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3. On the Solution of the Continuity Equation for Precipitating Electrons in Solar Flares

Author

Emslie, A. Gordon, Holman, Gordon D, and Litvinenko, Yuri E

Subjects
Space Sciences (General)
Abstract

Electrons accelerated in solar flares are injected into the surrounding plasma, where they are subjected to the influence of collisional (Coulomb) energy losses. Their evolution is modeled by a partial differential equation describing continuity of electron number. In a recent paper, Dobranskis & Zharkova claim to have found an "updated exact analytical solution" to this continuity equation. Their solution contains an additional term that drives an exponential decrease in electron density with depth, leading them to assert that the well-known solution derived by Brown, Syrovatskii & Shmeleva, and many others is invalid. We show that the solution of Dobranskis & Zharkova results from a fundamental error in the application of the method of characteristics and is hence incorrect. Further, their comparison of the "new" analytical solution with numerical solutions of the Fokker-Planck equation fails to lend support to their result.We conclude that Dobranskis & Zharkova's solution of the universally accepted and well-established continuity equation is incorrect, and that their criticism of the correct solution is unfounded. We also demonstrate the formal equivalence of the approaches of Syrovatskii & Shmeleva and Brown, with particular reference to the evolution of the electron flux and number density (both differential in energy) in a collisional thick target. We strongly urge use of these long-established, correct solutions in future works.

Published
2014
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10. The Compatibility of Friedmann Cosmological Models with Observed Properties of Gamma-Ray Bursts and a Large Hubble Constant

Author

Horack, John M, Koshut, Thomas M, Mallozzi, Robert S, Emslie, A. Gordon, and Meegan, Charles A

Subjects
Space Radiation
Abstract

The distance scale to cosmic gamma-ray bursts (GRB's) is still uncertain by many orders of magnitude; however, one viable scenario places GRB's at cosmological distances, thereby permitting them to be used as tracers of the cosmological expansion over a significant range of redshifts zeta. Also, several recent measurements of the Hubble constant H(sub 0) appearing in the referred literature report values of 70-80 km/s /Mpc. Although there is significant debate regarding these measurements, we proceed here under the assumption that they are evidence of a large value for H(sub 0). This is done in order to investigate the additional constraints on cosmological models that can be obtained under this hypothesis when combined with the age of the universe and the brightness distribution of cosmological gamma-ray bursts. We show that the range of cosmological models that can be consistent with the GRB brightness distribution, a Hubble constant of 70-80 km/s/Mpc, and a minimum age of the universe of 13-15 Gyr is constrained significantly, largely independent of a wide range of assumptions regarding the evolutionary nature of the burst population. Low-density, Lambda greater than 0 cosmological models with deceleration parameter in the range -1 less than q(sub 0) less than 0 and density parameter sigma(sub 0) in the range approximately equals 0.10-0.25(Omega(sub 0) approximately equals 0.2-0.5) are strongly favored.

Published
1996
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11. Force-free fields in thin coronal loops

Author

Emslie, A. Gordon and Wilkinson, L. K

Subjects
Astrophysics
Abstract

We solve the force-free equation J x B = 0 for fields which are toroidally symmetric. The technique utilizes an expansion about a cylindrical field and is therefore valid or tori with a large aspect ratio such as long, thin, coronal loops. The calculation is performed in spatial toroidal coordinates, rather than in the flux coordinates used by previous authors; this allows direct calculation of the loci of flux surfaces and of surfaces of constant magnetic pressure. Our solutions differ significantly from toroidal fields in laboratories, which are in general not force-free. They are characterized by field lines whose projections in the poloidal planes are circles with centers displaced by varying distances from the axis of the torus. In general, flux surfaces do not correspond to surfaces of constant magnetic pressure. We have examined solutions corresponding to simple analytic zero-order cylindrical fields. For moderate twists in the zero-order (cylindrical) field, the magnetic pressure is larger on the inner toroidal radius. However, this effect diminishes with twist angle and in fact, for extreme initial twists, the magnetic pressure can be larger on the outer radius. We compare our results with previous work utilizing flux coordinates.

Published
1994
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12. Integral-moment analysis of the BATSE gamma-ray burst intensity distribution

Author

Horack, John M and Emslie, A. Gordon

Subjects
Astrophysics
Abstract

We have applied the technique of integral-moment analysis to the intensity distribution of the first 260 gamma-ray bursts observed by the Burst and Transient Source Experiment (BATSE) on the Compton Gamma Ray Observatory. This technique provides direct measurement of properties such as the mean, variance, and skewness of the convolved luminosity-number density distribution, as well as associated uncertainties. Using this method, one obtains insight into the nature of the source distributions unavailable through computation of traditional single parameters such as V/V(sub max)). If the luminosity function of the gamma-ray bursts is strongly peaked, giving bursts only a narrow range of luminosities, these results are then direct probes of the radial distribution of sources, regardless of whether the bursts are a local phenomenon, are distributed in a galactic halo, or are at cosmological distances. Accordingly, an integral-moment analysis of the intensity distribution of the gamma-ray bursts provides for the most complete analytic description of the source distribution available from the data, and offers the most comprehensive test of the compatibility of a given hypothesized distribution with observation.

Published
1994
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