Spectral Diagnostics of Solar Photospheric Bright Points

By use of the high-resolution spectral data and the broadband imaging obtained with the Goode Solar Telescope at the Big Bear Solar Observatory on 2013 June 6, the spectra of three typical photospheric bright points (PBPs) have been analyzed. Based on the H$\alpha$ and Ca II 8542 \AA line profiles, as well as the TiO continuum emission, for the first time, the non-LTE semi-empirical atmospheric models for the PBPs are computed. The attractive characteristic is the temperature enhancement in the lower photosphere. The temperature enhancement is about 200 -- 500 K at the same column mass density as in the atmospheric model of the quiet-Sun. The total excess radiative energy of a typical PBP is estimated to be 1$\times$10$^{27}$ - 2$\times$10$^{27}$ ergs, which can be regarded as the lower limit energy of the PBPs. The radiation flux in the visible continuum for the PBPs is about 5.5$\times$10$^{10}$ ergs cm$^{-2}$ s$^{-1}$. Our result also indicates that the temperature in the atmosphere above PBPs is close to that of a plage. It gives a clear evidence that PBPs may contribute significantly to the heating of the plage atmosphere. Using our semi-empirical atmospheric models, we estimate self-consistently the average magnetic flux density $B$ in the PBPs. It is shown that the maximum value is about one kilo-Gauss, and it decreases towards both higher and lower layers, reminding us of the structure of a flux tube between photospheric granules.