Constraining the photon rest mass using timing observations of PSR J2241-5236

A precise measurement of the photon rest mass (mγ) would have profound implications for testing fundamental physical theories. In this study, we derive the theoretical expression for the propagation of photons with non-zero rest mass through a plasma. We find that the second-order time delay term contains a coupling relation between the plasma medium and the photon rest mass, which may constitute an important component of pulsar timing residual errors. Within this framework, we use high-precision, multi-band timing observations of the millisecond pulsar PSR J2241-5236, along with its distance estimates from different measurement methods, to give a tight upper limit on the photon rest mass: mγ≤3.14×10−47 kg (1.76×10−11 eV/c2). Our finding underscores that pulsars with precise distance measurements will play a critical role in constraining the photon mass. This result also provides a theoretical foundation for future campaigns to constrain the photon mass with large high-sensitivity radio telescopes and pulsar timing arrays.