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X-ray and Rotational Luminosity Correlation and Magnetic Heating of the Radio Pulsars

Previous works have suggested a correlation between the X-ray luminosity Lx and the rotational luminosity Lrot of the radio pulsars.However, none of the obtained regression lines are statistically acceptable due to large scatters. We construct a statistical model which has an intrinsic Lx-Lrot relation and reproduces the observed Lx distribution about it by using a Monte Carlo simulator, which takes into account the effects obscuring the intrinsic relation,i.e., the anisotropy of radiation, additional heating, uncertainty in distance and detection limit of the instruments. From the ATNF pulsar catalog we collect 57 `ordinary radio pulsars' with significant detection and 42 with upper limits.The sample does not include the high-magnetic field pulsars (>10^{13} G), which are separately analyzed. We obtain a statistically acceptable relation Lx (0.5 - 10 keV)= 10^{31.69} (Lrot / L_0)^{c_1} with c_1 = 1.03 \pm 0.27 and L_0 =10^{35.38}. The distribution about the obtained Lx-Lrot relation is reproduced well by the simulator. Pulsars with abnormally high Lx fall into two types: one is the soft gamma-ray pulsars, and the other is thermally bright pulsars in comparison with the standard cooling curve. On the other hand, pulsars showing low Lx are found to have dim pulsar wind nebulae. We argue that there is an unknown mechanism that governs both the magnetospheric emission and the pulsar wind nebulae, and it might involve the production rate of electron-positron pairs. The high-field pulsars form a distinctive population other than the ordinary pulsars due to their excess luminosities.