New numerical solver for flows at various Mach numbers

Many problems in stellar astrophysics feature flows at low Mach numbers. Conventional compressible hydrodynamics schemes frequently used in the field have been developed for the transonic regime and exhibit excessive numerical dissipation for these flows. While schemes were proposed that solve hydrodynamics strictly in the low Mach regime and thus restrict their applicability, we aim at developing a scheme that correctly operates in a wide range of Mach numbers. Based on an analysis of the asymptotic behavior of the Euler equations in the low Mach limit we propose a novel scheme that is able to maintain a low Mach number flow setup while retaining all effects of compressibility. This is achieved by a suitable modification of the well-known Roe solver. Numerical tests demonstrate the capability of this new scheme to reproduce slow flow structures even in moderate numerical resolution. Our scheme provides a promising approach to a consistent multidimensional hydrodynamical treatment of astrophysical low Mach number problems such as convection, instabilities, and mixing in stellar evolution.Comment: 16 pages, 8 figures, accepted for publication by A&

Three-dimensional simulations of the interaction between Type Ia supernova ejecta and their main sequence companions

The identity of the progenitor systems of SNe Ia is still uncertain. In the single-degenerate (SD) scenario, the interaction between the SN blast wave and the outer layers of a main sequence (MS) companion star strips off H-rich material which is then mixed into the ejecta. Strong contamination of the SN ejecta with stripped material could lead to a conflict with observations of SNe Ia. This constrains the SD progenitor model. In this work, our previous simulations based on simplified progenitor donor stars have been updated by adopting more realistic progenitor-system models that result from fully detailed, state-of-the-art binary evolution calculations. We use Eggleton's stellar evolution code including the optically thick accretion wind model and the possibility of the effects of accretion disk instabilities to obtain realistic models of companions for different progenitor systems. The impact of the SN blast wave on these companion stars is followed in three-dimensional hydrodynamic simulations employing the SPH code GADGET3. We find that the stripped masses range from 0.11 to 0.18 M_sun. The kick velocity is between 51 and 105 km/s. We find that the stripped mass and kick velocity depend on the ratio of the orbital separation to the radius of a companion. They can be fitted by a power law for a given companion model. However, the structure of the companion star is also important for the amount of stripped material. With more realistic companion star models than in previous studies, our simulations show that the H masses stripped from companions are inconsistent with the best observational limits (< 0.01 M_sun) derived from nebular spectra. However, a rigorous forward modeling based on impact simulations with radiation transfer is required to reliably predict observable signatures of the stripped H and to conclusively assess the viability of the considered SN Ia progenitor scenario.Comment: 14 pages, 13 figures, accepted for publication by A&

Turbulent dynamo action and its effects on the mixing at the convective boundary of an idealized oxygen-burning shell

Convection is one of the most important mixing processes in stellar interiors. Hydrodynamic mass entrainment can bring fresh fuel from neighboring stable layers into a convection zone, modifying the structure and evolution of the star. Under some conditions, strong magnetic fields can be sustained by the action of a turbulent dynamo, adding another layer of complexity and possibly altering the dynamics in the convection zone and at its boundaries. In this study, we used our fully compressible Seven-League Hydro code to run detailed and highly resolved three-dimensional magnetohydrodynamic simulations of turbulent convection, dynamo amplification, and convective boundary mixing in a simplified setup whose stratification is similar to that of an oxygen-burning shell in a star with an initial mass of $25\ M_\odot$. We find that the random stretching of magnetic field lines by fluid motions in the inertial range of the turbulent spectrum (i.e., a small-scale dynamo) naturally amplifies the seed field by several orders of magnitude in a few convective turnover timescales. During the subsequent saturated regime, the magnetic-to-kinetic energy ratio inside the convective shell reaches values as high as $0.33$, and the average magnetic field strength is ${\sim}10^{10}\,\mathrm{G}$. Such strong fields efficiently suppress shear instabilities, which feed the turbulent cascade of kinetic energy, on a wide range of spatial scales. The resulting convective flows are characterized by thread-like structures that extend over a large fraction of the convective shell. The reduced flow speeds and the presence of magnetic fields with strengths up to $60\%$ of the equipartition value at the upper convective boundary diminish the rate of mass entrainment from the stable layer by ${\approx}\,20\%$ as compared to the purely hydrodynamic case

Towards a self-consistent model of the convective core boundary in upper-main-sequence stars

There is strong observational evidence that convective cores of intermediate-mass and massive main-sequence stars are substantially larger than standard stellar-evolution models predict. However, it is unclear what physical processes cause this phenomenon or how to predict the extent and stratification of stellar convective boundary layers. Convective penetration is a thermal-time-scale process that is likely to be particularly relevant during the slow evolution on the main sequence. We use our low-Mach-number Seven-League Hydro (SLH) code to study this process in 2.5D and 3D geometries. Starting with a chemically homogeneous model of a $15$ M$_\odot$ zero-age main-sequence star, we construct a series of simulations with the luminosity increased and opacity decreased by the same factor ranging from $10^3$ to $10^6$. After reaching thermal equilibrium, all of our models show a clear penetration layer. Its thickness becomes statistically constant in time and it is shown to converge upon grid refinement. As the luminosity is decreased, the penetration layer becomes nearly adiabatic with a steep transition to a radiative stratification. This structure corresponds to the adiabatic ,,step overshoot'' model often employed in stellar-evolution calculations. The thickness of the penetration layer slowly decreases with decreasing luminosity. Depending on how we extrapolate our 3D data to the actual luminosity of the initial stellar model, we obtain penetration distances ranging from $0.09$ to $0.44$ pressure scale heights, which are broadly compatible with observations.Comment: 10 pages, 12 figures, submitted to A&

Three-Dimensional Simulations of Massive Stars: II. Age Dependence

We present 3D full star simulations, reaching up to 90% of the total stellar radius, for three $7M_\odot$ stars of different ages (ZAMS, midMS and TAMS). A comparison with several theoretical prescriptions shows the generation spectra for all three ages are dominated by convective plumes. Two distinct overshooting layers are observed, with most plumes stopped within the layer situated directly above the convective boundary (CB); overshooting to the second, deeper layer becomes increasingly more infrequent with stellar age. Internal gravity wave (IGW) propagation is significantly impacted in the midMS and TAMS models as a result of some IGWs getting trapped within their Brunt-V\"{a}is\"{a}l\"{a} frequency spikes. A fundamental change in the wave structure across radius is also observed, driven by the effect of density stratification on IGW propagation causing waves to become evanescent within the radiative zone, with older stars being affected more strongly. We find that the steepness of the frequency spectrum at the surface increases from ZAMS to the older models, with older stars also showing more modes in their spectra.Comment: 24 pages, 14 figures / Accepted at Ap