The synchrotron spectrum of fast cooling electrons revisited

Jonathan Granot, Tsvi Piran, Re'em Sari

Research output: Contribution to journalArticlepeer-review


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 has so far been described by four power-law segments divided by three break frequencies vsa < vc < vm. This is valid for a homogeneous electron distribution. However, hot electrons are located right after the shock, while most electrons are farther downstream and have cooled. This spatial distribution changes the optically thick part of the spectrum, introducing a new break frequency, vac < vsa, and a new spectral slope, Fv ∝ v 11/8 for vac < v < vsa. The familiar Fv ∝ v2 holds only for v < vac. This ordering of the break frequencies is relevant for typical gamma-ray burst (GRB) afterglows in an interstellar medium environment. Other possibilities arise for internal shocks or afterglows in dense circumstellar winds. We discuss the possible implications of this spectrum for GRBs and their afterglows in the context of the internal-external shock model. Observations of Fv oc ∝11/8 would enable us to probe scales much smaller than the typical size of the system and to constrain the amount of turbulent mixing behind the shock.

Original languageEnglish
Pages (from-to)L163-L166
JournalAstrophysical Journal
Issue number2 PART 2
StatePublished - 10 May 2000
Externally publishedYes

Bibliographical note

Funding Information:
This research was supported by the US-Israel BSF.


  • Gamma rays: bursts
  • Radiation mechanisms: nonthermal
  • Shock waves
  • Turbulence


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