Astrophysics implications of dense matter phase diagram

Transcription

1 Astrophysics implications of dense matter phase diagram Armen Sedrakian 1 1 Institute for Theoretical Physics, University of Frankfurt, Germany Hirschegg 2010 Januray 20, Hirschegg

2 Introduction Phase diagram of dense matter Phases: High-temperature QGP phase is probed in heavy ion colliders Low-density low-temperature nucleonic matter in nuclei and low-densities of neutron stars Low-temperature high density phase of dense matter may be in the quark state (compact stars) T heavy ion collider hadronic gas nuclear superfluid liq QGP non CFL neutron star CFL µ

3 Introduction Learning about the interiors of neutrons stars Key ideas: Quark matter and color superconductivity may have observational effect on neutron stars, e.g. (i) gravitation wave radiation, (ii) surface X-ray emission, (iii) timing anomalies in the radio emission This talk is focused on: Searches for the most favorable phase of color superconductor under charge, color neutrality and β-equilibrium Neutrino cooling of neutron stars with quark cores Gravitational radiation from strained superfluid compressed solid (CS) CS & free n npeµ M=1.4M O. npe π npek ΣΛ Ξ uds R = 10 [km] 9 1 S 0 n condensate 1 3 S p & P n condensate hypernuclear matter 15,2 14, log ρ = 1 π or K Bose condensate quark/strange matter [g/cm 3 ]

4 Stressed pairing Introduction -Initially isospin symmetric matter acquires d-quark excess via the inverse β-decay e + u d + ν, this implies shift in the Fermi spheres of by amount µ e = µ d µ u: - Appearance of strange quarks will have the same effect of shifting of Fermi-surfaces Standard BCS requires the numbers to be equal, coherence is optimal among the fermions bound in a Cooper pair Asymmetric BCS, shifted Fermi surfaces, coherence is destroyed LOFF phase, Finite momentum of the condensate, restores coherence. Simplest ansatz ( r) = exp(i r q). BCS: k = k, δµ = 0 ASYMMETRIC BCS: k = k, δ µ = / 0 rotational/transl. symmety rotational/symmetry, time reversal broken LOFF: k + P = k, δµ = / 0 DFS phase: k ~ k, δµ = / 0 rotational/trans sym. broken only rotational symmetry is broken to O(2)

5 Quark matter in compact stars Effective models of QCD Pairing ansatz: ψ T (x)cγ 5 τ 2 λ 2 ψ(x).

6 Quark matter in compact stars FFLO phase in quark matter Compact stars start at T T c 60 MeV and α 0 and evolve to T 0 and α = 0.9. They will entre the FF phase within short period of time

7 Quark matter in compact stars Pairing induced Fermi-surface deformations in QM Pomeranchuk-type instability of Fermi surfaces induced by asymmetric pairing Modelling the surfaces: µ f = P l ǫ lp l cos θ, where f = u, d refers to flavor Parameters ǫ l from minimum principle more details in PRL ; Phys. Rev. D

8 Quark matter in compact stars Shear modulus of CCS phase Important: The superconducting phase has a nonzero shear modulus, i. e. it can support quadrupole and higher order deformations mountains The key quantities are: Breaking strain 10 5 σ 10 2 Shear modulus Color superconducting phases can be solid with shear moduli by many orders exceeding that of the crusts. figure courtesy J. Bowers bcc superconducting lattice; «2 «2 µ = 2.47 MeV fm 3 µq, (1) 10 MeV 400 MeV (K. Rajagopal and R. Sharma: arxiv:hep-ph/ )

9 Quark matter in compact stars Equations of state 1.25e+39 1e+39 n [ cm -3 ] 7.5e+38 5e e+38 A A1 B 0 0 2e+35 4e+35 6e+35 8e+35 P [ dyn cm -2 ] The nuclear equation of state is taken from covariant BHF theory with two parameterizations (both stiff) The two quark equation of states differ by pressure normalization in the vacuum (slight vertical shift)

10 Constructing stellar configurations Stellar configurations A A1 B M/M O 1 M/M O model A model A1 model B 0 1e+15 2e+15 3e+15 ρ c [ g cm -3 ] 0.4 5e+14 1e e+15 2e e+15 ρ [g cm -3 ] Maximal masses are large 2M. Quark core masses are 0.8M. N. Ippolito et al Phys. Rev. D 77 (2008) , B. Knippel, et al Phys. Rev. D 79, (2009).

11 Constructing stellar configurations Stellar configurations A A1 B M/M O e+15 2e+15 3e+15 ρ c [ g cm -3 ] Unstable 2SC and CFL configuration vs our stable configurations

12 Neutrinos in quark matter Neutrinos in superconducting quark matter log(t s /K) θ=0 θ=π/2 T eff 1D code without heating log(τ/yr)

13 Neutrinos in quark matter Transport equations The S >,< propagators obey in non-equilibrium the KB equation ν-quasiparticle propagators: S < 0 (q, x) = iπγµ q h µ δ (q 0 ω ν( q)) f ν(q, x) ω ν( q) i δ (q 0 + ω ν( q))(1 f ν( q, x)). (2) ν and ν - Boltzmann equations with KB collision integrals h t + q ω ν( q) i x f ν( q, x) Z dq 0 = 0 2π Tr ˆΩ < (q, x)s > 0 (q, x) Ω> (q, x)s < 0 (q, x),

14 Self-energies Neutrinos in quark matter ν and ν-self-energies (second order in weak force) Z iω >,< (q 1, x) = d 4 q (2π) 4 d 4 q 2 (2π) 4 (2π)4 δ 4 (q 1 q 2 q) iγ µ L q is< 0 (q 2, x)iγ λ L q iπ>,< µλ (q, x), (3) the problem is to compute the polarization tensor!

15 Neutrinos in quark matter Neutrinos in a color superconductors energy loss per unit time and volume ǫ ν ν = d dt expressed through the collision integrals «G 2 X Z ǫ ν ν = f Z d 3 q [fν( q) + (2π) 3 f ν( q)] ων( q) (4) d 3 Z q 2 (2π) 3 2ω ν( q 2 ) d 3 Z q 1 (2π) 3 2ω ν( q 1 ) d 4 q (2π) 4 (2π) 4 δ 3 ( q 1 + q 2 q)δ(ω ν( q 1 ) + ω ν( q 2 ) q 0 ) [ω ν( q 1 ) + ω ν( q 2 )] g B (q 0 ) [1 f ν(ω ν( q 1 ))][1 f ν(ω ν( q 2 ))]Λ µλ (q 1, q 2 )Im Π R µλ (q).

16 Neutrinos in quark matter One loop results Polarization tensors Z Π µλ (q) = i Γ ± (q) = γ µ(1 γ 5 ) τ ± d 4 p (2π) 4 Tr [(Γ ) µs(p)(γ + ) λ S(p + q)] Λ + (p) S f=u,d = iδ ab p 2 0 (/p µ f γ 0 ), ǫ2 p F(p) = iǫ ab3 ǫ fg Λ+ (p) p 2 0 γ 5 C ǫ2 p

17 Neutrinos in quark matter ε ν /ε ζ = 2.0 ζ = 1.6 ζ = ε ν /ε ζ = 0.8 ζ = 0.4 ζ = T/T c ζ = /δµ, where δµ = µ d µ u = µ e. form P. Jaikumar, C. D. Roberts, and A. S., Phys. Rev. C 73 (2006)

18 Neutrinos in quark matter 36.0 M=1.0,1.4,1.6 M=1.0,1.4, log(l s /erg s -1 ) log(τ/yr) log(τ/yr) Cooling of neutron stars with Urca and pion-condensed cores. Onset at high densities with the drop of temperature of high mass stars.

19 Neutrinos in quark matter e14 5.1e14 8.2e e15 1.2e15 1.5e15 2.1e15 T obs [K] t [yrs] Cooling of hybrid color superconducting stars with constant ζ = 0.8. Blue - baryonic stars, red - hybrid stars.

20 Gravity wave Gravitation radiation Given a deformation the characteristic strain amplitude: h 0 = 16π2 G ǫi zzν 2 c 4, (5) r ǫ = (I xx I yy)/i zz is the equatorial ellipticity. Strain amplitude can be expressed in terms of the m = 2 mass quadrupole moment as Quadrupole moment Z Rcore Q 22 = 0 h 0 = 16π2 G c 4 «32π 1/2 Q 22 ν 2, (6) 15 r " drr 3 3 g(r) 2 (4 U)trr + 1 r 3 3 (6 U)t Λ + 8 3U U2 r 3 «du t r #, (7) dr where U = 2 + dlng(r)/dlnr and t rr, t Λ and t r are the coefficients of the expansion of the shear stress tensor in spherical harmonics.

21 Gravity wave Comparison with the previous work 4e+15 3e+15 ρ c [ g cm -3 ] 2e+15 1e r [ km ] L.-M. Lin, Phys. Rev. D 76, (R) (2007, incompressible models without nuclear crusts Haskell et al, Phys. Rev. Lett. 99, (2007), incompressible quark matter plus n = 1 polytrope B. Knippel, A. Sedrakian, Phys. Rev. D 79, (2009), microscopic equations of state

22 Strain amplitudes Gravity wave 6e-25 5e-25 A A1, B 4e-25 h 0 3e-25 2e-25 1e M core /M O GW strain amplitudes for breaking strain 10 4, Gaps from 10 to 50 MeV. Dashed line Crab pulsars upper limit from S5 run h 0 can pin down the product σ 2, currently σ max MeV 2 (under the assumptions of the present model).

23 Conclustions Summary, conclusions, and outlook Constructed hybrid configurations of CCS featuring compact stars The sequence contains entirely heavy mass (2 solar) objects with core masses 0.8 solar mass and radii up to 7 km. We think this is model independent (largely). If the core is maximally strained then the h 0 is detectable for realistic values σ 10 4 and 40 MeV. The spread in the cooling curves can be explained by the gaplessness of the spectrum. Questions for the feature Is there quark matter in the CCS state in compact stars? Is it strained and to which extent? What are the dynamic avenues for obtaining stressed cores? Other signatures of quark superconducting phases:

24 Thanks to Conclustions Bettina Knippel (ITP, Frankfurt-Main) Nicola Ippolito, Marco Ruggieri (INFN, Bari) Dirk Rischke (ITP, Frankfurt-Main) Fridolin Weber (San-Diego) Prashant Jaikumar (Cennei) Craig Roberts (Argonne)