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.
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 doi: 10.1086/184741
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 doi: 10.1111/j.1365-2966.2007.12083.x
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 doi: 10.1086/504415
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 doi: 10.1038/27155
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 doi: 10.1086/148444
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 doi: 10.1086/308371
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 doi: 10.1038/211468a0