Abstract
We study analytic core-envelope models obtained in Negi et al. (1989) under slow rotation. We have regarded in the present study, the lower bound on the estimate of moment of inertia of the Crab pulsar, ICrab,45≥2 (where I45=I/1045gcm2) obtained by Gunn and Ostriker (Astrophys. J. 157:1395, 1969) as a round off value of the recently estimated value of ICrab,45≥1.93 (Bejger and Haensel, Astron. Astrophys. 405:747, 2003) for the Crab pulsar. If this value of lower bound is combined with the other observational constraint obtained for the Crab pulsar (Crawford and Demianski, Astrophys. J. 595:1052, 2003), Gh=Icore/Itotal≥0.7 (where Gh is called the glitch healing parameter and represents the fractional moment of inertia of the core component in the starquake mechanism of glitch generation), the models yield the mass, M, and surface redshift, za, for the Crab pulsar in the range, M=1.79M⊙–1.88M⊙; za=0.374–0.393 (I45=2) for an assigned value of the surface density, Ea=2×1014gcm2 (like, Brecher and Caporaso, Nature 259:377, 1976). This assigned value of surface density, in fact, is an outcome of the first observational constraint imposed on our models that further yields the mass M=1.96M⊙ and surface redshift za= 0.414 (I45=2) for the values of Gh≈0.12, which actually belongs to the observed 'central' weighted mean value for the Vela pulsar. These values of mass and surface redshift predict the energy of a gravitationally redshifted electron-positron annihilation line, E(MeV)=0.511/(1+za) (Lindblom, Astrophys. J. 278:364, 1984) in the range about 0.396–401 MeV from the Crab and about 0.389 MeV from the Vela pulsar. The evidence of a line feature at about 0.40 MeV from the Crab pulsar (Leventhal et al., Astrophys. J. 216:491, 1977) agrees quite well with the finding of this study.