Toward an understanding of thermal X-ray emission of pulsars

We present a theoretical model for the thermal X-ray emission and cooling of isolated pulsars, assuming that pulsars are solid quark stars. We calculate the heat capacity for such a quark star, and the results show that the residual thermal energy cannot sustain the observed thermal X-ray luminosities seen in typical isolated X-ray pulsars. We conclude that other heating mechanisms must be in operation if the pulsars are in fact solid quark stars. Two possible heating mechanisms are explored. Firstly, for pulsars with little magnetospheric activities, accretion from the interstellar medium or from the material in the associated supernova remnants may power the observed thermal emission. In the propeller regime, a disk-accretion rate ${\dot M}\sim$1% of the Eddington rate with an accretion onto the stellar surface at a rate of $\sim 0.1% {\dot M}$ could explain the observed emission luminosities of the dim isolated neutron stars and the central compact objects. Secondly, for pulsars with significant magnetospheric activities, the pulsar spindown luminosities may have been as the sources of the thermal energy via reversing plasma current flows. A phenomenological study between pulsar bolometric X-ray luminosities and the spin energy loss rates presents the probable existence of a 1/2-law or a linear law, i.e. $L_{\rm bol}^{\infty}\propto\dot{E}^{1/2}$ or $L_{\rm bol}^{\infty}\propto\dot{E}$. This result together with the thermal properties of solid quark stars allow us to calculate the thermal evolution of such stars. Thermal evolution curves, or cooling curves, are calculated and compared with the `temperature-age' data obtained from 17 active X-ray pulsars. It is shown that the bolometric X-ray observations of these sources are consistent with the solid quark star pulsar model.