2021MNRAS.508L..48K

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 ≳10⁴⁴ erg. In this model, for an internal shock with a Lorentz factor ∼100, the normalized drift rate | DR_obs|/ν_mean is ∼10^–2 per ms, where ν_mean 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 x 10^–10 M_☉, which is considerably low compared to that ejected from SGR 1806-20 during the 2004 outburst.