Solar Chromospheric Temperature Diagnostics: A Joint ALMA-Hα Analysis

We present the first high-resolution, simultaneous observations of the solar chromosphere in the optical and millimeter wavelength ranges, obtained with the Atacama Large Millimeter Array (ALMA) and the Interferometric Bidimensional Spectrometer at the Dunn Solar Telescope. In this paper we concentrate on the comparison between the brightness temperature observed in ALMA Band 3 (3 mm; 100 GHz) and the core width of the Hα 6563 Å line, previously identified as a possible diagnostic of the chromospheric temperature. We find that in the area of plage, network and fibrils covered by our field of view, the two diagnostics are well correlated, with similar spatial structures observed in both. The strength of the correlation is remarkable, given that the source function of the millimeter radiation obeys local thermodynamic equilibrium, while the Hα line has a source function that deviates significantly from the local Planck function. The observed range of ALMA brightness temperatures is sensibly smaller than the temperature range that was previously invoked to explain the observed width variations in Hα. We employ analysis from forward modeling with the Rybicki-Hummer (RH) code to argue that the strong correlation between Hα width and ALMA brightness temperature is caused by their shared dependence on the population number n ₂ of the first excited level of hydrogen. This population number drives millimeter opacity through hydrogen ionization via the Balmer continuum, and Hα width through a curve-of-growth-like opacity effect. Ultimately, the n ₂ population is regulated by the enhancement or lack of downward Lyα flux, which coherently shifts the formation height of both diagnostics to regions with different temperature, respectively.