Implications from the Upper Limit of Radio Afterglow Emission of FRB 131104/Swift J0644.5-5111

A gamma-ray transient, Swift J0644.5-5111, has been claimed to be associated with FRB 131104. However, a long-term radio imaging follow-up observation only placed an upper limit on the radio afterglow flux of Swift J0644.5-5111. Applying the external shock model, we perform a detailed constraint on the afterglow parameters for the FRB 131104/ Swift J0644.5-5111 system. We find that for the commonly used microphysics shock parameters (e.g., epsilon(e) = 0.1, epsilon(B) = 0.01, and p - 2.3), if the fast radio burst (FRB) is indeed cosmological as inferred from its measured dispersion measure (DM), the ambient medium number density should be <= 10(-3)cm(-3), which is the typical value for a compact binary merger environment but disfavors a massive star origin. Assuming a typical ISM density, one would require that the redshift of the FRB be much smaller than the value inferred from DM (z << 0.1), implying a non-cosmological origin of DM. The constraints are much looser if one adopts smaller epsilon(B) and epsilon(e) values, as observed in some gamma-ray burst afterglows. The FRB 131104/Swift J0644.5-5111 association remains plausible. We critically discuss possible progenitor models for the system.National Basic Research Program ("973" Program) of China [2014CB845800]; National Natural Science Foundation of China [11543005, 11603003, 11633001]SCI(E)ARTICLE283