can neither prove nor disprove something with a single measurement, future observers will be able to draw upon my contribution and use this data to make a definite decision.

1.2 Variable Stars

The second of these projects involves Variable Stars. This research is also part of a larger project organized and directed by Michael Fitzgerald at Our Solar Siblings

[3]. Variables are stars that vary in magnitude (relative brightness of a star) in a predictable and oscillatory fashion. For some types of variable stars (like Cepheid and RR Lyrae variables) astronomers have created empirical and theoretical formulas that can relate the period of a star’s oscillation to its , making some variable stars reliable standards for measuring distances. Of course, we can’t expect these equations to be exact or perfect, and for this reason the organization Our

Solar Siblings has designed this research project to improve these derived formulas by taking into account other stellar properties such as .

Unlike binary stars, variable stars require much more attention to get decent information. Since the star oscillates in magnitude, we must observe it over a period of time. Once these observations are complete there is still much more to do. Since we are using physical instruments to take images of stars and environmental conditions are not identical from night to night, the magnitude of all the stars will appear to change from night to night. At this point we must use differential photometry to 1.2 Variable Stars 4 determine which stars in the night sky are truly constant. These will then be used as comparison stars to determine the true magnitude of the target star on any given night. Once that has been completed we can generate a light curve and then obtain the period of the variable star.

In my work I go through the above process for the star V0893 Her. I calculate a light curve for the star and extract a period. Theoretical distances are then calculated using the period and previously measured . In the end, I compare my calculated distances to the values taken from the GAIA space mission and discuss my

findings. Chapter 2

Binary Stars

2.1 Introduction

Binary stars have long been a topic of interest to astronomers. When stars are gravitationally bound, astronomers can calculate hard to determine properties such as stellar masses. Because we cannot measure the masses directly, astronomers must use indirect methods to do so. My contribution is through , which is the

”branch of astronomy concerned with the measurement of the positions and apparent motions of celestial objects in the sky and the factors that can affect them” [4].

In this project, the two measurements that we are interested in are the position angle and the separation distance. These values can be thought of as the compo- nents of a vector, with the vector starting at the primary star and ending at the secondary. The position angle is measured from the north and increases in the eastern direction. The separation distance is the angular separation measured in mil- liarcseconds between the two stars. With these two values and the coordinates of the primary star, an can fix both stars in the sky.

Of course, stars are not motionless in the sky. Each is moving under the grav-

5 2.2 Methods and Procedure 6 itational effects of other celestial bodies and each star has its own orbit within the . Even though these motions are very slight to earthly observers, over time the small changes add up. To account for all of these small motions, astronomers make use of the historical measurements of the stars to calculate orbits of possible binary systems.

Thanks to past observations and modern technology, the Washington Double Star catalog (WDS) holds historical records of millions of double stars. In addition to the catalog, other resources have been created that allow for easy searching of the WDS.

The tools that I use in this project are the online resource StelleDoppie [5] and the

WDS Double Star Selection Tool [6] developed through the collaborative efforts of

Alex Hewett, Dave Rowe and Richard Harshaw. StelleDoppie allows for easy searching of stars based on the coordinates of the primary star. The Double Star Selection Tool is used to find double star coordinates through specified search parameters such as magnitude difference and last measured separation distance.

2.2 Methods and Procedure

We began our study of binary stars by selecting a target. As there are millions of possible binary stars available, we wanted to choose a neglected system (last observed before 2015). Using the Double Star Selection tool, we searched for stars that fit the following criteria:

• between 9 and 14 hours. The Right Ascension places the star’s

eastern/western position in the sky, similar to longitude. The choice of these

parameters assures that our target will be visible in the night sky.

• Any declination. The Declination fixes the star’s northern/southern position in

the sky, similar to latitude. Since we are using remote telescopes to take images 2.2 Methods and Procedure 7

we don’t need to worry about choosing a star in the northern hemisphere.

• Primary Star Magnitude between 8 and 10. Any fainter than 10 and the star

may not be seen by the telescopes.

• The difference in magnitude (relative brightness) of the stars less than 3 mag-

nitudes. If the difference is any larger than this then the primary star will

outshine the secondary and we will not be able to take clear images of both

stars.

• Separation distance between 5 and 10 milliarcseconds. Less than 5 becomes

difficult to get accurate measurements and more than 10 makes it harder to

distinguish the secondary from the background stars. Doubles with separation

larger than 10 milliarcseconds are also less likely to be physical binaries.

• Maximum number of observations 10. We wanted a star that had not been

repeatedly studied.

• Most recent observation 2015. We wanted a star that hadn’t been observed

recently so that our measurements would show a change.

With these parameters in the selection tool we found the star 11080-6140 (Right

Ascension 11hrs, Declination −61◦). This star had only been observed a few times

and most recently in 2015 and is found in the .

Next we take images of the stars. This was done through the Las Cumbres Ob-

servatory (LCO) [7] remote telescopes. The LCO provides student researchers (and

other amateur astronomers) opportunities to use their telescopes remotely. Using the

LCO portal we put in the coordinates for our star, used a clear filter and submitted

a request. Using this method we took 10 images of our star. Unfortunately, when

we looked through the images we discovered that the actual separation distance was 2.2 Methods and Procedure 8 significantly smaller than what had been recorded previously. This meant that we would not be able to take decent measurements. This setback, frustrating though it was, provided us an opportunity to discover something new.

To double check that our images had accurately captured the right star, we used the French stargazing site VizieR. This site allowed us to look through complied star

field images from various missions and collect additional information about our target.

Sadly, the information provided by the Double Star Selection Tool was incorrect and these stars were too close together to resolve with the telescopes available to us. As we looked through the vicinity, however; two other sets of stars caught our attention.

These have the coordinates RA 11:06:30.6 DEC -46:10:28.97 and RA 11:06:34.7 DEC

-46:11:55.3. For simplicity I will define the system Double 1 to be the system with the primary star at RA 11:06:30.6 DEC -46:10:28.97, and Double 2 will be the system with primary star coordinates at RA 11:06:34.7 DEC -46:11:55.3. Figures 2.1, and

2.2 provide example images of the two systems.

Figure 2.1 Image of Double 1 taken from the Siding Spring Observatory on May 28 2020, boxed in red. The Siding Spring Observatory is located in Australia and is part of the LCO global telescope network.

Wanting to study these we searched the WDS to see what historical information was available to us. To our surprise, we couldn’t find anything. It appeared that these stars had not been previously identified as candidates for binary stars. Since 2.3 Results and Analysis 9

Figure 2.2 Image of Double 2 taken from the Siding Spring Observatory on May 28 2020, boxed in red. these two stars were in close angular proximity, we could capture both sets of stars in the same image. Following the same procedure as before, we submitted an image request to the LCO. Once the observations were complete, we retrieved our images, verified that our stars were distinguishable and proceeded to take measurements.

The program that we used is called AstroImageJ [8]. This program is an open source software available to the public that has many astrometry tools. Using As- troImageJ, I pulled up each of our ten starfields and took measurements. I took measurements by selecting the primary star of each system using an aperture tool and pairing it with its companion. From here, AstroImgaeJ was able to calculate the separation distance and position angle for each system. For each of the images, we measured the separation distance and position angle ten times (to assure consis- tency). The results of each of these measurements and the average of each is recorded in table 2.1. An example of the AstroImageJ interface can be seen in figure 2.3.

2.3 Results and Analysis

In addition to taking these measurements, we wanted to draw a few conclusions about the natures of these stars. Data from the GAIA space mission is freely available to the 2.3 Results and Analysis 10

Figure 2.3 An example of using AstroImageJ to take measurements of Dou- ble 1. public at https://gea.esac.esa.int/archive/. Using their searching software we located our stars and a few other properties of interest. The information used in this paper is contained in tables 2.2 and 2.3. The spectral type mentioned at the end of each table is a value that we determined by plotting the luminosity and surface temperature on the Hertzsprung-Russell (HR) diagram seen in figure 2.4.

Figure 2.4 The HR diagram we plotted on. We can see that the stars in Double 1 are both main sequence, whereas those of Double 2 are more likely on the giant branch.

Upon inspection of the GAIA data, we immediately notice that Double 2 is likely 2.3 Results and Analysis 11

Double 1 Double 2

Image θ (deg) ρ (arcsec) θ (deg) ρ (arcsec)

1 154.78 7.04 72.57 11.10

2 155.44 6.98 72.84 11.04

3 155.17 6.97 72.45 11.09

4 155.21 6.96 72.60 11.09

5 154.92 7.00 72.78 11.05

6 154.92 6.97 72.69 11.13

7 154.66 7.02 72.68 11.02

8 154.95 6.98 72.72 11.09

9 155.25 7.05 72.65 11.06

10 154.93 6.98 72.72 11.11

Mean 154.98 7.00 72.67 11.08

Std. Dev 0.30 0.031 0.11 0.034

Std. Err. of Mean 0.09 0.01 0.03 0.01

Table 2.1 Set of data collected by measuring the Position Angle and Sepa- ration distance collected through AstroImageJ. not a physical double. The two things that suggest this are the parallax angles and the proper motions. The parallax angles are close but in order to get any overlap we need to consider multiple standard deviations, compared with Double 1 that has overlapping parallax. The also suggests that these two may not be physical binaries. Typically if two stars are gravitationally bound they will also move through space together. The proper motion indicates how the stars are moving through space. We can see that in the case of Double 1 the proper motions are close, whereas those of Double 2 are significantly different. 2.3 Results and Analysis 12

GAIA source ID 5386565914691315968 5386565914691315712

Reference (yr) 2015.5 2015.5

Right ascension (deg) 166.63 ± 0.02 166.63 ± 0.02

Declination (deg) -46.17 ± 0.02 -46.18 ± 0.02

Parallax (mas) 2.053 ± 0.022 2.015 ± 0.030

Proper motion: right -20.745 ± 0.035 -20.87 ± 0.47 ascension (mas/yr)

Proper motion: decli- 5.050 ± 0.034 5.011 ± 0.045 nation (mas/yr)

Effective temperature 4920 ± 80 4790 ± 120 (K)

Lum (solLum) 0.353 ± 0.010 0.195 ± 0.008

Spectral Type (esti- K1 V K4 V mated)

Table 2.2 GAIA data for the primary and secondary stars in Double 1.

Since the GAIA data for Double 1 does not rule out the possibility of it being a true , we endeavor to compute a minimal . To do this we make use of the distances between the two stars in astronomical units (AU) and the masses of each star.

The distances are calculated through simple geometry. First we use the parallax angle in arcseconds to calculate the distance D to our primary star:

1AU D [] = (2.1) p 2.053 × 10−3arcseconds

This gives us 487.1 parsecs (pc) as the distance to the primary star. Now, using our 2.3 Results and Analysis 13

GAIA Source ID 538656512119495296 538656515877768800

Reference epoch (yr) 2015.5 2015.5

Right ascension (deg) 166.64 ± 0.02 166.65 ± 0.017

Declination (deg) -46.20 ± 0.02 -46.20 ± 0.02

Parallax (mas) 0.284 ± 0.030 0.236 ± 0.026

Proper motion: right -4.841 ± 0.047 -7.074 ± 0.038 ascension (mas/yr)

Proper motion: decli- (mas/yr) 3.200 ± 0.043 1.348 ± 0.036 nation

Effective temperature 4450 ± 210 4680 ± 200 (K)

Lum (solLum) 88.57± 15.90 26.29± 7.25

Spectral Type (esti- K1 III K1 IV mated)

Table 2.3 GAIA data for the primary and secondary stars in Double 2. measured separation angle in radians we can calculate the distance between the two.

Ds[pc] = D tan ρ (2.2)

−5 Ds = 487.1[pc] × tan 3.39 × 10 [rad] (2.3)

This puts the separation between the two stars at a distant of 0.0164 ± 0.00017 parcecs, which is equivalent to 3400 ± 36 AU. The next step will be to calculate the masses. We will use the mass luminosity relationship presented in Eker, et al [9].

log (L/L ) = 4.81 log (M/M ) − 0.026 (2.4)

log (L/L )+0.026 M = M × 10 4.841 (2.5) 2.4 Discussion 14

Using this formula and the data from GAIA we find the mass of the primary star

as Mp = 0.816M and the mass of the secondary as Ms = 0.722M , where M is the mass of the .

Now that we have the masses of the two stars in solar masses and the distance between the two in AU, we can calculate the minimal orbital period using Kepler’s

Third Law:

a3[AU] P 2[yrs] = (2.6) Mp + Ms s (3406[AU])3 P [yrs] = (2.7) 0.816[M ] + 0.722[M ]

P ≈ 160, 000yrs (2.8)

Should this be a physical binary, the calculated period assumes that the stars are

at their maximum separation and that we are observing from a non tilted plane.

2.4 Discussion

In this project, my group located two possible binary systems and measured each

system’s position angle and separation distance. Upon dissection of the available

GAIA data, we have determined that Double 2 is most likely an optical double,

though one that still warrants research. We have also shed light on what may be a

physical binary in Double 1 based on current GAIA data and our measurements. We

have calculated the minimum orbital period in order to give some idea of time frames

for future measurements.

Any future work that goes into this project will go towards collecting more data

on each binary system in order to confirm our suspicions about Double 2 and to

determine other orbital parameters for Double 1. Chapter 3

Variable Stars

3.1 Introduction

RR Lyrae stars are important in understanding galactic as they are one of the main distance indicators for Population II (metal poor) stars. RR Lyrae variables are old, low-mass, radially pulsating stars with periods in the range between 0.2 and

1 day. The classification of RR Lyrae is further subdivided into RRab and RRc type stars. RRab type stars have a steeper increase and more dramatic increase of magnitude. Their periods are also more consistent and reliable. An example of an

RRab light curve can be seen in figure 3.1. In the case of RRc type stars, these have a more sinusoidal light curve and tend to have more spread. This will be the focus of this project.

The Period-Luminosity (PL) relationship in RR Lyrae stars varies depending on what bandpass (filter) the star is studied in [10]. For this reason, researchers generally use an average relationship between absolute visual magnitude and metallicity [Fe/H] in applying the PL relationship of RR Lyrae stars. The metallicity of a star is an indicator of the relative abundance of elements heavier than . It is usually seen

15 3.1 Introduction 16

Figure 3.1 An example of a light curve for an RRab vairable star [1]. as a ratio of iron over [Fe/H].

However, because there is a strong dependence of the PL relationship on evolution effects [11], and a potential nonlinearity as a function of [Fe/H] [12], the use of the average relationship may provide inaccurate estimates of distance. Therefore, a better understanding of the PL relationship in RR Lyraes is warranted. Catelan et al. 2004, which will be referred to from now on as Catelan, presents a theoretical calibration of RR Lyrae PL relations in UBVRIJHK Johnson-Cousin-Glass filters.

This project, directed and overseen by Michael Fitzgerald at Our Solar Siblings, examines the light curves of the RR Lyrae V0893 Her. While V0893 Her is reported in several large surveys [13], no study has been carried out thus far for this particular star. Here we report on the light curves of V0893 Her in B, V, i, and z filters to study the period-luminosity relationship in more detail within these different band passes.

This project will also compare distances calculated using data gathered by the

GAIA spacecraft [14, 15] and the equations presented in Catelan to determine dis- tances based on the average magnitude in each filter. Basic statistics of this star are provided in Table 3.1. 3.2 Methods and Procedures 17

Property Value Source

Right ascension 16 20 04.075

Declination +45 12 59.969

Proper Motion RA -6.876 (mas/yr) GAIA DR2

Proper Motion Dec 11.566 (mas/yr) GAIA DR2

Parallax 2.6502 (mas) GAIA DR1

Other identifiers HIP 80020, SAO 46030

Spectral Type F2 AAVSO

Magnitude Range 9.2-9.38 AAVSO

Period 0.491812 d (11.8035 h) AAVSO

0.490 ± 0.002 d WISE

Table 3.1 Stellar properties of V0893 Her. This table includes basic information regarding V0893 Her. Note, the unit ‘mas’ is a milli-arc second and is a measurement of angular distance.

3.2 Methods and Procedures

In order to produce light curves for V0893 Her, we collected images in the B (blue),

V (visual/clear), i (infrared) and z (far infrared) filters using 0.4 m telescopes from the Las Cumbres Observatory [7] with the SBIG 6303 camera. We took preliminary exposures of 40 seconds in each filter to determine an appropriate exposure time, then adjusted accordingly so as to not overexpose our images. Our exposure times for each: 20 seconds in the B filter, 8 seconds in the V filter, 12 seconds in the i filter and 40 seconds in the z filter. Using these exposure times we created a cadence that ran between June 22, 2020 and July 5, 2020. This returned a total of 53 images for each filter.

A sample image from Aladin Sky is provided in Fig 3.2. 3.2 Methods and Procedures 18

Figure 3.2 An image of V0893 Her taken from the Aladin stargazing soft- ware.

Figure 3.3 An image of V0893 Her taken in the z filter from our cadence.

These images were processed using the Our Solar Siblings Pipeline [16]. The pipeline cleaned up the raw images, removing extra background noise as well as prepared the different types of photometry that are used later in this paper. In addition to using the pipeline, we manually sorted through our images to discard those that exhibited significant cloudiness or had otherwise poor quality. An example of a clean image of V0893 Her is provided in Fig 3.3

Using the python based scripts Autovar and Astrosource [17], provided by Michael 3.2 Methods and Procedures 19

Fitzgerald at Our Solar Siblings, we were able to extract information from our images.

Autovar and Astrosource are python scripts that are used to analyze the various types of photometry files (raw data for how much light is contained in each pixel) generated from our cadence. The programs analyze the star field surrounding the target star and identify suitable comparison stars - those of comparable magnitude and with little variance between images. Using these comparisons as a baseline, the programs extract magnitude and time information from the star files and compile these into a light curve. From the light curve we are then able to calculate the average magnitude, the period and the amplitude.

As part of the python script, two different methods are used to calculate the period from our light curve. These are Phase Dispersion Minimisation (PDM) [18] and the Distance Method (DM) [19]. Information regarding each of these methods can be found in their respective sources. These periods and magnitude information taken across the different photometry types are recorded in Table 3.2.

We used the Apt (Aperture photometry tool [20,21]) and Sex (aperture photom- etry) [22] photometry methods to analyze the star system. Aperture photometry is a method of determining a star’s light output. The method counts up all of the light within a certain radius (aperture) around the star and subtracts off the back ground light from outside the star. The Apt and Sex methods are different applications of this process. Apt is the most general, whereas Sex is a more specialized method that worked nicely for our images. Further information concerning of these methods can be found in their respective sources and will not be discussed in this thesis.

From this information we used the distance equations found in Catelan (see equa- tions 3.1, 3.2, and 3.3) and compared them to the distance data from GAIA and

WISE [23]. 3.3 Results and Analysis 20 3.3 Results and Analysis

While running Autovar and Astrosource for each filter we calculated an average period

and amplitude for each of the photometric filters, these values are recorded in table

3.2.

Filter B Error V Error i Error z Error

Middle Magnitude 9.396 0.071 9.082 0.020 8.958 0.0042 9.007 0.089

Period (DM) 0.4963 0.0056 0.4970 0.1500 0.4948 0.0058 0.4949 0.0050

Period (PDM) 0.4933 0.0048 0.4950 0.1100 0.4942 0.0051 0.4954 0.0050

Amplitude 0.358 - 0.300 - 0.339 - 0.341 -

Table 3.2 Average values of various results in each filter along with the errors of each.

Using the metallicity of the star ([Fe/H]=−1.445) [24] and Catelan’s equations for absolute magnitude:

2 Mv = 2.288 + 0.882 log(Z) + 0.108(log(Z)) (3.1)

Mi = 0.908 − 1.035 log(P ) + 0.220 log(Z) (3.2)

Mz = 0.839 − 1.295 log(P ) + 0.211 log(Z) (3.3)

where we have the following definitions:

log(Z) = [M/H] − 1.765 (3.4)

[M/H] = [F e/H] + log(0.638 × 100.3) + 0.362 (3.5) and P is the period. Using the metallicity and period values for each filter we get:

MV = 0.613 (3.6)

Mi = 0.429 (3.7)

Mz = 0.433 (3.8) 3.3 Results and Analysis 21

From here we can use the simple distance relationship to calculate the distance to the star for each filter.

d[pc] = 10(m−M−A+5)/5 (3.9)

Where A is the interstellar , a value related to the amount of dust between the observer and the star.

Using our measured and calculated values we get the results in Table 3.3.

Filter/Source Distance [pc] Error

GAIA 377.3 3.9

WISE 528 4

V 482 21

i 505 35

z 516 66

Viz 501 24

Table 3.3 Table of calculated distances. Viz is taken as an average of the other three.

In addition to calculating distances based on each filter, we generated light curves and estimated periods. These curves are included as Figures 3.4, 3.5 and 3.6 and a light curve generated using data taken with the Hipparcos satellite [25] is included as reference in Figure 3.7. It is to be noted that while our light curves are not as smooth as we would have hoped, this is not an issue since V0893 Her is an RRc type variable star which naturally exhibits more spread. We also noticed that the Hipparcos light curve has significant spread. This provides support that our light curves are accurate.

Taking the average of our period estimates in each filter we find that the period of V0893 Her based on our data is 0.495 ± 0.0036 days. 3.4 Discussion 22

Figure 3.4 Light curve in the i filter using the String Test to calculate the period and sex photometry

Figure 3.5 Light curve in the V filter using String Test to calculate the period and apt photometry

Figure 3.6 Light curve in the z filter using String Test to calculate the period and apt photometry

3.4 Discussion

As is evident in our distance measurements in Table 3.3, our values are significantly different from those collected by GAIA. We suspect that the cause of this discrepancy is excess light due to a companion star, an example of which can be seen in Figure

3.8. This was imaged by the Herschel Space Observatory [26] in the far infrared. 3.4 Discussion 23

Figure 3.7 Light curve generated with information from data collected by Hipparcos

The secondary star has a separation of 5.22 arcseconds and a position angle of 121.9 degrees.

Figure 3.8 An image of the V0893 Her system exhibiting its binary nature.

Due to this companion star and the limited resources available to us, we are 3.4 Discussion 24 unable to take the project further. Additional study would require researching the companion star and determining its spectrum then subtracting this light from that obtained through normal observation. After subtraction, the resultant light would be only that coming from the variable star and could be used to make more precise light curves. This, however, is beyond the scope of this project.

While our distance estimates are unusable, the periods that were calculated can be trusted: a secondary star will not change the period significantly provided it is not an eclipsing binary. The light curves produced in this project have noticeable spread unlike those presented in other papers. While this spread is common among RRc type stars it could stand to be improved. When looking at our raw images we find that many of these are cloudy and not as clear as we would have hoped. If we were to observe this star again in the future, we would take more images. This would give us a larger data pool and would allow us to discard poorer images without worrying about missing too many data points.

However, when compared with light curves taken by the Hipparcos spacecraft

(see Fig 3.7) it can be seen that these data points also exhibit a large spread, with many outliers. It would be interesting to explore further (with better equipment and funding) the variability of V0893 Her. Could the binary nature of the system have a more significant influence on the variability? Chapter 4

Conclusion

A major purpose of completing these projects was to give myself experience in real research. As such it is appropriate that I share some of the things that I learned from this experience.

4.1 Challenges is all things

For each of these projects I completed the entire research process. This consisted of finding and proposing to study a specific star that would be beneficial to the scientific community, completing all of the research, writing a paper for publication in a scientific journal and finally presenting the research. During these experiences I learned to appreciate the work of other scientist. The work was challenging. None of the steps were without challenges.

During the binary star project we were forced to redesign our plan when our desired target proved to be unusable. We ran into software errors while trying to take measurements on the stars. In the variable star project we spent weeks trying to determine why our measurements were not matching the predictions or theory, only

25 4.2 Future Rewards 26 after much digging did we determine that the secondary star must be influencing the of the variable. All of these things were challenging and showed me that research is not something to be taken lightly.

4.2 Future Rewards

As part of both projects, my work had no immediate impact on the scientific com- munity. The binary stars that I studied may or may not be added to the millions of others listed in the WDS. In my study of variable stars, we generated light curves that look very similar to those calculated for other stars. Does this mean that my work was wasted? Not at all.

While I was completing each of these projects, I relied on the research done by previous scientist. Thanks to their efforts I was able to have this experience. So while my work is not immediately useful, when future astronomers seek to study the binary system RA 11:06:30.6 DEC -46:11:55.3, they will find my measurements to be useful.

When a researcher wants to further explore the variability of V0893 Her, my work here will be appreciated. Bibliography

[1] G. Casali, Ph.D. thesis, 2020.

[2] “Institute for Student Astronomical Research,”, https://www.in4star.org/.

[3] “Our Solar Siblings,”, url/https://www.oursolarsiblings.com/, accessed: August

2020.

[4] J. Mitton, Cambridge dictionary of astronomy (2001).

[5] “StelleDoppie,”, https://www.stelledoppie.it/index2.php?section=1, accessed:

April and May 2020.

[6] “Double Star Selection Tool,”, https://boyce-astro-research-assistant.

herokuapp.com/, accessed: April and May 2020.

[7] T. Brown et al., “Las Cumbres Observatory global telescope network,” Publica-

tions of the Astronomical Society of the Pacific 125, 1031 (2013).

[8] K. A. Collins, J. F. Kielkopf, K. G. Stassun, and F. V. Hessman, “ASTROIM-

AGEJ: IMAGE PROCESSING AND PHOTOMETRIC EXTRACTION FOR

ULTRA-PRECISE ASTRONOMICAL LIGHT CURVES,” The Astronomical

Journal 153, 77 (2017).

27 BIBLIOGRAPHY 28

[9] Z. Eker, F. Soydugan, E. Soydugan, S. Bilir, E. Y. G¨ok¸ce,I. Steer, M. T¨uys¨uz,

T. S¸eny¨uz,and O. Demircan, “Main-sequence effective temperatures from a re-

vised mass–luminosity relation based on accurate properties,” The Astronomical

Journal 149, 131 (2015).

[10] M. Catelan, B. J. Pritzl, and H. A. Smith, “The RR Lyrae period-luminosity re-

lation. I. Theoretical calibration,” The Astrophysical Journal Supplement Series

154, 633 (2004).

[11] P. Demarque, R. Zinn, Y.-W. Lee, and S. Yi, “The metallicity dependence of

RR Lyrae absolute magnitudes from synthetic horizontal-branch models,” The

Astronomical Journal 119, 1398 (2000).

[12] M. Castellani, V. Castellani, L. Pulone, and A. Tornamb´e,“Theoretical hot

stars,” Astronomy and 282, 771–774 (1994).

[13] P. Kervella, A. Gallenne, N. R. Evans, L. Szabados, F. Arenou, A. Merand,

N. Nardetto, W. Gieren, and G. Pietrzynski, “Multiplicity of Galactic Cepheids

and RR Lyrae stars from Gaia DR2-II. Resolved common proper motion pairs,”

Astronomy & Astrophysics 623, A117 (2019).

[14] Gaia Collaboration, “Description of the Gaia mission (spacecraft, instruments,

survey and measurement principles, and operations),” Gaia Collaboration et

al.(2016a): Summary description of Gaia DR1 (2016).

[15] C. Gaia et al., “Gaia Data Release 2 Summary of the contents and survey prop-

erties,” Astronomy & Astrophysics 616 (2018).

[16] M. Fitzgerald, “The Our Solar Siblings Pipeline: Tackling the data issues of

the scaling problem for based astronomy education projects,”

(2018). BIBLIOGRAPHY 29

[17] M. Fitzgerald and E. Gomez, “astrosource,”, https://pypi.org/project/

astrosource/, Feb 25, 2021.

[18] R. F. Stellingwerf, “Period determination using phase dispersion minimization.,”

Astrophysical Journal 224, 953–960 (1978).

[19] M. Dworetsky, “A period-finding method for sparse randomly spaced observa-

tions or “How long is a piece of string?”,” Monthly Notices of the Royal Astro-

nomical Society 203, 917–924 (1983).

[20] R. R. Laher et al., “Aperture photometry tool versus SExtractor for noncrowded

fields,” Publications of the Astronomical Society of the Pacific 124, 764 (2012).

[21] R. R. Laher, V. Gorjian, L. M. Rebull, F. J. Masci, J. W. Fowler, G. Helou,

S. R. Kulkarni, and N. M. Law, “Aperture photometry tool,” Publications of the

Astronomical Society of the Pacific 124, 737 (2012).

[22] E. Bertin and S. Arnouts, “SExtractor: Software for source extraction,” Astron-

omy and Astrophysics Supplement Series 117, 393–404 (1996).

[23] T. Gavrilchenko, C. R. Klein, J. S. Bloom, and J. W. Richards, “A mid-infrared

study of RR Lyrae stars with the Wide-field Infrared Survey Explorer all-sky

data release,” Monthly Notices of the Royal Astronomical Society 441, 715–725

(2014).

[24] A. L. Luo, Y. H. Zhao, G. Zhao, and et al., “VizieR Online Data Catalog:

LAMOST DR5 catalogs (Luo+, 2019),” VizieR Online Data Catalog p. V/164

(2019).

[25] in ESA Special Publication, Vol. 1200 of ESA Special Publication (1997). BIBLIOGRAPHY 30

[26] E. Valiante et al., “The Herschel-ATLAS data release 1 - I. Maps, catalogues

and number counts,” Monthly Notices of the Royal Astronomical Society 462,

3146–3179 (2016).