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 in the blue-optical, 2) a smaller amount of Balmer continuum emission in the near-ultraviolet at λ ≤3 646 Å, and 3) an apparent pseudo-continuum of blended high-order Balmer lines between λ =3 646 Å and λ ≈3 900 Å. These properties are not reproduced by models that employ a typical "solar-type" flare heating level of ≤10¹¹ergcm−²s−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. The simulation produces bright near-ultraviolet and optical continuum emission from a dense (n >10¹⁵cm−³), hot (T ≈12 000 -13 500 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 blackbody-like continuum component and a low Balmer jump ratio result from optically thick Balmer (∞ →n =2 ) and Paschen recombination (∞ →n =3 ) radiation, and thus the properties of the flux spectrum are caused by blue (λ ≈4 300 Å) light escaping over a larger physical depth range than by red (λ ≈6 700 Å) and near-ultraviolet (λ ≈3 500 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.