Compression fronts from fast radio bursts

Abstract: When a fast radio burst (FRB) expands from its source through a surrounding tenuous plasma, it strongly heats and compresses the plasma at radii up to $\sim 10^{14}$cm. The likely central engines of FRBs are magnetars, and their ambient plasma at radii $r\gg 10^{10}$cm is a magnetized $e^\pm$ wind. We formulate equations describing the FRB-plasma interaction, solve them numerically, and provide an approximate analytical picture of the interaction. We find the following: (1) FRBs emitted at $r<r_{\rm stoch}\sim 10^{12}$cm induce fast stochastic heating and strong compression of the wind, sweeping it like a broom. The outcome of this interaction is determined by the energy losses of the radio wave. We evaluate the parameter space where the FRB survives its interaction with the wind. (2) At radii $r>r_{\rm stoch}$, the FRB induces regular heating to the Lorentz factor $\sim a_0$, where $a_0\propto r^{-1}$ is the wave strength parameter. At $r>r_\star\sim 10^{13}$cm, the FRB drives a quasisteady compression wave in the wind, with compression factor $C_\star\approx 1+a_0^2$. Both characteristic radii $r_{\rm stoch}$ and $r_\star$ scale with FRB luminosity $L$ as $L^{1/3}$. FRBs avoid damping if they are released into the wind medium outside $r_{\rm damp}\sim 10^{11}$cm.