Fast Radio Bursts from Induced Upscattering. I. Magnetar Polar Fireballs

Abstract

The extreme brightness temperatures of fast radio bursts (FRBs) demand a coherent process that converts magnetar burst energy into millisecond radio emission. We propose that FRBs can be produced within magnetar magnetospheres by induced (stimulated) upscattering in a relativistic fireball outflow. In this paper, we focus on induced Compton upscattering in an electron--positron fireball launched from the polar region of a magnetar. Radiation from the X-ray burst accelerates the polar fireball outflow to Lorentz factors of $Γ\sim10$--$10^3$. Low-frequency seed waves, such as fast magnetosonic or Alfvén waves, entering the outflow from the side or against its motion undergo induced scattering and are Lorentz-boosted by the relativistic bulk motion from $ν_0\sim10\mathrm{kHz}$ to $ν_{\rm obs}\simΓ^2ν_0\sim\mathrm{GHz}$. Combining the polar fireball dynamics with the linear growth and nonlinear saturation of the induced scattering instability, we derive the FRB luminosity $L_{\rm FRB}^{\rm iso}$ and fractional spectral bandwidth $Δν/ν_{\rm c}$. By considering the possible range of pair densities and temperatures, we find that this polar channel can account for the luminosity of Galactic FRB~20200428 and reach luminosities comparable to those of the brightest extragalactic FRBs. If the pair-loaded region is narrower than the relativistic beaming angle $1/Γ$, the model also produces a narrow spectrum and predicts $L_{\rm FRB}^{\rm iso}\propto(Δν/ν_{\rm c})^2$, a trend consistent with observations of repeating FRBs. The induced upscattering model thus connects magnetar X-ray bursts to FRBs through a coherent emission process grounded in plasma physics and makes observationally testable predictions.