H${\alpha}$ and H${\beta}$ emission in a C3.3 solar flare: comparison between observations and simulations

The Hydrogen Balmer series is a basic radiative loss channel from the flaring solar chromosphere. We report here on the analysis of an extremely rare set of simultaneous observations of a solar flare in the H${\alpha}$ and H${\beta}$ lines at high spatial and temporal resolution, which were acquired at the Dunn Solar Telescope. Images of the C3.3 flare (SOL2014-04-22T15:22) made at various wavelengths along the H${\alpha}$ line profile by the Interferometric Bidimensional Spectrometer (IBIS) and in the H${\beta}$ with the Rapid Oscillations in the Solar Atmosphere (ROSA) broadband imager are analyzed to obtain the intensity evolution. The H${\alpha}$ and H${\beta}$ intensity excesses in three identified flare footpoints are well correlated in time. We examine the ratio of H${\alpha}$ to H${\beta}$ flare excess, which was proposed by previous authors as a possible diagnostic of the level of electron beam energy input. In the stronger footpoints, the typical value of the the H${\alpha}$/H${\beta}$ intensity ratio observed is $\sim 0.4-0.5$, in broad agreement with values obtained from a RADYN non-LTE simulation driven by an electron beam with parameters constrained (as far as possible) by observation. The weaker footpoint has a larger H${\alpha}$/H${\beta}$ ratio, again consistent with a RADYN simulation but with a smaller energy flux. The H${\alpha}$ line profiles observed have a less prominent central reversal than is predicted by the RADYN results, but can be brought into agreement if the H${\alpha}$-emitting material has a filling factor of around 0.2--0.3.