New Insights into White-Light Flare Emission from Radiative-Hydrodynamic Modeling of a Chromospheric Condensation

The heating mechanism at high densities during M-dwarf flares is poorly understood. Spectra of M-dwarf flares in the optical and near-ultraviolet wavelength regimes have revealed three continuum components during the impulsive phase: 1) an energetically dominant blackbody component with a color temperature of T≈104K$T\approx10^{4}~\mbox{K}$ in the blue-optical, 2) a smaller amount of Balmer continuum emission in the near-ultraviolet at λ≤3646$\lambda\le3\,646$ Å, and 3) an apparent pseudo-continuum of blended high-order Balmer lines between λ=3646$\lambda=3\,646$ Å and λ≈3900$\lambda\approx3\,900$ Å. These properties are not reproduced by models that employ a typical “solar-type” flare heating level of ≤1011ergcm−2s−1${\le}\,10^{11}~\mbox{erg}\,\mbox{cm}^{-2}\,\mbox{s}^{-1}$ in nonthermal electrons, and therefore our understanding of these spectra is limited to a phenomenological three-component interpretation. We present a new 1D radiative-hydrodynamic model of an M-dwarf flare from precipitating nonthermal electrons with a high energy flux of 1013ergcm−2s−1$10^{13}~\mbox{erg}\,\mbox{cm}^{-2}\,\mbox{s}^{-1}$. The simulation produces bright near-ultraviolet and optical continuum emission from a dense (n>1015cm−3$n>10^{15}~\mbox{cm}^{-3}$), hot (T≈12000–13500K$T \approx12\,000\,\mbox{--}\,13\,500~\mbox{K}$) chromospheric condensation. For the first time, the observed color temperature and Balmer jump ratio are produced self-consistently in a radiative-hydrodynamic flare model. We find that a T≈104K$T\approx10^{4}~\mbox{K}$ blackbody-like continuum component and a low Balmer jump ratio result from optically thick Balmer (∞→n=2$\infty\rightarrow n=2$) and Paschen recombination (∞→n=3$\infty\rightarrow n=3$) radiation, and thus the properties of the flux spectrum are caused by blue (λ≈4300$\lambda\approx4\,300$ Å) light escaping over a larger physical depth range than by red (λ≈6700$\lambda\approx6\,700$ Å) and near-ultraviolet (λ≈3500$\lambda\approx3\,500$ Å) light. To model the near-ultraviolet pseudo-continuum previously attributed to overlapping Balmer lines, we include the extra Balmer continuum opacity from Landau–Zener transitions that result from merged, high-order energy levels of hydrogen in a dense, partially ionized atmosphere. This reveals a new diagnostic of ambient charge density in the densest regions of the atmosphere that are heated during dMe and solar flares.