Title: Time-dependent Stellar Flare Models of Deep Atmospheric Heating

Abstract: Optical flares have been observed from magnetically active stars for many decades; unsurprisingly, the spectra and temporal evolution are complicated. For example, the shortcomings of optically thin, static slab models have long been recognized when confronted with the observations. A less incorrect -- but equally simple -- phenomenological $T \approx 9000$ K blackbody model has instead been widely adopted in the absence of realistic (i.e., observationally-tested) time-dependent, atmospheric models that are readily available. We use the RADYN code to calculate a grid of 1D radiative-hydrodynamic stellar flare models that are driven by short pulses of electron-beam heating. The flare heating rates in the low atmosphere vary over many orders of magnitude in the grid, and we show that the models with high-energy electron beams compare well to the global trends in flux ratios from impulsive-phase stellar flare, optical spectra. The models also match detailed spectral line shape properties. We find that the pressure broadening and optical depths account for the broad components of the hydrogen Balmer $\gamma$ lines in a powerful flare with echelle spectra. The self-consistent formation of the wings and nearby continuum level provide insight into how high-energy electron beam heating evolves from the impulsive to the gradual decay phase in white-light stellar flares. The grid is publicly available, and we discuss possible applications.