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Register a new userUncertainties in models of stellar structure and evolution
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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.
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We summarize here the discussions around photospheric constraints, current uncertainties in models of stellar atmospheres, and reports on ongoing spectroscopic surveys. Rather than a panorama of the state of the art, we chose to present a list of open questions that should be investigated in order to improve future analyses.
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.
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.
In young dense clusters repeated collisions between massive stars may lead to the formation of a very massive star (above 100 Msun). In the past the study of the long-term evolution of merger remnants has mostly focussed on collisions between low-mass stars (up to about 2 Msun) in the context of blue-straggler formation. The evolution of collision products of more massive stars has not been as thoroughly investigated. In this paper we study the long-term evolution of a number of stellar mergers formed by the head-on collision of a primary star with a mass of 5-40 Msun with a lower mass star at three points in its evolution in order to better understand their evolution. We use smooth particle hydrodynamics (SPH) calculations to model the collision between the stars. The outcome of this calculation is reduced to one dimension and imported into a stellar evolution code. We follow the subsequent evolution of the collision product through the main sequence at least until the onset of helium burning. We find that little hydrogen is mixed into the core of the collision products, in agreement with previous studies of collisions between low-mass stars. For collisions involving evolved stars we find that during the merger the surface nitrogen abundance can be strongly enhanced. The evolution of most of the collision products proceeds analogously to that of normal stars with the same mass, but with a larger radius and luminosity. However, the evolution of collision products that form with a hydrogen depleted core is markedly different from that of normal stars with the same mass. They undergo a long-lived period of hydrogen shell burning close to the main-sequence band in the Hertzsprung-Russell diagram and spend the initial part of core helium burning as compact blue supergiants.
Stellar evolution computations provide the foundation of several methods applied to study the evolutionary properties of stars and stellar populations, both Galactic and extragalactic. The accuracy of the results obtained with these techniques is linked to the accuracy of the stellar models, and in this context the correct treatment of the transport of chemical elements is crucial. Unfortunately, in many respects calculations of the evolution of the chemical abundance profiles in stars are still affected by sometime sizable uncertainties. Here, we review the various mechanisms of element transport included in the current generation of stellar evolution calculations, how they are implemented, the free parameters and uncertainties involved, the impact on the models, and the observational constraints.
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