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

  • Solar and Stellar Flares
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Abstract

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 \(T\approx10^{4}~\mbox{K}\) in the blue-optical, 2) a smaller amount of Balmer continuum emission in the near-ultraviolet at \(\lambda\le3\,646\) Å, and 3) an apparent pseudo-continuum of blended high-order Balmer lines between \(\lambda=3\,646\) Å and \(\lambda\approx3\,900\) Å. These properties are not reproduced by models that employ a typical “solar-type” flare heating level of \({\le}\,10^{11}~\mbox{erg}\,\mbox{cm}^{-2}\,\mbox{s}^{-1}\) 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 \(10^{13}~\mbox{erg}\,\mbox{cm}^{-2}\,\mbox{s}^{-1}\). The simulation produces bright near-ultraviolet and optical continuum emission from a dense (\(n>10^{15}~\mbox{cm}^{-3}\)), hot (\(T \approx12\,000\,\mbox{--}\,13\,500~\mbox{K}\)) 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 \(T\approx10^{4}~\mbox{K}\) blackbody-like continuum component and a low Balmer jump ratio result from optically thick Balmer (\(\infty\rightarrow n=2\)) and Paschen recombination (\(\infty\rightarrow n=3\)) radiation, and thus the properties of the flux spectrum are caused by blue (\(\lambda\approx4\,300\) Å) light escaping over a larger physical depth range than by red (\(\lambda\approx6\,700\) Å) and near-ultraviolet (\(\lambda\approx3\,500\) 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.

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Notes

  1. A comprehensive study of NT rates was presented in the calculations of Ricchiazzi (1982) and Ricchiazzi and Canfield (1983), who found that the H i \(n=1 \rightarrow\infty\) and \(n=1 \rightarrow n=2\) rates are important, but that the \(n=2 \rightarrow\infty\) rate was negligible compared to the \(n=2 \rightarrow\infty\) thermal rates for their range of beam fluxes.

  2. The flux spectra for the F13 simulation are available upon request.

  3. The speed of sound in the CC at \(t=0.4~\mbox{s}\) is \(30~\mbox{km}\,\mbox{s}^{-1}\), whereas material is traveling at speeds of nearly \(100~\mbox{km}\,\mbox{s}^{-1}\).

  4. The differential \(\mathrm{d}I_{\lambda}/\mathrm{d}z\) in the definition of the contribution function is the same as the differential describing the variation of the specific intensity with height in the radiative-transfer equation; however, these differentials are not equivalent.

  5. \(j_{\nu}\) is often used to describe the emissivity in units of photons \(\mbox{cm}^{-3}\,\mbox{s}^{-1}\,\mbox{sr}^{-1}\) \(\mbox{Hz}^{-1}\), whereas \(\eta_{\nu}\) is used for the emissivity in units of \(\mbox{ergs}\,\mbox{cm}^{-3}\,\mbox{s}^{-1}\,\mbox{sr}^{-1}\,\mbox{Hz}^{-1}\); here, we use \(j_{\nu}\) to describe the emissivity in units of ergs \(\mbox{cm}^{-3}\,\mbox{s}^{-1}\,\mbox{sr}^{-1}\,\mbox{Hz}^{-1}\).

  6. See Section 3.4, there are additional opacities from photoionization of the higher levels of hydrogen, hydrogen free–free absorption, and opacity from the \(\mbox{H}^{-}\) ion that can also contribute towards the optical depth at these wavelengths.

  7. The value \(1.578\times10^{5}\) in the second exponential is 13.598 eV/\(k_{\mathrm{B}}\).

  8. Bengtson, Tannich, and Kepple (1970) provided results up to H12 using the theory of Kepple and Griem (1968) for one temperature and electron density. Bengtson (1996) provided higher order line profiles for the study of Johns-Krull et al. (1997), but these results have not been made publicly available to our knowledge.

  9. We compared the RH and RADYN predictions at \(t=2.2~\mbox{s}\) for the Balmer lines and continua that overlap, and we found satisfactory agreement.

  10. The S# refer to the time-sequential spectrum numbers over each flare analyzed in K13.

  11. We used the same continuum blue window (BW) wavelength regions and weighting as in K13.

  12. In addition to many faint metallic and helium emission lines.

  13. Assuming that the Balmer line emission does not originate at a different spatial location, for example from a larger area with a lower density, than the continuum emission.

  14. See the discussion in Hummer and Mihalas (1988) about how the theory of occupational probability differs from the Inglis–Teller relationship: the Landau–Zener transitions require fluctuations of the microfield around the critical field value.

  15. Emission model fits, e.g., with a blackbody function or RHD model spectra, give an indirect estimate of the flare area and energy flux requirements.

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Acknowledgements

Adam F. Kowalski thanks the Science Organizing Committee of the Solar and Stellar Flares meeting in Prague, Czech Republic for the opportunity to present this work. We thank an anonymous referee for clarifications and comments that helped improve this work. Adam F. Kowalski thanks Petr Heinzel and Hans Ludwig for bringing hot star modeling articles of Stark broadening to his attention. We thank Adrian Daw, Eric Agol, Ellen Zweibel, and Jeremiah Murphy for helpful discussions and William Abbett for several IDL routines used in the analysis. AFK also acknowledges helpful discussions at the International Space Science Institute with Lyndsay Fletcher’s Solar and Stellar Flares team and with Sven Wedemeyer-Bohm’s Magnetic Activity of M-type Dwarf Stars and the Influence on Habitable Extra-solar Planets team. This research was supported by an appointment to the NASA Postdoctoral Program at the Goddard Space Flight Center, administered by Oak Ridge Associated Universities through a contract with NASA, and by the University of Maryland Goddard Planetary Heliophysics Institute (GPHI) Task 132.

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Authors and Affiliations

  1. Department of Astronomy, University of Maryland, College Park, MD, 20742, USA

    Adam F. Kowalski

  2. NASA Goddard Space Flight Center, Heliophysics Science Division, Code 671, 8800 Greenbelt Rd., Greenbelt, MD, 20771, USA

    Adam F. Kowalski, J. C. Allred & G. Holman

  3. Department of Astronomy, University of Washington, Box 351580, Seattle, WA, 98195, USA

    S. L. Hawley

  4. Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029, Blindern, 0315, Oslo, Norway

    M. Carlsson

  5. National Solar Observatory, Sacramento Peak, P.O. Box 62, Sunpsot, NM, 88349, USA

    H. Uitenbroek

  6. Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD, 21218, USA

    R. A. Osten

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  1. Adam F. Kowalski
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  2. S. L. Hawley
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  3. M. Carlsson
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Correspondence to Adam F. Kowalski.

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Solar and Stellar Flares: Observations, Simulations, and Synergies

Guest Editors: Lyndsay Fletcher and Petr Heinzel

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Kowalski, A.F., Hawley, S.L., Carlsson, M. et al. New Insights into White-Light Flare Emission from Radiative-Hydrodynamic Modeling of a Chromospheric Condensation. Sol Phys 290, 3487–3523 (2015). https://doi.org/10.1007/s11207-015-0708-x

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