Abstract
We propose an accurate analytical model for the source of hard X-ray emission from a flare in the form of a “thick target” with a reverse current to explain the results of present-day observations of solar flares onboard the GOES, Hinode, RHESSI, and TRACE satellites. The model, one-dimensional in coordinate space and two-dimensional in velocity space, self-consistently takes into account the fact that the beam electrons lose the kinetic energy of their motion along the magnetic field almost without any collisions under the action of the reverse-current electric field. Some of the electrons return from the emission source to the acceleration region without losing the kinetic energy of their transverse motion. Based on the observed hard X-ray bremsstrahlung spectrum, the model allows the injection spectrum of accelerated electrons to be reconstructed with a high accuracy. As an example, we consider the white-light flare of December 6, 2006, which was observed with a high spatial resolution in the optical wavelength range at the main maximum of hard X-ray emission. Within the framework of our model, we show that to explain the hard X-ray spectrum, the flux density of the energy transferred by electrons with energies above 18 keV was ∼3 × 1013 erg cm−2 s−1. This exceeds the habitual values typical of the classical model of a thick target without a reverse current by two orders of magnitude. The electron density in the beam is also very high: ∼1011 cm−3. A more careful consideration of plasma processes in such dense electron beams is needed when the physical parameters of a flare are calculated.
Similar content being viewed by others
References
A. Asai, J. Kiyohara, H. Takasaki, N. Narukage, T. Yokoyama, S. Masuda, M. Shimojo, and H. Nakajima, Astrophys. J. 763, 87 (2013).
M. J. Aschwanden, Particle Acceleration and Kinematics in Solar Flares (Kluwer Academic Publ., Dordrecht, 2002), p. 227.
M. Battaglia and E. P. Kontar, Astrophys. J. 760, 142 (2013).
J. C. Brown, Solar Phys. 18, 489 (1971).
M. Casolino, M. de Simone, N. de Pascale, V. di Felice, L. Marcelli, M. Minori, P. Picozza, R. Sparvoli, et al., Nucl. Phys. 190, 293 (2009).
A. Caspi, S. Krucker, and R. P. Lin, Astrophys. J. 781, 43 (2014).
S.V. Diakonov and B.V. Somov, Solar Phys. 116, 119 (1988).
S. V. Diakonov and B. V. Somov, Kinem. Fiz. Nebesn. Tel 6, 48 (1990).
G. Elwert and E. Haug, Solar Phys. 15, 234 (1970).
L. Feng, T. Weigelmann, Y. Su, B. Inhester, Y. P. Li, X. D. Sun, and W. Q. Gan, Astrophys. J. 765, 37 (2013).
P. A. Gritsyk and B. V. Somov, Mosc. Univ. Phys. Bull. 66, 466 (2011).
H. Hudson and J. Ryan, Astrophys. J. 33, 239 (1995).
S. Ishikawa, S. Krucker, T. Takahashi, and R. P. Lin, Astrophys. J. 737, 48 (2011).
S. Krucker, H. S. Hudson, N. L. S. Jeffrey, M. Battaglia, E. P. Kontar, A. O. Benz, A. Csillaghy, and R. P. Lin, Astrophys. J. 739, 96 (2011).
Yu. E. Litvinenko and B. V. Somov, Solar Phys. 131, 319 (1991).
W. Liu, O. Chen, and V. Petrosia, Astrophys. J. 767, 168 (2013).
L. Nocera, Yu. I. Skrynnikov, and B. V. Somov, Solar Phys. 97, 81 (1985).
G. H. J. van den Oord, Astron. Astrophys. 234, 496 (1990).
A. V. Oreshina and B. V. Somov, Astron. Lett. 37, 726 (2011).
A. Y. Shih, R. P. Lin, and D. M. Smith, Astrophys. J. 698, 152 (2009).
P. J. A. Simões and E. P. Kontar, Astron. Astrophys. 551, 135 (2013).
B. V. Somov, Physical Processes in Solar Flares (Dordrecht, London, 1993), p. 249.
B. V. Somov, Cosmic Plasma Physics (Kluwer Academic, Dordrecht, 2000), p. 652.
B. V. Somov, Plasma Astrophysics. Part I: Fundamentals and Practice (Springer SBM, New York, 2012), p. 498.
B. V. Somov, Plasma Astrophysics Part II: Reconnection and Flares (Springer SBM, New York, 2013), p. 504.
B. V. Somov and P. A. Gritsyk, Mosc. Univ. Phys. Bull. 67, 102 (2012).
B. V. Somov and S. I. Syrovatskii, Sov. Phys. Usp. 19, 813 (1976).
L. Sui, G. D. Holman, and B. R. Dennis, Astrophys. J. 612, 546 (2004).
Z. Svestka, Solar Flares (D. Reidel, Dordrecht, 1976).
S. I. Syrovatskii and O. P. Shmeleva, Sov. Astron. 16, 273 (1972).
S. I. Syrovatskii and O. P. Shmeleva, in Solar Terrestrial Relations, Proceedings of the Conference, Calgary, Aug. 28–Sep. 1, 1972 (Univ. Calgary, 1973), p. 243.
S. Tsuneta, S. Masuda, T. Kosugi, and J. Sato, Astrophys. J. 478, 787 (1997).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © P.A. Gritsyk, B.V. Somov, 2014, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2014, Vol. 40, No. 8, pp. 554–565.
Rights and permissions
About this article
Cite this article
Gritsyk, P.A., Somov, B.V. Reverse-current effect in present-day models of solar flares: Theory and high-accuracy observations. Astron. Lett. 40, 499–509 (2014). https://doi.org/10.1134/S1063773714080040
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063773714080040