Free–free absorption in hot relativistic flows: application to fast radio bursts

Abstract

ABSTRACT Magnetic flares create hot relativistic shocks outside the light cylinder radius of a magnetized star. Radio emission produced in such a shock or at a radius smaller than the shock undergoes free–free absorption while passing through the shocked medium. In this work, we demonstrate that this free–free absorption can lead to a negative drift in the frequency-time spectra. Whether it is related to the downward drift pattern observed in fast radio bursts (FRBs) is unclear. However, if the FRB down-drifting is due to this mechanism then it will be pronounced in those shocks that have isotropic kinetic energies $ \gtrsim 10^{44}$ erg. In this model, for an internal shock with a Lorentz factor ∼100, the normalized drift rate $|{\rm DR_{\rm obs}}|/\nu _{\rm mean}$ is ∼10−2 per ms, where νmean is the central frequency of the radio pulses. The corresponding radius of the shocked shell is, therefore, in the range of 1010 cm and 1011 cm. This implies that, for an outflow consisting of hydrogen ion, the upper limit on the mass of the relativistic shocks is a few ×  10−10 M⊙, which is considerably low compared to that ejected from SGR 1806-20 during the 2004 outburst.