The increasing number and precision of measurements of neutron star masses, radii, and, in the near future, moments of inertia offer the possibility of precisely determining the neutron star equation of state (EOS). One way to facilitate the mapping of observables to the EOS is through a parametrization of the latter. We present here a generic method for optimizing the parametrization of any physically allowed EOS. We use mock EOS that incorporate physically diverse and extreme behavior to test how well our parametrization reproduces the global properties of the stars, by minimizing the errors in the observables of mass, radius, and the moment of inertia. We find that using piecewise polytropes and sampling the EOS with five fiducial densities between similar to 1-8 times the nuclear saturation density results in optimal errors for the smallest number of parameters. Specifically, it recreates the radii of the assumed EOS to within less than 0.5 km for the extreme mock EOS and to within less than 0.12 km for 95% of a sample of 42 proposed, physically motivated EOS. Such a parametrization is also able to reproduce the maximum mass to within 0.04 M-circle dot and the moment of inertia of a 1.338 M-circle dot. neutron star to within less than 10% for 95% of the proposed sample of EOS.

We present the first detailed 3D hydrodynamic implicit large eddy simulations of turbulent convection of carbon burning in massive stars. Simulations begin with radial profiles mapped from a carbon-burning shell within a 15M circle dot 1D stellar evolution model. We consider models with 128(3), 256(3), 512(3), and 1024(3) zones. The turbulent flow properties of these carbon-burning simulations are very similar to the oxygen-burning case. We performed a mean field analysis of the kinetic energy budgets within the Reynolds-averaged Navier-Stokes framework. For the upper convective boundary region, we find that the numerical dissipation is insensitive to resolution for linear mesh resolutions above 512 grid points. For the stiffer, more stratified lower boundary, our highest resolution model still shows signs of decreasing sub-grid dissipation suggesting it is not yet numerically converged. We find that the widths of the upper and lower boundaries are roughly 30 per cent and 10 per cent of the local pressure scaleheights, respectively. The shape of the boundaries is significantly different from those used in stellar evolution models. As in past oxygen-shell-burning simulations, we observe entrainment at both boundaries in our carbon-shell-burning simulations. In the large Peclet number regime found in the advanced phases, the entrainment rate is roughly inversely proportional to the bulk Richardson number, Ri(B) (alpha Ri(B)(-alpha) a, 0.5 less than or similar to alpha less than or similar to 1.0). We thus suggest the use of Ri(B) as a means to take into account the results of 3D hydrodynamics simulations in new 1D prescriptions of convective boundary mixing.

We explore the effects of rotation on convective carbon, oxygen, and silicon shell burning during the late stages of evolution in a 20 M-circle dot star. Using the Modules for Experiments in Stellar Astrophysics we construct one-dimensional (1D) stellar models both with no rotation and with an initial rigid rotation of 50% of critical. At different points during the evolution, we map the 1D models into 2D and follow the multidimensional evolution using the FLASH compressible hydrodynamics code for many convective turnover times until a quasi-steady state is reached. We characterize the strength and scale of convective motions via decomposition of the momentum density into vector spherical harmonics. We find that rotation influences the total power in solenoidal modes, with a slightly larger impact for carbon and oxygen shell burning than for silicon shell burning. Including rotation in 1D stellar evolution models alters the structure of the star in a manner that has a significant impact on the character of multidimensional convection. Adding modest amounts of rotation to a stellar model that ignores rotation during the evolutionary stage, however, has little impact on the character of the resulting convection. Since the spatial scale and strength of convection present at the point of core collapse directly influence the supernova mechanism, our results suggest that rotation could play an important role in setting the stage for massive stellar explosions.

Stellar models provide a vital basis for many aspects of astronomy and astrophysics. Recent advances in observational astronomy - through asteroseismology, precision photometry, high-resolution spectroscopy, and large-scale surveys - are placing stellar models under greater quantitative scrutiny than ever. The model limitations are being exposed and the next generation of stellar models is needed as soon as possible. The current uncertainties in the models propagate to the later phases of stellar evolution, hindering our understanding of stellar populations and chemical evolution. Here we give a brief overview of the evolution, importance, and substantial uncertainties of core helium burning stars in particular and then briefly discuss a range of methods, both theoretical and observational, that we are using to advance the modelling. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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