Full Polar Cap Cascade Scenario: Γ-ray and X-ray Luminosities from Spin-powered Pulsars

Canonical polar cap cascade models involve curvature radiation (CR) or inverse Compton scattering (ICS) of the primary particles and synchrotron radiation (SR) of the higher generation pairs. Here we modify such a cascade picture to include the ICS of the higher generation pairs. In such a “full-cascade” scenario, not only the perpendicular portion of the energy of the pairs goes to high energy radiation via SR, but the parallel portion of the energy of the pairs can also contribute to high energy emission via ICS with the soft thermal photons from either the full neutron star surface or the hot polar cap. The efficiency of converting particles’ kinetic energy to radiation by ICS is very high if the scatterings occur in the “resonant” regime. As a result, almost 100% of the energy input from the pulsar inner accelerators could be converted to high energy emission. An important output of such a scenario is that the soft tail of the ICS spectrum can naturally result in a non-thermal X-ray component which can contribute to the luminosities observed by ROSAT and ASCA. Here we present an analytic description of such a full polar cap cascade scenario using the recursion relationships between adjacent generations following the approach first proposed by Lu et al. (1994), but develop it to be able to delineate the complex full-cascade process. The acceleration model we adopted is the space-charge-limited flow model proposed by Harding & Muslimov (1998). We present the theoretical predictions of the γ-ray luminosities, the thermal and non-thermal X-ray luminosities for the known spin-powered X-ray pulsars (8 of them are also γ-ray pulsars), and compare them with the observations from CGRO, ROSAT and ASCA. We estimate the non-thermal X-ray luminosity by including all the possible ICS branches contributing to a certain energy band, and estimate both the full surface and hot polar cap thermal X-ray luminosities by adopting a standard neutron star cooling scenario, and by treating self-consistent polar cap heating in the Harding & Muslimov (1998) model, respectively. Our results show that the observed different dependences of the high energy luminosities on the pulsar spin-down luminosities, i.e., Lγ ∝ (Lsd) 1/2 and Lx ∼ 10 Lsd, are well reproduced. We found that, for normal pulsars, both the hard (ASCA band) and the soft (ROSAT band) X-ray luminosities are dominated by the non-thermal X-rays of ICS origin, although for some pulsars, thermal components due to either neutron star cooling or polar cap heating can have comparable luminosities so that they are detectable. For the millisecond pulsars, our predicted upper limits of the thermal luminosities due to polar cap heating are usually higher than the ICS-origin non-thermal components if there are no strong multipolar magnetic field components near the neutron star surface, thus the pulsed soft X-rays in the ROSAT band from most of the millisecond pulsars might be of thermal origin. Subject headings: pulsar: general radiation mechanism: non-thermal X-rays: stars