Astronomy and Astrophysics – Astrophysics
Scientific paper
2000-01-10
ApJL, 534 (2000), L163
Astronomy and Astrophysics
Astrophysics
9 pages, 1 figure. Revised version, Accepted for Publication in the Astrophysical Journal Letters
Scientific paper
10.1086/312661
We discuss the spectrum arising from synchrotron emission by fast cooling (FC) electrons, when fresh electrons are continually accelerated by a strong blast wave, into a power law distribution of energies. The FC spectrum was so far described by four power law segments divided by three break frequencies $\nu_{sa} < \nu_{c} < \nu_{m}$. This is valid for a homogeneous electron distribution. However, hot electrons are located right after the shock, while most electrons are farther down stream and have cooled. This spatial distribution changes the optically thick part of the spectrum, introducing a new break frequency, $\nu_{ac} < \nu_{sa}$, and a new spectral slope, $F_{\nu }\propto \nu^{11/8}$ for $\nu_{ac} < \nu < \nu_{sa}$. The familiar $F_{\nu }\propto \nu ^{2}$ holds only for $\nu < \nu_{ac}$. This ordering of the break frequencies is relevant for typical gamma-ray burst (GRB) afterglows in an ISM environment. Other possibilities arise for internal shocks or afterglows in dense circumstellar winds. We discuss possible implications of this spectrum for GRBs and their afterglows, in the context of the internal-external shock model. Observations of $F_{\nu} \propto \nu^{11/8}$ would enable us to probe scales much smaller than the typical size of the system, and constrain the amount of turbulent mixing behind the shock.
Granot Jonathan
Piran Tsvi
Sari Re'em
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