FRB 121102 Casts New Light on the Photon Mass

The photon mass, $m_\gamma$, can in principle be constrained using measurements of the dispersion measures (DMs) of fast radio bursts (FRBs), once the FRB redshifts are known. The DM of the repeating FRB 121102 is known to $< 1$\%, a host galaxy has now been identified with high confidence,and its redshift, $z$, has now been determined with high accuracy: $z = 0.19273(8)$. Taking into account the plasma contributions to the DM from the Intergalactic medium (IGM) and the Milky Way, we use the data on FRB 121102 to derive the constraint $m_\gamma \lesssim 2.2 \times 10^{-14}$ eV c$^{-2}$ ($3.9 \times 10^{-50}$ kg). Since the plasma and photon mass contributions to DMs have different redshift dependences, they could in principle be distinguished by measurements of more FRB redshifts, enabling the sensitivity to $m_\gamma$ to be improved.