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.

Rossby waves (r-modes) in rapidly rotating neutron stars are unstable because of the emission of gravitational radiation. As a result, the stellar rotational energy is converted into both gravitational waves and r-mode energy. The saturation level for the r-mode energy is a fundamental parameter needed to determine how fast the neutron star spins down, as well as whether gravitational waves will be detectable. In this paper we study saturation by nonlinear transfer of energy to the sea of stellar '' inertial '' oscillation modes that arise in rotating stars with negligible buoyancy and elastic restoring forces. We present detailed calculations of stellar inertial modes in the WKB limit, their linear damping by bulk and shear viscosity, and the nonlinear coupling forces among these modes. The saturation amplitude is derived in the extreme limits of strong or weak driving by radiation reaction, as compared to the damping rate of low-order inertial modes. In the weak driving case, energy can be stably transferred to a small number of modes, which damp the energy as heat or neutrinos. In the strong driving case, we show that a turbulent cascade develops, with a constant flux of energy to large wavenumbers and small frequencies where it is damped by shear viscosity. We find that the saturation energy is extremely small, at least 4 orders of magnitude smaller than that found by previous investigators. We show that the large saturation energy found in the simulations of Lindblom and coworkers is an artifact of their unphysically large radiation reaction force. In most physical situations of interest, for either nascent, rapidly rotating neutron stars or neutron stars being spun up by accretion in low-mass X-ray binaries (LMXBs), the strong driving limit is appropriate and the saturation energy is roughly E r mode =ð0:5Mr 2 Ã 2 Þ ' 0:1 gr = ' 10 À6 ð spin =10 3 HzÞ 5 , where M and r * are the stellar mass and radius, respectively, gr is the driving rate by gravitational radiation, is the angular velocity of the star, and spin is the spin frequency. At such a low saturation amplitude, the characteristic time for the star to exit the region of r-mode instability is e10 3 -10 4 yr, depending sensitively on the instability curve. Although our saturation amplitude is smaller than that found by previous investigators, it is still sufficiently large to explain the observed period clustering in LMXBs. We find that the r-mode signal from both newly born neutron stars and LMXBs in the spin-down phase of Levin's limit cycle will be detectable by enhanced LIGO detectors out to $100-200 kpc.

We develop the formalism required to study the nonlinear interaction of modes in rotating Newtonian stars, assuming that the mode amplitudes are only mildly nonlinear. The formalism is simpler than previous treatments of mode-mode interactions for spherical stars, and simplifies and corrects previous treatments for rotating stars. At linear order, we elucidate and extend slightly a formalism due to Schutz, show how to decompose a general motion of a rotating star into a sum over modes, and obtain uncoupled equations of motion for the mode amplitudes under the influence of an external force. Nonlinear effects are added perturbatively via three-mode couplings, which suffices for moderate amplitude modal excitations; the formalism is easy to extend to higher order couplings. We describe a new, efficient way to compute the modal coupling coefficients, to zeroth order in the stellar rotation rate, using spin-weighted spherical harmonics. The formalism is general enough to allow computation of the initial trends in the evolution of the spin frequency and differential rotation of the background star.We apply this formalism to derive some properties of the coupling coefficients relevant to the nonlinear interactions of unstable r-modes in neutron stars, postponing numerical integrations of the coupled equations of motion to a later paper. First, we clarify some aspects of the expansion in stellar rotation frequency Ω that is often used to compute approximate mode functions. We show that in zero-buoyancy stars, the rotational modes (those modes whose frequencies vanish as Ω → 0) are orthogonal to zeroth order in Ω. From an astrophysical viewpoint, the most interesting result of this paper is that many couplings of r−modes to other rotational modes are small: either they vanish altogether because of various selection rules, or they vanish to lowest order in Ω or in compressibility. In particular, in zero-buoyancy stars, the coupling of three r−modes is forbidden entirely and the coupling of two r-modes to one hybrid, or r-g rotational mode vanishes to zeroth order in rotation frequency. The coupling of any three rotational modes vanishes to zeroth order in compressibility and in Ω. In nonzero-buoyancy stars, coupling of the r-modes to each other vanishes to zeroth order in Ω . Couplings to regular modes (those modes whose frequencies are finite in the limit Ω → 0), such as f −modes, are not zero, but since the natural frequencies of these modes are relatively large in the slow rotation limit compared to those of the r-modes, energy transfer to those modes is not expected to be efficient.