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An Astrophysical Application of Crystalline Color Superconductivity

An Astrophysical Application of Crystalline Color Superconductivity. Roberto Anglani Physics Department - U Bari Istituto Nazionale di Fisica Nucleare, Italy. SM & FT 2006 XIII workshop on S tatistical M echanics and non perturbative F ield T heory. Direct and Modified URCA processes.

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An Astrophysical Application of Crystalline Color Superconductivity

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  1. An Astrophysical Application of Crystalline Color Superconductivity Roberto Anglani Physics Department- UBari Istituto Nazionale di Fisica Nucleare, Italy SM&FT2006 XIII workshop on Statistical Mechanics and non perturbative Field Theory

  2. Direct and Modified URCA processes Neutrino emission due to direct URCA process is the most efficient cooling mechanism for a neutron star in the early stage of its lifetime. In stars made of nuclear matter only modified URCA processes can take place [1] because the direct processes n → p + e +  and e+ p → n +  are not kinematically allowed. If hadronic density in the core of neutron stars is sufficiently large, deconfined quark matter could be found. Iwamoto [2] has shown that in quark matterdirect URCA process, d → u + e +  ande + u → d +  are kinematically allowed,consequently thisenhances drammatically the emissivity and the cooling of the star [1] Shapiro and Teukolski, White Dwarfs, Black Holes and Neutron Stars. J.Wiley (New York) [2] Iwamoto, Ann. Phys. 141 1 (1982) Anglani (U Bari)

  3. Color Superconductivity in the CS core Matter in the core could be in one of the possible Color Superconductive phases Aged compact stars T < 100 KeV TCS is of order of 10-20 MeV:. Relevantdensity for compact stars: not asymptotic! Asymptotical densities: Color-Flavor-Locked phase is favored. But direct URCA processes are strongly suppressed in CFL phase because thermally excited quasiquarks are exponentially rare. effects due to the strange quark mass ms must be included. β– equilibrium Color neutrality Electrical neutrality a mismatch between Fermi momenta of different quarks depending on the in-medium value of ms. GROUND STATE ?????????????? Anglani (U Bari)

  4. The Great Below of gapless phases μ Asymtptotia Temple T=0 Great below of GAPLESS phases CHROMOMAGNETC INSTABILITY DANGER Huang and Shovkovy, PR D70 051501 (2004) Casalbuoni, et al.,PL B605 362 (2005) Fukushima, PR D72 074002 (2005) AlforD and Wang, J. Phys. G31 719 (2005) BUT THERE IS SOMETHING THAT MAY ENLIGHT THE WAY Ciminale, et al., PL B636 317 (2006) Anglani (U Bari)

  5. Simplified models of toy stars Noninteracting nuclear matter 3 Normal quark matter n ~ 9 n0 LOFF matter n ~ 9 n0 2 n ~ 1.5 n0 1 5 km 5 km 10 km 10 km Noninteracting nuclear matter Alford and Reddy nucl-th/0211046 n0 = 0.16 fm-1 M = 1.4 MO. 12 km - n ~ 1.5 n0 Anglani (U Bari)

  6. Dispersion laws for (rd –gu) and (rs – bu) • LOFF phase is gapless • Dispersion laws around gapless modes could be considered as linear Anglani (U Bari)

  7. “The importance of being gapless” The contribution of gapped modes are exponentially suppressed since we work in the regime T<<D<<m Each gapless mode contributes to specific heat by a factor ~ T Anglani (U Bari)

  8. Neutrino Emissivity We consider the following b – decay process (1) for colora= r, g, b. Neutrino emissivity = the energy loss by b-neutrino emission per volume unit per time unit. Neutrino Energy (2) Electron capture process Thermal distributions Bogoliubov coefficients Transition rate Anglani (U Bari)

  9. Cooling laws (1) t < ~1Myr main mechanism is neutrino emission t > ~1Myr main mechanism is photon emission Anglani (U Bari)

  10. Results A star with LOFF matter core cools faster than a star made by nuclear matter only. REM.: Similarity between LOFF and unpaired quark matter follows from linearity of gapless dispersion laws : ε~T6 cV ~T. Normal quark matter curve: only for comparison between different models. Anglani (U Bari)

  11. Conclusions • We have shown that due to existence of gapless mode in the LOFF phase, a compact star with a quark LOFF core cools faster than a star made by ordinary nuclear matter only. • These results must be consideredpreliminary.The simple LOFF ansatz should be substituted by the favored more complex crystalline structure [Rajagopal and Sharma, hep-ph/0605316]. • In this case (2.) identification of the quasiparticle dispersion laws is a very complicated task but probable future work. For this reason it is also difficult to attempt a comparison with present observational data. Anglani (U Bari)

  12. Acknowledgments Thanks to M. Ruggieri, G. Nardulli and M. Mannarelli for the fruitful collaboration which has yielded the work hep-ph/0607341, whose results underlie the present talk In these matters the only certainty is that nothing is certain. PLINY THE ELDER Roman scholar and scientist (23 AD - 79 AD) Anglani (U Bari)

  13. A look at the HOT BOTTLE Alford et al. [astro-ph/0411560] Lg~ T2.2 Lg~ T2.2 cV~ D0.5T0.5 cV~ T P1bu P2bu Anglani (U Bari)

  14. LOFF3 Dispersion laws Sector 123 Sector 45 Sector 67 Sector 89 Every quasiquark is a mixing of coloured quarks, weighted by Bogolioubov – Valatin coefficients. “Coloured” components of quasiparticles can be easily found in the sectors of Gap Lagrangean in an appropriate color-flavor basis. det S –1 = 0 Dispersion laws Ref. prof. Buballa Anglani (U Bari)

  15. Larkin-Ovchinnikov-Fulde-Ferrel state of art The simplified ansatz crystal structure is Larkin and Ovchinnikov; Fulde and Ferrell (1964) (1) i, j = 1, 2, 3 flavor indices; ,  = 1, 2, 3 color indices; 2qI represents the momentum of Cooper pair andD1, D2, D3describe respectively d – s, u – s, u – d pairings. LOFF phase has been found energetically favored [1,2] with respect to the gCFL and the unpaired phases in a certain range of values of the mismatch between Fermi surfaces. [Ref. Ippolito’s talk and Buballa’s lecture]. [1] Casalbuoni, Gattoet al., PL B627 89 (2005) [2] Rajagopal et al., hep-ph/0603076 This phase resultschromomagnetically stable [3] [3] Ciminale, Gatto et al., PL B636 317 (2006) Anglani (U Bari)

  16. D1 = 0; D2 = D3 = D < 0.3 D0 [1] q2=q3=q = m2s/(8 m zq); zq ~ 0.83 [1] Neutral LOFF quark matter - 1 • Three light quarks u, d, s, in a color and electrically neutral state • Quark interactions are described employing a Nambu-Jona Lasinio model in a mean field approximation • We employ a Ginzburg-Landau expansion [1] [1] Casalbuoni et al., PL B627 89 (2005) Requiring color and electric neutrality, the energetically favored phase results in Rajagopal et al., hep-ph/0605316 (1) where D0is the CFL gap. The GL approximation is reliable in a region close to the second order phase transition point where the crystal structure is characterized by (2) Anglani (U Bari)

  17. D0 = 25 MeV m3 = m8 = 0 and me=ms2/4m [1] m = 500 MeV y= ms2/m  [130,150] MeV y = 140 MeV Neutral LOFF quark matter - 2 To the leading order approximation indm/mone obtains [1] Casalbuoni, Gatto, Nardulli et al., hep-ph/0606242 (1) The LOFF phase is energetically favored with respect to gCFL and normal phase in the range of chemical potential mismatch of (2) Finally, for our numerical estimates we use (3) (4) (5) Anglani (U Bari)

  18. Dispersion laws for (ru–gd –bs) Anglani (U Bari)

  19. Appendix A: Emissivity Anglani (U Bari)

  20. Appendix B: Specific Heat μ = 500 MeV; ms = (μ 140)1/2 MeV; D1 = 0; D2 = D3 = D~ 6 MeV. Anglani (U Bari)

  21. Appendix C: Dispersion laws Anglani (U Bari)

  22. Appendix D: Dispersion laws 3X3 Anglani (U Bari)

  23. Appendix E: Cooling laws Anglani (U Bari)

  24. Appendix F: Redifinition of gapless modes Anglani (U Bari)

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