Center-to-limb observations of the Sun with ALMA Implications for solar atmospheric models

Aims. We seek to derive information on the temperature structure of the solar chromosphere and compare these results with existing models. Methods. We measured the center-to-limb variation of the brightness temperature, T-b, from ALMA full-disk images at two frequencies and inverted the solution of the transfer equation to obtain the electron temperature, T-e as a function of optical depth, tau. Results. The ALMA images are very similar to AIA images at 1600 angstrom. The brightness temperature at the center of the disk is 6180 and 7250K at 239 and 100 GHz, respectively, with dispersions of 100 and 170 K. Plage regions stand out clearly in the 239/100 GHz intensity ratio, while faculae and filament lanes do not. The solar disk radius, reduced to 1AU, is 961.1 +/- 2.5" and 964.1 +/- 4.5" at 239 and 100 GHz, respectively. A slight but statistically significant limb brightening is observed at both frequencies. Conclusions. The inversion of the center-to-limb curves shows that Te varies linearly with the logarithm of optical depth for 0 : 34 < tau(100GHz) < 12, with a slope dT(e)/dln tau= -608 K. Our results are 5% lower than predicted by the average quiet Sun model C of Fontenla et al. (1993, ApJ, 406, 319), but do not confirm previous reports that the mm-lambda solar spectrum is better fitted with models of the cell interior.