Constraining the Environmental Properties of FRB 131104 Using the Unified Dynamical Afterglow Model

Abstract

Multi-band observations of the fast radio burst (FRB) 131104 show that this burst may be associated with a gamma-ray transient entitled Swift J0644.5-5111. Follow-up observations for potential X-ray and radio counterparts of FRB 131104/Swift J0644.5-5111 got null results and provided the upper limits of the emission flux at 5.5 GHz, 7.5 GHz, $U$-band, and X-ray band. By assuming this association and using these upper limits, environmental properties (the fraction of energyin a magnetic field $\varepsilon_{\rm B}$ and the number density $n$) of the progenitor system of FRB 131104/Swift J0644.5-5111 were constrained in the context of the standard afterglow model that neglects the non-relativistic effect and jet effect by several groups. In this paper, we adopt a unified afterglow model that takes into account the non-relativistic effect and jet effect and use the upper limits of four bands (5.5 GHz, 7.5 GHz, $U$-band, and X-ray) to obtain more stringent constraints on the parameter space spanned by $\varepsilon_{\rm B}$ and $n$. We thus suggest that FRB 131104/Swift J0644.5-5111 might originate from a black hole-neutron star merger event. Moreover, we calculate multi-band emissions from a kilonova powered by the radioactivity of $r$-process elements synthesized in the ejected neutron-rich material and find that the $U$-band emission from the putative kilonova is significantly lower than the upper limit of the observations.