Fourier Analysis

1. Preliminary Analysis of RR Lyrae Light Curves in the Globular Cluster M15 Timothy DeHaas • Andy Missert and Shashi Kanbur (University of Rochester and SUNY Oswego Abstract RR Lyraes are found mostly in globular clusters in the halo of spiral galaxies. Knowledge of their absolute magnitude as a function of metallicity leads to constraints on the theory of galaxy formation. Thus, it is important to study RR Lyraes in a range of environments. We present an initial analysis of the BVI light curves of RRab stars within the metal poor Oosterhoff II globular cluster M15 using Fourier analysis. We compare the resultant period-color relations at minimum light with similar period-color relations from the metal rich Oosterhoff I globular cluster M3. Using Fourier analysis to define the maximum and minimum magnitude of RRab light curves, it was found that minimum light, the slope of period-color relation is level. At maximum light, the period-color relation is sloped in the positive direction. Fourier Analysis Fourier analysis is an important part to analyzing scientific data from RRab light curves. It is a mathematical process by which a curve is fit through data using an infinite, or partial, sum of sinusoidal frequencies. In this scientific analysis, a Fourier decomposition was used to define a light curve, rather than individual point, so that maximum and minimum magnitude can be take. A partial sum for each light curve was taken. The order was star and color specific. The equation used in this analysis is below. Introduction Globular clusters, like M15, are characterized as a spherical, density group of stars that orbit a galactic core as a satellite. Globular clusters can be found in the halo of a galaxy and have a well defined age, older than any object in that galaxy. For this reason, it is important to study globular clusters as it helps to understand stellar and globular evolution as well as understand the formation history of galaxies and nearby satellites. RR Lyrae variable star, or in this case RRab stars, can be found within globular clusters. They are the focus of this preliminary study because of their importance of defining an age and distance of a particular cluster. They are easily identifiable, for their light curves are well define, and they are bright enough to be observed at considerable distances. In globular cluster M15, the RRab stars are known as being metal-poor, or an Oosterhoff type II. The purpose of this preliminary analysis is to study the light curves of these Oosterhoff type II variables so that the period-color (PC) relation of these stars can be compared with the period-color relation of globular cluster M3, a metal-rich cluster, or Oosterhoff type II. Sample Light Curves Period Color Relation Acknowledgments The authors thank the following for support: NSF grant OISE 0755646, HST grant HST-AR-10673.04-A, The 2006 Chretien Award of the American Astronomical Society to SMK, Laboratorio Nacional de Astrofisica, Brasil, SUNY Oswego, The Grupo de Astrofisica, Universidade Federal de Santa Catarina. Conclusion Using Fourier analysis to describe light curves of RR Lyraes in M15, maximum and minimum magnitude of these light curves were found. .Period color relations of RR Lyraes that at minimum light was plotted versus phase. The slope is level. The period color relations at maximum light versus phase has a slope that is in the positive direction. Further studies will compare the slopes of maximum and minimum period color relations of metal-poor M15 versus metal-rich M3.