We substantially update the capabilities of the open source software package Modules for Experiments in Stellar Astrophysics (MESA), and its one-dimensional stellar evolution module, MESA star. Improvements in MESA star's ability to model the evolution of giant planets now extends its applicability down to masses as low as one-tenth that of Jupiter. The dramatic improvement in asteroseismology enabled by the space-based Kepler and CoRoT missions motivates our full coupling of the ADIPLS adiabatic pulsation code with MESA star. This also motivates a numerical recasting of the Ledoux criterion that is more easily implemented when many nuclei are present at non-negligible abundances. This impacts the way in which MESA star calculates semi-convective and thermohaline mixing. We exhibit the evolution of 3-8 M stars through the end of core He burning, the onset of He thermal pulses, and arrival on the white dwarf cooling sequence. We implement diffusion of angular momentum and chemical abundances that enable calculations of rotating-star models, which we compare thoroughly with earlier work. We introduce a new treatment of radiation-dominated envelopes that allows the uninterrupted evolution of massive stars to core collapse. This enables the generation of new sets of supernovae, long gamma-ray burst, and pair-instability progenitor models. We substantially modify the way in which MESA star solves the fully coupled stellar structure and composition equations, and we show how this has improved the scaling of MESA's calculational speed on multi-core processors. Updates to the modules for equation of state, opacity, nuclear reaction rates, and atmospheric boundary conditions are also provided. We describe the MESA Software Development Kit (SDK) that packages all the required components needed to form a unified, maintained, and well-validated build environment for MESA. We also highlight a few tools developed by the community for rapid visualization of MESA star results.

We determine an empirical dense matter equation of state from a heterogeneous dataset of six neutron stars: three type I X-ray bursters with photospheric radius expansion, studied bÿ Ozel et al., and three transient low-mass X-ray binaries. We critically assess the mass and radius determinations from the X-ray burst sources and show explicitly how systematic uncertainties, such as the photospheric radius at touchdown, affect the most probable masses and radii. We introduce a parameterized equation of state and use a Markov Chain Monte Carlo algorithm within a Bayesian framework to determine nuclear parameters such as the incompressibility and the density dependence of the bulk symmetry energy. Using this framework we show, for the first time, that these parameters, predicted solely on the basis of astrophysical observations, all lie in ranges expected from nuclear systematics and laboratory experiments. We find significant constraints on the mass-radius relation for neutron stars, and hence on the pressure-density relation of dense matter. The predicted symmetry energy and the equation of state near the saturation density are soft, resulting in relatively small neutron star radii around 11-12 km for M = 1.4 M ⊙ . The predicted equation of state stiffens at higher densities, however, and our preferred model for X-ray bursts suggests that the neutron star maximum mass is relatively large, 1.9-2.2 M ⊙ . Our results imply that several commonly used equations of state are inconsistent with observations.

Nuclear reactions occurring at densities ≈ 10 12 g cm −3 in the crust of a transiently accreting neutron star efficiently maintain the core at a temperature ≈ (5-10) × 10 7 K. When accretion halts, the envelope relaxes to a thermal equilibrium set by the flux from the hot core, as if the neutron star were newly born. For the time-averaged accretion rates ( ∼ < 10 −10 M ⊙ yr −1 ) typical of low-mass X-ray transients, standard neutrino cooling is unimportant and the core thermally reradiates the deposited heat. The resulting luminosity is ∼ 5×10 32 -5×10 33 ergs s −1 and agrees with many observations of transient neutron stars in quiescence. Confirmation of this mechanism would strongly constrain rapid neutrino cooling mechanisms for neutron stars (e.g., a pion condensate). Thermal emission had previously been dismissed as a predominant source of quiescent emission since blackbody spectral fits implied an emitting area much smaller than a neutron star's surface. However, as with thermal emission from radio pulsars, fits with realistic emergent spectra will imply a substantially larger emitting area. Other emission mechanisms, such as accretion or a pulsar shock, can also operate in quiescence and generate intensity and spectral variations over short timescales. Indeed, quiescent accretion may produce gravitationally redshifted metal photoionization edges in the quiescent spectra (detectable with AXAF and XMM ). We discuss past observations of Aql X-1 and note that the low luminosity (< 10 34 ergs s −1 ) X-ray sources in globular clusters and the Be star/X-ray transients are excellent candidates for future study.