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Neutron star interiors: are we there yet?. Gordon Baym, University of Illinois. Workshop on Supernovae and Gamma-Ray Bursts YIPQS Kyoto ’ October 28, 2013. Neutron star interior. Mountains < 1 mm. Mass ~ 1.4-2 M sun Radius ~ 10-12 km Temperature ~ 10 6 -10 9 K Surface gravity

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## Neutron star interiors: are we there yet?

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**Neutron star interiors: are we there yet?**Gordon Baym, University of Illinois Workshop on Supernovae and Gamma-Ray Bursts YIPQS Kyoto’ October 28, 2013**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**_**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? Being explored at rare isotope accelerators, RIKEN, GSI, FRIB, KORIA**Valley of b stability**in neutron stars neutron drip line**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**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: kFT = Thomas-Fermi screening length For k > kFT screening by electron less effective. Critical wavenumber above which pp interaction is attractive:**Most unstable direction determined from**modification of elastic constants J. Cahn, Acta Metallurgica 10, 179 (1962) Possibly leads to BaTiO3 -like structure: Similar to pasta phases of nuclei, rearrangement of lattice structure affects 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.**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, ...**QMD simulations of pasta phases**Sonoda, Watanabe, Sato, Yasuoka and Ebisuzaki, Phys. Rev. C77 (2008) 035806 0.10 0.20 0.39 0.49 0.58 T=0 T>0 Pasta phase diagram**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**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**Energy per nucleon in pure neutron matter**Akmal, Pandharipande and Ravenhall, Phys. Rev. C58 (1998) 1804 p0 condensate**Neutron star models using static interactions between**nucleons Maximum neutron star mass Mass vs. central density Mass vs. radius Akmal, Pandharipande and Ravenhall, 1998**Equation of state vs. neutron star structure**from J. Lattimer**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?**Hyperons in dense matter**Produce hyperon X of baryon no. A and charge eQ when Amn - Qme > mX (plus interaction corrections). mn = baryon chemical potential and me = 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.**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~ 0.4n 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!**Lattice gauge theory**calculations of equation of state of QGP Not useful yet for realistic chemical potentials**Learning about dense matter from neutron star observations**Challenges to nuclear theory!!**High 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**Second high mass neutron star, PSRJ0348+0432 -- in neutron**star-white dwarf binary Antonidas et al., Science 340 1233232 (April 26, 2013) Spin period = 39 ms; orbital period = 2.46 hours Inclination =40.2o Mneutron star =2.01 ± 0.04M ; Mwhite dwarf= 0.172 ±0.003M Significant gravitational radiation 400 Myr to coalescence!**A third high mass neutron star, PSR J1311-3430 -- in neutron**star - flyweight He star binary Romani et al., Ap. J. Lett., 760:L36 (2012) Mneutron star > 2.0 M ; Mcompanion~ 0.01-0.016M Uncertainties arising from internal dynamics of companion**Mass vs. radius determination of neutron stars in burst**sources M vs R from bursts, Ozel at al, Steiner et al.**J. Poutanan, at Trento workshop on**Neutron-rich matter and neutron stars, 30 Sept. 2013**Or perhaps overestimated, since**R. Rutledge, at Trento workshop on Neutron-rich matter and neutron stars, 30 Sept. 2013**Phase diagram of equilibrated quark gluon plasma**Critical point Asakawa-Yazaki 1989. 1st order crossover Karsch & Laermann, 2003**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 ~10nm -- would not be reached in neutron stars given observation of high mass PSR J1614-2230 with M = 1.97M=> no quark matter cores**BCS-BEC**crossover BCS paired quark matter Hadrons Normal Color SC BEC-BCS crossover in QCD phase diagram 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) Hadronic (as ms increases) Small quark pairs are “diquarks”**Continuous evolution from nuclear to quark matter**K. Masuda, T. Hatsuda, & T. Takatsuka, Ap. J.764, 12 (2013)**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**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: PNJL phase diagram K and K’ from axial anomaly**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: 5 1.5 pressure 1 0 baryon density mass density**Neutron star equation of state vs. phenomenological**fits to observed masses and radii Lines from bottom to top: gV /G = 0, 1, 1.5, 5 Cross-hatched region = Ozel et al. (2010) Shaded region = Steiner et al. (2010)**Masses and radii of neutron stars vs. central mass density**from integrating the TOV equation 5 1.5 1 gv/G= 0 Mass vs. central density: only stars on rising curves are stable M vs. R: only stars on rapidly rising curves are stable**Maximum neutron star mass vs. gV**PNJL accomodates large mass neutron stars as well as strange quarks -- avoiding the “hyperon problem” -- and is consistent with observed masses and radiii**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 gv 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 + Cpf4 , with B ~ 100-200 MeV/fm3. Then the pressure is P = -B + Cpf4 /3. Effect of B on maximum neutron star mass? Need to calculate gluon contributions accurately to pin down B.

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