Surface Temperature of a Magnetized Neutron Star and Interpretation of the ROSAT Data. II.

Abstract

We complete our study of pulsarsÏ nonuniform surface temperature and its e †ects on their soft X-ray thermal emission. Our previous work showed that, because of the e †ect of gravitational lensing, dipolar Ðelds cannot reproduce the strong pulsations observed in the four nearby pulsars for which surface thermal radiation has been detected : PSR 0833[45 (Vela), PSR 0656]14, PSR 0630]178 (Geminga), and PSR 1055[52. Assuming a standard neutron star mass of 1.4 we show here that the inclusion M _ , of a quadrupolar component, if it is suitably oriented, is sufficient to increase substantially the pulsed fraction, PF, up to or above the observed values if the stellar radius is 13 km or even 10 km. For models with a radius of 7 km, the maximum pulsed fraction obtainable with (isotropic) blackbody emission is of the order of 15% for orthogonal rotators (Vela, Geminga, and PSR 1055[52) and only 5% for an inclined rotator such as PSR 0656]14. Given the observed values, this may indicate that the neutron stars in Geminga and PSR 0656]14 have radii signiÐcantly larger than 7 km, and given that very spe-ciÐc quadrupolar components are required to reproduce the large observed PF, even radii of the order of 10 km may be unlikely in all four cases. However, e †ects not included in our study might seriously invalidate this tentative conclusion. We conÐrm our previous Ðnding that the pulsed fraction always increases with photon energy, up to D1 keV, when blackbody emission is used, and we show that this is due to the hardening of the black-body spectrum with increasing temperature. The observed decrease of the pulsed fraction may thus suggest that the emitted spectrum is softer in the warmest regions than in colder ones and that this observed e †ect must be of magnetospheric origin, probably due to the magnetic Ðeld. Finally, we apply our model to reassess the magnetic ÐeldÏs e †ect on the outer boundary condition used in neutron star cooling models and show that, in contradistinction to several previous claims, it is a small e †ect.