Radio Non-Detection of the SGR 1806-20 Giant Flare and Implications for Fast Radio Bursts

We analyse archival data from the Parkes radio telescope which was observing a location 35.6$^\circ$ away from SGR 1806-20 during its giant $γ$-ray flare of 2004 December 27. We show that no FRB-like burst counterpart was detected, and set a radio limit of 110\,MJy at 1.4 GHz, including the estimated 70\,dB suppression of the signal due to its location in the far side lobe of Parkes and the predicted scattering from the interstellar medium. The upper limit for the magnetar giant flare radio to $γ$-ray fluence ratio is $η_\mathrm{SGR} \lesssim 10^{7}\,\mathrm{Jy\,ms\,erg^{-1}\,cm^{2}}$. Based on the non-detection of a short and prompt $γ$-ray counterpart of fifteen FRBs in $γ$-ray transient monitors, we set a lower limit on the fluence ratios of FRBs to be $η_\mathrm{FRB} \gtrsim 10^{7-9}\,\mathrm{Jy\,ms\,erg^{-1}\,cm^{2}}$. The fluence ratio limit for \sgr\ is inconsistent with all but one of the fifteen FRBs. We discuss possible variations in the magnetar-FRB emission mechanism and observational caveats that may reconcile the theory with observations.