Comparing Catelan’s equations to distances from GAIA using an

RR Lyrae type , SW Andromedae

by

Talon Dow

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 Physics

Brigham Young University - Idaho

March 2021

1 Copyright ©2021 Talon Dow All Rights Reserved

2 BRIGHAM YOUNG UNIVERSITY - IDAHO

DEPARTMENT APPROVAL

of a senior thesis submitted by

Talon Dow

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 Stephen Turcotte, Committee Member

Date Brian Tonks, Committee Member

Date R. Todd Lines, Chair

3 Abstract

COMPARING CATELAN’S EQUATIONS TO DISTANCES FROM GAIA USING AN RR LYRAE TYPE STAR, SW ANDROMEDAE

Talon Dow Department of Physics and Astronomy Bachelor of Science

In this project, we try to establish how accurate Catelans’ equations are using a RR Lyrae star, SW

Andromedae. Utilizing telescopes from the Las Cumbres Observatory, we took data of the star over two weeks in the V, i, Z and B filters. Using that data and metallicity obtained from several different journal articles, we obtain an average distance to the star of 447 + / − 30 . That distance is not within the

distance recorded by GAIA which is 562 + / − 52 parsecs. Our methodology is explained and can be duplicated to rerun our measurements.

4 Acknowledgements

I would like to thank Michael Fitzgerald, the creator of this project and the time he spent creating the videos for us to learn of off. I would also like to thank Brother McNeil for guiding me through this whole project and contacting Michael Fitzgerald in our behalf. I would also like to thank my wife, Brittany

Smith, and my cat, Greg. Both stayed up late with me and provided me with emotional support while my wife helped me correct all the mistakes in this thesis. Finally I would like to thank my parents for believing in me and that I would eventually reach this point.

5 Contents

1 Introduction 7

1.1 RR Lyrae Variable ...... 7

1.2 Standard Candles and Catelan’s Equations ...... 8

1.3 GAIA Distance Measurement ...... 9

1.4 SW Andromedae General Properties ...... 10

1.5 Problems with Metallicity ...... 10

2 Observations 12

2.1 Las Cumbres Observatory ...... 12

2.2 Photometry, Bands, and Intervals ...... 12

2.3 The Filtering Process ...... 13

3 Methods 14

3.1 Photometry Types ...... 14

3.2 Coding in Astrosource ...... 14

3.3 Issues with Coding ...... 16

4 Results 18

5 Discussion 20

6 Future Work 21

7 Conclusion 22

6 1 Introduction

1.1 RR Lyrae Variable Stars

Once a star is born, depending on a multitude of factors, it will evolve and move along the H-R diagram throughout it’s lifetime. These stars are low mass stars that have moved through the giant phase to the horizontal branch and into the instability strip. They will then evolve into variable stars. Variable stars are not in hydrostatic equilibrium; the gravity caused by the star going inwards and the pressure going outwards from the core are not equal. This causes the of the star to change as the star swells from the pressure and shrink from the gravity. For this project we are going to be looking at a specific type of , RR Lyrae. In the H-R diagram below, the instability strip is in white and the section where RR Lyrae are found is in blue.

Figure 1: HR Diagram for Variable Stars [19]

While RR Lyrae are variable stars, they are different from others. They typically only have a period of around 0.2 - 1.0 days. Due to the nature of how they evolve and are created, RR Lyrae have a minimum age of 10 gigayears. There are three different sub classes for RR Lyrae; a, b and c. The a and b sub classes can be grouped together as Type AB because they have larger amplitudes and longer periods. Compared to Type C they have short periods, low amplitudes, and symmetric light curves. In figure 2, each RR Lyrae type is labeled to show how they look.

7 Figure 2: RR Lyrae Types ab and c [15]

1.2 Standard Candles and Catelan’s Equations

Standard candles are used in astronomy to help us determine distances to objects far out in space.[26]

Some variable stars are good candidates for standard candles, like Cepheid Variables, because they generally have a high luminosity and have a period luminosity relationship. This means that there is a simple relation- ship between the of the star and the length of time from maximum to minimum back to maximum brightness. However, RR Lyrae don’t have a strong period-luminosity relationship, but they have a good relation between the absolute magnitude and the metallicity to allow for distance measurements. As mentioned prior, RR Lyraes are over 10 gigayears old and most will be found in globular clusters that are over 10 gigayears old. With this information, we can figure out both the age and the distance from these types of stars.

Due to there being a weaker period-luminosity relationship between RR Lyrae to other variable stars,

Marcio Catelan derived three separate equations to more accurately describe a relationship for RR Lyrae in magnitude and metallicity. In this paper published in 2004 [2], an equation was derived for the magnitude in the V filter. The Mv is the absolute magnitude in the V filter.

2 Mv = 2.28 + 0.882LogZ + 0.108(LogZ) (1)

In 2008, Catelan derived two more equations for the magnitude in both the i and the Z filter. [1]

Mi = 0.908 − 1.035LogP + 0.220LogZ (2)

8 Mz = 0.839 − 1.296LogP + 0.211LogZ (3)

The relation for metallicity comes from the LogZ as a conversion from metallicity as shown below. The

F e 0.3 LogP is the Log of the period. The H is the metallicity and the f is a constant equal to 10 .

M F e [ ] = [ ] + Log(0.638f + 0.362) (4) H H

M LogZ = [ ] − 1.765 (5) H

These equations give us another way to measure our absolute magnitude for a star and then use the

distance modulus to acquire a distance to the star.

1.3 GAIA Distance Measurement

The GAIA spacecraft was made with the intention to spend its time in space and map and survey one

percent of the stars in our , the Milky Way.[6] To do this it was outfit with two identical telescopes

for , blue and red filters for photometry, and a radial-velocity spectrometer. Gaia was launched

into space on December 19, 2013 and was set to orbit at the L2 point which lies at approximately 1.5 million

kilometers from Earth.[5] This specific orbit allows Gaia to never be subject to any eclipses while scanning

the galaxy and Gaia has an uninterrupted view of the galaxy for the entire . Using the two telescopes

mentioned before and the advantage of being in space to get a clearer image, Gaia is able to attain a distance

to stars with an accuracy of about 24 microarcseconds.[7]

9 Figure 3: An Artist Rendition of GAIA Telescope. Credit: ESA/ATG medialab [25]

1.4 SW Andromedae General Properties

The star that we chose for this project is SW Andromedae. As seen below in Table 1, the general properties of SW Andromedae are listed. These were obtained from the astronomical database SIMBAD,

Set of Identifications, Measurements and Bibliography for Astronomical Data, on a basic query search for

SW Andromedae.[24]

Table 1: General Information of SW And Right Ascension 00:23:43.09 +29:24:03.63 Period(Days) 0.4422 Radial Velocity(Km/s) -20.80 Spectral Type A7III m F0 C

1.5 Problems with Metallicity

The main issue that was run into in this project was finding a good value for the metallicity, [F e/H], for our star. In stars, metallicity is defined as the abundance of metals that are heavier than hydrogen and helium. RR Lyrae stars can be either metal-rich(Population I) or metal-poor(Population II) type stars.[9]

Since metallicity is directly correlated to our absolute magnitude, as shown above in equations, 1, 2, and

3, we need an accurate value to properly test our predictions. The metallicity value for SW Andromedae is mentioned in a multitude of papers as shown in Table 2. As shown in equation 4, the metallicity is needed for the Catelan equations. Since the listed papers all have different methods and different values for the

10 metallicity, our calculations may not be accurate. Listed along side each value is how it was measured in each correlating paper and an N/A is put there if it didn’t specifically put a method used. Using an analysis of the spectroscopy has shown to be accurate in brighter stars and the Fourier correlation is the next accurate.[2]

Due to those two being the most accurate, we decided to use the -0.06 and the -0.38 for our metallicity as a high and then a low, respectively.

Table 2: Calculated Metallicity Value Measurement -0.07 N/A [18] -0.06 N/A [4] -0.24 N/A [22] -0.24 N/A [8] -0.06 Spectra [17] -0.06 Spectra [16] -0.06 Blazhko Effect -0.38 Fourier Correlation [28] -0.15 N/A [27] 0.05 Period Relation [29] -0.09 Previously Measured [3]

11 2 Observations

2.1 Las Cumbres Observatory

We are lucky enough to have the ability to access a network of telescopes through the Las Cumbres

Observatory[23]. The network consists of many different telescopes, but for our star we used three specific telescopes that are located in the Northern Hemisphere. The first was the Teide Observatory located in the

Canary Islands, Spain with two 0.4 meter telescopes. The second was the McDonald observatory in Fort

Davis, Texas with a 0.4 meter telescope. The last telescope was the Haleakala Observatory in Maui, Hawaii with two 0.4 meter telescopes.[23]

2.2 Photometry, Bands, and Intervals

Photometry is defined as the measurement of light. There are many different optical filters that we can view stars in to get a different view of the light that they give off. We are able to view stars in ultraviolet, visible, and the infrared on the electromagnetic spectrum. For this project, however, we will use two filters in the visible spectra and two filters from the infrared spectra.[10] Shown in the subscripts of Catelan’s equations, 1, 2, and 3, we need the V (green), i (infrared), and the Z (infrared) bands. For our fourth band we will use the B(blue) band as well. While Catelan’s equations specifically use the V, i, and Z bands, there is not one for the B band, yet we are still going to be taking measurements for it. When asking the creator of our project, Michael Fitzgerald, about why we are not using a B band equation, but still taking the measurements, he said, ”The B band equation is garbage. We don’t use it.” Because the B equation seems to be inaccurate, there is potential for future research to look at the B equation specifically to identify the issues in it.

Now that we know which bands we want to take our photos in, we must figure out how often we are going to be taking our data. Because each band deals with a different wavelength of light, each band needs to have their own set time to take a data set and images. To do this, we must first take a test image of our star in each band and estimate an exposure time for each one. Once those images have returned we can move them into a program named AstroImageJ which will allows us to look at both the star in the image and how much light we have collect overall to make sure we do not have an overexposed image. The telescopes can only handle a certain amount of measured light(counts) across the area of the telescope to get an accurate measurement. If too much light is collected, meaning the exposure time was too long, there is no added benefit to the measurement and we waste exposure time. If there is too little light collected meaning too short exposure time, our measurement becomes inaccurate. Because we are looking at a variable star, we

12 must remember that the star will sometimes be dimmer and sometimes be brighter, so we have to be sure that at the maxima and minima of the period there is an appropriate amount of measured light(counts).

The cut-off point for the low counts is 10,000 while the high point is around 1 million. Using the aperture photometry tool from AstroImageJ, simply clicking on our star will give us an output of all of our measured data from this star, including our counts. Now we will take the amount of counts that we are given and divide it by our estimated exposure time to give us a ”counts per second”. With that number, we are able to estimate an accurate exposure time that will give us an appropriate number of counts for our exposure times.[13]

For each band, the above process must be done to get a good exposure time. The times that we calculated are listed below.

Band Exposure Time(Seconds) B 22 i 12 V 16 Z 38

Once all this information was acquired, we submitted a request on the LCO website to get our measure- ments. It was approved and were performed from October 5, 2020 to October 18, 2020.

2.3 The Filtering Process

The final filter process our images had to go through was a visual analysis to make sure they were good images. The telescopes are placed on Earth, so there are bound to be problems like wind or other bad weather and atmospheric distortion that can cause bad images. In our pictures, if stars are out of focus, blobby, or a little cloudy in the picture, we are still able to use them. Images that need to be tossed are ones that are obviously overexposed, bad weather like clouds that completely wash out the star field, bad weather like wind pushing the telescope and it having to redirect itself, or if the stars are no longer circular and have darker sides to them. For our data set we did not have to throw out any data, but we did have some less decent pictures that were still capable of giving us accurate data.[12]

13 3 Methods

3.1 Photometry Types

For the photometry on our star, we used six different types. They are called the APT, SEK, SEX, DAO,

DOP, and PSX. APT, SEK, and SEX are based on aperture photometry while DOP, DAO, and PSX are based on PSF, Point Spread Function, photometry.[14]

Aperture photometry is simple. Basically, we define an area around our star and we count all of the measured light within that circle. This type of photometry is much simpler to use even though it is a little less accurate. It can be used for any shape of star and can easily be used on one star.[14]

PSF Photometry will make a gridded pattern to the pixels on the image of the star. Using that pattern it will create a function for the light in all three dimensions, X, Y and Z, and count the amount of light that is under that generated curve. This type is more accurate, but it is more complicated to use. Using this will allow us to get better measurements on stars that are located in a dense globular cluster, are part of a binary system, or are dimmer when compared to neighbors.[14]

For this project we used aperture photometry because SW Andromedae is a single bright star in an easy group of bright stars and not part of a binary system. The last decision for our data to be made is if we are going to be using the APT, SEK, or the SEX data set. The APT type is better used when our star is more of a different shape than a circle like an oval so it gets tossed out. To choose between SEK and SEX, we simply made a quick light curve using our code listed below in each of the filters and chose the one that had the most data points to give us a more accurate measurement. This turned out to be our SEK data set so this is the one that will be the focus of the rest of our research.

3.2 Coding in Astrosource

To turn these photometry files into usable data we are going to be running it through Anaconda. Using

Anaconda, we are going to be running an environment using Astrosource. It is a program set up for this type of research to create light curves. A basic commandline is listed below for Astrosource.

astrosource --ra 5.929 --dec 29.40085 --indir C:\Users\Doug\SW_And\sekB

--full --format sek --imgreject 0.01 --period --verbose

We call astrosource from the library first and list the celestial coordinates for our star, SW And, in right ascension and declination. Then we list where our target files are in our directory and the correct path to our target files. The format is the type of photomtery we are using; in this case it is SEK. We then choose if

14 we want to reject any images based on the number of comparison stars, to be explained later. The final two

inputs are telling the program that we are focusing on the periods of our data and verbose lets the program know we want to see all of the information it will be outputting as it does it.[20] This program will first off take the files in the directory and convert them to files to be run a little quicker or else this program would take a long time to run. Once it does that, it will look at each one and choose the best image with the most amount of stars to compare our star, SW And, to. Then it will compare the best file to every other file and check to see which stars are present and measured in each file, because the program will eventually compare our star, SW And, to other stars to help get our light curve. This means that all the files that we will use for our data must have every comparison star. Then it accesses the AAVSO, American Association of Variable

Star Observers, website and sees if there are any variable stars along with our star in the image. Once this is complete, our loop begins. All of our comparison star candidates undergo a process where our program looks at all of their data and compares that data against itself to see how much the amount of light the star gives off varies. If the variation of light is too much, that star is no longer a good candidate to compare against and gets eliminated. In general for this program, we only want a couple percent of variability for our comparison stars. Once this is done, our program will choose a certain number of stars to compare our target star, SW And, to. For the final step, it will go through and measure our star to the comparison stars and calibrate the comparison stars to get better measurements.[11]

Once this has fully run through for the given filter, it will give us a plot showing our period and light curve measured in two different fashions and a text document with the maximum and minimum magnitudes.

It also gives us our error in our calibration stars, period of SW And, and magnitude for SW And. Also listed there are the star images that the program deemed unusable and the images it chose to use.

Figure 4: B Filter Light Curve

15 Figure 5: V filter Light Curve

Figure 6: Z Filter Light Curve

3.3 Issues with Coding

The main issue in the code is that my computer would always filter out too many stars. When comparing the light curves in the B filter shown above and the light curve in the B filter shown below, you can see the above one has many more points and a lot better of a curve to follow. After tinkering with Astrosource, I could not figure out what was going wrong so I had a group member do it on their computer since he had it working well. We also had an issue with our i band where it would give us a lot bigger numbers in our period when compared to our other filters. We also ran into the same problem where no matter what we did, it was not working for Astrosource. Brother McNeil, my research and thesis advisor, emailed Michael

Fitzgerald and asked for help. He directed Brother McNeil to use PANstarss instead. Brother McNeil was kind enough to quickly do that himself and emailed me the plot and it matches our other data, with the plot listed below.

16 Figure 7: My B Light Curve

Figure 8: I Filter Light Curve in PANstarss

17 4 Results

Now that we have established everything that our code does and allows us to do, let’s take a look at

the results that it gives. Specifically, our top priorities from this code are the magnitude, the error in that

measurement, and the period.

Table 3: Magnitude and Period Band Magnitude Magnitude Error Period(Days) B 9.568 0.020 0.443 V 9.081 0.079 0.443 i 9.111 0.082 0.442 Z 9.617 0.063 0.442

As a reminder, the purpose of this project is to determine the validity of Catelans’ new equations for RR

Lyrae stars and compare their distances to accurate instruments like GAIA. Looking back at section 1.1,

Catelans’ equations are listed out there as equations 1, 2, and 3. As explained before, those equations will

simply give us the absolute magnitude of our star in each of the three filters we are using, the V, i and Z.

The B measurements are provided in that filter even though there are no equations for it. To convert these

magnitudes into a distance, we must use an equation called the distance modulus. The distance modulus is

an equation that relates our apparent and absolute magnitude using logarithms. The regular equation looks

as follows with m being our , M being our absolute magnitude, and d being the distance

in parsecs.

d = 10(m−M+5)/5 (6)

For our research however, we are going to be using an altered version of the equation by adding in one

factor, interstellar reddening.

d = 10(m−M−A+5)/5 (7)

The new variable, A, is our reddening. We have to account for dust grains in the interstellar medium.

The average size of those grains are the same wavelength that we detect blue light at. This means that as blue light is coming to Earth from our star, the blue light is being absorbed and scattered by the dust in the interstellar medium and not making it all the way down to be measured by the telescope. This causes the light we are seeing to be more red than it actually is. We used the data from the Infrared Science Archive [21] for our extinction, which gave us a value of 0.039 + / − 0.001. Now that we finally have all of our pieces, we are able to get our distances. Referring back to section 1.5, we are going to be using our low and high

18 metallicity values, -0.06 and -0.38, as there we was not an accurately measured one.

Table 4: High Metallicty Distance (-0.06) Band Magnitude Distance(Pc) Error V 1.147 447 33 i 0.920 413 30 Z 0.958 414 26

Table 5: Low Metallicty Distance (-0.38) Band Magnitude Distance(Pc) Error V 1.055 467 33 i 0.881 420 39 Z 0.920 421 37

19 5 Discussion

As you can see from Tables 4 and 5, all of our equations have given us accurate distances within the error of each other. Now that we have our own calculated distances we can compare to GAIA. GAIA lists the distance to SW Andromedae as 562 parsecs with an error of 52. When comparing this to our own distances, the only one that comes close is the V band, with a low metallicity, and at the very top of the error. Looking at another telescope, WISE, it gives a distance as 557 parsecs with an error of +/- 11. Even comparing to the second telescope, we are not within our error.

Now we need to know why our predictions were far off from the prior measured distance. The main factor that we have looked at is our metallicity. As we did not have an accurate measurement for the metallicity, that number could have messed up our measurements. Maybe using different methods it could be even higher than what is measured or alternatively lower than what we are using. After reading too many journal articles published with a metallicity value listed, we came to the conclusion to use the values that we did.

Now, there are plenty more papers that have values listed, and have a more accurate number measured in a different method but the value varies so much that we believed the metal to be the best choice. For reference on accuracy in measurements, the period was also measured and it lines up perfectly when compared to data obtained from VIZIER.

20 6 Future Work

In the context of our project, there may not be anymore work done on our star. There is still work that has to be done though. Because we are led to believe that the issue of our distances is the metallicity, we need an accurately measured value for it. Once this value has been acquired, then we are able to go back through and run this experiment with greater accuracy and more reliable results.

Another possibility is that because we are decently far off the previously measured distance, we might return and rerun our data again just as a safe measure. Another factor not discussed in the previous section is if Catelans equations just do not work. As it stands, the project that allows this research to happen, Our

Solar Siblings, has a spreadsheet of multitudes of RR Lyrae stars waiting to be catalogued. We simply chose one star that would be good for this time of year. With a catalogue of stars as big as the one provided, at the end there will be more than enough stars to decide on how accurate these equations really are. Our star is only one small piece of this puzzle to prove the validity of Catelans equations.

21 7 Conclusion

As stated previously, the goal behind this project is to determine the validity of Catelans’ equations for

RR Lyrae stars. Based on our data that we acquired, our distance to our star is calculated as over 100 parsecs off when compared to the distances measured by both GAIA and WISE. Based on our results our star does not fit the equations, but we believe that this is due to not having an accurately measured value for metallicity. If a value is measured and proven to be accurate, coming back to this star and rerunning our data may provide a different result.

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25