Abstract
We investigate the possible occurrence of a Bose-Einstein condensed phase of matter within neutron stars due to the formation of Cooper pairs among the superfluid neutrons. To this end we study the condensation of bosonic particles under the influence of both a short-range contact and a long-range gravitational interaction in the framework of a Hartree-Fock theory. We consider a finite-temperature scenario, generalizing existing approaches, and derive macroscopic and astrophysically relevant quantities like a mass limit for neutron stars.
Similar content being viewed by others
References
M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, E.A. Cornell, Science 269, 198 (1995)
K.B. Davis, M.O. Mewes, M.R. Andrews, M.J.V. Druten, D.S. Durfee, D.M. Kurn, W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995)
S.N. Bose, Z. Phys. 26, 178 (1924)
A. Einstein, Sitz.ber. Preuss. Akad. Wiss. 1, 3 (1925)
B. Kleihaus, J. Kunz, S. Schneider, Phys. Rev. D 85, 024045 (2012)
O.G. Benvenuto, M.A. Vito, JCAP 2, 033 (2011)
N. Nag, S. Chakrabarty, arXiv:astro-ph/0008477 (2000)
P.H. Chavanis, T. Harko, Phys. Rev. D 86, 064011 (2012)
R.C. Tolman, Phys. Rev. 55, 364 (1939)
J.R. Oppenheimer, G.M. Volkoff, Phys. Rev. 55, 374 (1939)
P.B. Demorest, T. Pennucci, S.M. Ransom, M.S.E. Roberts, J.W.T. Hessels, Nature 467, 1081 (2010)
P. Haensel, A.Y. Potekhin, D.G. Yakovlev, Neutron Stars 1: Equation of State and Structure (Springer, 2007)
R. Belvedere, D. Pugliese, J.A. Rueda, R. Ruffini, S.S. Xue, Nucl. Phys. A 883, 1 (2012)
D. Page, M. Prakash, J.M. Lattimer, A.W. Steiner, Phys. Rev. Lett. 106, 081101 (2011)
C.A.R.S. de Melo, M. Randeria, J.R. Engelbrecht, Phys. Rev. Lett. 71, 3202 (1993)
J.R. Engelbrecht, M. Randeria, C.A.R.S. de Melo, Phys. Rev. B 55, 15153 (1997)
M. Greiner, C.A. Regal, D.S. Jin, Nature 426, 537 (2003)
G.E. Astrakharchik, J. Boronat, J. Casulleras, S. Giorgini, Phys. Rev. Lett. 95, 230405 (2005)
M. Matsuo, Phys. Rev. C 73, 044309 (2006)
J. Margueron, H. Sagawa, K. Hagino, Phys. Rev. C 76, 064316 (2007)
L. Salasnich, J. Phys.: Conf. Ser. 497, 012026 (2014)
C.F.V. Weizsäcker, Zeitschr. Phys. 96, 431 (1935)
D.M. Brink, R.A. Broglia, Nuclear Superfluidity: pairing in finite systems (Cambridge University Press, 2010)
R. Ruffini, S. Bonazzola, Phys. Rev. 187, 1767 (1969)
T. Harko, G. Mocanu, Phys. Rev. D 85, 084012 (2012)
P.H. Chavanis, Phys. Rev. D 84, 063518 (2011)
T. Harko, Phys. Rev. D 83, 123515 (2011)
X.Y. Li, T. Harko, K.S. Cheng, JCAP 6, 001 (2012)
T. Matos, A. Suarez, Europhys. Lett. 96, 56005 (2011)
L.D. Landau, E.M. Lifshitz, Statistical Physics, 3rd edn. (Elsevier, 1980)
J.M. Lattimer, M. Prakash, Astrophys. J. 550, 426 (2001)
P. Oehberg, S. Stenholm, J. Phys. B 30, 2749 (1997)
I.S. Gradshteyn, I.M. Ryzhik, in Table of integrals, series and products, (Academic Press Inc., 1965), Eq. (3.361)
F.K. Lamb, in Proc. Accreting Neutron Stars (Max Planck Institute, 1982), pp. 316–332
J. van Paradijs, W.H.G. Lewin, A&A 172, L20 (1987)
A. Wolszczan, D.A. Frail, Nature 355, 145 (1992)
J. Antoniadis et al., Science 340, 6131 (2013)
J.M. Lattimer, M. Prakash, Phys. Rep. 442, 109 (2007)
B. Kiziltan, A. Kottas, M.D. Yoreo, S.E. Thorsett, Astrophys. J. 778, 66 (2013)
G.P. Horedt, Polytropes: Applications In Astrophysics And Related Fields (Springer, 2004)
A.L. Fetter, Rev. Mod. Phys. 81, 647 (2009)
H. Kleinert, V. Schulte-Frohlinde, Critical Properties of φ4 Theories (World Scientific, 2001)
H. Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets (World Scientific, 2009)
G.C. Wick, Phys. Rev. 80, 268 (1950)
P. Stevenson, Phys. Rev. D 23, 2916 (1981)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gruber, C., Pelster, A. A theory of finite-temperature Bose-Einstein condensates in neutron stars. Eur. Phys. J. D 68, 341 (2014). https://doi.org/10.1140/epjd/e2014-50380-3
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjd/e2014-50380-3