Abstract
Isolated neutron stars undergoing non-radial oscillations are expected to emit gravitational waves in the kilohertz frequency range. To date, radio astronomers have located about 1,300 pulsars, and can estimate that there are about 2×108 neutron stars in the galaxy. Many of these are surely old and cold enough that their interiors will contain matter in the superfluid or superconducting state. In fact, the so-called glitch phenomenon in pulsars (a sudden spin-up of the pulsar's crust) is best described by assuming the presence of superfluid neutrons and superconducting protons in the inner crusts and cores of the pulsars. Recently there has been much progress on modelling the dynamics of superfluid neutron stars in both the Newtonian and general relativistic regimes. We will discuss some of the main results of this recent work, perhaps the most important being that superfluidity should affect the gravitational waves from neutron stars (emitted, for instance, during a glitch) by modifying both the rotational properties of the background star and the modes of oscillation of the perturbed configuration. Finally, we present an analysis of the so-called zero-frequency subspace (i.e., the space of time-independent perturbations) and determine that it is spanned by two sets of polar (or spheroidal) and two sets of axial (or toroidal) degenerate perturbations for the general relativistic system. As in the Newtonian case, the polar perturbations are the g-modes which are missing from the pulsation spectrum of a non-rotating configuration, and the axial perturbations should lead to two sets of r-modes when the degeneracy of the frequencies is broken by having the background rotate.
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REFERENCES
D. R. Lorimer, “Binary and millisecond pulsars at the new millenium,” Living Reviews. Relativity 4, 5 (2001). [Online article]: cited on 15 Aug 2001 http://www.livingreviews. org/Articles/Volume4/2001-5lorimer/.
U. Lombardo, in Nuclear Methods and Nuclear Equations of State, M. Baldo, ed. (World Scientific, Singapore, 1999), pp. 458–510.
U. Lombardo and H.-J. Schulze, preprint LANL archive astro-ph/0012209.
V. Radhakrishnan and R. N. Manchester, Nature 244, 228 (1969).
A. G. Lyne, in Pulsars as Physics Laboratories, R. D. Blandford, A. Hewish, A. G. Lyne, and L. Mestel, eds. (Oxford University Press, New York, 1993).
P. E. Reichley and G. S. Downs, Nature 222, 229 (1969).
G. Baym, C. Pethick, D. Pines, and M. Ruderman, Nature 224, 872 (1969).
P. W. Anderson and N. Itoh, Nature 256, 25 (1975).
M. A. Alpar, P. W. Anderson, D. Pines, and J. Shaham, Ap. J. 276, 325 (1984).
M. A. Alpar, P. W. Anderson, D. Pines, and J. Shaham, Ap. J. 278, 791 (1984).
J. S. Tsakadze and S. J. Tsakadze, J. Low Temp. Phys. 39, 649 (1980).
D. R. Tilley and J. Tilley, Superfluidity and Superconductivity, 2nd edn. (Adam Hilger, Bristol, 1986).
D. L. Goodstein, States of Matter (Dover, New York, 1985).
J. A. Sauls, in Timing Neutron Stars, H. Ögelman and E. P. J. van den Heuvel, eds. (Kluwer Academic, Dordrecht, 1989), pp. 457–490.
A. B. Migdal, Nucl. Phys. 13, 655 (1959).
M. Hoffberg, A. E. Glassgold, R. W. Richardson, and M. Ruderman, Phys. Rev. Lett. 24, 175 (1970).
M. Alpar, S. A. Langer, and J. A. Sauls, Ap. J. 282, 533 (1984).
M. A. Alpar and J. A. Sauls, Ap. J. 327, 723 (1988).
A. F. Andreev and E. P. Bashkin, Sov. Phys. JETP 42(1), 164 (1975).
G. A. Vardanyan and D. M. Sedrakian, Soviet Physics-JETP 54, 919 (1981).
G. Mendell and L. Lindblom, Ann. Phys. 205, 110 (1991).
G. Mendell, Ap. J. 380, 515 (1991); 530 (1991).
L. Lindblom and G. Mendell, Ap. J. 421, 689 (1994).
L. Lindblom and G. Mendell, Ap. J. 444, 804 (1995).
R. Prix, in preparation (2002).
B. Carter, in A Random Walk in General Relativity and Cosmology, N. Dadhich, J. Krishna Rao, J. V. Narlikar, and C. V. Vishveshwar, eds. (IAGRG, 1985), pp. 48.
B. Carter, in Lecture Notes in Mathematics 1385: Relativistic Fluid Dynamics, A. Anile and Y. Choquet-Bruhat (Springer, Heidelberg, 1989), pp. 1–64.
G. L. Comer and D. Langlois, Class. and Quant. Grav. 10, 2317 (1993).
G. L. Comer and D. Langlois, Class. and Quant. Grav. 11, 709 (1994).
B. Carter and D. Langlois, Phys. Rev. D 51, 5855 (1995).
B. Carter and D. Langlois, Nucl. Phys. B 454, 402 (1998).
B. Carter and D. Langlois, Nucl. Phys. B 531, 478 (1998).
D. Langlois, A. Sedrakian, and B. Carter, Mon. Not. R. Astron. Soc. 297, 1189 (1998).
B. Carter, D. Langlois, and D. M. Sedrakian, Astron. Astrophys. 361, 795 (2000).
R. Prix, Phys. Rev. D 62, 103005 (2000).
N. Andersson, G. L. Comer, and D. Langlois, Phys. Rev. D 66, 104002 (2002); also available as preprint LANL archive gr-qc/0203039.
N. Andersson, Ap. J. 502, 708 (1998).
J. L. Friedman and S. M. Morsink, Ap. J. 502, 714 (1998).
S. Chandrasekhar, Phys. Rev. Lett. 24, 611 (1970).
J. L. Friedman and B. F. Schutz, Ap. J. 221, 937 (1978); 222, 281 (1978).
J. L. Friedman, Commun. Math. Phys. 62, 247 1978.
L. Lindblom, B. Owen, and S. M. Morsink, Phys. Rev. Lett. 80, 4843 (1998).
B. J. Owen, L. Lindblom, C. Cutler, B. F. Schutz, A. Vecchio, and N. Andersson, Phys. Rev. D 58, 084020 (1998).
N. Andersson, K. D. Kokkotas, and B. F. Schutz, Ap. J. 510, 846 (1999).
L. Lindblom and G. Mendell, Phys. Rev. D 61, 104003 (2000).
N. Andersson and G. L. Comer, Mon. Not. R. Astron. Soc. 328, 1129 (2001).
R. I. Epstein, Ap. J. 333, 880 (1988).
N. Andersson and G. L. Comer, Class. and Quant. Grav. 18, 969 (2001).
R. Prix, G. L. Comer, and N. Andersson, Astron. Astrophys. 381, 178 (2002).
P. Haensel, Astron. Astrophys. 262, 131 (1992).
G. L. Comer, D. Langlois, and L. M. Lin, Phys. Rev. D 60, 104025 (1999).
S. J. Putterman, Superfluid Hydrodynamics (North-Holland, Amsterdam, 1974).
A. Akmal, V. R. Panharipande, and D. G. Ravenhall, Phys. Rev. C 58, 1804 (1998).
D. Pines and P. Nozières, The Theory of Quantum Liquids, Vol. 1 (Benjamin, New York, 1966).
M. Borumand, R. Joynt, and W. Kluźniak, Phys. Rev. C 54, 2745 (1996).
O. Sjöberg, Nucl. Phys. A 265, 511 (1976).
B. Carter, J. Math. Phys. 10, 70 (1969).
B. Carter, Comm. Math. Phys. 17, 233 (1970).
S. Bonazzola, E. Gourgoulhon, M. Salgado, and J.-A. Marck, Astron. Astrophys. 278, 421 (1993).
N. Stergioulas, “Rotating Stars in Relativity,” Living Reviews. Relativity 1 (1998). 8. [Online article]: cited on 15 Aug 2001 http://www.livingreviews.org/Articles/Volumel/ 1998-8stergio/.
E. Gourgoulhon, P. Haensel, R. Livine, E. Paluch, S. Bonazzola, and J.-A. Marck, Astron. Astrophys. 349, 851 (1999).
R. Prix, Astron. Astrophys. 352, 623 (1999).
J. B. Hartle, Ap. J. 150, 1005 (1967).
J. B. Hartle and K. S. Thorne, Ap. J. 163, 807 (1968).
S. Chandrasekar, Mon. Not. R. Astron. Soc. 93, 390 (1933).
E. A. Milne, Mon. Not. R. Astron. Soc. 83, 118 (1923).
M. Prakash, J. M. Lattimer, and T. L. Ainsworth, Phys. Rev. Lett. 61, 2518 (1988).
J. Font, T. Goodale, S. Iyer, M. Miller, L. Rezolla, E. Seidel, N. Stergioulas, W. Suen, and M. Tobias, Phys. Rev. D 65, 084024 (2002).
K. H. Lockitch and J. L. Friedman, Ap. J. 521, 764 (1999).
K. H. Lockitch, N. Andersson, and J. L. Friedman, Phys. Rev. D 63, 024019 (2001).
U. Lee, Astron. Astrophys. 303, 515 (1995).
A. Sedrakian and I. Wasserman, Phys. Rev. D 63, 024016 (2000).
R. Prix and M. Rieutord, preprint LANL archive astro-ph/0204520.
P. N. McDermott, H. M. Van Horn, and C. J. Hansen, Ap. J. 325, 725 (1988).
A. Reisenegger and P. Goldreich, Ap. J. 395, 240 (1992).
W. Unno, Y. Osaki, H. Ando, and H. Shibahashi, Nonradial Oscillations of Stars (University of Tokyo Press, 1989).
N. Andersson and G. L. Comer, Phys. Rev. Lett. 24, 241101 (2001).
V. V. Khodel, V. A. Khodel, and J. W. Clark, Nuc. Phys. A 679, 827 (2001).
T. Regge and J. A. Wheeler, Phys. Rev. 108, 1063 (1957).
S. Chandrasekhar, Ap. J. 140, 417 (1964).
K. S. Thorne and A. Campolattaro, Ap. J. 149, 591 (1967).
R. Price and K. S. Thorne, Ap. J. 155, 163 (1969).
K. S. Thorne, Ap. J. 158, 1 (1969).
K. S. Thorne, Ap. J. 158, 997 (1969).
A. Campolattaro and K. S. Thorne, Ap. J. 159, 847 (1970).
L. Lindblom and S. L. Detweiler, Ap. J. Supplement Series 53, 73 (1983).
S. L. Detweiler and L. Lindblom, Ap. J. 292, 12 (1985).
K. D. Kokkotas and B. F. Schutz, Mon. Not. R. Astron. Soc. 268, 119 (1992).
N. Andersson, K. D. Kokkotas, and B. F. Schutz, Mon. Not. R. Astron. Soc. 280, 1230 (1996).
Proceedings of the SOHO 10/GONG 2000 Workshop: Helio-and asteroseismology at the dawn of the millennium, A. Wilson, ed. (ESA Publications Division, 2001).
N. Andersson and K. D. Kokkotas, Phys. Rev. Lett. 77, 4134 (1996).
N. Andersson and K. D. Kokkotas, Mon. Not. R. Astron. Soc. 299, 1059 (1998).
K. D. Kokkotas, T. Apostolatos, and N. Andersson, Mon. Not. R. Astron. Soc. 302, 307 (2001).
P. R. Brady, T. Creighton, C. Cutler, and B. F. Schutz, Phys. Rev. D 57, 2101 (1998).
L. M. Franco, B. Link, and R. I. Epstein, Ap. J. 543, 987 (2000).
D. Hartmann, K. Hurley, and M. Niel, Ap. J. 387, 622 (1992).
I. H. Stairs, A. G. Lyne, and S. L. Shemar, Nature 406, 484 (2000). 1942 Comer
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Comer, G.L. Do Neutron Star Gravitational Waves Carry Superfluid Imprints?. Foundations of Physics 32, 1903–1942 (2002). https://doi.org/10.1023/A:1022322801696
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DOI: https://doi.org/10.1023/A:1022322801696