Robust Limits on Photon Mass from Statistical Samples of Extragalactic Radio Pulsars

The photon zero-mass hypothesis has been investigated for a long time using the frequency-dependent time delays of radio emissions from astrophysical sources. However, the search for a rest mass of the photon has been hindered by the similarity between the frequency-dependent dispersions due to the plasma and nonzero photon mass effects. Considering the contributions to the observed dispersion measure from both the plasma and nonzero photon mass effects, and assuming the dispersion induced by the plasma effect is an unknown constant, we obtain a robust limit on the photon mass by directly fitting a combination of the dispersion measures of radio sources. Using the observed dispersion measures from two statistical samples of extragalactic pulsars, here we show that at the 68\% confidence level, the constraints on the photon mass can be as low as $m_{\gamma}\leq1.51\times10^{-48}~\rm kg\simeq8.47\times10^{-13}~{\rm eV}/c^{2}$ for the sample of 22 radio pulsars in the Large Magellanic Cloud and $m_{\gamma}\leq1.58\times10^{-48}~\rm kg\simeq8.86\times10^{-13} {\rm eV}/c^{2}$ for the other sample of 5 radio pulsars in the Small Magellanic Cloud, which are comparable with that obtained by a single extragalactic pulsar. Furthermore, the statistical approach presented here can also be used when more fast radio bursts with known redshifts are detected in the future.