Middle Aged Gamma-Ray Pulsar J1957+5033 In X-Rays: Pulsations, Thermal Emission, And Nebula

We analyse new XMM-Newton and archival Chandra observations of the middle-aged gamma-ray radio-quiet pulsar J1957+5033. We detect, for the first time, X-ray pulsations with the pulsar spin period of the point-like source coinciding by position with the pulsar. This confirms the pulsar nature of the source. In the 0.15-0.5keV band, there is a single pulse per period and the pulsed fraction is approximate to 18 +/- 6 per cent. In this band, the pulsar spectrum is dominated by a thermal emission component that likely comes from the entire surface of the neutron star, while at higher energies (greater than or similar to 0.7keV) it is described by a power law with the photon index Gamma approximate to 1.6. We construct new hydrogen atmosphere models for neutron stars with dipole magnetic fields and non-uniform surface temperature distributions with relatively low effective temperatures. We use them in the spectral analysis and derive the pulsar average effective temperature of approximate to(2-3) x 10(5)K. This makes J1957+5033 the coldest among all known thermally emitting neutron stars with ages below 1Myr. Using the interstellar extinction-distance relation, we constrain the distance to the pulsar in the range of 0.1-1kpc. We compare the obtained X-ray thermal luminosity with those for other neutron stars and various neutron star cooling models and set some constraints on the latter. We observe a faint trail-like feature, elongated similar to 8arcmin from J1957+5033. Its spectrum can be described by a power law with a photon index Gamma = 1.9 +/- 0.5 suggesting that it is likely a pulsar wind nebula powered by J1957+5033.