Aims. We extend semi-analytical computations of excitation rates for solar oscillation modes to those of other solar-like oscillating stars to compare them with recent observations Methods. Numerical 3D simulations of surface convective zones of several solar-type oscillating stars are used to characterize the turbulent spectra as well as to constrain the convective velocities and turbulent entropy fluctuations in the uppermost part of the convective zone of such stars. These constraints, coupled with a theoretical model for stochastic excitation, provide the rate P at which energy is injected into the p-modes by turbulent convection. These energy rates are compared with those derived directly from the 3D simulations.Results. The excitation rates obtained from the 3D simulations are systematically lower than those computed from the semi-analytical excitation model. We find that P max , the P maximum, scales as (L/M) s where s is the slope of the power law and L and M are the mass and luminosity of the 1D stellar model built consistently with the associated 3D simulation. The slope is found to depend significantly on the adopted form of χ k , the eddy time-correlation; using a Lorentzian, χ L k , results in s = 2.6, whereas a Gaussian, χ G k , gives s = 3.1. Finally, values of V max , the maximum in the mode velocity, are estimated from the computed power laws for P max and we find that V max increases as (L/M) sv . Comparisons with the currently available ground-based observations show that the computations assuming a Lorentzian χ k yield a slope, sv, closer to the observed one than the slope obtained when assuming a Gaussian. We show that the spatial resolution of the 3D simulations must be high enough to obtain accurate computed energy rates.
We simulate the rise through the upper convection zone and emergence through the solar surface of initially uniform, untwisted, horizontal magnetic flux, with the same entropy as the nonmagnetic plasma, that is advected into a domain 48 Mm wide by 20 Mm deep. The magnetic field is advected upward by the diverging upflows and pulled down in the downdrafts, which produces a hierarchy of loop-like structures of increasingly smaller scale as the surface is approached. There are significant differences between the behavior of fields of 10 kG and 20 or 40 kG strength at 20 Mm depth. The 10 kG fields have little effect on the convective flows and show small magnetic-buoyancy effects, reaching the surface in the typical fluid rise time from 20 Mm depth of 32 hours. 20 and 40 kG fields significantly modify the convective flows, leading to long, thin cells of ascending fluid aligned with the magnetic field and their magnetic buoyancy makes them rise to the surface faster than the fluid rise time. The 20 kG field produces a large-scale magnetic loop that as it emerges through the surface leads to the formation of a bipolar, pore-like structure.
Recent progress in realistic simulations of solar convection have given us an unprecedented opportunity to evaluate the robustness of solar interior structures and dynamics obtained by methods of local helioseismology. We present results of testing the time-distance method using realistic simulations. By computing acoustic wave propagation time and distance relations for different depths of the simulated data, we confirm that acoustic waves propagate into the interior and then turn back to the photosphere. This demonstrates that in the numerical simulations properties of acoustic waves (p-modes) are similar to the solar conditions, and that these properties can be analyzed by the time-distance technique. For the surface gravity waves (f -mode), we calculate perturbations of their travel times, caused by localized downdrafts, and demonstrate that the spatial pattern of these perturbations (representing so-called sensitivity kernels) is similar to the patterns obtained from the real Sun, displaying characteristic hyperbolic structures. We then test the time-distance measurements and inversions by calculating acoustic travel times from a sequence of vertical velocities at the photosphere of the simulated data, and inferring a mean 3D flow fields by performing inversion based on the ray approximation. The inverted horizontal flow fields agree very
Abstract. The amplitude of solar-like oscillations results from a balance between excitation and damping. As in the sun, the excitation is attributed to turbulent motions that stochastically excite the p modes in the uppermost part of the convective zone. We present here a model for the excitation mechanism. Comparisons between modeled amplitudes and helio and stellar seismic constraints are presented and the discrepancies discussed. Finally the possibility and the interest of detecting such stochastically excited modes in pre-main sequence stars are also discussed.
We apply time-distance helioseismology, local correlation tracking and Fourier spatial-temporal filtering methods to realistic supergranule scale simulations of solar convection and compare the results with high-resolution observations from the SOHO Michelson Doppler Imager (MDI). Our objective is to investigate the surface and sub-surface convective structures and test helioseismic measurements. The size and grid of the computational domain are sufficient to resolve various convective scales from granulation to supergranulation. The spatial velocity spectrum is approximately a power law for scales larger than granules, with a continuous decrease in velocity amplitude with increasing size. Aside from granulation no special scales exist, although a small enhancement in power at supergranulation scales can be seen. We calculate the time-distance diagram for f -and p-modes and show that it is consistent with the SOHO/MDI observations. From the simulation data we calculate travel time maps for surface gravity waves (f -mode). We also apply correlation tracking to the simulated vertical velocity in the photosphere to calculate the corresponding horizontal flows. We compare both of these to the actual large-scale (filtered) simulation velocities. All three methods reveal similar large scale convective patterns and provide an initial test of time-distance methods.
Abstract. P-mode oscillations in the Sun and stars are excited stochastically by Reynolds stress and entropy fluctuations produced by convection in their outer envelopes. The excitation rate of radial oscillations of stars near the main sequence from K to F and a subgiant K IV star have been calculated from numerical simulations of their surface convection zones. P-mode excitation increases with increasing effective temperature (until envelope convection ceases in the F stars) and also increases with decreasing gravity. The frequency of the maximum excitation decreases with decreasing surface gravity.
Abstract.Results of realistic simulations of solar surface convection on the scale of supergranules (96 Mm wide by 20 Mm deep) are presented. The simulations cover only 10% of the geometric depth of the solar convection zone, but half its pressure scale heights. They include the hydrogen, first and most of the second helium ionization zones. The horizontal velocity spectrum is a power law and the horizontal size of the dominant convective cells increases with increasing depth. Convection is driven by buoyancy work which is largest close to the surface, but significant over the entire domain. Close to the surface buoyancy driving is balanced by the divergence of the kinetic energy flux, but deeper down it is balanced by dissipation. The damping length of the turbulent kinetic energy is 4 pressure scale heights. The mass mixing length is 1.8 scale heights. Two thirds of the area is upflowing fluid except very close to the surface. The internal (ionization) energy flux is the largest contributor to the convective flux for temperatures less than 40,000 K and the thermal energy flux is the largest contributor at higher temperatures. THE SIMULATIONSolar surface convection on supergranular scales (96 Mm wide by 20 Mm deep) was simulated by solving the conservation equations for mass, momentum and internal energy. Spatial derivatives were evaluated using sixth order finite differences [1] and the time advance was by a low memory, third order Runge-Kutta scheme [2]. The calculations were performed on a grid of 1000 2
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