Surface Temperature of a Magnetized Neutron Star and Interpretation of the Rosat Data. Ii

We complete our study of pulsars’ non-uniform surface temperature and of its effects on their soft X-ray thermal emission. Our previous work had shown that, due to the effect of gravitational lensing, dipolar fields 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 M⊙ , we show here that the inclusion 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 as PSR 0656+14. Given the observed values, this may indicate that the neutron stars in Geminga and PSR 0656+14 have radii significantly larger than 7 km and, given that very specific quadrupole components are required to increase Pf , even radii of the order of 10 km may be unlikely in all four cases. However, effects not included in our study may possibly seriously invalidate this temptative conclusion. We confirm our previous finding that the pulsed fraction always increases with photon energy, below about 1 keV, when blackbody emission is used and we show that it is due to the hardenning of the blackbody spectrum with increasing temperature. The observed decrease of pulsed fraction may thus suggest that the emitted spectrum softens with increasing temperature and that this observed effect must be of atmospheric origin. Finally, we apply our model to reassess the magnetic field effect on the outer boundary condition used in neutron star cooling models and show that, in contradistinction to several previous claims, it is very small and most probably results in a slight reduction of the heat flow through the envelope. Submitted to The Astrophysical Journal. Subject headings: stars: neutron — pulsars: individual: Vela, 0656+14, Geminga, 1055-52 — X-rays: stars — dense matter — stars: magnetic fields