主要内容:
即f_nu~nu^0
用不同角度由于多普勒效应而看起来不同温度，合起来就是nu的0次方了。（我曾经考虑过的，即相对论性膨胀的同温球，观测者看起来依然是一个温度的黑体谱！也就是低能段是nu^2,而不是nu^0. 不过他这里考虑了等时面效应，不知道是不是这个原因导致他这儿就成立了。）
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文章信息:
- · arXiv e-print (arXiv:1008.4590)
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| Title: |
| A Theory of Mulicolor Black Body Emission from Relativistically Expanding Plasmas |
| Authors: |
| Pe'er, Asaf; Ryde, Felix |
| Publication: |
| eprint arXiv:1008.4590 |
| Publication Date: |
| 08/2010 |
| Origin: |
| ARXIV |
| Keywords: |
| Astrophysics - High Energy Astrophysical Phenomena |
| Comment: |
| 8 pages, 2 figures; submitted for publication in Ap.J |
| Bibliographic Code: |
| 2010arXiv1008.4590P |
Abstract
We consider the emission of photons from the inner parts of a relativistically expanding plasma outflow, characterized by a constant Lorentz factor, Gamma. Photons that are injected in regions of high optical depth are advected with the flow until they escape at the photosphere. Due to multiple scattering below the photosphere, the locally emerging comoving photon distribution is thermal. However, as an observer sees simultaneously photons emitted from different angles, hence with different Doppler boosting, the observed spectrum is a multi-color black-body. We calculate here the properties of the observed spectrum at different observed times. Due to the strong dependence of the photospheric radius on the angle to the line of sight, for parameters characterizing gamma-ray bursts (GRBs) thermal photons are seen up to tens of seconds following the termination of the inner engine. At late times, following the inner engine termination, both the number flux and energy flux of the thermal spectrum decay as F ~ t^{-2}. At these times, the multicolor black body emission results in a power law at low energies (below the thermal peak), with power law index F_\nu ~ \nu^{0}. This result is remarkably similar to the average value of the low energy spectral slope index (``\alpha'') seen in fitting the spectra of large GRB sample.
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