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 no
nlocal 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.
Solar-like oscillations have been observed by {{it Kepler}} and CoRoT in several solar-type stars. We study the variations of stellar p-mode linewidth as a function of effective temperature. Time series of 9 months of Kepler data have been used.
The power spectra of 42 cool main-sequence stars and subgiants have been analysed using both Maximum Likelihood Estimators and Bayesian estimators, providing individual mode characteristics such as frequencies, linewidths and mode heights. Here we report on the mode linewidth at maximum power and at maximum mode height for these 42 stars as a function of effective temperature. We show that the mode linewidth at either maximum mode height or maximum amplitude follows a scaling relation with effective temperature, which is a combination of a power law plus a lower bound. The typical power law index is about 13 for the linewidth derived from the maximum mode height, and about 16 for the linewidth derived from the maximum amplitude while the lower bound is about 0.3 microHz and 0.7 microHz, respectively. We stress that this scaling relation is only valid for the cool main-sequence stars and subgiants, and does not have predictive power outside the temperature range of these stars.
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 mod
es 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.
We report on the analysis of high-precision space-based photometry of the roAp (rapidly oscillating Ap) stars HD 9289, HD 99563, and HD134214. All three stars were observed by the MOST satellite for more than 25 days, allowing unprecedented views of
their pulsation. We find previously unknown candidate frequencies in all three stars. We establish the rotation period of HD 9289 (8.5 d) for the first time and show that the star is pulsating in two modes that show different mode geometries. We present a detailed analysis of HD 99563s mode multiplet and find a new candidate frequency which appears independent of the previously known mode. Finally, we report on 11 detected pulsation frequencies in HD 134214, 9 of which were never before detected in photometry, and 3 of which are completely new detections. Thanks to the unprecedentedly small frequency uncertainties, the p-mode spectrum of HD 134214 can be seen to have a well-defined large frequency spacing similar to the well-studied roAp star HD 24712 (HR 1217).
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.
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 auth
ors, 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.
Context: We present 31.2 days of nearly continuous MOST photometry of the roAp star 10Aql. Aims:The goal was to provide an unambiguous frequency identification for this little studied star, as well as to discuss the detected frequencies in the contex
t of magnetic models and analyze the influence of the magnetic field on the pulsation. Methods: Using traditional Fourier analysis techniques on three independent data reductions, intrinsic frequencies for the star are identified. Theoretical non-adiabatic axisymmetric modes influenced by a magnetic field having polar field strengths Bp = 0-5kG were computed to compare the observations to theory. Results: The high-precision data allow us to identify three definite intrinsic pulsation frequencies and two other candidate frequencies with low S/N. Considering the observed spacings, only one (50.95microHz) is consistent with the main sequence nature of roAp stars. The comparison with theoretical models yields a best fit for a 1.95Msun model having solar metallicity, suppressed envelope convection, and homogenous helium abundance. Furthermore, our analysis confirms the suspected slow rotation of the star and sets new lower limits to the rotation period (Prot>1 month) and inclination (i>30pm10deg.). Conclusions:The observed frequency spectrum is not rich enough to unambiguously identify a model. On the other hand, the models hardly represent roAp stars in detail due to the approximations needed to describe the interactions of the magnetic field with stellar structure and pulsation. Consequently, errors in the model frequencies needed for the fitting procedure can only be estimated. Nevertheless, it is encouraging that models which suppress convection and include solar metallicity, in agreement with current concepts of roAp stars, fit the observations best.
The identification of increasingly smaller signal from objects observed with a non-perfect instrument in a noisy environment poses a challenge for a statistically clean data analysis. We want to compute the probability of frequencies determined in va
rious data sets to be related or not, which cannot be answered with a simple comparison of amplitudes. Our method provides a statistical estimator for a given signal with different strengths in a set of observations to be of instrumental origin or to be intrinsic. Based on the spectral significance as an unbiased statistical quantity in frequency analysis, Discrete Fourier Transforms (DFTs) of target and background light curves are comparatively examined. The individual False-Alarm Probabilities are used to deduce conditional probabilities for a peak in a target spectrum to be real in spite of a corresponding peak in the spectrum of a background or of comparison stars. Alternatively, we can compute joint probabilities of frequencies to occur in the DFT spectra of several data sets simultaneously but with different amplitude, which leads to composed spectral significances. These are useful to investigate a star observed in different filters or during several observing runs. The composed spectral significance is a measure for the probability that none of coinciding peaks in the DFT spectra under consideration are due to noise. Cinderella is a mathematical approach to a general statistical problem. Its potential reaches beyond photometry from ground or space: to all cases where a quantitative statistical comparison of periodicities in different data sets is desired. Examples for the composed and the conditional Cinderella mode for different observation setups are presented.
Aims. Despite photometry and spectroscopy of its oscillations obtained over the past 25 years, the pulsation frequency spectrum of the rapidly oscillating Ap (roAp) star gamma Equ has remained poorly understood. Better time-series photometry, combine
d with recent advances to incorporate interior magnetic field geometry into pulsational models, enable us to perform improved asteroseismology of this roAp star. Methods. We obtained 19 days of continuous high-precision photometry of gamma Equ with the MOST (Microvariability & Oscillations of STars) satellite. The data were reduced with two different reduction techniques and significant frequencies were identified. Those frequencies were fitted by interpolating a grid of pulsation models that include dipole magnetic fields of various polar strengths. Results. We identify 7 frequencies in gamma Equ that we associate with 5 high-overtone p-modes and 1st and 2nd harmonics of the dominant p-mode. One of the modes and both harmonics are new discoveries for this star. Our best model solution (1.8 M_sun, log T_eff ~ 3.882; polar field strength ~8.1 kG) leads to unique mode identifications for these frequencies (ell = 0, 1, 2 and 4). This is the first purely asteroseismic fit to a grid of magnetic models. We measure amplitude and phase modulation of the primary frequency due to beating with a closely spaced frequency which had never been resolved. This casts doubts on theories that such modulation - unrelated to the rotation of the star - is due to a stochastic excitation mechanism.
