Convective core entrainment in 1D main sequence stellar models

3D hydrodynamics models of deep stellar convection exhibit turbulent entrainment at the convective-radiative boundary which follows the entrainment law, varying with boundary penetrability. We implement the entrainment law in the 1D Geneva stellar evolution code. We then calculate models between 1.5 and 60 M$_{odot}$ at solar metallicity ($Z=0.014$) and compare them to previous generations of models and observations on the main sequence. The boundary penetrability, quantified by the bulk Richardson number, $Ri_{mathrm{B}}$, varies with mass and to a smaller extent with time. The variation of $Ri_{mathrm{B}}$ with mass is due to the mass dependence of typical convective velocities in the core and hence the luminosity of the star. The chemical gradient above the convective core dominates the variation of $Ri_{mathrm{B}}$ with time. An entrainment law method can therefore explain the apparent mass dependence of convective boundary mixing through $Ri_{mathrm{B}}$. New models including entrainment can better reproduce the mass dependence of the main sequence width using entrainment law parameters $A sim 2 times 10^{-4}$ and $n=1$. We compare these empirically constrained values to the results of 3D hydrodynamics simulations and discuss implications.

Stellar ages and convective cores in field main-sequence stars: first asteroseismic application to two Kepler targets

Using asteroseismic data and stellar evolution models we make the first detection of a convective core in a Kepler field main-sequence star, putting a stringent constraint on the total size of the mixed zone and showing that extra mixing beyond the formal convective boundary exists. In a slightly less massive target the presence of a convective core cannot be conclusively discarded, and thus its remaining main-sequence life time is uncertain. Our results reveal that best-fit models found solely by matching individual frequencies of oscillations corrected for surface effects do not always properly reproduce frequency combinations. Moreover, slightly different criteria to define what the best-fit model is can lead to solutions with similar global properties but very different interior structures. We argue that the use of frequency ratios is a more reliable way to obtain accurate stellar parameters, and show that our analysis in field main-sequence stars can yield an overall precision of 1.5%, 4%, and 10% in radius, mass and age, respectively. We compare our results with those obtained from global oscillation properties, and discuss the possible sources of uncertainties in asteroseismic stellar modeling where further studies are still needed.

The slowly pulsating B-star 18 Peg: A testbed for upper main sequence stellar evolution

The predicted width of the upper main sequence in stellar evolution models depends on the empirical calibration of the convective overshooting parameter. Despite decades of discussions, its precise value is still unknown and further observational constraints are required to gauge it. Based on a photometric and preliminary asteroseismic analysis, we show that the mid B-type giant 18 Peg is one of the most evolved members of the rare class of slowly pulsating B-stars and, thus, bears tremendous potential to derive a tight lower limit for the width of the upper main sequence. In addition, 18 Peg turns out to be part of a single-lined spectroscopic binary system with an eccentric orbit that is greater than 6 years. Further spectroscopic and photometric monitoring and a sophisticated asteroseismic investigation are required to exploit the full potential of this star as a benchmark object for stellar evolution theory.

Forward asteroseismic modeling of stars with a convective core from gravity-mode oscillations: parameter estimation and stellar model selection

We propose a methodological framework to perform forward asteroseismic modeling of stars with a convective core, based on gravity-mode oscillations. These probe the near-core region in the deep stellar interior. The modeling relies on a set of observed high-precision oscillation frequencies of low-degree coherent gravity modes with long lifetimes and their observational uncertainties. Identification of the mode degree and azimuthal order is assumed to be achieved from rotational splitting and/or from period spacing patterns. This paper has two major outcomes. The first is a comprehensive list and discussion of the major uncertainties of theoretically predicted gravity-mode oscillation frequencies based on linear pulsation theory, caused by fixing choices of the input physics for evolutionary models. Guided by a hierarchy among these uncertainties of theoretical frequencies, we subsequently provide a global methodological scheme to achieve forward asteroseismic modeling. We properly take into account correlations amongst the free parameters included in stellar models. Aside from the stellar mass, metalicity and age, the major parameters to be estimated are the near-core rotation rate, the amount of convective core overshooting, and the level of chemical mixing in the radiative zones. This modeling scheme allows for maximum likelihood estimation of the stellar parameters for fixed input physics of the equilibrium models, followed by stellar model selection considering various choices of the input physics. Our approach uses the Mahalanobis distance instead of the often used $chi^2$ statistic and includes heteroscedasticity. It provides estimation of the unknown variance of the theoretically predicted oscillation frequencies.