Photon diffusion in a relativistically expanding sphere

Abstract

A relativistically expanding sphere exists in many explosive astrophysical systems, including gammaray bursts, neutron star mergers, and some supernovae. In this paper we investigate the photon diffusion process in a relativistically expanding sphere, which is important for understanding the energetic and radiative characters of the above mentioned explosive systems. The following contents are discussed in the frame work of special relativity: random walks of photons by scattering with electrons, photospheres, photon diffusion, and the energy flux density emerging from the surface of the expanding sphere. Some of the results are also applicable to the Universe since the Universe is also a spherical expanding system.

Keywords

special relativity / explosive processes / gamma-ray bursts / supernovae / neutron star mergers / radiative transfer / scattering / cosmology

References

[1] L. X. Li and B. Paczyński, Transient events from neutron star mergers, Astrophys. J., 1998, 507(1): L59

[2] P. Mészáros, Gamma-ray bursts, Rep. Prog. Phys., 2006, 69(8): 2259

[3] S. L. Shapiro and S. A. Teukolsky, Black Holes, White Dwarfs, and Neutron Stars, Weinheim: Wiley-VCH, 2004

[4] B. Zhang and P. Mészáros, Gamma-ray bursts: Progress, problems & prospects, Int. J. Mod Phys. A, 2004, 19: 2385

[5] S.W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time, Cambridge: Cambridge University Press, 1975

[6] R. M. Wald, General Relativity, Chicago: University of Chicago Press, 1984

[7] S. Weinberg, Gravitation and Cosmology, New York: John Wiley & Sons, 1972

[8] J. Goodman, Are gamma-ray bursts optically thick? Astrophys. J., 1986, 308: L47

[9] L. X. Li, Gamma-ray burst precursors as the remnant of the thermal radiation initially trapped in the fireball, Mon. Not. R. Astron. Soc., 2007, 380(2): 621

[10] P. A. Mazzali, J. Deng, E. Pian, D. Malesani, N. Tominaga, K. Maeda, K. Nomoto, G. Chincarini, S. Covino, M. Della Valle, D. Fugazza, G. Tagliaferri, and A. Gal-Yam, Models for the Type Ic Hypernova SN 2003lw associated with GRB 031203, Astrophys. J., 2006, 645(2): 1323

[11] K. Nomoto, K. Iwamoto, P. A. Mazzali, H. Umeda, , A hypernova model for the supernova associated with the γ-ray burst of 25 April 1998, Nature, 1998, 395(6703): 672

[12] W. Rindler, Essential Relativity: Special, General, and Cosmological, New York: Springer-Verlag, 1977

[13] J. E. Gunn and B. A. Peterson, On the density of neutral hydrogen in intergalactic space, Astrophys. J., 1965, 142: 1633

[14] B. W. Carroll and D. A. Ostlie, An Introduction to Modern Astrophysics, New York: Addison-Wesley, 1996

[15] P. Mészáros and M. J. Rees, Steep slopes and preferred breaks in gamma-ray burst spectra: The role of photospheres and comptonization, Astrophys. J., 2000, 530(1): 292

[16] I. D. Novikov and K. S. Thorne, in: Black Holes, edited by C. DeWitt and B. DeWitt, Paris: Gordoan and Breach, 1973

[17] M. J. Rees, Appearance of relativistically expanding radio sources, Nature, 1966, 211(5048): 468

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg