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Register a new userConfronting uncertainties in stellar physics II. exploring differences in main-sequence stellar evolution tracks
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R. J. Stancliffe
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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.
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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.
In the era of advanced electromagnetic and gravitational wave detectors, it has become increasingly important to effectively combine and study the impact of stellar evolution on binaries and dynamical systems of stars. Systematic studies dedicated to exploring uncertain parameters in stellar evolution are required to account for the recent observations of the stellar populations. We present a new approach to the commonly used Single-Star Evolution (SSE) fitting formulae, one that is more adaptable: Method of Interpolation for Single Star Evolution (METISSE). It makes use of interpolation between sets of pre-computed stellar tracks to approximate evolution parameters for a population of stars. We have used METISSE with detailed stellar tracks computed by the Modules for Experiments in Stellar Astrophysics (MESA), Bonn Evolutionary Code (BEC) and Cambridge STARS code. METISSE better reproduces stellar tracks computed using the STARS code compared to SSE, and is on average three times faster. Using stellar tracks computed with MESA and BEC, we apply METISSE to explore the differences in the remnant masses, the maximum radial expansion, and the main-sequence lifetime of massive stars. We find that different physical ingredients used in the evolution of stars, such as the treatment of radiation dominated envelopes, can impact their evolutionary outcome. For stars in the mass range 9 to 100 M$_odot$, the predictions of remnant masses can vary by up to 20 M$_odot$, while the maximum radial expansion achieved by a star can differ by an order of magnitude between different stellar models.
We present interferometric diameter measurements of 21 K- and M- dwarfs made with the CHARA Array. This sample is enhanced by literature radii measurements to form a data set of 33 K-M dwarfs with diameters measured to better than 5%. For all 33 stars, we compute absolute luminosities, linear radii, and effective temperatures (Teff). We develop empirical relations for simK0 to M4 main- sequence stars between the stellar Teff, radius, and luminosity to broad-band color indices and metallicity. These relations are valid for metallicities between [Fe/H] = -0.5 and +0.1 dex, and are accurate to ~2%, ~5%, and ~4% for Teff, radius, and luminosity, respectively. Our results show that it is necessary to use metallicity dependent transformations to convert colors into stellar Teffs, radii, and luminosities. We find no sensitivity to metallicity on relations between global stellar properties, e.g., Teff-radius and Teff-luminosity. Robust examinations of single star Teffs and radii compared to evolutionary model predictions on the luminosity-Teff and luminosity-radius planes reveals that models overestimate the Teffs of stars with Teff < 5000 K by ~3%, and underestimate the radii of stars with radii < 0.7 Rodot by ~5%. These conclusions additionally suggest that the models overestimate the effects that the stellar metallicity may have on the astrophysical properties of an object. By comparing the interferometrically measured radii for single stars to those of eclipsing binaries, we find that single and binary star radii are consistent. However, the literature Teffs for binary stars are systematically lower compared to Teffs of single stars by ~ 200 to 300 K. Lastly, we present a empirically determined HR diagram for a total of 74 nearby, main-sequence, A- to M-type stars, and define regions of habitability for the potential existence of sub-stellar mass companions in each system. [abridged]
Numerous physical aspects of stellar physics have been presented in Ses- sion 2 and the underlying uncertainties have been tentatively assessed. We try here to highlight some specific points raised after the talks and during the general discus- sion at the end of the session and eventually at the end of the workshop. A table of model uncertainties is then drawn with the help of the participants in order to give the state of the art in stellar modeling uncertainties as of July 2013.
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.
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