TP-04

The Synchrotron spectrum of Fast Cooling Electrons Revisited

Jonathan Granot¹, Tsvi Piran¹ and Re'em Sari^2
1Racah Institute, Hebrew University, Jerusalem 91904, Israel
²Theoretical Astrophysics, California Institute of Technology, Pasadena, CA 91125, USA.

We discuss the spectrum arising from synchrotron emission by fast cooling electrons, which are continually accelerated into relativistic thermal energies by a strong blast wave. The fast cooling spectrum was so far believed to consist of four power law segments divided by three break frequencies: $\nu_{sa}<\nu_c<\nu_m$. We show that emission from different depths behind the shock front, where the electrons had suffered a different degree of cooling, results in a new spectral slope and a new break frequency in the optically thick regime: $\nu_{ac}<\nu_{sa}<\nu_c<\nu_m$, $F_{\nu}\propto\nu^{11/8}$ for $\nu_{ac}<\nu<\nu_{sa}$ and $F_{\nu}\propto\nu^2$ for $\nu<\nu_{ac}$. It is shown that different relative orderings of the break frequencies result in two additional cases for the shape of the spectrum: $\nu_{ac}<\nu_{sa}<\nu_m$ and $\nu_m<\nu_{sa}$. We discuss possible applications for GRBs and their afterglow, in the context of the internal-external shock model, and provide useful expressions for the various break frequencies and the flux density.