NICER study of pulsed thermal X-rays from Calvera: a neutron star born in the Galactic halo?

Calvera (1RXS J141256.0+792204) is an isolated neutron star detected only through its thermal X-ray emission. Its location at high Galactic latitude ($b=+37^\circ$) is unusual if Calvera is a relatively young pulsar, as suggested by its spin period (59 ms) and period derivative ($3.2 \times 10^{-15}$ Hz s$^{-1}$). Using the Neutron Star Interior Composition Explorer (NICER), we obtained a phase-connected timing solution spanning four years which allowed us to measure the second derivative of the frequency $\ddot\nu = -2.5 \times 10^{-23}$ Hz s$^{-2}$ and to reveal timing noise consistent with that of normal radio pulsars. A magnetized hydrogen atmosphere model, covering the entire star surface, provides a good description of the phase-resolved spectra and energy-dependent pulsed fraction. However, we find that a temperature map more anisotropic than that produced by a dipole field is required, with a hotter zone concentrated towards the poles. By adding two small polar caps, we find that the surface effective temperature and that of the caps are ~0.1 and ~0.36 keV, respectively. The inferred distance is ~3.3 kpc. We confirm the presence of an absorption line at 0.7 keV associated to the emission from the whole star surface, difficult to interpret as a cyclotron feature and more likely originating from atomic transitions. We searched for pulsed $\gamma$-ray emission by folding seven years of Fermi-LAT data using the X-ray ephemeris, but no evidence for pulsations was found. Our results favour the hypothesis that Calvera is a normal rotation-powered pulsar, with the only peculiarity of being born at a large height above the Galactic disk.