Skip to main content
SpringerLink
Log in

Effects of temperature on the structure of neutron stars at high temperature

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

In Newtonian physics, higher temperature leads to higher thermal pressure, which provides stronger support against the gravitational contraction of stars. However, in the temperature range of tens of MeV involved in the evolution of a proto-neutron star or a higher massive neutron star, the effects of temperature are richer. We showed that, for a high temperature neutron star (HTNS) constructed with a realistic equation of state (EOS), the HTNS may expand or contract during cooling, the central density may increase or decrease, the quasi-normal mode oscillation frequencies may increase or decrease, and in particular, (i) independent of the EOS, for a HTNS of a given mass, there exists a maximum temperature \(T_{max}\) that it could ever attend at birth (with the value of \(T_{max}\) different for different EOS), and (ii) for the Hempel EOS and the Shen EOS, there is a range of mass that the HTNS may gravitationally collapse after a period of radiative cooling; however, for the Lattimer–Swesty EOS and Banik EOS, no delayed collapse is possible. Our study, which describes the cooling of HTNSs with simple quasi-stationary TOV sequences, provides an understanding of the effects of the thermal energy/pressure at high temperature, and a demonstration that different EOSs can lead to qualitatively different evolution paths.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Notes

  1. We thank a referee of this paper for highlighting this point.

References

  1. Burrows, A., Lattimer, J.M.: The birth of neutron stars. Astrophys. J. 307, 178 (1986)

    Article  ADS  Google Scholar 

  2. Burrows, A.: Supernova neutrinos. Astrophys. J. 334, 891 (1988)

    Article  ADS  MATH  Google Scholar 

  3. Burrows, A.: Neutrinos from supernova explosions. Ann. Rev. Nucl. Sci. 40, 181 (1990)

    Article  ADS  Google Scholar 

  4. Pons, J.A., Reddy, S., Prakash, M., Lattimer, J.M., Miralles, J.A.: Evolution of proto-neutron stars. Astrophys. J. 513, 780 (1999)

    Article  ADS  Google Scholar 

  5. Pons, J.A., Miralles, J.A., Prakash, M., Lattimer, J.M.: Evolution of proto-neutron stars with kaon condensates. Astrophys. J. 553, 382 (2001)

    Article  ADS  Google Scholar 

  6. Pons, J.A., Steiner, A.W., Prakash, M., Lattimer, J.M.: Evolution of proto-neutron stars with quarks. Phys. Rev. Lett. 86, 5223 (2001)

    Article  ADS  Google Scholar 

  7. Oppenheimer, J.R., Volkoff, G.M.: On massive neutron cores. Phys. Rev. 55, 374 (1939)

    Article  ADS  MATH  Google Scholar 

  8. Tolman, R.C.: Static solutions of Einstein’s field equations. Phys. Rev. 55, 364 (1939)

    Article  ADS  MATH  Google Scholar 

  9. Tolman, R.C.: On the weight of heat and thermal equilibrium in general relativity. Phys. Rev. 35, 904 (1930)

    Article  ADS  MATH  Google Scholar 

  10. Wilson, J.R., Mayle, R.W.: The Nuclear Equation of State, Part A, vol. 731. Plenum Press, New York (1989)

    Google Scholar 

  11. Keil, W., Janka, H.T.: Hadronic phase transitions at supranuclear densities and the delayed collapse of newly formed neutron stars. Astron. Astrophys. 296, 145 (1995)

    ADS  Google Scholar 

  12. Fisher, T., Whitehouse, S.C., Mezzacappa, A., Thielemann, F.-K., Liebendörfer, M.: Protoneutron star evolution and the neutrino-driven wind in general relativistic neutrino radiation hydrodynamics simulations. Astron. Astrophys. 517, A80 (2010)

    Article  ADS  MATH  Google Scholar 

  13. Ferrari, V., Miniutti, G., Pons, J.A.: Gravitational waves from newly born, hot neutron stars. Mon. Not. R. Astron. Soc. 342, 629 (2003)

    Article  ADS  Google Scholar 

  14. Ferrari, V., Gualtieri, L., Pons, J.A., Stavridis, A.: Gravitational waves from rotating proto-neutron stars. Class. Quantum Grav. 21S, 515 (2004)

    Article  ADS  MATH  Google Scholar 

  15. Ferrari, V., Gualtieri, L., Pons, J.A.: Unstable g-modes in proto-neutron Stars. Class. Quantum Grav. 24, 5093 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Burgio, G.F., Ferrari, V., Gualtieri, L., Schulze, H.-J.: Oscillations of hot, young neutron stars: gravitational wave frequencies and damping times. Phys. Rev. D 84, 044017 (2011)

    Article  ADS  Google Scholar 

  17. Glendenning, N.K.: Neutron stars are giant hypernuclei? Astrophys. J. 293, 470 (1985)

    Article  ADS  Google Scholar 

  18. Lattimer, J.M., Prakash, M.: The equation of state of hot, dense matter and neutron stars. Phys. Rep. 621, 127 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  19. O’Connor, E., Ott, C.D.: Black hole formation in failling core-collapse supernovae. Astrophys. J. 730, 70 (2011)

    Article  ADS  Google Scholar 

  20. Oechslin, R., Janka, H.-T., Marek, A.: Relativistic neutron star merger simulations with non-zero temperature equations of state. I. Variation of binary parameters and equation of state. Astron. Astrophys. 467, 395 (2007)

    Article  ADS  Google Scholar 

  21. Hempel, M., Fischer, T., Schaffner-Bielich, J., Liebendorfer, M.: New equations of state in simulations of core-collapse supernovae. Astrophys. J. 748, 27 (2012) (The version of the table we use is \(Hempel_{-}TMAEOS_{-}rho234_{-}temp\) \(180_{-}ye60_{-}version_{-}1.1_{-}20120817.h5\), as given in http://www.stellarcollapse.org/equationofstate)

  22. Shen, G., Horowitz, C.J., Teige, S.: A new equation of state for astrophysical simulations. Phys. Rev. C 83, 035802 (2011)

    Article  ADS  Google Scholar 

  23. Shen, G., Horowitz, C.J., O’Connor, E.: A second relativistic mean field and virial equation of state for astrophysical simulations. Phys. Rev. C 83, 065808 (2011) (The version of the table we use is \(GShenFSU_{-}2.1EOS_{-}rho280_{-}temp180_{-}ye52_{-}version_{-}\) \(1.1_{-}20120824.h5\), as given in http://www.stellarcollapse.org/equationofstate)

  24. Lattimer, J.M., Swesty, F.D.: A generralized equation of state for hot, dense matter. Nucl. Phys. A 535, 331 (1991) (The version of the table we use is \(LS220_{-}234r_{-}\) \(136t_{-}50y_{-}analmu_{-}20091212_{-}SVNr26.h5\), as given in http://www.stellarcollapse.org/equationofstate)

  25. Banik, S., Hempel, M., Bandyopadhyay, D.: New hyperon equations of state for supernovae and neutron stars in density dependent hadron field theory. Astrophys. J. Suppl. 214, 22 (2014) (The version of the table we use is \(BHB_{-}1pEOS_{-}rho234_{-}temp180_{-}ye60_{-}version_{-}\) \(1.02_{-}20140422.h5\), as given in http://www.stellarcollapse.org/equationofstate)

  26. Lu, J.L., Wan, M.B.: Oscillation and collapses of proto-neutron stars. Chin. Phys. Lett. 26, 010402 (2009)

    Article  ADS  Google Scholar 

  27. Bauswein, A., Janka, H.-T., Oechslin, R.: Testing approximations of thermal effects in neutron star merger simulations. Phys. Rev. D 82, 084043 (2010)

    Article  ADS  Google Scholar 

  28. Constantinou, C., Muccioli, B., Prakash, M., Lattimer, J.M.: Thermal properties of hot and dense matter with finite range interactions. Phys. Rev. C 92, 025801 (2015)

    Article  ADS  MATH  Google Scholar 

  29. Constantinou, C., Prakash, M.: Enforcing causality in nonrelativistic equations of state at finite temperature. Phys. Rev. C 95, 055802 (2017)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank Professors Wai-Mo Suen and Kenneth Young for useful discussions.

Author information

Authors and Affiliations

  1. Department of Physics, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China

    Liang-gui Zhu, Jun-Li Lu & Li Wang

Authors
  1. Liang-gui Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jun-Li Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Li Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jun-Li Lu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhu, Lg., Lu, JL. & Wang, L. Effects of temperature on the structure of neutron stars at high temperature. Gen Relativ Gravit 50, 11 (2018). https://doi.org/10.1007/s10714-017-2327-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-017-2327-3

Keywords

Search

Navigation