# UR: Phase Difference and Metallicity of RR Lyrae Variable Stars

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Anna McElhannon

University of Kentucky

Anna McElhannon is a rising junior studying physics, mathematics, and creative writing at the University of Kentucky. This research was conducted as part of a physics REU at the University of Kentucky under the supervision of Dr. Ronald Wilhelm. When she isn’t doing her homework, you can find her drawing, writing, or watching tornado videos.

RR Lyrae stars are radially pulsating stars classified into two types: “ab” and “c”. These stars occupy the instability strip in the Hertzsprung-Russell diagram. The RR Lyrae ab (RRab) variable stars oscillate at the fundamental mode while the RR Lyrae c (RRc) stars pulsate in the first overtone. This means that the light curve of the RRab star looks like a saw tooth curve, while the lightcurve of the RRc star looks like a sine wave.

In order to obtain a better understanding of RR Lyrae stars, we want to ultimately create theoretical pulsation models which will inform us of the physical processes that occur during a pulsation cycle. To constrain the model, various stellar input parameters are required, one of which is the metallicity

For my project, I worked to obtain the metallicity parameter by establishing a relationship with the phase difference of RRab stars. I used lightcurve data from the Transiting Exoplanet Survey Satellite (TESS) and calculated the phase differences using the program Period 04. A phase difference comes from a Fourier transform — which transforms a wave into its individual frequencies to help identify repeating patterns within it. The first frequency is the most prominent in the lightcurve and is known as the fundamental frequency, containing the first phase. The second frequency contains the second phase and so on. Prior research suggests that the phase difference between phase one and three of the Fourier transform of an RRab star’s light curve coincides with the metallicity.

I used the program Period04 to find the phases for RRab stars and compared the first and third phase difference to the stellar metallicity, either from the literature or from our own observations. I spent the summer trying to recreate the experimental results of previous research papers to confirm the success of our process. This research is still being conducted, and we hope to establish a relationship between the phase difference and stellar metallicity, and therefore the metallicity parameter, in the incoming months.

Figure 1: This is an example of the Fourier transform (the black wave) fitting to the TESS lightcurve as additional Fourier coefficients are added in the Period04 program. The left graph is from the first calculation and contains phase one while the right graph is of the third calculation and contains up to phase three. This shows how each calculation of the fourier transform adds fourier coefficients to reach a graph similar to that of the lightcurve. The same lightcurve is shown in both subfigures, where each red circle shows the observed flux of the RR Lyrae star taken every two minutes by TESS. As RR Lyrae stars have pulsation periods anywhere from a few hours to a few days, having data points every couple of minutes gives us clean and precise curves.

This research includes data collected by the TESS mission. Funding for the TESS mission is provided by the NASA’s Science Mission Directorate.

Astrobite edited by: Emma Foxell