Accurate modelling of solar-like oscillators requires that modelled mode frequencies are corrected for the systematic shift caused by improper modelling of the near-surface layers, known as the surface effect. ... We investigate how much additional u
ncertainty is introduced to stellar model parameters by our uncertainty about the functional form of the surface effect. At the same time, we test whether any of the parametrizations is significantly better or worse at modelling observed subgiants and low-luminosity red giants. We model six stars observed by Kepler that show clear mixed modes. We fix the input physics of the stellar models and vary the choice of surface correction ... Models using a solar-calibrated power law correction consistently fit the observations more poorly than the other four corrections. Models with the remaining four corrections generally fit ... about equally well, with the combined surface correction by Ball & Gizon perhaps being marginally superior. The fits broadly agree on the model parameters within about the $2sigma$ uncertainties, with discrepancies between the modified Lorentzian and free power law corrections occasionally exceeding the $3sigma$ level. Relative to the best-fitting values, the total uncertainties on the masses, radii and ages of the stars are all less than 2, 1 and 6 per cent, respectively. A solar-calibrated power law ... appears unsuitable for use with more evolved solar-like oscillators. Among the remaining surface corrections, the uncertainty in the model parameters introduced by the surface effects is about twice as large as the uncertainty in the individual fits for these six stars. Though the fits are thus somewhat less certain because of our uncertainty of how to manage the surface effect, these results also demonstrate that it is feasible to model the individual mode frequencies of subgiants and low-luminosity red giants. ...
... [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 equilibriu
m 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.
