There is a discrepancy between the observed p-mode frequencies and the eigenfrequencies calculated
from one-dimensional models. Part of this difference occurs because convection enlarges the
p-mode resonant cavity and lowers the frequencies of the higher frequency modes with turning
points in the photosphere (Figure 42). This is due to two effects: First, the turbulent pressure
is about 15% of the gas pressure near the top of the convection zone and the extra pressure
support raises the atmosphere about half a scale height. Second, because of the high temperature
sensitivity of the H^{–} opacity, one does not see the hotter gas at the surface. Optical depth
unity lies higher in hotter regions where the temperature decreasing outward is lower. Thus the
horizontally averaged temperature is actually higher than obtained with a 1D model having the same
effective temperature. The higher temperature means the scale height is larger, which raises the
atmosphere another half scale height. The total effect is an atmosphere that is extended by a
scale height compared to 1D models (Figure 42). The larger cavity reduces the discrepancy
between the observed and theoretical mode frequencies as calculated from 1D models (Figure 43)
(Rosenthal et al., 1999). The frequency residuals of the f-mode (which is nearly independent of the
hydrostatic structure) are unchanged. The residuals of the p-modes from the simulation now
are the same order of magnitude as for the f-mode and change sign. This indicates that the
remaining discrepancies are due to mode physics effects and depend on depth or frequency or
both.

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