1. Neutron stars and quark matter Gordon Baym University of Illinois, Urbana 21 st Century COE Workshop: Strongly Correlated Many-Body Systems from Neutron Stars to Cold Atoms 19 January 2006 東京大学

2. Mass ~ 1.4 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 Mountains < 1 mm Density ~ 2x10 14 g/cm 3 Cross section of a neutron star

3. Properties of matter 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 3

4. 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).

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

6. Akmal, Pandharipande and Ravenhall, 1998 Mass vs. central density Mass vs. radius Maximum neutron star mass 2.2M ¯

7. Accurate for n » n 0. n À 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? Fundamental limitations of equation of state based on nucleon interactions alone:

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

9. もしほんの一つ二つクレイジーな仮定をすれば、 あなたは私の言動のすべてが正しいと解るよ。

10. neutron stars?Solid state physics Low energy nuclear physics (1983)

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12. Phase diagram of quark gluon plasma Karsch & Laermann, hep-lat/0305025 2nd order tricritical pt. 1st order

13. Hatsuda, Tachibana, Yamamoto & GB, PRL 97, 122001 (2006) New critical point in phase diagram : induced by chiral condensate – diquark pairing coupling via axial anomaly Hadronic Normal Color SC (as m s increases)

14. Predictions of phase transition at finite  Lattice gauge theory Strong coupling qcd Kawamoto et al., hep-lat/0512023 Effective (NJL) theories Ratti,Thaler,&Weise, nucl-th/0604025 N f =2 de Forcrand & Kratochvila hep-lat/0602024

15. Onset of quark matter at low temperatures difficult to predict via lattice gauge theory.  c » 5-10  nm Observations of massive neutron stars, M » 2M ¯ => equation of state stiff, and central density so low that sharp transition to bulk quark liquid unlikely. Quark droplets in nuclear matter. Gradual onset of quark degrees of freedom.

16. Quark Droplets in Nuclear Matter Glendenning; Heiselberg; Pethick, Ravenhall and Staubo Favorable to form negatively charged quark droplets n u ~100, n d ~n s ~300, R~5fm Q~ -150|e| at lower densities than quark-hadron transition since they 1) reduce no. of electrons in matter 2) increase fraction of protons in nuclear matter Neutron stars likely to have such mixed phase cores, but results are very model dependent

17. In fact, expect similar pasta phases of quark droplets: Structure, neutrino emissivity?

18. a)Masses of neutron stars: equation of state b)Glitches: probe n,p superfluidity and crust c)Cooling of n-stars: search for exotica d)Burst oscillations: probe nuclear physics to ~10 9 g/cm 3 Learning about dense matter from neutron star observations

19. Infer masses from periods and Doppler shifts

20. 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 ± 0.15M ¯ allow some softening PSR J0751+1807: M » 2.1 M ¯ no softening QPO 4U1820-30: M » 2.2-2.3 M ¯ challenge microscopic e.o.s.

21. Measured neutron star masses in radio pulsars Thorsett and Chakrabarty, Ap. J. 1998 neutron star - neutron star binaries M=1.35  0.04M ¯ Hulse-Taylor 1.18M ¯ < M < 1.44M ¯

22. Hulse-Taylor binary Measured neutron star masses in radio pulsars (from I. Stairs) Possible path to compact binary system (Bart & Kalogera) NICE

23. 22-ms pulsar J0737  3039A +2.7-sec pulsar J0737  3039B companion orbital period = 2.4 hours! NEW BINARY PULSAR SYSTEM Lyne et al., Science 303, 1153 (2004) Highly-relativistic double-neutron-star system See eclipsing of A by B Laboratory for gravitational physics!

24. See orbit almost edge-on:

25. Mass determinations: Stellar masses A=1.337(5)M ¯, B=1.250(5)M ¯

26. Vela X-1 (LMXB) light curves Serious deviation from Keplerian radial velocity Excitation of (supergiant) companion atmosphere? 1.4M ¯ M=1.86  0.33 (2  )M ¯ M. H. van Kerkwijk, astro-ph/0403489 1.75M ¯ <M<2.44M ¯ Quaintrell et al., A&A 401, 313 (2003)

27. PSR J0751+1807 3.4 ms. pulsar in circular 6h binary w. He white dwarf Nice et al., Ap.J. 634, 1242 (2005) M=2.1M ¯ Pulsar slowing down due to gravitational radiation: dP/dt = 6.4 £ 10 -14 Shapiro delay of signal due to gravitational field of companion:  t = - (2Gm 2 /c 3 ) ln(1-cos  )  = angle between ns and wd seen by observer Measurements free (?) of uncertainties from possible atmospheric distortion in companion 

28. Additional physics that allows one to pin down the masses from D. Nice

29. Neutron star (pulsar) - white dwarf binaries Nice et al., Ap.J. 634, 1242 (2005), Splaver et al., Ap.J 620, 405 (2005).

30. Observations of white dwarf companion C. G. Bassa, van Kerkwijk, & Kulkarni, astro-ph/0601205 Companion is very red: T eff » 4000K. Implies w.d. has He or He-H atmosphere. Two mysteries: 1) Evolutionary models suggest companion should have hot (burning) H atmosphere. 2) The pulsar does not seem to heat the w.d. atmosphere. Absorbed and re-emitted radiation < 15%. Need more detailed observations of spectra of white dwarf

31. Neutron-Star Low Mass X-ray Binaries

32. X-ray flux power density spectrum Wijnands et al. (1998) Kilohertz quasiperiodic oscillations (QPOs) in accreting neutron stars Detected in ~ 25 neutron stars QPOs remarkably coherent (Q = /d ~ 30–200) Large amplitude Usually see 2 simultaneous kHz QPOs (never 3) Frequencies of the two QPOs can vary by hundreds of Hz in few hundred seconds, but Separation QPO = QPO2 - QPO1 of the two QPOs fairly constant ≈ spin or ≈ spin /2 Sco X-1

33. Strong evidence that higher frequency QPO2 is the ISCO frequency, Then have direct measurement of neutron star mass: M * = c 3 /(6 3/2 £ 2  QPO2 G   2198/ QPO2 (Hz) )M ¯ R   c/(6  £ 2  QPO2 ) Ex.: QPO 4U1820-30, QPO2 = 1170 Hz => M~ 2.2-2.3 M ¯ innermost circular stable orbit (ISCO) in GR: R=6MG/c 2 Implies very stiff equation of state. Central density ~ 1.0 fm -3 ~ 6  nm (Miller, Lamb, & Psaltis 1997)

34. EXO0748-676: low mass x-ray binary thermonuclear burst source z=redshift of Fe and O lines hypothetical star: 1.8M ¯, R=10km M ' 2.1 § 0.28 M ¯ R ' 13.8 § 1.8 km F. Özel, astro-ph//0605106

35. Akmal, Pandharipande and Ravenhall, 1998

36. Present observations of neutron stars masses M ' M max ' 2.2 M ¯ beginning to confront microscopic nuclear physics. High mass neutron stars => very stiff equation of state, with n c < 7n 0. At this point for nucleonic equation of state, sound speed c s = (  P/  ) 1/2  c. Naive theoretical predictions based on sharp deconfinement transition seemingly inconsistent with presence of (soft) bulk quark matter in neutron stars. Further degrees of freedom, e.g., hyperons, mesons, or quarks at n matter less stiff. Quark cores possible, only if quark matter is very stiff. » »

37. Outside material adds ~ 0.1 M ¯ Maximum mass of a neutron star Say that we believe equation of state up to mass density   but e.o.s. is uncertain beyond Weak bound: a) core not black hole => 2M c G/c 2 < R c b) M c = s 0 R c d 3 r  (r)  (4  /3)  0 R c 3 => c 2 R c /2G  M c  (4  /3)  0 R c 3 M c max = (3M ¯ /4  0 R s ¯ 3 ) 1/2 M ¯  R c ) =  0 M max  13.7 M ¯ £ (10 14 g/cm 3 /  0 ) 1/2 R s ¯ =2M ¯ G/c 2 = 2.94 km 4  0 R c 3 /3

38. Strong bound: require speed of sound, c s, in matter in core not to exceed speed of light: Maximum core mass when c s = c Rhodes and Ruffini (PRL 1974) c s 2 =  P/   c 2 WFF (1988) eq. of state => M max = 6.7M ¯ (10 14 g/cm 3 /  0 ) 1/2 V. Kalogera and G.B., Ap. J. 469 (1996) L61  0 = 4  nm => M max = 2.2 M ¯ 2  nm => 2.9 M ¯

39. Can M max be larger? Larger M max requires larger sound speed c s at lower n. For nucleonic equation of state, c s -> c at n » 7n 0. Further degrees of freedom, e.g., hyperons, mesons, or quarks at n » 7n 0 lower E/A => matter less stiff. Stiffer e.o.s. at lower n => larger M max. If e.o.s. very stiff beyond n ' 2n 0, M max can be as large as 2.9 M ¯. Stiffer e.o.s. => larger radii (cf. EXO0748-676).

40. Gradual onset of quark degrees of freedom Quarks degrees of freedom -- not accounted for by nucleons interacting via static potentials -- expected to play role. As nucleons begin to overlap, matter percolates at (Quarks can still be bound even if deconfined!) Transition to quark matter likely crossover at low T n perc » 0.34 (3/4  r n 3 ) Hadronic Normal Color SC Hatsuda, Tachibana, Yamamoto & GB, PRL 97, 122001 (2006)

41. Gradual onset of quark degrees of freedom Quarks degrees of freedom -- not accounted for by nucleons interacting via static potentials -- expected to play role. As nucleons begin to overlap, matter percolates at (Quarks can still be bound even if deconfined!) Transition to quark matter likely a crossover at low T n perc » 0.34 (3/4  r n 3 ) Hadronic Normal Color SC Hatsuda, Tachibana, Yamamoto & GB, PRL 97, 122001 (2006)