Discovery of 3 s pulsations from the Brightest Hard X-ray Source in M31

We report the discovery with XMM-Newton of 3-s X-ray pulsations from 3XMM J004232.1+411314, a dipping source that dominates the hard X-ray emission of M31. This finding unambiguously assesses the neutron star (NS) nature of the compact object. We also measured an orbital modulation of 4.15 h and a projected semi-axis at $a_{mathrm{X}} sin i= 0.6$ lt-s, which implies a low-mass companion of about 0.2$-$0.3$M_{odot}$ assuming a NS of 1.5 $M_{odot}$ and an orbital inclination $i=70^{circ}-80^{circ}$. The barycentric orbit-corrected pulse period decreased by $sim$28 ms in about 16 yr, corresponding to an average spin-up rate of $dot{P} sim -6 times 10^{-11}$ s s$^{-1}$ ; pulse period variations, probably caused to by X-ray luminosity changes, were observed on shorter time scales. We identify two possible scenarios for the source: a mildly magnetic NS with $B_{mathrm{p}}simeq$ few $times10^{10}$ G if the pulsar is far from its equilibrium period $P_{mathrm{eq}}$, and a relatively young highly magnetic NS with $B_{mathrm{eq}}simeq 10^{13}$ G if spinning close to $P_{mathrm{eq}}$.