... [C]urrent stellar models predict oscillation frequencies that are systematically affected by simplified modelling of the near-surface layers. 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. ... 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. 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 the two-term fit by Ball & Gizon (2014) 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. ... 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.
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