Massive neutron star models with parabolic cores

  • P. S. NegiEmail author
Original Article


The results of the investigation of the core-envelope model presented in Negi et al. (Gen. Relativ. Gravit. 22:735, 1990) have been discussed in view of the reference (Negi et al. in Gen. Relativ. Gravit. 51:131, 2019). It is seen that there are significant changes in the results to be addressed. In addition, I have also calculated the gravitational binding energy, causality and pulsational stability of the structures which were not considered in Negi et al. (Gen. Relativ. Gravit. 22:735, 1990). The modified results have important consequences to model neutron stars and pulsars. The maximum neutron star mass obtained in this study corresponds to the mean value of the classical results obtained by Rhoades and Ruffini (Phys. Rev. Lett. 32:324, 1974) and the upper bound on neutron star mass obtained by Kalogera and Baym (Astrophys. J. 470:L61, 1996) and is much closer to the most recent theoretical estimate made by Sotani (Phys. Rev. C 95:025802, 2017). On one hand, when there are only few equations of state (EOSs) available in the literature which can fulfil the recent observational constraint imposed by the largest neutron star masses around 2\(M_{\odot }\) (Demorest et al. in Nature 467:1081, 2010; Antoniadis et al. in Science 340:6131, 2013; Cromartie et al. in Nat. Astron. 4:72, 2020), the present analytic models, on the other hand, can comfortably satisfy this constraint. Furthermore, the maximum allowed value of compactness parameter \(u\) (\(\equiv M/a\); mass to size ratio in geometrized units) \(\leq 0.30\) obtained in this study is also consistent with an absolute maximum value of \(u_{\mathrm{max}} = 0.333^{+0.001}_{-0.005}\) resulting from the observation of binary neutron stars merger GW170817 (see, e.g. Koliogiannis and Moustakidis in Astrophys. Space Sci. 364:52, 2019).


Static spherical structures Analytic solutions Neutron stars 



The author is grateful to anonymous referee for his valuable comments, suggestions and comprehensive reviewing of the present paper.

Conflict of interest

The Author declares that there is no conflict of interest.


  1. Antoniadis, J., Freire, P.C., Wex, N., et al.: Science 340, 6131 (2013) ADSCrossRefGoogle Scholar
  2. Bauswein, A., Just, O., Janka, H.T., Stergioulas, N.: Astrophys. J. Lett. 850, L34 (2017) ADSCrossRefGoogle Scholar
  3. Brecher, K., Caporaso, G.: Nature 259, 377 (1976) ADSCrossRefGoogle Scholar
  4. Chandrasekhar, S.: Astrophys. J. 140, 417 (1964a) ADSMathSciNetCrossRefGoogle Scholar
  5. Chandrasekhar, S.: Astrophys. J. 140, 417 (1964b) ADSMathSciNetCrossRefGoogle Scholar
  6. Cromartie, H.T., Fonseca, E., et al.: Nat. Astron. 4, 72 (2020) ADSCrossRefGoogle Scholar
  7. Demorest, P.B., Pennucci, R., Ransom, S.M., Roberts, M.S.E., Hessels, J.W.T.: Nature 467, 1081 (2010) ADSCrossRefGoogle Scholar
  8. Durgapal, M.C., Pande, A.K.: Indian J. Pure Appl. Phys. 18, 171 (1980) ADSGoogle Scholar
  9. Haensel, P., Potekhin, A.Y., Yakovlev, D.G.: Neutron Stars 1. Equation of State and Structure. Springer, Berlin (2006) Google Scholar
  10. Kalogera, V., Baym, G.: Astrophys. J. 470, L61 (1996) ADSCrossRefGoogle Scholar
  11. Knutsen, H.: Astrophys. Space Sci. 162, 315 (1989) ADSCrossRefGoogle Scholar
  12. Koliogiannis, P.S., Moustakidis, C.C.: Astrophys. Space Sci. 364, 52 (2019) ADSCrossRefGoogle Scholar
  13. Lai, X.Y., Xu, R.X.: Mon. Not. R. Astron. Soc. 398, L31 (2009) ADSCrossRefGoogle Scholar
  14. Margalit, B., Metzger, B.D.: Astrophys. J. Lett. 850, L19 (2017) ADSCrossRefGoogle Scholar
  15. Negi, P.S.: Gen. Relativ. Gravit. 39, 529 (2007) ADSCrossRefGoogle Scholar
  16. Negi, P.S., Durgapal, M.C.: Gen. Relativ. Gravit. 31, 13 (1999) ADSCrossRefGoogle Scholar
  17. Negi, P.S., Durgapal, M.C.: Astrophys. Space Sci. 275, 185 (2001) ADSCrossRefGoogle Scholar
  18. Negi, P.S., Pande, A.K., Durgapal, M.C.: Gen. Relativ. Gravit. 22, 735 (1990) ADSCrossRefGoogle Scholar
  19. Negi, P.S., Pande, A.K., Durgapal, M.C.: Gen. Relativ. Gravit. 51, 131 (2019). ADSCrossRefGoogle Scholar
  20. Rhoades, C.E. Jr., Ruffini, R.: Phys. Rev. Lett. 32, 324 (1974) ADSCrossRefGoogle Scholar
  21. Shapiro, S.L., Teukolsky, S.A.: Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects. Wiley, New York (1983) CrossRefGoogle Scholar
  22. Sotani, H.: Phys. Rev. C 95, 025802 (2017) ADSCrossRefGoogle Scholar
  23. Zeldovich, Ya.B., Novikov, I.D.: Relativistic Astrophysics, Vol. I. University of Chicago Press, Chicago (1978) Google Scholar

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© Springer Nature B.V. 2020

Authors and Affiliations

  1. 1.Department of PhysicsKumaun UniversityNainitalIndia

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