Bayesian framework to constrain the photon mass with a catalog of fast radio bursts

Abstract

A hypothetical photon mass, mγ, gives an energy-dependent light speed in a Lorentz-invariant theory. Such a modification causes an additional time delay between photons of different energies when they travel through a fixed distance. Fast radio bursts (FRBs), with their short time duration and cosmological propagation distance, are excellent astrophysical objects to constrain mγ. Here for the first time we develop a Bayesian framework to study this problem with a catalog of FRBs. Those FRBs with and without redshift measurement are both useful in this framework, and can be combined in a Bayesian way. A catalog of 21 FRBs (including 20 FRBs without redshift measurement, and one, FRB 121102, with a measured redshift z=0.19273±0.00008) give a combined limit mγ≤8.7×10-51 kg, or equivalently mγ≤4.9×10-15 eV/c2 (mγ≤1.5×10-50 kg, or equivalently mγ≤8.4×10-15 eV/c2) at 68% (95%) confidence level, which represents the best limit that comes purely from kinematics. The framework proposed here will be valuable when FRBs are observed daily in the future. Increment in the number of FRBs, and refinement in the knowledge about the electron distributions in the Milky Way, the host galaxies of FRBs, and the intergalactic medium, will further tighten the constraint.