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

4. Summary

We have used a three-dimensional outer gap model to calculate the observed light curves and spectra of the Crab-like pulsars: PSR B1509-58 and PSR B0540-69. According to our model, there are three components for X-ray emission for Crab-like pulsars: thermal X-rays from the stellar surface, non-thermal X-rays produced near the stellar surface through synchrotron radiation and non-thermal photons produced above the outer gap through a synchrotron self-Compton mechanism. We have calculated the light curves and spectra of these three components for PSR B1509-58 and PSR B0540-69 respectively. Compared to non-thermal components, the thermal component can be negligible. Furthermore, the non-thermal photon emission above the outer gap dominates the non-thermal photons produced near the stellar surface. The light curves and spectra depend on the inclination angle (), viewing angle () as well as the thickness of the emission region. We found that the inclination and viewing angles are and respectively and the mean thickness of the photon emission region is for PSR B1509-58, and and respectively and for PSR B0540-68. However, we stress that the observed light curves of these two pulsars are broader than our model light curves. If the radio beam is actually wider than or radio emission comes from the region very near the stellar surface where multiple field dominates the dipolar field, a smaller inclination angle is allowed and this gives a wider X-ray light curves (cf. Fig. 6 of CRZ).

Using the CHR model, Cheng & Ding (1994) and Cheng & Wei (1995) have calculated the phase-averaged spectrum of PSR B1509-58 by assuming that it is a Vela-like and a Crab-like pulsar respectively. Generally, if the mean distance to the outer gap approaches the light cylinder radius, and then the smaller magnetic field makes the Vela-like mechanism more favorable, otherwise the Crab-like mechanism is more likely. In their calculations, however, they did not consider the offset of the X-rays/-rays with respect to the radio pulse. Romani & Yadigaroglu (1995) have considered the observed offset and concluded that and based on the geometry of the outer gap, which is consistent with our result. For PSR B0540-69, Cheng & Wei (1995) have calculated the phase-averaged spectrum by assuming that it is a Crab-like pulsar, which is consistent with our findings.

© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000
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