Tight constraint on photon mass from pulsar spindown

Pulsars are magnetized rotating compact objects. They spin down due to magnetic dipole radiation and wind emission. If photon has a nonzero mass, the spin down rate would be smaller than the zero mass case. We show that an upper limit of the photon mass, i.e. $m_\gamma\lesssim h/Pc^2$, could be placed if a pulsar with period $P$ is observed to spin down. Recently, a white dwarf (WD) --- M dwarf binary, AR Scorpii was found to emit pulsed broadband emission with pulses (Marsh et al. 2016). The spin-down luminosity of the WD can comfortably power the non-thermal radiation from the system. Applying our results to the WD pulsar with $P=117~\rm{s}$, we obtain a stringent upper limit of the photon mass of $m_\gamma<6.3\times10^{-50}~\rm{g}$ assuming vacuum dipole spindown, or $m_\gamma<6.7\times10^{-50}~\rm{g}$ for $\eta=0.5$ assuming wind spindown, where $\eta$ is the ratio of wind spindown luminosities between the cases with and without photon mass.

Comments: 6 pages, 5 figures, 1 table. Comments are welcomed

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