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

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

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

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

Bayesian asteroseismology

xvi, 172 leaves : ill. (some col.) ; 29 cm.Includes abstract.Includes bibliographical references.This thesis presents a new probabilistic method for the asteroseismic analysis of stellar structure and evolution with the goal of providing a universal tool to improve our knowledge of stellar modelling. This new method implements the advantages of Bayesian analysis, such as the treatment of systematic errors and nuisance parameters, the modular structure of Bayesian analysis, and the correct normalization of all probabilities. First, a general introduction to asteroseismology is provided, followed by an comprehensive guide to Bayesian analysis. The derivation of the new method then follows, and its subsequent application to current problems in asteroseismology is also presented. An in-depth analysis of the Sun is performed in order to investigate long standing problems with the solar chemical composition. This also reveals the presence of systematic problems in the modelling of the Sun, potentially requiring new developments in solar modelling. Finally, the new method is also applied to 23 stars that were observed with the Kepler satellite, in order to perform a comparative investigation with respect to published results from other teams, and to study systematic errors in the stellar models

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

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

Asteroseismic modelling of the roAp star gamma Equulei based on observations obtained by the MOST satellite

roAp (rapidly oscillating Ap) Sterne sind pulsierende Sterne mit starken organisierten Magnetfeldern, die zur Gruppe der (im Allgemeinen nicht pulsierenden) Ap Sterne gehören. Erst wenige Objekte dieser Art wurden bisher entdeckt. Mit ihren chemisch–pekuliaren Sternatmosphären, ihren heterogenen Eigenschaften, was Rotation, Magnetfeldstärke und Pulsationscharakteristik betrifft, sowie ihrer geringen Anzahl, stellen roAp Sterne ein interessantes aber sehr komplexes Thema in der stellaren Astronomie dar. Eine äußerst vielversprechende Möglichkeit, die Vielzahl an physikalischen Effekten aufzulösen, die in diesen Objekten eine Rolle spielen, ist die Astero- seismologie. Sie untersucht, was Pulsationen über den Sternaufbau verraten. Diese Magisterarbeit berichtet vom Versuch, bei einem roAp Stern erstmalig lediglich mittels der Pulsation auf die Fundamentalparameter und den Aufbau des Sterns rückzuschließen. Mit Hilfe des MOST–Asteroseismologiesatelliten wurden Helligkeitsschwankungen des roAp Sterns γ Equulei (γ Equ) über 19 Tage lang gemessen, wobei insgesamt beinahe ca. 50000 Datenpunkte gewonnen werden konnten. Diese Daten wurden dann mit den aktuellsten Pulsationsmodellen dieses Sterntyps verglichen. Der MOST-Datensatz ermöglicht durch seine außergewöhnliche Qualität zum ersten Mal eine eindeutige Auflösung von γ Equ’s Frequenzen, und liefert somit die Grundbedingung für eine derartige Untersuchung.roAp (rapidly oscillating Ap) stars are pulsating stars with strong, organized magnetic fields. They belong to the larger group of (in general non-pulsating) Ap stars. Only a few objects of this class are known up to now. Due to the many convoluted effects, like their peculiar atmospheres, there heterogeneity concerning rotation, magnetic field strength, and pulsation characteristics, they are interesting but difficult stars to study. One of the most promising tools to improve our understanding of this class of stars is asteroseismology, which tries to infer details of stellar structure simply from a star’s pulsation. This thesis reports on the first attempt to use asteroseismology for a roAp star as way to derive the fundamental stellar parameters from pulsation modes alone. With the help of the MOST–satellite, which was explicitly designed for asterseismological purposes, the varying brightness of the roAp star γ Equulei (γ Equ) has been monitored for over 19 days. All in all, about 50000 measurements were obtained. These were then compared to the latest generation of roAp pulsation models. Due to its impressive quality, the MOST–data set fulfils the requirements for such a study by being the first to unambiguously resolve γ Equ’s frequencies

The connection between stellar granulation and oscillation as seen by the Kepler mission

The long and almost continuous observations by Kepler show clear evidence of a granulation background signal in a large sample of stars, which is interpreted as the surface manifestation of convection. It has been shown that its characteristic timescale and rms intensity fluctuation scale with the peak frequency (\nu_{max}) of the solar-like oscillations. Various attempts have been made to quantify the observed signal, to determine scaling relations, and to compare them to theoretical predictions. We use a probabilistic method to compare different approaches to extracting the granulation signal. We fit the power density spectra of a large set of Kepler targets, determine the granulation and global oscillation parameter, and quantify scaling relations between them. We establish that a depression in power at about \nu_{max}/2, known from the Sun and a few other main-sequence stars, is also statistically significant in red giants and that a super-Lorentzian function with two components is best suited to reproducing the granulation signal in the broader vicinity of the pulsation power excess. We also establish that the specific choice of the background model can affect the determination of \nu_{max}, introducing systematic uncertainties that can significantly exceed the random uncertainties. We find the characteristic background frequency and amplitude to tightly scale with \nu_{max} for a wide variety of stars, and quantify a mass dependency of the latter. To enable comparison with theoretical predictions, we computed effective timescales and intensity fluctuations and found them to approximately scale as \tau_{eff} \propto g^{-0.85}\,T^{-0.4} and A_{gran} \propto (g^2M)^{-1/4}, respectively. Similarly, the bolometric pulsation amplitude scales approximately as A_{puls} \propto (g^2M)^{-1/3}, which implicitly verifies a separate mass and luminosity dependence of A_{puls}.Comment: 18 pages, 12 figures, accepted for A&