426 research outputs found
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&
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 . 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 , and
the average magnetic field strength is . 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 of the equipartition
value at the upper convective boundary diminish the rate of mass entrainment
from the stable layer by as compared to the purely
hydrodynamic case
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 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
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 M zero-age
main-sequence star, we construct a series of simulations with the luminosity
increased and opacity decreased by the same factor ranging from to
. 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 to
pressure scale heights, which are broadly compatible with observations.Comment: 10 pages, 12 figures, submitted to A&
Fully compressible simulations of waves and core convection in main-sequence stars
Context. Recent, nonlinear simulations of wave generation and propagation in
full-star models have been carried out in the anelastic approximation using
spectral methods. Although it makes long time steps possible, this approach
excludes the physics of sound waves completely and rather high artificial
viscosity and thermal diffusivity are needed for numerical stability. Direct
comparison with observations is thus limited. Aims. We explore the capabilities
of our compressible multidimensional hydrodynamics code SLH to simulate stellar
oscillations. Methods. We compare some fundamental properties of internal
gravity and pressure waves in 2D SLH simulations to linear wave theory using
two test cases: (1) an interval gravity wave packet in the Boussinesq limit and
(2) a realistic stellar model with a convective core and a
radiative envelope. Oscillation properties of the stellar model are also
discussed in the context of observations. Results. Our tests show that
specialized low-Mach techniques are necessary when simulating oscillations in
stellar interiors. Basic properties of internal gravity and pressure waves in
our simulations are in good agreement with linear wave theory. As compared to
anelastic simulations of the same stellar model, we can follow internal gravity
waves of much lower frequencies. The temporal frequency spectra of velocity and
temperature are flat and compatible with observed spectra of massive stars.
Conclusion. The low-Mach compressible approach to hydrodynamical simulations of
stellar oscillations is promising. Our simulations are less dissipative and
require less luminosity boosting than comparable spectral simulations. The
fully-compressible approach allows the coupling of gravity and pressure waves
to be studied too.Comment: Accepted for publication in A&
Well-balanced treatment of gravity in astrophysical fluid dynamics simulations at low Mach numbers
Accurate simulations of flows in stellar interiors are crucial to improving
our understanding of stellar structure and evolution. Because the typically
slow flows are merely tiny perturbations on top of a close balance between
gravity and the pressure gradient, such simulations place heavy demands on
numerical hydrodynamics schemes. We demonstrate how discretization errors on
grids of reasonable size can lead to spurious flows orders of magnitude faster
than the physical flow. Well-balanced numerical schemes can deal with this
problem. Three such schemes were applied in the implicit, finite-volume
Seven-League Hydro (SLH) code in combination with a low-Mach-number numerical
flux function. We compare how the schemes perform in four numerical experiments
addressing some of the challenges imposed by typical problems in stellar
hydrodynamics. We find that the - and deviation well-balancing
methods can accurately maintain hydrostatic solutions provided that
gravitational potential energy is included in the total energy balance. They
accurately conserve minuscule entropy fluctuations advected in an isentropic
stratification, which enables the methods to reproduce the expected scaling of
convective flow speed with the heating rate. The deviation method also
substantially increases accuracy of maintaining stationary orbital motions in a
Keplerian disk on long timescales. The Cargo-LeRoux method fares substantially
worse in our tests, although its simplicity may still offer some merits in
certain situations. Overall, we find the well-balanced treatment of gravity in
combination with low Mach number flux functions essential to reproducing
correct physical solutions to challenging stellar slow-flow problems on
affordable collocated grids.Comment: Accepted for publication in A&
Do electron-capture supernovae make neutron stars? First multidimensional hydrodynamic simulations of the oxygen deflagration
Context. In the classical picture, electron-capture supernovae and the accretion-induced collapse of oxygen-neon white dwarfs undergo an oxygen deflagration phase before gravitational collapse produces a neutron star. These types of core collapse events are postulated to explain several astronomical phenomena. In this work, the oxygen deflagration phase is simulated for the first time using multidimensional hydrodynamics.
Aims. By simulating the oxygen deflagration with multidimensional hydrodynamics and a level-set-based flame approach, new insights can be gained into the explosive deaths of 8−10 M⊙ stars and oxygen-neon white dwarfs that accrete material from a binary companion star. The main aim is to determine whether these events are thermonuclear or core-collapse supernova explosions, and hence whether neutron stars are formed by such phenomena.
Methods. The oxygen deflagration is simulated in oxygen-neon cores with three different central ignition densities. The intermediate density case is perhaps the most realistic, being based on recent nuclear physics calculations and 1D stellar models. The 3D hydrodynamic simulations presented in this work begin from a centrally confined flame structure using a level-set-based flame approach and are performed in 2563 and 5123 numerical resolutions.
Results. In the simulations with intermediate and low ignition density, the cores do not appear to collapse into neutron stars. Instead, almost a solar mass of material becomes unbound from the cores, leaving bound remnants. These simulations represent the case in which semiconvective mixing during the electron-capture phase preceding the deflagration is inefficient. The masses of the bound remnants double when Coulomb corrections are included in the equation of state, however they still do not exceed the effective Chandrasekhar mass and, hence, would not collapse into neutron stars. The simulations with the highest ignition density (log 10ρc = 10.3), representing the case where semiconvective mixing is very efficient, show clear signs that the core will collapse into a neutron star
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