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Register a new userThe dependence of convective core overshooting on stellar mass: semi-empirical determination using the diffusive approach with two different element mixtures
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Convective core overshooting has a strong influence on the evolution of stars of moderate and high mass. Studies of double-lined eclipsing binaries and stellar oscillations have renewed interest in the possible dependence of overshooting on stellar mass, which has been poorly constrained by observations so far. Here we have used a sample of 29 well-studied double-lined eclipsing binaries in key locations of the H-R diagram to establish the explicit dependence of f(ov) on mass, where f(ov) is the free parameter in the diffusive approximation to overshooting. Measurements of the masses, radii, and temperatures of the binary components were compared against stellar evolution calculations based on the MESA code to infer semi-empirical values of f(ov) for each component. We find a clear mass dependence such that f(ov) rises sharply from zero in the range 1.2--2.0 solar masses, and levels off thereafter up to the 4.4 solar mass limit of our sample. Tests with two different element mixtures indicate the trend is the same, and we find it is also qualitatively similar to the one established in our previous study with the classical step-function implementation of overshooting characterized by the free parameter alpha(ov). Based on these measurements we infer an approximate relationship between the two overshooting parameters of alpha(ov)/f(ov) = 11.36 +/- 0.22, with a possible dependence on stellar properties.
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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.
Overshooting from the convective cores of stars more massive than about 1.2 M(Sun) has a profound impact on their subsequent evolution. And yet, the formulation of the overshooting mechanism in current stellar evolution models has a free parameter (f[ov] in the diffusive approximation) that remains poorly constrained by observations, affecting the determination of astrophysically important quantities such as stellar ages. In an earlier series of papers we assembled a sample of 37 well-measured detached eclipsing binaries to calibrate the dependence of f[ov] on stellar mass, showing that it increases sharply up to a mass of roughly 2 M(Sun), and remains constant thereafter out to at least 4.4 M(Sun). Recent claims have challenged the utility of eclipsing binaries for this purpose, on the basis that the uncertainties in f[ov] from the model fits are typically too large to be useful, casting doubt on a dependence of overshooting on mass. Here we reexamine those claims and show them to be too pessimistic, mainly because they did not account for all available constraints --- both observational and theoretical --- in assessing the true uncertainties. We also take the opportunity to add semi-empirical f[ov] determinations for 13 additional binaries to our previous sample, and to update the values for 9 others. All are consistent with, and strengthen our previous conclusions, supporting a dependence of f[ov] on mass that is now based on estimates for a total of 50 binary systems (100 stars).
Many current stellar evolution models assume some dependence of the strength of convective core overshooting on mass for stars more massive than 1.1-1.2 solar masses, but the adopted shapes for that relation have remained somewhat arbitrary for lack of strong observational constraints. In previous work we compared stellar evolution models to well-measured eclipsing binaries to show that, when overshooting is implemented as a diffusive process, the fitted free parameter f(ov) rises sharply up to about 2 solar masses, and remains largely constant thereafter. Here we analyze a new sample of eight binaries selected to be in the critical mass range below 2 solar masses where f(ov) is changing the most, nearly doubling the number of individual stars in this regime. This interval is important because the precise way in which f(ov) changes determines the shape of isochrones in the turnoff region of 1-5 Gyr clusters, and can thus affect their inferred ages. It also has a significant influence on estimates of stellar properties for exoplanet hosts, on stellar population synthesis, and on the detailed modeling of interior stellar structures, including the calculation of oscillation frequencies that are observable with asteroseismic techniques. We find that the derived f(ov) values for our new sample are consistent with the trend defined by our earlier determinations, and strengthen the relation. This provides an opportunity for future series of models to test the new prescription, grounded on observations, against independent observations that may constrain overshooting in a different way.
Classical Cepheids are powerful probes of both stellar evolution and near-field cosmology thanks to their high luminosities, pulsations, and that they follow the Leavitt (Period-Luminosity) Law. However, there still exist a number of questions regarding their evolution, such as the role of rotation, convective core overshooting and winds. ln particular, how do these processes impact Cepheid evolution and the predicted fundamental properties such as stellar mass. In this work, we compare a sample of period change that are real-time observations of stellar evolution with new evolution models to test the impact of these first two processes. In our previous study we found that enhanced mass loss is crucial for describing the sample, and here we continue that analysis but for rotational mixing and core overshooting. We show that, while rotation is important for stellar evolution studies, rotation, itself, is insufficient to model the distribution of period change rates from the observed sample. On the other hand, convective core overshooting is needed to explain the magnitude of the rates of period change, but does not explain the number of stars with positive and negative period change rates. In conclusion, we determine that convective core overshooting and stellar rotation alone are not enough to account for the observed distribution of Cepheid rates of period change and another mechanism, such as pulsation-driven mass-loss, may be required.
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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