2021MNRAS.501.4998Z

We analyse new XMM-Newton and archival Chandra observations of the middle-aged γ-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 0.15-0.5 keV band, there is a single pulse per period and the pulsed fraction is ≃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 (>=0.7 keV) it is described by a power law with the photon index Γ ≃ 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 ≃(2-3) x 10⁵ K. This makes J1957+5033 the coldest among all known thermally emitting neutron stars with ages below 1 Myr. Using the interstellar extinction-distance relation, we constrain the distance to the pulsar in the range of 0.1-1 kpc. 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 ∼8 arcmin from J1957+5033. Its spectrum can be described by a power law with a photon index Γ = 1.9 ± 0.5 suggesting that it is likely a pulsar wind nebula powered by J1957+5033.