Characterization of white-light enhancements under umbral conditions in one-dimensional simulations of solar flares

Solar flares with signatures in the optical continuum (white light, WL) pose a challenge to the standard flare model and to solar flare simulations. In particular, simulations are so far not able to convincingly reproduce observed WL enhancements. We investigate the effect of different electron beams on an umbral atmosphere and what the differences and similarities to the quiet-Sun response are. We characterized WL emission in one-dimensional simulations of solar flares using the radiation hydrodynamics code RADYN. We used a similar setup as the F-CHROMA grid, but with a starting atmosphere describing umbral conditions. We investigated the influence of different temporal profiles of an electron beam on this umbral atmosphere. Our simulations show maximum WL increases between 40 and 335%, which is comparable to observed values. The reduced umbral background is the main reason for these large increases. We identify hydrogen recombination in an optically thin chromosphere as the dominant process responsible for the increases, with the radiation from the heated photosphere becoming substantial in the later stages due to the longer timescale of the cooling of the photosphere compared to hydrogen recombination in the chromosphere. Shorter, more intense beams (i.e., beams with a higher maximum energy flux) lead to a faster and more dramatic atmospheric evolution. Such beams also cause larger WL enhancements due to a higher electron density in the relevant layers. Both the Balmer ratio and the Paschen ratio are substantially higher in our simulations compared to simulations with a quiet-Sun atmosphere. The detectability and amplitude of WL enhancements depends on the spectral and temporal structure of the electron beam as well as the underlying background radiation. The combination of a short, intense beam and an umbral atmosphere provides an excellent seed for substantial WL enhancements.