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Neutrino emission from Goldstone modes in dense quark matter

Prashanth Jaikumar and Madappa Prakash

Thomas Schäfer

  • Department of Physics & Astronomy, SUNY at Stony Brook, New York 11794

  • Department of Physics & Astronomy, SUNY at Stony Brook, New York 11794
  • Department of Physics, Duke University, Durham, North Carolina 27708
  • Riken-BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973

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Phys. Rev. D 66, 063003 – Published 12 September, 2002

DOI: https://doi.org/10.1103/PhysRevD.66.063003

Abstract

We calculate neutrino emissivities from the decay and scattering of Goldstone bosons in the color-flavor-locked (CFL) phase of quarks at high baryon density. Interactions in the CFL phase are described by an effective low-energy theory. For temperatures in the tens of keV range, relevant to the long-term cooling of neutron stars, the emissivities involving Goldstone bosons dominate over those involving quarks, because gaps in the CFL phase are ∼100MeV while the masses of Goldstone modes are on the order of 10 MeV. For the same reason, the specific heat of the CFL phase is also dominated by the Goldstone modes. Notwithstanding this, both the emissivity and the specific heat from the massive modes remain rather small, because of their extremely small number densities. The values of the emissivity and the specific heat imply that the time scale for the cooling of the CFL core is ∼1026yr, which makes the CFL phase invisible as the exterior layers of normal matter surrounding the core will continue to cool through significantly more rapid processes. If the CFL phase appears during the evolution of a protoneutron star, neutrino interactions with Goldstone bosons are expected to be significantly more important since temperatures are high enough (∼20–40MeV) to admit large number densities of Goldstone modes.

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References (55)

  1. M. Prakash, J.M. Lattimer, R.F. Sawyer, and R.R. Volkas, Annu. Rev. Nucl. Part. Sci. 51, 295 (2001).
  2. A. Burrows, Nature (London) 403, 727 (2000).
  3. A. Burrows and J.M. Lattimer, Astrophys. J. 307, 178 (1986); W. Keil and H.T. Janka, Astron. Astrophys. 296, 145 (1995); J.A. Pons, S. Reddy, M. Prakash, J.M. Lattimer, and J.A. Miralles, Astrophys. J. 513, 780 (1999); J.A. Pons, A.W. Steiner, M. Prakash, and J.M. Lattimer, Phys. Rev. Lett. 86, 5223 (2001).
  4. C.J. Pethick, Rev. Mod. Phys. 64, 1133 (1992); M. Prakash, Phys. Rep. 242, 297 (1994); ibid.D.G. Yakovlev, A.D. Kaminker, O.Y. Gnedin, and P. Haensel, 354, 1 (2001).
  5. J.C. Collins and M.J. Perry, Phys. Rev. Lett. 30, 1353 (1975).
  6. S. C. Frautschi, in Proceedings of the Workshop on Hadronic Matter at Extreme Energy Density, edited by N. Cabibbo and L. Sertorio (Plenum, New York, 1978), p. 18.
  7. B.C. Barrois, Nucl. Phys. B129, 390 (1977).
  8. F. Barrois, Ph. D. thesis, California Institute of Technology, UMI 79-04847-mc (microfiche).
  9. D. Bailin and A. Love, Phys. Rep. 107, 325 (1984).
  10. M. Alford, K. Rajagopal, and F. Wilczek, Phys. Lett. B 422, 247 (1998).
  11. R. Rapp, T. Schäfer, E.V. Shuryak, and M. Velkovsky, Phys. Rev. Lett. 81, 53 (1998).
  12. M.G. Alford, K. Rajagopal, and F. Wilczek, Nucl. Phys. B537, 443 (1999).
  13. R. Rapp, T. Schäfer, E.V. Shuryak, and M. Velkovsky, Ann. Phys. (N.Y.) 280, 35 (2000).
  14. T. Schäfer, Nucl. Phys. B575, 269 (2000).
  15. N. Evans, J. Hormuzdiar, S.D. Hsu, and M. Schwetz, Nucl. Phys. B581, 391 (2000).
  16. D. Blaschke, T. Klahn, and D.N. Voskresensky, Astrophys. J. 533, 406 (2000).
  17. D. Page, M. Prakash, J.M. Lattimer, and A. Steiner, Phys. Rev. Lett. 85, 2048 (2000).
  18. M.G. Alford, J.A. Bowers, and K. Rajagopal, J. Phys. G 27, 541 (2001).
  19. G.W. Carter and S. Reddy, Phys. Rev. D 62, 103002 (2000).
  20. M. Prakash, J.R. Cooke, and J.M. Lattimer, Phys. Rev. D 52, 661 (1995); M. Prakash et al., Phys. Rep. 280, 1 (1997); A.W. Steiner, M. Prakash, and J.M. Lattimer, Phys. Lett. B 509, 10 (2001); see also [33].
  21. P. Jaikumar and M. Prakash, Phys. Lett. B 516, 345 (2001).
  22. D.K. Hong, M. Rho, and I. Zahed, Phys. Lett. B 468, 261 (1999).
  23. R. Casalbuoni and R. Gatto, Phys. Lett. B 464, 111 (1999).
  24. D.T. Son and M.A. Stephanov, Phys. Rev. D 61, 074012 (2000).
  25. M. Rho, A. Wirzba, and I. Zahed, Phys. Lett. B 473, 126 (2000).
  26. R. Casalbuoni, Z. Duan, and F. Sannino, Phys. Rev. D 63, 114026 (2001).
  27. D.K. Hong, H.K. Lee, M.A. Nowak, and M. Rho, First KIAS Workshop on Astrophysics, Seoul, 2000, hep-ph/0010156.
  28. T. Schäfer, Phys. Rev. D 65, 094033 (2002).
  29. T. Schäfer, Phys. Rev. D 65, 074006 (2002).
  30. P.F. Bedaque and T. Schäfer, Nucl. Phys. A697, 802 (2002).
  31. K. Zarembo, Phys. Rev. D 62, 054003 (2000).
  32. K. Rajagopal and F. Wilczek, Phys. Rev. Lett. 86, 3492 (2001).
  33. D.B. Kaplan and S. Reddy, Phys. Rev. D 65, 054042 (2002).
  34. M. Alford, K. Rajagopal, S. Reddy, and F. Wilczek, Phys. Rev. D 64, 074017 (2001).
  35. N. Iwamoto, Phys. Rev. Lett. 44, 1637 (1980).
  36. N. Iwamoto, Ann. Phys. (N.Y.) 141, 1 (1982).
  37. J.B. Adams, M.A. Ruderman, and C.-H. Woo, Phys. Rev. 129, 1383 (1963).
  38. E. Braaten, Phys. Rev. Lett. 66, 1655 (1991).
  39. E. Braaten and D. Segel, Phys. Rev. D 48, 1478 (1993).
  40. D.F. Litim and C. Manuel, Phys. Rev. D 64, 094013 (2001).
  41. P. Jaikumar, R. Rapp, and I. Zahed, Phys. Rev. C 65, 055205 (2002).
  42. T. Schäfer, Phys. Rev. Lett. 85, 5531 (2000).
  43. P.F. Bedaque, Phys. Lett. B 524, 137 (2002).
  44. J.N. Bahcall and R.A. Wolf, Phys. Rev. 140, B1445 (1965).
  45. B. Friman and O. Maxwell, Astrophys. J. 293, 470 (1985).
  46. D.T. Son, hep-ph/0204199.
  47. M.A. Nowak, M. Rho, A. Wirzba, and I. Zahed, Phys. Lett. B 497, 85 (2001).
  48. M. E. Peskin and D. V. Schroeder, Quantum Field Theory (Addison-Wesley, Redwood City, CA, 1995).
  49. J.M. Lattimer, K.A. Van Riper, M. Prakash, and Manju Prakash, Astrophys. J. 425, 802 (1994).
  50. J.M. Lattimer, C.J. Pethick, M. Prakash, and P. Haensel, Phys. Rev. Lett. 66, 2701 (1991).
  51. M. Prakash, Manju Prakash, J.M. Lattimer, and C.J. Pethick, Astrophys. J. Lett. 390, L77 (1992).
  52. D. Page and V.V. Usov, astro-ph/0204275.
  53. V.V. Usov, Phys. Rev. Lett. 80, 230 (1998).
  54. S. Reddy, M. Sadzikowski, and M. Tachibana, nucl-th/0203011.
  55. I.A. Shovkovy and P.J. Ellis, Phys. Rev. C 66, 015802 (2002).

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Phys. Rev. D 66, 063003– Published 12 September, 2002
  • Received 6 March 2002

© 2002 American Physical Society

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