Fridolin Weber San Diego State University and University of California at San Diego San Diego, California

Transcription

1 Fridolin Weber San Diego State University and University of California at San Diego San Diego, California INT Program INT-16-2b The Phases of Dense Matter, July 11 August 12, 2016 EMMI Rapid Reaction Task Force Meeting, FIAS, October 7-9, 2013

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3 Ø Ø Ø Ø Ø Ø Ø Strange Stars versus Neutron Stars Distinguishing features Quark-Hadron Phase Transition inside Pulsars Current status Possible signal of quark deconfinement D populations Rotating Neutron Stars Rotation in GR Rotation-driven compositional changes Quark-hadron Lattices Non-rotating but nevertheless deformed? Summary

4 Strange Quark Stars

5 Strange Quark Star Neutron Star Surface Hydrogen/Helium plasma Iron nuclei Outer Crust Core Surface u,d,s quarks electrons F. Weber (SDSU, 2012) I Color superconducting quarks Radii < 10 km Masses ~1 to 2 M Outer Crust Ions Electron gas Ø Made entirely of deconfined quarks Ø Self-bound (M ~ R 3 ) Ø Electron dipole layer at surface (ultra-strong electric fields) Ø Either bare or dressed Ø Only outer crusts Ø No inner crusts Inner Crust Heavy ions Relativistic electron gas Superfluid neutrons Outer Core Neutrons, protons Electrons, muons Ø Two-parameter stellar sequence Inner Core Neutrons Superconducting protons Radii > 10 km Electrons, muons Alcock, Farhi, Olinto, ApJ Hyperons 310 (1986) (Σ, 261; Λ, Ξ) Alcock & Olinto, Ann. Rev. Nucl. Part. Sci. 38 (1988) 161; sun Madsen, Lecture Notes Deltas Phys. 516 ( ) (1999) 162; Proc. of Strange Quark Boson Matter (π, in K) Physics condensates and Astrophysics, J. Madsen & P. Haensel, Deconfined NPB (Proc. Suppl. (u,d,s) 24B quarks (1991); / color- V. Usov, ApJ 559 (2001), superconducting 550 (2001) quark matter

6 Schematic illustration of a quark star carrying a nuclear crust Quark matter core Electric field Color superconducting quark matter (CFL, 2SC) Nuclear crust Iron

7 Mass-radius relationship of neutron stars and strangequark stars d bc b a d b a b a Glendenning, Kettner, FW, ApJ 450 (1995) 253; PRL 74 (1995) 3519 FW, Prog Part Nucl Phys 54 (2005) 193

8 M/M sun Mass-radius relationship of neutron stars Black holes 1 Neutron stars void of compact stars 2 unstable equilibrium 3 configurations White dwarfs R (km) Planets

9 Rotation at Sub-Millisecond Periods Kepler Period (msec) Observed masses and rotational periods Strange quark stars

10 Photons Electron sea Electron sea may perform global oscillations Oscillation frequencies calculated by R. Xu et al. (PRD 85 (2012) ). Related to spectral absorption lines observed for CCOs and XDINs?

11 Pavlov, Sanwal & Teter (2004); Halpern & Gotthelf (2010) Oscillation frequencies (R. Xu et al. (2012))

12 Absorption features detected in the thermal X-ray spectrum of 1E at 0.7, 1.4 and 2.1 kev* 0.7 kev 1.4 kev 2.1 kev *G. F. Bignami, P. A. Caraveo, A. De Luca, & S. Mereghetti, Nature 423 (2003) 725

13 Quark-Hadron Phase Transition

14 Modeling the Quark-Hadron Phase Transition in the Cores of Neutron Stars q Baryonic matter (Schroedinger-based, RMF, RHF, RBHF,...) q Quark matter (MIT bag model, NJL) P h (µ, µ e, )=P q (µ, µ e, ), V q /(V q + V h ) Gibbs or Maxwell? q Electric charge neutrality (global versus local) q Chemical equilibrium

15 RMF Local/ non-local NJL models M. Orsario et al; Blaschke et al., Sedrakianet al., Lugones et al., Kashiwa, Hell & Weise,

16 1 G v = 0.1 G s Model neutron star matter composition Relative Particle Y i Fractions 0,1 0,01 p µ - e n Σ 0 Ξ - Σ + Σ - Λ 0 ρ u ρ d ρ s 1E ρ/ρ G v = 0.1 G s Hadronic Phase Mixed Phase Quark Phase Associated equation of state P [MeV.fm -3 ] µ e [MeV] µ B [MeV] Milva Orsaria et al. (2012, 2014)

17 A Possible Signal of Quark Deconfinement in isolated Pulsars during spin-down J = Z d 3 xt 3 0 p g Backbending 200 Hz (5 ms) Glendenning, Pei, FW, PRL 79 (1997) 1603 Chubarian, Grigorian, Poghosyan, Blaschke, A&A 357 (2000) FW, Prog. Nucl. Part. Phys. 54 (2005) 193

18 Backbending - well known in Nuclear Physics... and from the Olympics Backbending predicted in 1960 by Mottelson & Valatin Observed in 1972 by Stephens & Simon

19 Braking index of a pulsar n( ) 2 =3 3I 0 + I I + I 0 Backbending 200 Hz (5 ms) Glendenning, Pei, FW, PRL 79 (1997) 1603 Chubarian, Grigorian, Poghosyan, Blaschke, A&A 357 (2000) FW, Prog. Nucl. Part. Phys. 54 (2005) 193

20 Braking index of a pulsar n( ) 2 =3 3I 0 + I I + I 0 Signals of quark deconfinement Ø Braking indices of pulsars < n < + Ø Spin-up of isolated MSPs Backbending 200 Hz (5 ms) Glendenning, Pei, FW, PRL 79 (1997) 1603 Chubarian, Grigorian, Poghosyan, Blaschke, A&A 357 (2000) FW, Prog. Nucl. Part. Phys. 54 (2005) 193

21 D s populations

22 M-R relationship of non-rotating neutron stars EOS: DD2 (Typel, 2010) W. Spinella (2016) Saturation parameters: n 0 = fm -3 : E/A = MeV, K 0 = MeV, a sym = MeV, L 0 = 56.7 MeV, m* = 0.56 Couplin constants: g σy fixed to hypernuclearpotentials at n 0 : U Λ (N) = -28 MeV, U Σ (N) = +30 MeV, U Ξ (N) = -18 MeV g ωy at n 0 : x ωλ = x ωσ = 0.79, x ωξ = 0.59 (Rijken et al., 2010, Mayatsuet al., 2013) R [km]

23 Hadronic EoS with Delta Baryons Mass-Radius+Constraints with Hyperons+Deltas High density EoS remains sufficiently stiff Δ - softens EoS W. Spinella (2016)

24 Hadronic EoS with Delta Baryons Mass-Radius+Constraints with Hyperons+Deltas 90% confidence on 1.4 MSun NS from Lattimer et al σ, 2σ, and 1σ limits on radii and 1σ limits on mass of PSR J σ (dashed) and 2σ (solid) bounds on LMXB radii from Steiner et al W. Spinella (2016)

25 Hadronic EoS with Delta Baryons Delta Baryons Favored D s in Neutron Star Matter Δ - appears at 0.27 fm -3 Δ 0 appears at 0.69 fm -3 W. Spinella (2016)

26 Rotating Neutron Stars

27 Number of Neutron Stars R. Mellinger (2016)

28 Source: Jodrell Bank Centre for Astrophysics

29 Rotation in General Relativity ( r,, ) Problems to deal with Ø 2-D system Ø Dragging of local inertial frames (Lense-Thirringeffect) Ø Maximum rotational frequency

30 Differential rotation

31 Einstein's Field Equations for Rotating Compact Objects q Metric: ds 2 = e 2ν dt 2 + e 2(α+β ) r 2 sin 2 q (dφ N φ dt) 2 + e 2(α β) (dr 2 + r 2 dq 2 ) q Christoffelsymbols: Г σ µν= g σλ ( ν g µλ + µ g νλ λ g µν ) / 2 q Riemann tensor: R τ µνσ = ν Гτ µσ σ Гτ µν + Гκ µσ Гτ κν Γκ µν Γτ κσ Friedman, Ipser & Parker (1986) q Ricci tensor: R µν = R τ µtν q Scalar curvature: R = R µν g µν q Kepler frequency: Ω K = r 1 e ν α β U K + N φ Newtonian limit! p M/R 3 q Differential rotation/uniform rotation at 0 < W < W K Stellar properties: M, R p, R eq, I, z, Ω K, ω, P(r), e(r), r(r)

32 Central stellar density R. Mellinger (2016)

33 Rotation-driven compositional changes inside of neutron stars Polar direction (km) Nucleons and Hyperons R. Mellinger (2015) Quark-Hadron mixed phase Equatorial direction (km)

34 Rotation-driven compositional changes inside of neutron stars Polar direction (km) Equatorial deformation (km)

35 Rotation-driven compositional changes inside of neutron stars Deconfined quarks No free quarks Rotational Frequency (Hz) R. Mellinger (2016)

36 Quark-Hadron Lattices

37 Geometrical Structures in the mixed Quark-Hadron Phase N. K. Glendenning, PRD 46 (1992) 1274 mixed phase Ø Competition between Coulomb and surface energies in the mixed phase Ø Mixed quark-hadron phase may develop geometrical structures

38 Quark-Hadron Mixed Phase in Cores of Neutron Stars? Quark blobs Hadronic blobs Leads to changes the heat capacity, thermal conductivity, neutrino emissivity!

39 W. Spinella et al. (EPJA 52 (2016) 61) See also Glendenning Phys Rep 342 (2001) 393; X. Na et al., PRD 86 (2012)

40 Electron-Quark Scattering leads to Bremsstrahlung e + (Z,A) e + (Z,A) + ν + ν _ Quark blobs/rods/slabs For the scattering of neutrinos from quark droplets, see S. Reddy, G. Bertsch, M. Prakash, PLB 475 (2000) 1

41 Electron-Quark Scattering leads to Bremsstrahlung e + (Z,A) e + (Z,A) + ν + ν _ Sub-nuclear NS matter (electrons + heavy atomic nuclei): Haensel Kaminker, Yakovlev (1996) Yakovlev, Kaminker (1996) Kaminker, Pethick, Potekhin, Thorsson, Yakovlev (1999)

42 Modified URCA: n+n n+p+e+ν Nucleon Bremsstrahlung: n+n n+n+ν+ν Electron-quark blob Bremsstrahlung: e+(z,a) e+(z,a)+ν+ν- W. Spinella (2015); see also X. Na et al., PRD 86 (2012)

43 Non-rotating but nevertheless Deformed? Anisotropic equations of state (see E. J. Ferrer et al., PRC 82 (2010) )

44 Metric of spherically symmetric mass distributions (Schwarzschild metric) ds 2 = e 2 dt 2 + e 2 dr 2 + r 2 d 2 + r 2 sin 2 d 2 isotropic case

45 More on the isotropic case Rank-2 tensor transformation T µ =( + P )u µ u + g µ P

46 Tolman-Oppenheimer-Volkoff equation dp dr = 1+ P m r 2 1 2m r 1+ 4 Pr3 m m(r) =4 Z r 0 r 02 (r 0 ) dr 0

47 Energy-momentum tensor of non-isotropic matter z x f r y

48 Energy-momentum tensor of non-isotropic matter z x f r y

49 Full Stellar Structure Equations of Deformed NSs h k ( + P k = 2 r +4 r3 1 P k 2 1 r r 1 2 2M(r,z) h z dp ( + P? )? dz = 2 +4 z3 z P? 2 z 1 2 r 2M(r,z) z 1 2M(r,z) r i, 2M(r,z) z i O. Zubairi (2015) M(r, z) (r, z) r2 z P k (r = R) =0 P? (r = Z) =0

50 O. Zubairi (2015)

51 O. Zubairi (2015)

52 O. Zubairi (2015)

53 O. Zubairi (2015)

54 Ø Ø Ø Ø Ø Ø Composition and structure of rotating neutron stars depend on rotational frequency (neutron-to-proton ratio, hyperon population, boson condensates, quark-hadron composition) MSPs & NSs in LMXBs may be ideal objects to look for phase transitions (e.g., stellar backbending) D s in NS matter? (open issue) Broad collection of quark-hybrid EOSs -> all predict a mixed phase Quark-hadron lattices in NSs may lead to enhanced cooling of older NSs Anisotropic EOSs may impact maximum mass.