摘要：Context. Space-based observations of solar-like oscillators have
identified large numbers of stars in which many individual mode frequencies can be
precisely measured. However, current stellar models predict oscillation frequencies that
are systematically affected by simplified modelling of the near-surface layers.
Aims. We use three-dimensional radiation hydrodynamics simulations to
better model the near-surface equilibrium structure of dwarfs with spectral types F3, G2,
K0 and K5, and examine the differences between oscillation mode frequencies computed in
stellar models with and without the improved near-surface equilibrium structure.
Methods. We precisely match stellar models to the simulations’ gravities
and effective temperatures at the surface, and to the temporally- and
horizontally-averaged densities and pressures at their deepest points. We then replace the
near-surface structure with that of the averaged simulation and compute the change in the
oscillation mode frequencies. We also fit the differences using several parametric models
currently available in the literature.
Results. The surface effect in the stars of solar-type and later is
qualitatively similar and changes steadily with decreasing effective temperature. In
particular, the point of greatest frequency difference decreases slightly as a fraction of
the acoustic cut-off frequency and the overall scale of the surface effect decreases. The
surface effect in the hot, F3-type star follows the same trend in scale (i.e. it is larger
in magnitude) but shows a different overall variation with mode frequency. We find that a
two-term fit using the cube and inverse of the frequency divided by the mode inertia is
best able to reproduce the surface terms across all four spectral types, although the
scaled solar term and a modified Lorentzian function also match the three cooler
simulations reasonably well.
Conclusions. Three-dimensional radiation hydrodynamics simulations of
near-surface convection can be averaged and combined with stellar structure models to
better predict oscillation mode frequencies in solar-like oscillators. Our simplified
results suggest that the surface effect is generally larger in hotter stars (and
correspondingly smaller in cooler stars) and of similar shape in stars of solar type and
cooler. However, we cannot presently predict whether this will remain so when other
components of the surface effect are included.
