FRB$-$SRB$-$XRB: Geometric and Relativistic Beaming Constraints of Fast Radio Bursts from the Galactic Magnetar SGR J1935+2154

Abstract: The detection of a fast radio burst (FRB), FRB 200428, coincident with an X-ray burst (XRB) from the Galactic magnetar soft gamma repeater (SGR) SGR J1935+2154 suggests that magnetars can produce FRBs. Many XRBs have been detected from the source, but very few were found to be associated with bursty radio emission. Meanwhile, a number of weaker radio bursts have been detected from the source, which could in principle be slow radio bursts (SRBs): FRBs detected at viewing angles outside the FRB jet cone. In this paper, we use these X-ray and radio observations to constrain the geometric and relativistic beaming factors of FRBs under two hypotheses. First, we assume that all SRBs should be associated with XRBs like FRB 200428. We use the FRB-SRB closure relations to identify two SRBs and derive that FRB beaming must be geometrically narrow, $\theta_j \lesssim 10^{-2}$ rad, and follow $\theta_j\Gamma\sim2$. Second, we assume a less stringent constraint for SRBs by not requiring that they are associated with XRBs. We identify a total of seven SRBs, five of which have Gaussian-like spectra, and derive that FRB beaming factors again follow $\theta_j\Gamma\sim2$.