A comparison of Bayesian and Fourier methods for frequency determination in asteroseismology

Bayesian methods are becoming more widely used in asteroseismic analysis. In particular, they are being used to determine oscillation frequencies, which are also commonly found by Fourier analysis. It is important to establish whether the Bayesian methods provide an improvement on Fourier methods. We compare, using simulated data, the standard iterative sine-wave fitting method against a Markov Chain Monte Carlo (MCMC) code that has been introduced to infer purely the frequencies of oscillation modes (Brewer et al. 2007). A uniform prior probability distribution function is used for the MCMC method. We find the methods do equally well at determining the correct oscillation frequencies, although the Bayesian method is able to highlight the possibility of a misidentification due to aliasing, which can be useful. In general, we suggest that the least computationally intensive method is preferable.Comment: 11 pages, 8 figures, accepted for publication in Communications in Asterosesimolog

The treatment of mixing in core helium burning models - I. Implications for asteroseismology

The detection of mixed oscillation modes offers a unique insight into the internal structure of core helium burning (CHeB) stars. The stellar structure during CHeB is very uncertain because the growth of the convective core, and/or the development of a semiconvection zone, is critically dependent on the treatment of convective boundaries. In this study we calculate a suite of stellar structure models and their non-radial pulsations to investigate why the predicted asymptotic g-mode $\ell = 1$ period spacing $\Delta\Pi_1$ is systematically lower than is inferred from Kepler field stars. We find that only models with large convective cores, such as those calculated with our newly proposed "maximal-overshoot" scheme, can match the average $\Delta\Pi_1$ reported. However, we also find another possible solution that is related to the method used to determine $\Delta\Pi_1$: mode trapping can raise the observationally inferred $\Delta\Pi_1$ well above its true value. Even after accounting for these two proposed resolutions to the discrepancy in average $\Delta\Pi_1$, models still predict more CHeB stars with low $\Delta\Pi_1$ ($< 270$ s) than are observed. We establish two possible remedies for this: i) there may be a difficulty in determining $\Delta\Pi_1$ for early CHeB stars (when $\Delta\Pi_1$ is lowest) because of the effect that the sharp composition profile at the hydrogen burning shell has on the pulsations, or ii) the mass of the helium core at the flash is higher than predicted. Our conclusions highlight the need for the reporting of selection effects in asteroseismic population studies in order to safely use this information to constrain stellar evolution theory.Comment: 24 pages. 24 figures. Published in MNRA

Solar-like oscillations in a metal-poor globular cluster with the HST

We present analyses of variability in the red giant stars in the metal-poor globular cluster NGC6397, based on data obtained with the Hubble Space Telescope. We use an non-standard data reduction approach to turn a 23-day observing run originally aimed at imaging the white dwarf population, into time-series photometry of the cluster's highly saturated red giant stars. With this technique we obtain noise levels in the final power spectra down to 50 parts per million, which allows us to search for low amplitude solar-like oscillations. We compare the observed excess power seen in the power spectra with estimates of the typical frequency range, frequency spacing and amplitude from scaling the solar oscillations. We see evidence that the detected variability is consistent with solar-like oscillations in at least one and perhaps up to four stars. With metallicities two orders of magnitude lower than of the Sun, these stars present so far the best evidence of solar-like oscillations in such a low metallicity environment.Comment: 7 pages, 6 figures, accepted by Ap