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Neutron stars and the properties of matter at high density

Neutron stars and the properties of matter at high density. Gordon Baym, University of Illinois. Future Prospects of Hadron Physics at J-PARC and Large Scale Computational Physics ’ 11 February 2012. Neutron star interior. Mountains < 1 mm. Mass ~ 1.4-2 M sun Radius ~ 10-12 km

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Neutron stars and the properties of matter at high density

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  1. Neutron stars and the properties of matter at high density Gordon Baym, University of Illinois Future Prospects of Hadron Physics at J-PARC and Large Scale Computational Physics’ 11 February 2012

  2. Neutron star interior Mountains < 1 mm Mass ~ 1.4-2 Msun Radius ~ 10-12 km Temperature ~ 106-109 K Surface gravity ~1014 that of Earth Surface binding ~ 1/10 mc2 Density ~ 2x1014g/cm3

  3. Masses ~ 1-2 M Baryon number ~ 1057 Radii ~ 10-12 km Magnetic fields ~ 106 - 1015G Made in gravitational collapse of massive stars (supernovae) Central element in variety of compact energetic systems: pulsars, binary x-ray sources, soft gamma repeaters Merging neutron star-neutron star and neutron star-black hole sources of gamma ray bursts Matter in neutron stars is densest in universe: r up to ~ 5-10 r0 (r0= 3X1014g/cm3 = density of matter in atomic nuclei) [cf. white dwarfs: r~ 105-109 g/cm3] Supported against gravitational collapse by nucleon degeneracy pressure Astrophysical laboratory for study of high density matter complementary to accelerator experiments What are states in interior? Onset of quark degrees of freedom! Do quark stars, as well as strange stars exist?

  4. The liquid interior Neutrons (likely superfluid)~ 95% Non-relativistic Protons (likely superconducting) ~ 5% Non-relativistic Electrons (normal, Tc~ Tf e-137) ~ 5% Fully relativistic Eventually muons, hyperons, and possibly exotica: pion condensation kaon condensation quark droplets bulk quark matter n0 = baryon density in large nuclei 0.16 fm-3 1fm = 10-13cm Phase transition from crust to liquid at nb 0.7 n0 0.09 fm-3 or r = mass density ~ 2 X1014g/cm3

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

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

  7. Three body forces in polarized pd and dp scattering 135 MeV/A (RIKEN) (K. Sekiguchi 2007) Blue = 2 body forces Red = 2+3 body forces

  8. Energy per nucleon in pure neutron matter Akmal, Pandharipande and Ravenhall, Phys. Rev. C58 (1998) 1804 p0 condensate

  9. Energy per nucleon in pure neutron matter Morales, (Pandharipande) & Ravenhall, in progress p0 condensate AV-18 + UIV 3-body (IL 3-body too attractive) Improved FHNC algorithms. Two minima! E/A slightly higher than Akmal, Pandharipande and Ravenhall, Phys. Rev. C58 (1998) 1804

  10. Maximum neutron star mass Mass vs. central density Mass vs. radius Akmal, Pandharipande and Ravenhall, 1998

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

  12. Fundamental limitations of equation of state based on nucleon-nucleon interactions alone: Accurate for n~ n0. n >> n0: -can forces be described with static few-body potentials? -Force range ~ 1/2m => relative importance of 3 (and higher) body forces ~n/(2m)3~ 0.4nfm-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!

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

  14. New critical point in phase diagram: induced by chiral condensate – diquark pairing coupling via axial anomaly Normal QGP Hadronic Color SC Hatsuda, Tachibana, Yamamoto & GB, PRL 97, 122001 (2006) Yamamoto, Hatsuda, Tachibana & GB, PRD76, 074001 (2007) GB, Hatsuda, Tachibana, & Yamamoto. J. Phys. G: Nucl. Part. 35 (2008) 10402 Abuki, GB, Hatsuda, & Yamamoto,Phys. Rev. D81, 125010 (2010) (as ms increases)

  15. BCS-BEC crossover BCS paired quark matter Hadrons Normal Color SC BEC-BCS crossover in QCD phase diagram J. Phys.G: Nucl. Part. Phys. 35 (2008) Hadronic (as ms increases) Small quark pairs are “diquarks”

  16. 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, arXiv:1111.5911 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: PNJL phase diagram K and K’ from axial anomaly

  17. Spatially ordered chiral transition = quarkyonic phase Kojo, Hidaka, Fukushima, McLerran, & Pisarski ,arXiv:1107.2124 Structure deduced in limit of large number of colors, Nc

  18. Well beyond nuclear matter density Onset of new degrees of freedom: mesonic, D’s, quarks and gluons, ... Properties of matter in this extreme regime determine maximum neutron star mass. Large uncertainties! Hyperons: S, L, ... Meson condensates: p-, p0, K- Quark matter in droplets in bulk Color superconductivity Strange quark matter absolute ground state of matter?? strange quark stars?

  19. Hyperons in dense matter Produce hyperon X of baryon no. A and charge eQ when Amn - Qme > mX (plus interaction corrections) Djapo, Schaefer & Wambach, PhysRev C81, 035803 (2010)

  20. Pion condensed matter Softening of collective spin-isospin oscillation of nuclear matter Above critical density have transition to new state with nucleons rotated in isospin space: with formation of macroscopic pion field

  21. Strangeness (kaon) condensates Analogous to p condensate Chiral SU(3) X SU(3) symmetry of strong interactions => effective low energy interaction Kaplan and Nelson (1986), Brown et al. (1994) “Effective mass” term lowers K energies in matter => condensation =>

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

  23. Learning about dense matter from neutron star observations

  24. Learning about dense matter from neutron star observations Masses of neutron stars Binary systems: stiff eos Thermonuclear bursts in X-ray binaries => Mass vs. Radius, strongly constrains eos Glitches: probe n,p superfluidity and crust Cooling of n-stars: search for exotica

  25. Dense matter from neutron star mass determinations Softer equation of state => lower maximum mass and higher central density Binary neutron stars ~ 1.4 M consistent with soft e.o.s. Cyg X-2: M=1.78 ± 0.23M Vela X-1: M=1.86 ± 0.33Mallow some softening PSR J1614-2230 M=1.97 ± 0.04M allows no softening; begins to challenge microscopic e.o.s.

  26. Neutron Star Masses ca. 2007

  27. 1.4 M 1.4 M Vela X-1 (LMXB) light curves Serious deviation from Keplerian radial velocity Excitation of (supergiant) companion atmosphere? M=1.86 ± 0.33 M¯ M. H. van Kerkwijk, astro-ph/0403489 1.7 M <M<2.4 M Quaintrell et al., A&A 401, 313 (2003)

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

  29. Highest mass neutron star M= 1.97±0.04 M

  30. Akmal, Pandharipande and Ravenhall, 1998

  31. Can Mmax be larger? Larger Mmax requires larger sound speed cs at lower n. For nucleonic equation of state, cs -> c at n ~7n0. Further degrees of freedom, e.g., hyperons, mesons, or quarks at n ~7n0 lower E/A => matter less stiff. Stiffer e.o.s. at lower n => larger Mmax. If e.o.s. very stiff beyond n =2n0, Mmax can be as large as 2.9 M. Stiffer e.o.s. => larger radii .

  32. Eddington Luminosity Apparent Radius Time (s) Measuring masses and radii of neutron stars in thermonuclear bursts in X-ray binaries Ozel et al., 2006-20l2 Measurements of apparent surface area, & flux at Eddington limit (radiation pressure = gravity), combined with distance to star constrains M and R.

  33. Mass vs. radius determination of neutron stars in burst sources Ozel et al., ApJ 2009-2011 4U 1820-30 in globular cluster NGC 6624, D = 6.8 - 9.6 kpc 4U 1608-52 in NGC 6624 EXO 1745-248 in globular cluster Terzan 5, D = 6.30.6 kpc (HST) KS 1731-260 Galactic bulge source

  34. M vs R from bursts, Ozel at al, Steiner et al.

  35. Pressure vs. mass density of cold dense matter inferred from neutron star observations Fit equation of state with polytropes above Ozel, GB, & Guver Steiner, Lattimer, & Brown PRD 82 (2010) Ap. J. 722 (2010) - little stiffer Results ~ consistent with each other and with maximum mass ~ 2 M

  36. 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. ex. nuclear matter using 2 & 3 body interactions, vs. pert. expansion or bag models. Akmal, Pandharipande, Ravenhall 1998 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

  37. More realistically, expect gradual onset of quark degrees of freedom in dense matter Normal Hadronic Color SC New critical point suggests transition to quark matter is a crossover at low T Consistent with percolation picture that as nucleons begin to overlap, quarks percolate [GB, Physics 1979] nperc ~ 0.34 (3/4 rn3) fm-3 Quarks can still be bound even if deconfined. Calculation of equation of state remains a challenge for theorists

  38. More realistically, expect gradual onset of quark degrees of freedom in dense matter Normal Hadronic Color SC New critical point suggests transition to quark matter is a crossover at low T Consistent with percolation picture that as nucleons begin to overlap, quarks percolate [GB, Physics 1979] nperc ~ 0.34 (3/4 rn3) fm-3 Quarks can still be bound even if deconfined. Calculation of equation of state remains a challenge for theorists

  39. Present observations of high mass neutron stars M ~ 2Mbegin to confront microscopic nuclear physics. High mass neutron stars => very stiff equation of state, with nc < 7n0. At this point for nucleonic equation of state, sound speed cs = ( P/)1/2  c. Naive theoretical predictions based on sharp deconfinement transition would be inconsistent with presence of (soft) bulk quark matter in neutron stars. Further degrees of freedom, e.g., hyperons, mesons, or quarks at n < 7n0 lower E/A => matter less stiff. Quark cores would require very stiff quark matter. Expect gradual onset of quark degrees of freedom.

  40. どうもありがとう

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

  42. Valley of b stability in neutron stars neutron drip line

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

  44. Neutron Star Models E = energy density = r c2 nb = baryon density P(r) = pressure = nb2¶(E/nb)/¶ nb Equation of state: Tolman-Oppenheimer-Volkoff equation of hydrostatic balance: general relativistic corrections = mass within radius r 1) Choose central density: r(r=0) = rc 2) Integrate outwards until P=0 (at radius R) 3) Mass of star

  45. Maximum mass of a neutron star Say that we believe equation of state up to mass density r0 but e.o.s. is uncertain beyond r(Rc) = r0 Weak bound: a) core not black hole => 2McG/c2 < Rc b) Mc = s0Rc d3r r(r) ³ (4p/3) r0Rc3 => c2Rc/2G ³ Mc ³ (4p/3) r0Rc3 Rs¯=2M¯ G/c2 = 2.94 km Mcmax = (3M¯/4pr0Rs¯3)1/2M¯ Mmax ³ 13.7 M¯ £(1014g/cm3/r0)1/2 4pr0Rc3/3 Outside material adds ~ 0.1 M¯

  46. Strong bound:require speed of sound, cs, in matter in core not to exceed speed of light: cs2 = ¶P/¶r£ c2 Maximum core mass when cs = c Rhodes and Ruffini (PRL 1974) WFF (1988) eq. of state => Mmax= 6.7M¯(1014g/cm3/r0)1/2 V. Kalogera and G.B., Ap. J. 469 (1996) L61 r0 = 4rnm => Mmax = 2.2 M¯ 2rnm => 2.9 M¯

  47. Neutron drip Beyond density rdrip~ 4.3 X 1011 g/cm3 neutron bound states in nuclei become filled. Further neutrons must go into continuum states. Form degenerate neutron Fermi sea. Neutrons in neutron sea are in equilibrium with those inside nucleus Protons never drip, but remain in bound states until nuclei merge into interior liquid. Free neutrons form 1S0 BCS paired superfluid

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