Solving the discrepancy between the seismic and photospheric solar radius

Two methods are used to observationally determine the solar radius: One is the observation of the intensity profile at the limb, the other one uses f-mode frequencies to derive a 'seismic' solar radius which is then corrected to optical depth unity. The two methods are inconsistent and lead to a difference in the solar radius of $\sim$0.3 Mm. Because of the geometrical extention of the solar photosphere and the increased path lengths of tangential rays the Sun appears to be larger to an observer who measures the extent of the solar disk. Based on radiative transfer calculations we show that this discrepancy can be explained by the difference between the height at disk center where $\tau_{\mathrm{5000}}=1$ ($\tau_{\mathrm{Ross}}=2/3$) and the inflection point of the intensity profile on the limb. We calculate the intensity profile of the limb for the MDI continuum and the continuum at 5000 {\AA} for two atmosphere structures and compare the position of the inflection points with the radius at $\tau_{\mathrm{5000}}=1$ ($\tau_{\mathrm{Ross}}=2/3$). The calculated difference between the 'seismic' radius and the inflection point is $0.347\pm 0.06$ Mm with respect to $\tau_{\mathrm{5000}}=1$ and $0.333\pm 0.08$ Mm with respect to $\tau_{\mathrm{Ross}}=2/3$. We conclude that the standard solar radius in evolutionary models has to be lowered by $0.333\pm 0.08$ Mm and is 695.66 Mm. Furthermore, this correction reconciles inflection point measurements and the 'seismic' radii within the uncertainty.