Ultraluminous x-ray sources (ULXs) in nearby galaxies shine brighter than any X-ray source in our Galaxy. ULXs are usually modeled as stellar-mass black holes (BHs) accreting at very high rates or intermediate-mass BHs. We present observations showing that NGC 5907 ULX is instead an x-ray accreting neutron star (NS) with a spin period evolving from 1.43 s in 2003 to 1.13 s in 2014. It has an isotropic peak luminosity of ∼1000 times the Eddington limit for a NS at 17.1 Mpc. Standard accretion models fail to explain its luminosity, even assuming beamed emission, but a strong multipolar magnetic field can describe its properties. These findings suggest that other extreme ULXs (x-ray luminosity ≥1041 erg s −1 ) might harbor NSs.Ultraluminous x-ray sources (ULXs) are observed in off-nucleus regions of nearby galaxiesand have x-ray luminosities in excess of a few 10 39 erg s −1 , which is the Eddington luminosity (L Edd ) for a black hole (BH) of 10 M (1). The L Edd sets an upper limit on the accretion luminosity (L acc ) of a compact object steadily accreting, since for L acc > L Edd accretion will be halted by radiation forces. For spherical accretion of fully ionized hydrogen, the limit can be written as, where σ T is the Thomson scattering cross section, m p is the proton mass, and M/M is the compact object mass in solar masses; for a 1.4 M neutron star (NS), the maximum accreting luminosity is ∼2×10 38 erg s −1 .The high luminosity of ULXs has thus been explained as accretion at or above the Eddington luminosity onto BHs of stellar origin (<80-100 M ), or onto intermediate-mass (10BHs (2, 3). However, if the emission of ULXs were beamed over a fraction b < 1 of the sky, their true luminosity, and thus also the compact object mass required not to exceed L Edd , would be reduced by the same factor. This possibility, together with the recent identification of two accreting NSs associated with the ∼10 40 erg s −1 M82 X-2 (4) and NGC 7793 P13 (5, 6) x-ray sources, have brought support to the view that most low-luminosity ULXs likely host a NS (7) 2 or a stellar-mass BH (8). For the most extreme ULXs with x-ray luminosity exceeding a few ×10 40 erg s −1 , BHs with masses in excess of 100 M are still commonly considered (9, 10).Despite several searches for coherent x-ray pulsations,no other ultraluminous x-ray source has been found to host a NS so far (11).Within the framework of "Exploring the X-ray Transient and variable Sky", EXTraS (12) Fig. 1 and Table 1). In all cases, a strong first period derivative term is present (see Table 1). The pulse shape is nearly sinusoidal, while the pulsed fraction (the semi-amplitude of the sinusoid divided by the average count rate)is energy dependent and increases from about 12% at low energies (<2.5 keV) to ∼20% in the hard band (>7 keV; Fig. 1).To derive constraints on the orbital period (P orb ), we applied a likelihood analysis to the two 2014 NuSTAR observations (see supplementary online text), which have the longest baseline.
3By assuming a circular orbit (as in the case of M...
