  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 simulations in 1D have shown that
high energy deposition rates from electron beams produce two flaring layers at
T~10^4 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 a time to
come. We have developed a prescription for predicting the approximate evolved
states, continuum optical depth, and the emergent continuum flux spectra of
radiative-hydrodynamic 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-Mar-29 X1 solar flare and that variation in m_ref from 0.001 to
0.02 g/cm2 reproduces most of the observed range of the optical continuum flux
ratios at the peaks of M dwarf flares.
