Using asteroseismology to determine membership of stellar clusters observed by the Kepler Mission

Abstract If we can measure the speed of sound in a gas, we have information about the pressure and density of that gas. From the equation of state, we can constrain the temperature and chemical composition. Therefore, by measuring the sound speed in stars we can deduce these same characteristics of the star being measured. The goal of asteroseismology is to use oscillations to measure this sound speed throughout the star to determine these fundamental stellar parameters. Asteroseismology accomplishes this by extracting the oscillation frequencies of the sound at the stellar surface, and combining this with models to infer the sound speed and density inside the star. The Kepler space telescope has initiated a revolution in asteroseismology. The Kepler mission is a NASA space-based photometric telescope, designed to detect Earth-size planets around Sun-like stars. Kepler has observed one patch of sky for a continuous four year period. The high photometric precision of the data in conjunction with the long time span also makes it ideal for measuring the frequencies of the sound-wave induced by oscillations at the stellar surface. I use a new technique to determine the cluster membership of red giant stars in two open clusters using asteroseismology. By determining the oscillation frequencies of a number of red giants in the region of two clusters in the Kepler field, I can determine whether they are consistent with membership of the cluster or are field stars in the foreground or background. This thesis focuses on the evolved stars, which have left the hydrogen-core burning phase on the main sequence to become hydrogen shell-burning subgiants, or red giants. I was able to use the Kepler long-cadence (29.4 min) data to measure the oscillation frequencies of the red giants, and thus infer their fundamental stellar parameters. Stars in a cluster are believed to share a common age and initial composition, being formed from the same interstellar cloud. This allows for membership to be inferred from photometric studies by using models of isochrones in a color-magnitude diagram. As a result, this technique is dependent on knowing distance and interstellar extinction. Alternatively, the common space velocity can also be used to determine membership status, however, this relies on the field stars not randomly aligning with the cluster motion. Recently, Stello et al. (2010b) introduced a new technique based on asteroseismology to determine cluster membership that is dependent only on the internal properties of the stars. I detect the oscillation frequencies to measure the frequency of maximum oscillation power, vmax and the large frequency separation, ∆v. These parameters are related to surface gravity and the mean density of the star respectively, and are therefore known to scale with the M, L and Teff (where M is the mass, L is the luminosity and Teff is the surface temperature) of the star (Ulrich 1986; Kjeldsen & Bedding 1995). The common initial conditions of the cluster allow us to compare the parameters of individual stars in the vicinity of the cluster with the mean of the cluster. A ratio of 1.0 for the measured to scaled parameter indicates a likely member of the cluster independent of distance or interstellar absorption. I analysed over 400 red giant stars in the vicinity of two clusters in the Kepler field of view, NGC 6791 and NGC 6819. By measuring the asteroseismic parameters of each star and comparing them with the solar scaled values, I was able to confirm the members of Stello et al. (2011b) and to identify 45 new red giant members distributed over the two clusters. This has increased the red giant population by almost 40% for NGC 6791 and almost 10% for NGC 6819, which will allow stellar evolution models to be constrained