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Register a new userThe asteroseismic surface effect from a grid of 3D convection simulations. I. Frequency shifts from convective expansion of stellar atmospheres
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We analyse the effect on adiabatic stellar oscillation frequencies of replacing the near-surface layers in 1D stellar structure models with averaged 3D stellar surface convection simulations. The main difference is an expansion of the atmosphere by 3D convection, expected to explain a major part of the asteroseismic surface effect; a systematic overestimation of p-mode frequencies due to inadequate surface physics. We employ pairs of 1D stellar envelope models and 3D simulations from a previous calibration of the mixing-length parameter, alpha. That calibration constitutes the hitherto most consistent matching of 1D models to 3D simulations, ensuring that their differences are not spurious, but entirely due to the 3D nature of convection. The resulting frequency shift is identified as the structural part of the surface effect. The important, typically non-adiabatic, modal components of the surface effect are not included in the present analysis, but relegated to future papers. Evaluating the structural surface effect at the frequency of maximum mode amplitude, $ u_{rm max}$, we find shifts from $delta u$=-0.8 microHz for giants at $log g$=2.2 to -35 microHz for a ($T_{rm eff}=6901$ K, $log g$=4.29) dwarf. The fractional effect $delta u( u_{rm max})/ u_{rm max}$, ranges from -0.1% for a cool dwarf (4185 K, 4.74) to -6% for a warm giant (4962 K, 2.20).
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Relations between temperature, T, and optical depth, tau, are often used for describing the photospheric transition from optically thick to optically thin in stellar structure models. We show that this is well justified, but also that currently used T(tau) relations are often inconsistent with their implementation. As an outer boundary condition on the system of stellar structure equations, T(tau) relations have an undue effect on the overall structure of stars. In this age of precision asteroseismology, we need to re-assess both the method for computing and for implementing T(tau) relations, and the assumptions they rest on. We develop a formulation for proper and consistent evaluation of T(tau) relations from arbitrary 1D or 3D stellar atmospheres, and for their implementation in stellar structure and evolution models. We extract radiative T(tau) relations, as described by our new formulation, from 3D simulations of convection in deep stellar atmospheres of late-type stars from dwarfs to giants. These simulations employ realistic opacities and equation of state, and account for line-blanketing. For comparison, we also extract T(tau) relations from 1D MARCS model atmospheres using the same formulation. T(tau)-relations from our grid of 3D convection simulations display a larger range of behaviours with surface gravity, compared with those of conventional theoretical 1D hydrostatic atmosphere models. Based on this, we recommend no longer to use scaled solar T(tau) relations. Files with T(tau) relations for our grid of simulations are made available to the community, together with routines for interpolating in this irregular grid. We also provide matching tables of atmospheric opacity, for consistent implementation in stellar structure models.
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