Bayesian Asteroseismology of 23 Solar-Like Kepler Targets

We study 23 previously published Kepler targets to perform a consistent grid-based Bayesian asteroseismic analysis and compare our results to those obtained via the Asteroseismic Modelling Portal (AMP). We find differences in the derived stellar parameters of many targets and their uncertainties. While some of these differences can be attributed to systematic effects between stellar evolutionary models, we show that the different methodologies deliver incompatible uncertainties for some parameters. Using non-adiabatic models and our capability to measure surface effects, we also investigate the dependency of these surface effects on the stellar parameters. Our results suggest a dependence of the magnitude of the surface effect on the mixing length parameter which also, but only minimally, affects the determination of stellar parameters. While some stars in our sample show no surface effect at all, the most significant surface effects are found for stars that are close to the Sun's position in the HR diagram.Comment: 14 pages, 9 figures, accepted for publication in MNRA

Modeling Convective Core Overshoot and Diffusion in Procyon Constrained by Asteroseismic Data

We compare evolved stellar models, which match Procyons mass and position in the HR diagram, to current ground-based asteroseismic observations. Diffusion of helium and metals along with two conventional core overshoot descriptions and the Kuhfuss nonlocal theory of convection are considered. We establish that one of the two published asteroseismic data reductions for Procyon, which mainly differ in their identification of even versus odd l-values, is a significantly more probable and self-consistent match to our models than the other. The most probable models according to our Bayesian analysis have evolved to just short of turnoff, still retaining a hydrogen convective core. Our most probable models include Y and Z diffusion and have conventional core overshoot between 0.9 and 1.5 pressure scale heights, which increases the outer radius of the convective core by between 22% to 28%, respectively. We discuss the significance of this comparatively higher than expected core overshoot amount in terms of internal mixing during evolution. The parameters of our most probable models are similar regardless of whether adiabatic or nonadiabatic model p-mode frequencies are compared to the observations, although, the Bayesian probabilities are greater when the nonadiabatic model frequencies are used. All the most probable models (with or without core overshoot, adiabatic or nonadiabatic model frequencies, diffusion or no diffusion, including priors for the observed HRD location and mass or not) have masses that are within one sigma of the observed mass 1.497+/-0.037 Msun

Asteroseismic Stellar Modelling with AIMS

The goal of AIMS (Asteroseismic Inference on a Massive Scale) is to estimate stellar parameters and credible intervals/error bars in a Bayesian manner from a set of asteroseismic frequency data and so-called classical constraints. To achieve reliable parameter estimates and computational efficiency, it searches through a grid of pre-computed models using an MCMC algorithm -- interpolation within the grid of models is performed by first tessellating the grid using a Delaunay triangulation and then doing a linear barycentric interpolation on matching simplexes. Inputs for the modelling consist of individual frequencies from peak-bagging, which can be complemented with classical spectroscopic constraints. AIMS is mostly written in Python with a modular structure to facilitate contributions from the community. Only a few computationally intensive parts have been rewritten in Fortran in order to speed up calculations.Comment: 11 pages, 4 figures. Tutorial presented at the IVth Azores International Advanced School in Space Sciences on "Asteroseismology and Exoplanets: Listening to the Stars and Searching for New Worlds" (arXiv:1709.00645), which took place in Horta, Azores Islands, Portugal in July 201

On the detection of Lorentzian profiles in a power spectrum: A Bayesian approach using ignorance priors

Aims. Deriving accurate frequencies, amplitudes, and mode lifetimes from stochastically driven pulsation is challenging, more so, if one demands that realistic error estimates be given for all model fitting parameters. As has been shown by other authors, the traditional method of fitting Lorentzian profiles to the power spectrum of time-resolved photometric or spectroscopic data via the Maximum Likelihood Estimation (MLE) procedure delivers good approximations for these quantities. We, however, show that a conservative Bayesian approach allows one to treat the detection of modes with minimal assumptions (i.e., about the existence and identity of the modes). Methods. We derive a conservative Bayesian treatment for the probability of Lorentzian profiles being present in a power spectrum and describe an efficient implementation that evaluates the probability density distribution of parameters by using a Markov-Chain Monte Carlo (MCMC) technique. Results. Potentially superior to "best-fit" procedure like MLE, which only provides formal uncertainties, our method samples and approximates the actual probability distributions for all parameters involved. Moreover, it avoids shortcomings that make the MLE treatment susceptible to the built-in assumptions of a model that is fitted to the data. This is especially relevant when analyzing solar-type pulsation in stars other than the Sun where the observations are of lower quality and can be over-interpreted. As an example, we apply our technique to CoRoT observations of the solar-type pulsator HD 49933.Comment: 12 pages, 11 figures, accepted for publication in Astronomy and Astrophysic

Pulsation models for the roAp star HD 134214

Precise time-series photometry with the MOST satellite has led to identification of 10 pulsation frequencies in the rapidly oscillating Ap (roAp) star HD 134214. We have fitted the observed frequencies with theoretical frequencies of axisymmetric modes in a grid of stellar models with dipole magnetic fields. We find that, among models with a standard composition of $(X,Z) = (0.70,0.02)$ and with suppressed convection, eigenfrequencies of a $1.65\,{\rm M}_\odot$ model with $\log T_{\rm eff} = 3.858$ and a polar magnetic field strength of 4.1kG agree best with the observed frequencies. We identify the observed pulsation frequency with the largest amplitude as a deformed dipole ($\ell = 1$) mode, and the four next-largest-amplitude frequencies as deformed $\ell = 2$ modes. These modes have a radial quasi-node in the outermost atmospheric layers ($\tau \sim 10^{-3}$). Although the model frequencies agree roughly with observed ones, they are all above the acoustic cut-off frequency for the model atmosphere and hence are predicted to be damped. The excitation mechanism for the pulsations of HD 134214 is not clear, but further investigation of these modes may be a probe of the atmospheric structure in this magnetic chemically peculiar star.Comment: 9 pages, 6 figures; accepted for publication in MNRA

gamma Doradus pulsation in two pre-main sequence stars discovered by CoRoT

Pulsations in pre-main sequence stars have been discovered several times within the last years. But nearly all of these pulsators are of delta Scuti-type. gamma Doradus-type pulsation in young stars has been predicted by theory, but lack observational evidence. We present the investigation of variability caused by rotation and (gammaDoradus-type) pulsation in two pre-main sequence members of the young open cluster NGC2264 using high-precision time series photometry from the CoRoT satellite and dedicated high-resolution spectroscopy. Time series photometry of NGC2264VAS20 and NGC 2264VAS87 was obtained by the CoRoT satellite during the dedicated short run SRa01 in March 2008. NGC2264VAS87 was re-observed by CoRoT during the short run SRa05 in December 2011 and January 2012. Frequency analysis was conducted using Period04 and SigSpec. The spectral analysis was performed using equivalent widths and spectral synthesis. The frequency analysis yielded 10 and 14 intrinsic frequencies for NGC2264VAS20 and NGC2264VAS 87, respectively, in the range from 0 to 1.5c/d which are attributed to be caused by a combination of rotation and pulsation. The effective temperatures were derived to be 6380$\pm$150K for NGC2264VAS20 and 6220$\pm$150K for NGC2264VAS87. Membership of the two stars to the cluster is confirmed independently using X-ray fluxes, radial velocity measurements and proper motions available in the literature. The derived Li abundances of log n(Li)=3.34 and 3.54 for NGC2264VAS20 and NGC2264VAS87, respectively, are in agreement with the Li abundance for other stars in NGC2264 of similar Teff reported in the literature. We conclude that the two objects are members of NGC2264 and therefore are in their pre-main sequence evolutionary stage. Assuming that part of their variability is caused by pulsation, these two stars might be the first pre-main sequence gamma Doradus candidates.Comment: 11 pages, 10 figures, A&A accepte

Photometry of GSC 762-110, a new triple-mode radially pulsating star

Stars pulsating in three radial modes are very rare; only three examples are known in the Galaxy. These stars are very useful since their periods may be measured very precisely, and this will constrain the global stellar parameters and the models of the star's interior. The purpose of this paper is to present a new example of the class of triple-mode radial pulsators. A search for candidate multi-mode pulsators was carried out in public survey data. Time-series photometry of one of the candidates, GSC 762-110, was performed. GSC 762-110 was found to be a triple-mode radial pulsator, with a fundamental period of 0.1945d and period ratios of 0.7641 and 0.8012. In addition two non-radial modes were found, for which the amplitude has diminished considerably over the last few years.Comment: Accepted for publication in Astronomy & Astrophysic

Toward a New Kind of Asteroseismic Grid Fitting

Recent developments in instrumentation (e.g., in particular the Kepler and CoRoT satellites) provide a new opportunity to improve the models of stellar pulsations. Surface layers, rotation, and magnetic fields imprint erratic frequency shifts, trends, and other non-random behavior in the frequency spectra. As our observational uncertainties become smaller, these are increasingly important and difficult to deal with using standard fitting techniques. To improve the models, new ways to compare their predictions with observations need to be conceived. In this paper we present a completely probabilistic (Bayesian) approach to asteroseismic model fitting. It allows for varying degrees of prior mode identification, corrections for the discrete nature of the grid, and most importantly implements a treatment of systematic errors, such as the "surface effects." It removes the need to apply semi- empirical corrections to the observations prior to fitting them to the models and results in a consistent set of probabilities with which the model physics can be probed and compared. As an example, we show a detailed asteroseismic analysis of the Sun. We find a most probable solar age, including a 35 +- 5 million year pre-main sequence phase, of 4.591 billion years, and initial element mass fractions of X_0 = 0.72, Y_0 = 0.264, Z_0 = 0.016, consistent with recent asteroseismic and non-asteroseismic studies.Comment: 15 pages, 5 figures, accepted for publication in The Astrophysical Journal; v2 contains minor changes made in the proofs (updated references & corrected typos

The nature of p-modes and granulation in HD 49933 observed by CoRoT

Context: Recent observations of HD49933 by the space-photometric mission CoRoT provide photometric evidence of solar type oscillations in a star other than our Sun. The first published reduction, analysis, and interpretation of the CoRoT data yielded a spectrum of p-modes with l = 0, 1, and 2. Aims: We present our own analysis of the CoRoT data in an attempt to compare the detected pulsation modes with eigenfrequencies of models that are consistent with the observed luminosity and surface temperature. Methods: We used the Gruberbauer et al. frequency set derived based on a more conservative Bayesian analysis with ignorance priors and fit models from a dense grid of model spectra. We also introduce a Bayesian approach to searching and quantifying the best model fits to the observed oscillation spectra. Results: We identify 26 frequencies as radial and dipolar modes. Our best fitting model has solar composition and coincides within the error box with the spectroscopically determined position of HD49933 in the H-R diagram. We also show that lower-than-solar Z models have a lower probability of matching the observations than the solar metallicity models. To quantify the effect of the deficiencies in modeling the stellar surface layers in our analysis, we compare adiabatic and nonadiabatic model fits and find that the latter reproduces the observed frequencies better.Comment: accepted to be published in A&A, 9 pages, 5 figure