Magnetar giant flare origin for GRB 200415A inferred from a new scaling relation and its implications

Soft gamma-ray repeaters (SGRs) are mainly a Galactic population and originate from neutron stars with intense ($B\simeq 10^{15}{\rm \ G}$) magnetic fields ('magnetars'). Occasionally, a giant flare occurs with enormous intensity, displaying a short hard spike, followed by a weaker, oscillatory phase which exhibits the rotational period of the neutron star. If the magnetar giant flares occur in nearby galaxies, they would appear as cosmic short-hard gamma-ray bursts (GRBs) without detecting the weak oscillatory phase. Recently, a short-hard GRB named GRB 200415A was detected, with a position coincident with the Sculptor Galaxy (NGC 253), rasing the question whether it is a classic short GRB or a magentar giant flare. Here we show that magnetar giant flares follow a scaling relation between the spectral peak energy and the isotropic energy in $1\,{\rm keV} - 10\,{\rm MeV}$, i.e., $E_{\rm p}\propto E_{\rm iso}^{1/4}$, and locate in a distinct region of the $E_{\rm p}-E_{\rm iso}$ plane from that of classic short GRBs. The relation can be well understood in the model that giant flares arise from the photosphere emissions of relativistically expanding fireball. GRB 200415A, together with two other candidate giant flares (GRB 051103 and GRB 070201) follow this relation, which strongly favor the giant flare origin of these GRBs. The GeV emission detected by \emph{Fermi}/LAT from GRB 200415A at $18-285 \,$s can also be explained in the giant flare scenario. The total energy in the GeV emission implies a baryon load of $\sim 10^{23}{\rm g}$ in the giant flare fireball of GRB 200415A.