Abstract
The gravitational radiation has been proposed a long time before, as an explanation for the observed relatively low spin frequencies of young neutron stars and of accreting neutron stars in low-mass X-ray binaries as well. In the present work we studied the effects of the neutron star equation of state on the \(r\)-mode instability window of rotating neutron stars. Firstly, we employed a set of analytical solution of the Tolman-Oppenheimer-Volkoff equations with special emphasis on the Tolman VII solution. In particular, we tried to clarify the effects of the bulk neutron star properties (mass, radius, density distribution, crust size and elasticity) on the \(r\)-mode instability window. We found that the critical angular velocity \(\varOmega_{c}\) depends mainly on the neutron star radius. The effects of the gravitational mass and the mass distribution are almost negligible. Secondly, we studied the effect of the elasticity of the crust, via to the slippage factor \(S\) and also the effect of the nuclear equation of state, via the slope parameter \(L\), on the instability window. We found that the crust effects are more pronounced, compared to those originated from the equation of state. Moreover, we proposed simple analytical expressions which relate the macroscopic quantity \(\varOmega_{c}\) to the radius, the parameter \(L\) and the factor \(\mathcal{S}\). We also investigated the possibility to measure the radius of a neutron star and the factor \(\mathcal{S}\) with the help of accurate measures of \(\varOmega_{c}\) and the neutron star temperature. Finally, we studied the effects of the mutual friction on the instability window and discussed the results in comparison with previous similar studies.
Similar content being viewed by others
References
Adler, R.J.: J. Math. Phys. 15, 727 (1974)
Alford, M.G., Mahmoodifar, S., Schwenzer, K.: Phys. Rev. D 85, 044051 (2012)
Alford, M.G., Schwenzer, K.: Phys. Rev. Lett. 113, 251102 (2014)
Andersson, N.: Astrophys. J. 502, 708 (1998)
Andersson, N.: Class. Quantum Gravity 20, R105 (2003)
Andersson, N., Kokkotas, K.D.: Int. J. Mod. Phys. D 10, 381 (2001)
Andersson, N., Kokkotas, K.D., Schutz, B.F.: Astrophys. J. 510, 846 (1999)
Andersson, N., Jones, D.I., Kokkotas, K.D., Stergioulas, N.: Astrophys. J. 534, L75 (2000)
Andersson, N., Haskell, B., Comer, G.L.: Phys. Rev. D 82, 023007 (2010)
Bildsten, L., Ushomirsky, G.: Astrophys. J. Lett. 529, L33 (2000)
Bondarescu, R., Teukolsky, S.A., Wasserman, I.: Phys. Rev. D 79, 10403 (2009)
Buchdahl, H.A.: Astrophys. J. 147, 310 (1967)
Chirenti, C., de Souza, G.H., Kastaun, W.: Phys. Rev. D 91, 044034 (2015)
Chatterjee, D., Bandyopadhyay, D.: Astrophys. Space Sci. 308, 451 (2007)
Delgaty, M.S.R., Lake, K.: Comput. Phys. Commun. 115, 395 (1998)
Demorest, P.B., Pennucci, R., Ransom, S.M., Roberts, M.S.E., Hessels, J.W.T.: Nature 467, 1081 (2010)
Fattoyev, F.J., Newton, W.G., Li, B.A.: Eur. Phys. J. A 50, 45 (2014)
Friedman, J.L., Morsink, S.M.: Astrophys. J. 502, 714 (1998)
Friedman, J.L., Lockitch, K.H.: Prog. Theor. Phys. Suppl. 136, 121 (1999)
Glampedakis, K., Andersson, N.: Phys. Rev. D 74, 044040 (2006)
Glendenning, N.K.: Compact Stars: Nuclear Physics, Particle Physics, and General Relativity. Springer, Berlin (2000)
Gusakov, M.E., Chugunov, A.I., Kantor, E.M.: Phys. Rev. D 90, 063001 (2014)
Gusakov, M.E., Kantor, E.M., Chugunov, A.I., Gualtieri, L.: Mon. Not. R. Astron. Soc. 428, 1518 (2013)
Haensel, P., Potekhin, A.Y., Yakovlev, D.G.: Neutron Stars 1: Equation of State and Structure. Springer, New York (2007)
Haskell, B.: Int. J. Mod. Phys. E 24, 1541007 (2015)
Haskell, B., Degenaar, N., Ho, W.C.G.: Mon. Not. R. Astron. Soc. 424, 93 (2012)
Haskell, B., Andersson, N., Jones, D.L., Samuelsson, L.: Phys. Rev. Lett. 99, 1101 (2007)
Haskell, B., Andersson, N., Passamonti, A.: Mon. Not. R. Astron. Soc. 397, 1464 (2009)
Ho, W.C.G., Andersson, N., Haskell, B.: Phys. Rev. Lett. 107, 101101 (2011)
Idrisy, A., Owen, B.J., Jones, D.I.: Phys. Rev. D 91, 024001 (2015)
Keek, L., Galloway, D.K., in’t Zand, J.J.M., Heger, A.: Astrophys. J. 718, 292 (2010)
Kinney, J., Mendell, G.: Phys. Rev. D 67, 024032 (2003)
Kobyakov, D., Pethick, C.J.: Mon. Not. R. Astron. Soc. 449, L110 (2015)
Kokkotas, K.D., Stergioulas, N.: Astron. Astrophys. 341, 110 (1999)
Kokkotas, K.D., Schwenzer, K.: (2015). arXiv:1510.07051 [gr-qc]
Kolomeitsev, E.E., Voskresensky, D.N.: Eur. Phys. J. A 50, 180 (2014)
Lattimer, J.M.: Annu. Rev. Nucl. Part. Sci. 62, 485 (2012)
Lattimer, J.M., Prakash, M.: Astrophys. J. 550, 426 (2001)
Lattimer, J.M., Prakash, M.: Phys. Rep. 442, 109 (2007)
Lattimer, J.M., Lim, Y.: Astrophys. J. 771, 51 (2013)
Lattimer, J.M.: Neutron Stars, lectures delivered at the 33rd Summer Institute on Particle Physics, SSI 2005 (unpublished)
Lattimer, J.M., Prakash, M.: Phys. Rep. 333–334, 121 (2000)
Lattimer, J.M., Prakash, M.: Phys. Rev. Lett. 94, 1105 (2005)
Lee, U., Yoshida, S.: Astrophys. J. 586, 403 (2003)
Levin, Y., Ushomirsky, G.: Mon. Not. R. Astron. Soc. 324, 917 (2001)
Lindblom, L., Owen, B.J., Ushomirsky, G.: Phys. Rev. D 62, 084030 (2000a)
Lindblom, L., Mendell, G.: Phys. Rev. D 61, 104003 (2000b)
Lindblom, L., Owen, B.J.: Phys. Rev. D 65, 063006 (2002)
Lindblom, L., Owen, B.J., Morsink, S.M.: Phys. Rev. Lett. 80, 4843 (1998)
Mahmoodifar, S., Strohmayer, T.: Astrophys. J. 773, 140 (2013)
Matese, J., Whitman, M.: Phys. Rev. D 22, 1270 (1980)
Moustakidis, Ch.C.: Phys. Rev. C 91, 035804 (2015)
Mytidis, A., Coughlin, M., Whiting, B.: Astrophys. J. 810, 27 (2015)
Nariai, H.: Sci. Rep. Tohoku Univ., Ser. 1 34, 160 (1950)
Nariai, H.: Sci. Rep. Tohoku Univ., Ser. 1 35, 62 (1951)
Nariai, H.: Gen. Relativ. Gravit. 31, 951 (1999)
Newton, W.G., Hooker, J., Gearheart, M., Murphy, K., Wen, D.H., Fattoyev, F.J., Li, B.A.: Eur. Phys. J. A 50, 41 (2014)
Owen, B.J., Lindblom, L., Cutler, C., Schutz, B.F., Vecchio, A., Andersson, N.: Phys. Rev. D 58, 084020 (1998)
Prakash, M.: Nucl. Phys. A 928, 260 (2014)
Prakash, M.: The Equation of State and Neutron Stars, lectures delivered at the Winter School held in Puri India, 1994 (unpublished)
Postnikov, S., Prakash, M., Lattimer, J.M.: Phys. Rev. D 82, 024016 (2010)
Raghoonundun, A.M., Hobill, D.W.: Phys. Rev. D 92, 124005 (2015)
Read, J.S., Markakis, C., Shibata, M., Uryu, K., Creighton, J.D.E., Friedman, J.L.: Phys. Rev. D 79, 0124033 (2009a)
Read, J.S., Lackey, B.D., Owen, B.J., Friedman, J.L.: Phys. Rev. D 79, 0124032 (2009b)
Rieutord, M.: (2000). astro-ph/0003171
Rupak, G., Jaikumar, P.: Phys. Rev. C 88, 065801 (2013)
Schutz, B.F.: A First Course in General Relativity. Cambridge University Press, Cambridge (1985)
Shapiro, S.L., Teukolsky, S.A.: Black Holes, White Dwarfs, and Neutron Stars. John Wiley and Sons, New York (1983)
Takami, K., Rezzolla, L., Baiotti, L.: Phys. Rev. Lett. 113, 091104 (2014)
Tolman, R.C.: Phys. Rev. 55, 364 (1939)
Vidaña, I.: Phys. Rev. C 85, 045808 (2012). Erratum: Phys. Rev. C 90, 029901 (2014)
Watts, A.L., Krishnam, B., Bildsten, L., Schutz, B.F.: Mon. Not. R. Astron. Soc. 389, 839 (2008)
Watts, A.L., et al.: (2016). arXiv:1602.01081 [astro-ph.HE]
Wen, D.H., Newton, W.G., Li, B.A.: Phys. Rev. C 85, 025801 (2012)
Yagi, K., Stein, L.C., Pappas, G., Yunes, N., Apostolatos, T.: Phys. Rev. D 90, 063010 (2014)
Acknowledgements
This work was supported by the Aristotle University of Thessaloniki Research Committee under Contract No. 89286.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Papazoglou, M.C., Moustakidis, C.C. R-mode constraints from neutron star equation of state. Astrophys Space Sci 361, 98 (2016). https://doi.org/10.1007/s10509-016-2692-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10509-016-2692-5