We construct for the first time , the sequences of stable neutron star ( NS ) models capable of explaining simultaneously , the glitch healing parameters , Q , of both the pulsars , the Crab ( Q \geq 0.7 ) and the Vela ( Q \leq 0.2 ) , on the basis of starquake mechanism of glitch generation , whereas the conventional NS models can not give such consistent explanation .
Furthermore , our models also yield an upper bound on NS masses similar to those obtained in the literature for a variety of modern equations of state ( EOSs ) compatible with causality and dynamical stability .
If the lower limit of the observational constraint of ( i ) Q \geq 0.7 for the Crab pulsar and ( ii ) the recent value of the moment of inertia for the Crab pulsar ( evaluated on the basis of time-dependent acceleration model of the Crab Nebula ) , I _ { Crab, 45 } \geq 1.93 ( where I _ { 45 } = I / 10 ^ { 45 } { g . cm } ^ { 2 } ) , both are imposed together on our models , the models yield the value of matching density , E _ { b } = 9.584 \times 10 ^ { 14 } { g cm } ^ { -3 } at the core-envelope boundary .
This value of matching density yields a model-independent upper bound on neutron star masses , M _ { max } \leq 2.22 M _ { \odot } , and the strong lower bounds on surface redshift z _ { R } \simeq 0.6232 and mass M \simeq 2.11 M _ { \odot } for the Crab ( Q \simeq 0.7 ) and the strong upper bound on surface redshift z _ { R } \simeq 0.2016 , mass M \simeq 0.982 M _ { \odot } and the moment of inertia I _ { Vela, 45 } \simeq 0.587 for the Vela ( Q \simeq 0.2 ) pulsar .
However , for the observational constraint of the ‘ central ’ weighted mean value Q \approx 0.72 , and I _ { Crab, 45 } > 1.93 , for the Crab pulsar , the minimum surface redshift and mass of the Crab pulsar are slightly increased to the values z _ { R } \simeq 0.655 and M \simeq 2.149 M _ { \odot } respectively , whereas corresponding to the ‘ central ’ weighted mean value Q \approx 0.12 for the Vela pulsar , the maximum surface redshift , mass and the moment of inertia for the Vela pulsar are slightly decreased to the values z _ { R } \simeq 0.1645 , M \simeq 0.828 M _ { \odot } and I _ { Vela, 45 } \simeq 0.459 respectively .
These results set an upper and lower bound on the energy of a gravitationally redshifted electron-positron annihilation line in the range of about 0.309 - 0.315 MeV from the Crab and in the range of about 0.425 - 0.439 MeV from the Vela pulsar .