Astron. Astrophys. 363, 575-584 (2000)

1. Introduction

It is commonly accepted that a three dimensional outer gap model is necessary in order to explain the observed light curves and phase-resolved spectra of -ray pulsars. Outer gaps, which are powerful acceleration regions, can form in the vicinity of a "null charge surface" () (Holloway 1973; Cheng et al. 1976) because the charge carriers on each side of the null charge surface have opposite charges. Current passing through this surface removes charge in the vicinity of the null surface and a charge vacuum forms there. Cheng et al. (1986a, 1986b, hereafter CHR I and CHR II) proposed an outer gap model to explain the observed data of the Crab and Vela pulsars (also see Ho 1989). Their model assumed that the radiation regions are thin in the longitudinal direction. The double peak structure in the pulse profile predicted by the model results from two topologically disconnected outer gaps, each of which is associated with different magnetic poles. However, Romani and co-workers (Chiang & Romani 1992, 1994; Romani & Yadigaroglu 1995; Romani 1996) have shown that one outer gap with only outgoing current can itself produce a broad, irregularly-shaped emission beam which is particularly dense near the edge, so that two -ray peaks would be observed when the line of sight from the Earth crosses these enhanced -ray beam regions; the inner region of the beam provides a significant amount of emission between the peaks. Recently, Cheng et al. (2000) (hereafter CRZ) have re-considered conditions in the three dimensional magnetosphere using various physical processes to determine the three-dimensional geometry of the outer gap (including pair production which depends sensitively on the local electric field, the local radius of curvature, surface field structure, and reflection of pairs because of mirroring and resonant scattering). They have shown that two outer gaps and both outgoing and incoming currents are, in principle, allowed, but that outgoing currents dominate the emitted radiation intensities. The observed features of the Crab pulsar can be well explained by this model.

Based on the outer gap model of high-energy radiation from the pulsars which we have proposed (Zhang & Cheng 1997; see also Cheng et al. 1998), we (Cheng & Zhang 1999) have studied in detail the X-ray production near or on the pulsar surface due to backflow high-energy electrons/positrons from the outer gaps. In particular, the soft thermal X-ray spectra of Geminga and PSR B1055-52 are consistent with this backflow current heating model. Here we report the X-ray emissions in the three dimensional magnetosphere, and give X-ray light-curves and spectra, which would be tested by measurements by newly launched satellites, e.g. XMM, Chandra etc. For the known -ray pulsars, two pulsars may be Crab-like pulsars: PSR B0540-69 and PSR B1509-58. PSR B0540-69 in the Large Magellanic Cloud (LMC) is one of the youngest and most luminous rotation-powered pulsars, its period and period derivative are 50 ms and  s s^-1, which implies a characteristic age of yr. PSR B1509-58 is a pulsar with a period of 150 ms and period derivative of  s s^-1. Its characteristic age of yr makes it the second youngest known pulsar behind only the Crab pulsar. In Sect. 2, we describe an outer gap model of Crab-like pulsars, and then apply this model in Sect. 3 to explain the light curves and spectra of PSR B1509-58 and PSR B0540-69. Our results are summarized in Sect. 4.

© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000
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