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Register a new userConfronting uncertainties in stellar physics: calibrating convective overshooting with eclipsing binaries
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Richard J. Stancliffe
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As part of a larger program aimed at better quantifying the uncertainties in stellar computations, we attempt to calibrate the extent of convective overshooting in low to intermediate mass stars by means of eclipsing binary systems. We model 12 such systems, with component masses between 1.3 and 6.2 solar masses, using the detailed binary stellar evolution code STARS, producing grids of models in both metallicity and overshooting parameter. From these, we determine the best fit parameters for each of our systems. For three systems, none of our models produce a satisfactory fit. For the remaining systems, no single value for the convective overshooting parameter fits all the systems, but most of our systems can be well described with an overshooting parameter between 0.09 and 0.15, corresponding to an extension of the mixed region above the core of about 0.1-0.3 pressure scale heights. Of the nine systems where we are able to obtain a good fit, seven can be reasonably well fit with a single parameter of 0.15. We find no evidence for a trend of the extent of overshooting with either mass or metallicity, though the data set is of limited size. We repeat our calculations with a second evolution code, MESA, and we find general agreement between the two codes. For the extension of the mixed region above the convective core required by the MESA models is about 0.15-0.4 pressure scale heights. For the system EI Cep, we find that MESA gives an overshooting region that is larger than the STARS one by about 0.1 pressure scale heights for the primary, while for the secondary the difference is only 0.05 pressure scale heights.
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We assess the systematic uncertainties in stellar evolutionary calculations for low- to intermediate-mass, main-sequence stars. We compare published stellar tracks from several different evolution codes with our own tracks computed using the stellar codes STARS and MESA. In particular, we focus on tracks of 1 and 3 solar masses at solar metallicity. We find that the spread in the available 1 solar mass tracks (computed before the recent solar composition revision by Asplund et al.) can be covered by tracks between 0.97-1.01 solar masses computed with the STARS code. We assess some possible causes of the origin of this uncertainty, including how the choice of input physics and the solar constraints used to perform the solar calibration affect the tracks. We find that for a 1 solar mass track, uncertainties of around 10% in the initial hydrogen abundance and initial metallicity produce around a 2% error in mass. For the 3 solar mass tracks, there is very little difference between the tracks from the various different stellar codes. The main difference comes in the extent of the main sequence, which we believe results from the different choices of the implementation of convective overshooting in the core. Uncertainties in the initial abundances lead to a 1-2% error in the mass determination. These uncertainties cover only part of the total error budget, which should also include uncertainties in the input physics (e.g., reaction rates, opacities, convective models) and any missing physics (e.g., radiative levitation, rotation, magnetic fields). Uncertainties in stellar surface properties such as luminosity and effective temperature will further reduce the accuracy of any potential mass determinations.
Convective core overshooting extends the main-sequence lifetime of a star. Evolutionary tracks computed with overshooting are quite different from those that use the classical Schwarzschild criterion, which leads to rather different predictions for the stellar properties. Attempts over the last two decades to calibrate the degree of overshooting with stellar mass using detached double-lined eclipsing binaries have been largely inconclusive, mainly due to a lack of suitable observational data. Here we revisit the question of a possible mass dependence of overshooting with a more complete sample of binaries, and examine any additional relation there might be with evolutionary state or metal abundance Z. We use a carefully selected sample of 33 double-lined eclipsing binaries strategically positioned in the H-R diagram, with accurate absolute dimensions and component masses ranging from 1.2 to 4.4 solar masses. We compare their measured properties with stellar evolution calculations to infer semi-empirical values of the overshooting parameter alpha(ov) for each star. Our models use the common prescription for the overshoot distance d(ov) = alpha(ov) Hp, where Hp is the pressure scale height at the edge of the convective core as given by the Schwarzschild criterion, and alpha(ov) is a free parameter. We find a relation between alpha(ov) and mass that is defined much more clearly than in previous work, and indicates a significant rise up to about 2 solar masses followed by little or no change beyond this mass. No appreciable dependence is seen with evolutionary state at a given mass, or with metallicity at a given mass despite the fact that the stars in our sample span a range of a factor of ten in [Fe/H], from -1.01 to +0.01.
Many short-period binary stars have distant orbiting companions that have played a role in driving the binary components into close separation. Indirect detection of a tertiary star is possible by measuring apparent changes in eclipse times of eclipsing binaries as the binary orbits the common center of mass. Here we present an analysis of the eclipse timings of 41 eclipsing binaries observed throughout the NASA Kepler mission of long duration and precise photometry. This subset of binaries is characterized by relatively deep and frequent eclipses of both stellar components. We present preliminary orbital elements for seven probable triple stars among this sample, and we discuss apparent period changes in seven additional eclipsing binaries that may be related to motion about a tertiary in a long period orbit. The results will be used in ongoing investigations of the spectra and light curves of these binaries for further evidence of the presence of third stars.
We report differential photometric observations and radial-velocity measurements of the detached, 1.69-day period, double-lined eclipsing binary AQ Ser. Accurate masses and radii for the components are determined to better than 1.8% and 1.1%, respectively, and are M1 = 1.417 +/- 0.021 MSun, M2 = 1.346 +/- 0.024 MSun, R1 = 2.451 +/- 0.027 RSun, and R2 = 2.281 +/- 0.014 RSun. The temperatures are 6340 +/- 100 K (spectral type F6) and 6430 +/- 100 K (F5), respectively. Both stars are considerably evolved, such that predictions from stellar evolution theory are particularly sensitive to the degree of extra mixing above the convective core (overshoot). The component masses are different enough to exclude a location in the H-R diagram past the point of central hydrogen exhaustion, which implies the need for extra mixing. Moreover, we find that current main-sequence models are unable to match the observed properties at a single age even when allowing the unknown metallicity, mixing length parameter, and convective overshooting parameter to vary freely and independently for the two components. The age of the more massive star appears systematically younger. AQ Ser and other similarly evolved eclipsing binaries showing the same discrepancy highlight an outstanding and largely overlooked problem with the description of overshooting in current stellar theory.
The extent of mixed regions around convective zones is one of the biggest uncertainties in stellar evolution. 1D overshooting descriptions introduce a free parameter ($f_{ov}$) that is in general not well constrained from observations. Especially in small central convective regions the value is highly uncertain due to its tight connection to the pressure scale height. Long-term multi-dimensional hydrodynamic simulations can be used to study the size of the overshooting region and the involved mixing processes. Here we show how one can calibrate an overshooting parameter by performing 2D Maestro simulations of Zero-Age-Main-Sequence stars ranging from $1.3$ to $3.5 M_odot$. The simulations cover the convective cores of the stars and a large fraction of the surrounding radiative envelope. We follow the convective flow for at least 20 convective turnover times, while the longest simulation covers 430 turnover time scales. This allows us to study how the mixing as well as the convective boundary evolve with time, and how the resulting entrainment can be interpreted in terms of overshooting parameters. We find that increasing the overshooting parameter $f_{ov}$ beyond a certain value in the initial model of our simulations, changes the mixing behaviour completely. This result can be used to put limits on the overshooting parameter. We find $0.010 < f_{ov} < 0.017$ to be in good agreement with our simulations of a $3.5 M_odot$ mass star. We also identify a diffusive mixing component due to internal gravity waves (IGW) that is active throughout the convectively stable layer, but likely overestimated in our simulations. Furthermore, applying our calibration method to simulations of less massive stars suggests a need for a mass-dependent overshooting description where the mixing in terms of the pressure scale height is reduced for small convective cores.
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