Advertisement

Constraints on the equation of state from the stability condition of neutron stars

  • P. S. Koliogiannis
  • C. C. MoustakidisEmail author
Original Article
  • 92 Downloads

Abstract

The stellar equilibrium and collapse, including mainly white dwarfs, neutron stars and super massive stars, is an interplay between general relativistic effects and the equation of state of nuclear matter. In the present work, we use the Chandrasekhar criterion of stellar instability by employing a large number of realistic equations of state (EoSs) of neutron star matter. We mainly focus on the critical point of transition from stable to unstable configuration. This point corresponds to the maximum neutron star mass configuration. We calculate, in each case, the resulting compactness parameter, \(\beta =GM/c^{2}R\), and the corresponding effective adiabatic index, \(\gamma _{\mathrm{cr}}\). We find that there is a model-independent relation between \(\gamma _{ \mathrm{cr}}\) and \(\beta \). This statement is strongly supported by the large number of EoSs, and it is also corroborated by using analytical solutions of the Einstein field equations. In addition, we present and discuss the relation between the maximum rotation rate and the adiabatic index close to the instability limit. Accurate observational measurements of the upper bound of the neutron star mass and the corresponding radius, in correlation with present predictions, may help to impose constraints on the high density part of the neutron star equation of state.

Keywords

Neutron stars Nuclear equation of state Stability condition Adiabatic index 

Notes

Acknowledgements

Ch.C.M. would like to thank the Theoretical Astrophysics Department of the University of Tuebingen, where part of this work was performed, for the warm hospitality and Professor K. Kokkotas for his constructive comments and insights during the preparation of the manuscript. This work was partially supported by the COST action PHAROS (CA16214) and the DAAD Germany–Greece grant ID 57340132.

References

  1. Abbott, B.P., et al.: Phys. Rev. Lett. 119, 161101 (2017a) ADSCrossRefGoogle Scholar
  2. Abbott, B.P., et al.: Astrophys. J. 12, 848 (2017b) Google Scholar
  3. Akmal, A., Pandharipande, V.R., Ravenhall, D.G.: Phys. Rev. C 58, 1804 (1998) ADSGoogle Scholar
  4. Alsing, J., Silva, H.O., Berti, E.: Mon. Not. R. Astron. Soc. 478, 1377 (2018) ADSGoogle Scholar
  5. Antoniadis, J., Freire, P.C., Wex, N., Tauris, T.M., Lynch, R.S., et al.: Science 340, 1233232 (2013) Google Scholar
  6. Balberg, S., Shapiro, S.L.:. astro-ph/0004317 (2000)
  7. Bardeen, J.M., Thorne, K.S., Meltzer, D.W.: Astrophys. J. 145, 505 (1966) ADSGoogle Scholar
  8. Bauswein, A., Just, O., Janka, H.T., Stergioulas, N.: Astrophys. J. Lett. 850, L34 (2017) ADSGoogle Scholar
  9. Bludman, S.A.: Astrophys. J. 183, 637 (1973a) ADSGoogle Scholar
  10. Bludman, S.A.: Astrophys. J. 183, 649 (1973b) ADSGoogle Scholar
  11. Bombaci, I., Logoteta, D.: Astron. Astrophys. 609, A128 (2018) ADSGoogle Scholar
  12. Bourke, T.L., et al.: In: Proceedings of Science, Advancing Astrophysics with the Square Kilometre Array (AASKA14). SISSA, Trieste (2015). http://pos.sissa.it/cgi-bin/reader/conf.cgi?confid=215 Google Scholar
  13. Bowers, R.L., Gleeson, A.M., Pedigo, R.D.: Phys. Rev. D 12, 3056 (1975) ADSGoogle Scholar
  14. Breu, C., Rezzolla, L.: Mon. Not. R. Astron. Soc. 459, 646 (2016) ADSGoogle Scholar
  15. Buchdahl, H.A.: Phys. Rev. 116, 1027 (1959) ADSMathSciNetGoogle Scholar
  16. Buchdahl, H.A.: Astrophys. J. 147, 310 (1967) ADSGoogle Scholar
  17. Chabanat, E., Bonche, P., Haensel, P., Meyer, J., Schaeffer, R.: Nucl. Phys. A 627, 710 (1997) ADSGoogle Scholar
  18. Chan, R., Herrera, L., Santos, N.O.: Mon. Not. R. Astron. Soc. 267, 637 (1994) ADSGoogle Scholar
  19. Chandrasekhar, S.: Astrophys. J. 140, 417 (1964a) ADSMathSciNetGoogle Scholar
  20. Chandrasekhar, S.: Phys. Rev. Lett. 12, 114 (1964b) ADSGoogle Scholar
  21. Chen, W.C., Piekarewicz, J.: Phys. Rev. Lett. 115, 161101 (2015) ADSGoogle Scholar
  22. Demorest, P., Pennucci, T., Ransom, S., Roberts, M., Hessels, J.: Nature (London) 467, 1081 (2010) ADSGoogle Scholar
  23. Douchin, F., Haensel, P.: Astron. Astrophys. 380, 151 (2001) ADSGoogle Scholar
  24. Farine, M., Pearson, J.M., Tondeur, F.: Nucl. Phys. A 615, 135 (1997) ADSGoogle Scholar
  25. Friedman, J.L., Stergioulas, N.: Rotating Relativistic Stars. Cambridge University Press, Cambridge (2013) zbMATHGoogle Scholar
  26. Gaertig, E., Kokkotas, K.D.: Phys. Rev. D 80, 064026 (2009) ADSGoogle Scholar
  27. Gaitanos, T., Kaskulov, M.: Nucl. Phys. A 899, 133 (2013) ADSGoogle Scholar
  28. Gaitanos, T., Kaskulov, M.: Nucl. Phys. A 940, 181 (2015) ADSGoogle Scholar
  29. Glass, E.N., Harpaz, A.: Mon. Not. R. Astron. Soc. 202, 159 (1983) ADSGoogle Scholar
  30. Glendenning, N.K.: Compact Stars: Nuclear Physics, Particle Physics, and General Relativity. Springer, Berlin (2000) zbMATHGoogle Scholar
  31. Haensel, P., Lasota, J.P., Zdunik, J.L.: Astron. Astrophys. 344, 151 (1999) ADSGoogle Scholar
  32. Haensel, P., Potekhin, A.Y., Yakovlev, D.G.: Neutron Stars 1: Equation of State and Structure. Springer, New York (2007) Google Scholar
  33. Haensel, P., Bejger, M., Fortin, M., Zdunic, L.: Eur. Phys. J. A 52, 59 (2016) ADSGoogle Scholar
  34. Hambaryan, V., Suleimanov, V., Haberl, F., Schwope, A.D., Neuhauser, R., Hohle, M., Werner, K.: Astron. Astrophys. 601, A108 (2017) ADSGoogle Scholar
  35. Harrison, B.K., Thorne, K.S., Wakano, M., Wheeler, J.A.: Gravitational Theory and Gravitational Collapse. Chigago University Press, Chigago (1965) Google Scholar
  36. Hebeler, K., Lattimer, J.M., Pethick, C.J., Schwenk, A.: Astrophys. J. 773, 11 (2013) ADSGoogle Scholar
  37. Heiselberg, H., Hjorth-Jensen, M.: Phys. Rep. 328, 237 (2000) ADSGoogle Scholar
  38. Herrera, L., Le Denmat, G., Santos, N.O.: Mon. Not. R. Astron. Soc. 237, 257 (1989) ADSGoogle Scholar
  39. Hessels, J.W.T., Ransom, S.M., Stairs, I.H., et al.: Science 311, 1901 (2006) ADSGoogle Scholar
  40. Hiscock, W.A., Lindblom, L.: Ann. Phys. 151, 466 (1983) ADSGoogle Scholar
  41. Ipser, J.R.: Astrophys. Space Sci. 7, 361 (1970) ADSGoogle Scholar
  42. Kokkotas, K.D., Ruoff, J.: Astron. Astrophys. 366, 565 (2001) ADSGoogle Scholar
  43. Lasota, J.P., Haensel, P., Abramowicz, M.A.: Astrophys. J. 456, 300 (1996) ADSGoogle Scholar
  44. Lattimer, J.M., Prakash, M.: Astrophys. J. 550, 426 (2001) ADSGoogle Scholar
  45. Lattimer, J.M., Prakash, M.: Phys. Rev. Lett. 94, 111101 (2005) ADSGoogle Scholar
  46. Lindblom, L., Detweiler, S.L.: Astrophys. J. Suppl. Ser. 53, 73 (1983) ADSGoogle Scholar
  47. Madappa, P., Bombaci, I., Manju, P., Ellis, P.J., Lattimer, J.M., Knorren, R.: Phys. Rep. 280, 1 (1997) ADSGoogle Scholar
  48. Margalit, B., Metzger, B.D.: Astrophys. J. Lett. 850, L19 (2017) ADSGoogle Scholar
  49. Maselli, A., Pnigouras, P., Nielsen, N.G., Kouvaris, C., Kokkotas, K.D.: Phys. Rev. D 96, 023005 (2017) ADSGoogle Scholar
  50. Merafina, M., Ruffini, R.: Astron. Astrophys. 221, 4 (1989) ADSGoogle Scholar
  51. Miller, M.C., Lamb, F.K.: Astrophys. J. Lett. 499, L37 (1998) ADSGoogle Scholar
  52. Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. Freeman, San Francisco (1973) Google Scholar
  53. Moustakidis, Ch.C., Panos, C.P.: Phys. Rev. C 79, 045806 (2009) ADSGoogle Scholar
  54. Moustakidis, Ch.C.: Gen. Relativ. Gravit. 49, 68 (2017) ADSMathSciNetGoogle Scholar
  55. Nariai, H.: Sci. Rep. Tohoku Univ. Ser. 1(34), 160 (1950) ADSMathSciNetGoogle Scholar
  56. Nariai, H.: Sci. Rep. Tohoku Univ. Ser. 1(35), 62 (1951) MathSciNetGoogle Scholar
  57. Nariai, H.: Gen. Relativ. Gravit. 31, 951 (1999) ADSMathSciNetGoogle Scholar
  58. Negi, P.S., Durgapal, M.C.: Gen. Relativ. Gravit. 31, 13 (1999) ADSGoogle Scholar
  59. Negi, P.S., Durgapal, M.C.: Astrophys. Space Sci. 275, 185 (2001) ADSGoogle Scholar
  60. Oppenheimer, J.R., Volkoff, G.M.: Phys. Rev. 55, 374 (1939) ADSGoogle Scholar
  61. Pandharipande, V.R., Smit, R.A.: Phys. Lett. B 59, 15 (1975) ADSGoogle Scholar
  62. Papazoglou, M.C., Moustakidis, Ch.C.: Astrophys. Space Sci. 361, 98 (2016) ADSGoogle Scholar
  63. Raghoonundun, A.M., Hobill, D.W.: Phys. Rev. D 92, 124005 (2015) ADSGoogle Scholar
  64. Rosso, A.G., Vissani, F., Volpe, M.C.: J. Cosmol. Astron. Phys. 36 (2017) Google Scholar
  65. Ravenhall, D.G., Pethick, C.J.: Astrophys. J. 424, 846 (1994) ADSGoogle Scholar
  66. Schutz, B.F.: A First Course in General Relativity. Cambridge University Press, Cambridge (1985) Google Scholar
  67. Shapiro, S.L., Teukolsky, S.A.: Black Holes, White Dwarfs, and Neutron Stars. Wiley, New York (1983) Google Scholar
  68. Sharif, M., Yousaf, Z.: Astrophys. Space Sci. 355, 317 (2015) ADSGoogle Scholar
  69. Sharma, B.K., Centelles, M., Vinas, X., Baldo, M., Burgio, G.F.: Astron. Astrophys. 584, A103 (2015) ADSGoogle Scholar
  70. Silva, H.O., Sotani, H., Berti, E.: Mon. Not. R. Astron. Soc. 459, 4378 (2016) ADSGoogle Scholar
  71. Silva, H.O., Yunes, N.: Class. Quantum Gravity 35, 015005 (2018) ADSGoogle Scholar
  72. Sotani, H., Kokkotas, K.D.: Phys. Rev. D 97, 124034 (2018) ADSGoogle Scholar
  73. Tolman, R.C.: Phys. Rev. 55, 364 (1939) ADSGoogle Scholar
  74. Tooper, R.F.: Astrophys. J. 140, 434 (1964) ADSMathSciNetGoogle Scholar
  75. Tooper, R.F.: Astrophys. J. 142, 1541 (1965) ADSMathSciNetGoogle Scholar
  76. Walecka, J.D.: Ann. Phys. 83, 491 (1974) ADSGoogle Scholar
  77. Watts, A.L., et al.: Rev. Mod. Phys. 88, 021001 (2016) ADSGoogle Scholar
  78. Weinberg, S.: Gravitational and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley, New York (1972) Google Scholar
  79. Wiringa, R.B., Fiks, V., Fabrocini, A.: Phys. Rev. C 38, 1010 (1988) ADSGoogle Scholar
  80. Yagi, K., Yunes, N.: Science 341, 365 (2013a) ADSGoogle Scholar
  81. Yagi, K., Yunes, N.: Phys. Rev. D 88, 023009 (2013b) ADSGoogle Scholar
  82. Yagi, K., Stein, L.C., Pappas, G., Yunes, N., Apostolatos, T.A.: Phys. Rev. D 90, 063010 (2014) ADSGoogle Scholar
  83. Yagi, K., Yunes, N.: Phys. Rep. 681, 1–72 (2017) ADSMathSciNetGoogle Scholar
  84. Yousaf, Z., Bhatti, M.Z.: Eur. Phys. J. C 76, 267 (2016) ADSGoogle Scholar
  85. Zeldovich, Ya.B., Novikov, I.D.: Relativistic Astrophysics, vol. I. University of Chigago Press, Chicago (1978) Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsAristotle University of ThessalonikiThessalonikiGreece
  2. 2.Theoretical Astrophysics, IAATEberhard-Karls University of TuebingenTuebingenGermany

Personalised recommendations