2018ApJ...852...61K

The origin of the near-ultraviolet and optical continuum radiation in flares is critical for understanding particle acceleration and impulsive heating in stellar atmospheres. Radiative-hydrodynamic (RHD) simulations in 1D have shown that high energy deposition rates from electron beams produce two flaring layers at T ∼ 10⁴ K that develop in the chromosphere: a cooling condensation (downflowing compression) and heated non-moving (stationary) flare layers just below the condensation. These atmospheres reproduce several observed phenomena in flare spectra, such as the red-wing asymmetry of the emission lines in solar flares and a small Balmer jump ratio in M dwarf flares. The high beam flux simulations are computationally expensive in 1D, and the (human) timescales for completing NLTE models with adaptive grids in 3D will likely be unwieldy for some time to come. We have developed a prescription for predicting the approximate evolved states, continuum optical depth, and emergent continuum flux spectra of RHD model flare atmospheres. These approximate prescriptions are based on an important atmospheric parameter: the column mass (m_ref) at which hydrogen becomes nearly completely ionized at the depths that are approximately in steady state with the electron beam heating. Using this new modeling approach, we find that high energy flux density (>F11) electron beams are needed to reproduce the brightest observed continuum intensity in IRIS data of the 2014 March 29 X1 solar flare, and that variation in m_ref from 0.001 to 0.02 g cm^–2 reproduces most of the observed range of the optical continuum flux ratios at the peak of M dwarf flares.