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Comparing Catelan's equations to distances from GAIA using an RR Lyrae type star, 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 parsecs. 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 Stars . 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 luminosity 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 variable star, 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 absolute magnitude 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 galaxy, the Milky Way.[6] To do this it was outfit with two identical telescopes for astrometry, 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 year. 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 Declination +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].

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