1. Neutron star interiors: are we there yet? Gordon Baym, University of Illinois Workshop on Supernovae and Gamma-Ray Bursts YIPQS Kyoto’ October 28, 2013

2. Mass ~ 1.4-2 M sun Radius ~ 10-12 km Temperature ~ 10 6 -10 9 K Surface gravity ~10 14 that of Earth Surface binding ~ 1/10 mc 2 Density ~ 2x10 14 g/cm 3 Neutron star interior Mountains < 1 mm

3. Nuclei before neutron drip e - +p n +  makes nuclei neutron rich as electron Fermi energy increases with depth n p+ e - + : not allowed if e - state already occupied _ Beta equilibrium:  n =  p +  e Shell structure (spin-orbit forces) for very neutron rich nuclei? Do N=50, 82 remain magic numbers? Being explored at rare isotope accelerators, RIKEN, GSI, FRIB, KORIA

4. Valley of  stability in neutron stars neutron drip line

5. RIKEN, H. Sakurai 2013

6. No shell effect for Mg(Z=12), Si(14), S(16), Ar(18) at N=20 and 28 Loss of shell structure for N >> Z even

7. Instability of bcc lattice in the inner crust D. Kobyakov and C. J. Pethick, ArXiv 1309.1891 BCC: Lower energy than FCC or simple cubic. Predicted (pre-pasta) Coulomb structure at crust-liquid interface GB, H. A. Bethe, C. J. Pethick, Nucl. Phys. A 175, 225 (1971) But effective finite wavenumber proton-proton interaction strongly modified by screening: k FT = Thomas-Fermi screening length For k > k FT screening by electron less effective. Critical wavenumber above which pp interaction is attractive:

8. Most unstable direction determined from modification of elastic constants J. Cahn, Acta Metallurgica 10, 179 (1962) Possibly leads to BaTiO 3 -like structure: Similar to pasta phases of nuclei, rearrangement of lattice structure a ffects thermodynamic and transport properties of crust; effects on cooling and glitches, pinning of n vortices, crust bremsstrahlung of neutrinos. Modifies elastic properties of crust (breaking strains, modes,...) affect on precursors of γ-ray bursts in NS mergers, and generation of gravitational radiation.

9. Pasta Nuclei over half the mass of the crust !! onset when nuclei fill ~ 1/8 of space Lorentz, Pethick and Ravenhall. PRL 70 (1993) 379 Iida, Watanabe and Sato, Prog Theo Phys 106 (2001) 551; 110 (2003) 847 Important effects on crust bremsstrahlung of neutrinos, pinning of n vortices,...

10. Sonoda, Watanabe, Sato, Yasuoka and Ebisuzaki, Phys. Rev. C77 (2008) 035806 QMD simulations of pasta phases T=0 0.10 0.20 0.39 0.49 0.58 T>0 Pasta phase diagram

11. Properties of liquid interior near nuclear matter density Determine N-N potentials from - scattering experiments E<300 MeV - deuteron, 3 body nuclei ( 3 He, 3 H) ex., Paris, Argonne, Urbana 2 body potentials Solve Schrödinger equation by variational techniques Two body potential alone: Underbind 3 H: Exp = -8.48 MeV, Theory = -7.5 MeV 4 He: Exp = -28.3 MeV, Theory = -24.5 MeV Large theoretical extrapolation from low energy laboratory nuclear physics at near nuclear matter density

12. Importance of 3 body interactions Attractive at low density Repulsive at high density Stiffens equation of state at high density Large uncertainties Various processes that lead to three and higher body intrinsic interactions (not described by iterated nucleon-nucleon interactions).

13.  0 condensate Energy per nucleon in pure neutron matter Akmal, Pandharipande and Ravenhall, Phys. Rev. C58 (1998) 1804

14. Akmal, Pandharipande and Ravenhall, 1998 Mass vs. central density Mass vs. radius Maximum neutron star mass Neutron star models using static interactions between nucleons

15. Equation of state vs. neutron star structure from J. Lattimer

16. Well beyond nuclear matter density Hyperons: , ,... Meson condensates:  -,  0, K - Quark matter in droplets in bulk Color superconductivity Strange quark matter absolute ground state of matter?? strange quark stars? Onset of new degrees of freedom: mesonic,  ’s, quarks and gluons,... Properties of matter in this extreme regime determine maximum neutron star mass. Large uncertainties!

17. Hyperons in dense matter Produce hyperon X of baryon no. A and charge eQ when A  n - Q  e > m X (plus interaction corrections).  n = baryon chemical potential and  e = electron chemical potential Ex. Relativistic mean field model w. baryon octet + meson fields, w. input from double-Λ hypernuclei. Bednarek et al., Astron & Astrophys 543 (2012) A157 Y = number fraction vs. baryon density Significant theoretical uncertainties in forces! Hard to reconcile large mass neutron stars with softening of e.o.s due to hyperons -- the hyperon problem. Requires stiff YN interaction.

18. Accurate for n ~ n 0. n >> n 0 : -can forces be described with static few-body potentials? -Force range ~ 1/2m  => relative importance of 3 (and higher) body forces ~ n/(2m  ) 3 ~ 0.4n fm-3. -No well defined expansion in terms of 2,3,4,...body forces. -Can one even describe system in terms of well-defined ``asymptotic'' laboratory particles? Early percolation of nucleonic volumes! Fundamental limitations of equation of state based on nucleon-nucleon interactions alone:

19. Lattice gauge theory calculations of equation of state of QGP Not useful yet for realistic chemical potentials

20. Learning about dense matter from neutron star observations Challenges to nuclear theory!!

21. High mass neutron star, PSR J1614-2230 -- in neutron star-white dwarf binary Spin period = 3.15 ms; orbital period = 8.7 day Inclination = 89:17 o ± 0:02 o : edge on M neutron star =1.97 ± 0.04M  ; M white dwarf = 0.500 ±006M  (Gravitational) Shapiro delay of light from pulsar when passing the companion white dwarf Demorest et al., Nature 467, 1081 (2010); Ozel et al., ApJ 724, L199 (2010).

22. Second high mass neutron star, PSRJ0348+0432 -- in neutron star-white dwarf binary Spin period = 39 ms; orbital period = 2.46 hours Inclination =40.2 o M neutron star =2.01 ± 0.04M  ; M white dwarf = 0.172 ±0.003M  Significant gravitational radiation 400 Myr to coalescence! Antonidas et al., Science 340 1233232 (April 26, 2013)

23. A third high mass neutron star, PSR J1311-3430 -- in neutron star - flyweight He star binary M neutron star > 2.0 M  ; M companion ~ 0.01-0.016M  Romani et al., Ap. J. Lett., 760:L36 (2012) Uncertainties arising from internal dynamics of companion

24. Akmal, Pandharipande and Ravenhall, 1998

25. M vs R from bursts, Ozel at al, Steiner et al. Mass vs. radius determination of neutron stars in burst sources

26. J. Poutanan, at Trento workshop on Neutron-rich matter and neutron stars, 30 Sept. 2013

27. Or perhaps overestimated, since R. Rutledge, at Trento workshop on Neutron-rich matter and neutron stars, 30 Sept. 2013

30. Phase diagram of equilibrated quark gluon plasma Karsch & Laermann, 2003 Critical point Asakawa-Yazaki 1989. 1 st order crossover

31. Quark matter cores in neutron stars Canonical picture: compare calculations of eqs. of state of hadronic matter and quark matter. Crossing of thermodynamic potentials => first order phase transition. Typically conclude transition at  ~ 10  nm -- would not be reached in neutron stars given observation of high mass PSR J1614-2230 with M = 1.97M  => no quark matter cores ex. nuclear matter using 2 & 3 body interactions, vs. pert. expansion or bag models. Akmal, Pandharipande, Ravenhall 1998

32. Fukushima & Hatsuda, Rep. Prog. Phys. 74 (2011) 014001

33. K. Fukushima (IPad)

34. BEC-BCS crossover in QCD phase diagram Normal Color SC (as m s increases) BCS paired quark matter BCS-BEC crossover Hadrons Hadronic Small quark pairs are “diquarks” GB, T.Hatsuda, M.Tachibana, & Yamamoto. J. Phys. G: Nucl. Part. 35 (2008) 10402 H. Abuki, GB, T. Hatsuda, & N. Yamamoto,Phys. Rev. D81, 125010 (2010)

35. Continuous evolution from nuclear to quark matter K. Masuda, T. Hatsuda, & T. Takatsuka, Ap. J.764, 12 (2013)

36. Hadron-quark crossover equation of state K. Masuda, T. Hatsuda, &T. Takatsuka, Ap. J.764, 12 (2013) Neutron matter at low density with smooth interpolation to Nambu Jona-Lasinino model of quark matter at high density quark content vs. density E.o.s. with interpolation between 2 - 4

37. Model calculations of phase diagram with axial anomaly, pairing, chiral symmetry breaking & confinement NJL alone: H. Abuki, GB, T. Hatsuda, & N. Yamamoto, PR D81, 125010 (2010). NPL with Polyakov loop description of confinement: P. Powell & GB PR D 85, 074003 (2012) Couple quark fields together with effective 4 and 6 quark interactions: At mean field level, effective couplings of chiral field φ and pairing field d: K and K’ from axial anomaly PNJL phase diagram

38. Model calculations of neutron star matter and neutron stars within NJL model NJL Lagrangian supplemented with universal repulsive quark-quark vector coupling K. Masuda, T. Hatsuda, & T. Takatsuka, Ap. J.764, 12 (2013) GB, T. Hatsuda, P. Powell,... (to be published) Include up, down, and strange quarks with realistic masses and spatially uniform pairing wave functions Smoothly interpolate from nucleonic equation of state (APR) to quark equation of state: 0 5 1 1.5 pressure baryon density mass density

39. Neutron star equation of state vs. phenomenological fits to observed masses and radii Lines from bottom to top: g V /G = 0, 1, 1.5, 5 Cross-hatched region = Ozel et al. (2010) Shaded region = Steiner et al. (2010)

40. Masses and radii of neutron stars vs. central mass density from integrating the TOV equation 0 1 1.5 5 g v /G= Mass vs. central density: only stars on rising curves are stable M vs. R: only stars on rapidly rising curves are stable

41. Maximum neutron star mass vs. g V PNJL accomodates large mass neutron stars as well as strange quarks -- avoiding the “hyperon problem” -- and is consistent with observed masses and radiii

42. But we are not quite there yet: Uncertainties in interpolating from nuclear matter to quark matter lead to errors in maximum neutron star masses and radii. Uncertainties in the vector coupling g v The NJL model does not treat gluon effects well, which leads to uncertainties in the “bag constant” B of quark matter: At very high baryon density, the energy density is E = B + Cp f 4, with B ~ 100-200 MeV/fm 3. Then the pressure is P = -B + Cp f 4 /3. Effect of B on maximum neutron star mass? Need to calculate gluon contributions accurately to pin down B.

43. どうもありがとう