Analytic core-envelope models with continuity of density at the boundary

Monthly Notices of the Royal Astronomical Society

2008

We show that the mass–radius (M–R) relation corresponding to the stiffest equation of state (EOS) does not provide the necessary and sufficient condition of dynamical stability for equilibrium configurations, because such configurations cannot satisfy the ‘compatibility criterion’. In this regard, we construct sequences composed of core–envelope models such that, like the central condition belonging to the stiffest EOS, each member of these sequences satisfies the extreme case of the causality condition, v=c= 1, at the centre. We thereafter show that the M–R relation corresponding to the said core–envelope model sequences can provide the necessary and sufficient condition of dynamical stability only when the ‘compatibility criterion’ for these sequences is ‘appropriately’ satisfied. However, the ‘compatibility criterion’ can remain satisfied even when the M–R relation does not provide the necessary and sufficient condition of dynamical stability for the equilibrium configurations. In continuation of the results of a previous study, these results explicitly show that the ‘compatibility criterion’independently provides, in general, the necessary and sufficient condition of hydrostatic equilibrium for any regular sequence. In addition to its fundamental result, this study can explain simultaneously the higher and the lower values of the glitch healing parameter observed for the Crab‐like and Vela‐like pulsars respectively, on the basis of the starquake model of glitch generation.

Section: Results and Conclusionmentioning

confidence: 99%

Section: Removal Of Abnormalities From the Stiffest Eos And Boundamentioning

confidence: 99%

Hydrostatic equilibrium of causally consistent and dynamically stable neutron star models

Monthly Notices of the Royal Astronomical Society

2008

“…Examples of such two-density models are also available in the literature (see, e.g., ref. [22] (2) the central density of the configuration should be independent of the surface density. Obviously, the condition (1) will be satisfied by the configurations pertaining to an infinite value of the central density (that is, the singular solutions), and/or by the two-density (or multiple-density) distributions corresponding to a surface density which turns out to be independent of the central density (because, the regular configurations governed by a single exact solution or EOS pertaining to this category are not possible).…”

Section: Boundary Conditions: the Valid And Invalid Assumptions For Mmentioning

confidence: 99%

“…The future study of such core-envelope models [see, for example, the models described in [22] and [23]], based upon the criterion obtained in [20] could be interesting regarding two density structures of neutron stars and other stellar objects compatible with the structure of GR.…”

Section: Criterion For Static Spherical Configurations To Be Consis-tmentioning

confidence: 99%

Exact Solutions of Einstein's Field Equations

2006

Int J Theor Phys

We examine various well known exact solutions available in the literature to investigate the recent criterion obtained in ref. [20] which should be fulfilled by any static and spherically symmetric solution in the state of hydrostatic equilibrium.It is seen that this criterion is fulfilled only by (i) the regular solutions having a vanishing surface density together with the pressure, and (ii) the singular solutions corresponding to a non-vanishing density at the surface of the configuration . On the other hand, the regular solutions corresponding to a non-vanishing surface density do not fulfill this criterion. Based upon this investigation, we point out that the exterior Schwarzschild solution itself provides necessary conditions for the types of the density distributions to be considered inside the mass, in order to obtain exact solutions or equations of state compatible with the structure of general relativity.The regular solutions with finite centre and non-zero surface densities which do not fulfill the criterion [20], in fact, can not meet the requirement of the 'actual mass' set up by exterior Schwarzschild solution. The only regular solution which could be possible in this regard is represented by uniform (homogeneous) density distribution.The criterion [20] provides a necessary and sufficient condition for any static and spherical configuration (including core-envelope models) to be compatible with the structure of general relativity. Thus, it may find application to construct the appropriate core-envelope models of stellar objects like neutron stars and may be used to 1 test various equations of state for dense nuclear matter and the models of relativistic stellar structures like star clusters.

“…

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, I Crab,45 ≥ 2 (where I 45 = I/10 45 gcm 2 ) obtained by Gunn and Ostriker (1969) as a round off value of the recently estimated value of I Crab,45 ≥ 1.93 (Bejger & Haensel 2003) for the Crab pulsar.

…”

mentioning

confidence: 99%

Analytic core envelope models for the Crab and the Vela pulsars

2019

Astrophys Space Sci

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, I Crab,45 ≥ 2 (where I 45 = I/10 45 gcm 2 ) obtained by Gunn and Ostriker (1969) as a round off value of the recently estimated value of I Crab,45 ≥ 1.93 (Bejger & Haensel 2003) for the Crab pulsar. If this value of lower bound is combined with the other observational constraint obtained for the Crab pulsar (Crawford & Demiansky 2003), G h = I core /I total ≥ 0.7 ( where G h 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, z a , for the Crab pulsar in the range, M = 1.79M − 1.88M ; z a = 0.374 − 0.393 (I 45 = 2) for an assigned value of the surface density, E a = 2 × 10 14 gcm −3 (like, Brecher and Caporaso 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 z a = 0.414 (I 45 = 2) for the values of G h ≈ 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 + z a ) (Lindblom 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 0.40MeV from the Crab pulsar (Leventhal et al. 1977) agrees quite well with the finding of this study.