  ... [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.
