SURFACE-TEMPERATURE OF A MAGNETIZED NEUTRON-STAR AND INTERPRETATION OF THE ROSAT DATA .1. DIPOLAR FIELDS

We model the temperature distribution at the surface of a magnetized neutron star and study the effects on the observed X-ray spectra and light curves. Generalrelativistic effects, i.e., redshift and lensing, are fully taken into account. Atmospheric effects on the emitted spectral flux are not included: we consider only blackbody emission at the local effective temperature. In this first paper we restrict ourselves to dipolar fields. General features are studied and compared with the ROSAT data from the pulsars 0833-45 (Vela), 0656+14, 0630+178 (Geminga), and 1055-52, the four cases for which there is strong evidence that thermal radiation from the stellar surface is detected. The composite spectra we obtain are not very different from a blackbody spectrum at the star's effective temperature. We conclude that, as far as blackbody spectra are considered, temperature estimates using single-temperature models give results practically identical to our composite models. The change of the (composite blackbody) spectrum with the star's rotational phase is also not very large and may be unobservable in most cases. Gravitational lensing strongly suppresses the light curve pulsations. If a dipolar field is assumed, pulsed fractions comparable to the observed ones can be obtained only with stellar radii larger than those which are predicted by current models of neutron star structure, or with low stellar masses. Moreover, the shapes of the theoretical light curves with dipolar fields do not correspond to the observations. The use of magnetic spectra may raise the pulsed fraction sufficiently but will certainly make the discrepancy with the light curve shapes worse: dipolar fields are not sufficient to interpret the data. Many neutron star models with a meson condensate or hyperons predict very small radii, and hence very strong lensing, which will require highly nondipolar fields to be able to reproduce the observed pulsed fractions, if possible at all: this may be a new tool to constrain the size of neutron stars. The pulsed fractions obtained in all our models increase with photon energy: the strong decrease observed in Geminga at energies 0.3-0.5 keV is definitely a genuine effect of the magnetic field on the spectrum in contradistinction to the magnetic effects on the surface temperature considered her. Thus, a detailed analysis of thermal emission from the four pulsars we consider will require both complex surface held configurations and the inclusion of magnetic effects in the atmosphere (i.e., on the emitted spectrum).