Quark hybrid Stars: how can we identify them? Prof. Mark Alford Washington University in St. Louis Alford, Han, Prakash, arXiv:1302.4732 Alford, Schwenzer, arXiv:1310.3524
Schematic QCD phase diagram T heavy ion collider QGP non−CFL hadronic = color− superconducting CFL gas liq quark matter nuclear µ compact star superfluid /supercond M. Alford, K. Rajagopal, T. Sch¨ afer, A. Schmitt, arXiv:0709.4635 (RMP review) A. Schmitt, arXiv:1001.3294 (Springer Lecture Notes)
Signatures of quark matter in compact stars ← Microphysical properties Observable (and neutron star structure) ← Phases of dense matter Property Nuclear phase Quark phase known unknown; mass, radius eqn of state ε ( p ) up to ∼ n sat many models
Signatures of quark matter in compact stars ← Microphysical properties Observable (and neutron star structure) ← Phases of dense matter Property Nuclear phase Quark phase known unknown; mass, radius eqn of state ε ( p ) up to ∼ n sat many models bulk viscosity Depends on Depends on spindown shear viscosity phase: phase: (spin freq, age) n p e unpaired n p e , µ CFL heat capacity cooling CFL- K 0 neutrino emissivity n p e , Λ, Σ − (temp, age) n superfluid 2SC thermal cond. p supercond CSL shear modulus glitches π condensate LOFF vortex pinning (superfluid, K condensate 1SC energy crystal) . . .
Nucl/Quark EoS ε ( p ) ⇒ Neutron star M ( R ) GR MS0 2.5 MPA1 < AP3 P � PAL1 ENG y t i l a AP4 MS2 s u Recent a c 2.0 J1614-2230 measurement: SQM3 MS1 FSU J1903+0327 Mass (solar) SQM1 GM3 PAL6 1.5 M = 1 . 97 ± 0 . 04 M ⊙ J1909-3744 GS1 Double NS Systems Demorest et al, 1.0 Nature 467, 1081 (2010). rotation 0.5 Nucleons Nucleons+ExoticStrange Quark Matter 0.0 7 8 9 10 11 12 13 14 15 Radius (km) Can neutron stars contain quark matter cores?
Constraining QM EoS by observing M ( R ) Does a 2 M ⊙ star rule out quark matter cores (hybrid stars)? Lots of literature on this question, with various models of quark matter ◮ MIT Bag Model; (Alford, Braby, Paris, Reddy, nucl-th/0411016 ) ◮ NJL models; (Paoli, Menezes, arXiv:1009.2906 ) ◮ PNJL models (Blaschke et. al, arXiv:1302.6275 ; Orsaria et. al.; arXiv:1212.4213 ) ◮ hadron-quark NL σ model (Negreiros et. al., arXiv:1006.0380 ) ◮ 2-loop perturbation theory (Kurkela et. al., arXiv:1006.4062 ) ◮ MIT bag, NJL, CDM, FCM, DSM (Burgio et. al., arXiv:1301.4060 ) We need a model-independent parameterization of the quark matter EoS: ◮ framework for relating different models to each other ◮ observational constraints can be expressed in universal terms
CSS: a fairly generic QM EoS Model-independent parameterization with Constant Speed of Sound (CSS) ε ( p ) = ε trans + ∆ ε + c − 2 QM ( p − p trans ) Quark Matter Energy Density QM EoS params: -2 c QM ε 0,QM Slope = Δε p trans /ε trans ε trans ∆ ε/ε trans c 2 Nuclear QM Matter p trans Pressure Zdunik, Haensel, arXiv:1211.1231 ; Alford, Han, Prakash, arXiv:1302.4732
Hybrid star M ( R ) Hybrid star branch in M ( R ) relation has 4 typical forms “Connected” “Both” M M ∆ ε < ∆ ε crit small energy density jump at phase transition R R “Absent” “Disconnected” M M ∆ ε > ∆ ε crit large energy density jump at phase transition R R
“Phase diagram” of hybrid star M ( R ) Soft NM + CSS( c 2 QM =1) Schematic n trans /n 0 2.0 3.0 4.0 5.0 n causal 6.0 1.2 A 1 D Δε/ε trans = λ-1 ∆ε ε trans 0.8 B 0.6 C 0.4 0.2 0 trans ε p 0 0.1 0.2 0.3 0.4 0.5 trans p trans /ε trans ∆ ε crit = 1 2 + 3 p trans Above the red line (∆ ε > ∆ ε crit ), ε trans 2 ε trans connected branch disappears (Seidov, 1971; Schaeffer, Zdunik, Haensel, 1983; Lindblom, gr-qc/9802072 ) Disconnected branch exists in regions D and B.
Sensitivity to NM EoS and c 2 QM c 2 c 2 QM =1 / 3 QM =1 1.2 1.2 A A 1 NL3 1 NL3 D D HLPS 0.8 0.8 Δε/ε trans Δε/ε trans B HLPS B 0.6 0.6 C C 0.4 0.4 0.2 0.2 0 0 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 p trans /ε trans p trans /ε trans • NM EoS (HLPS=soft, NL3=hard) does not make much difference. • Higher c 2 QM favors disconnected branch.
n trans /n 0 2.0 3.0 4.0 5.0 n causal 6.0 1.2 A 1 D -4 B 0.8 Δ M = 10 M ๏ Δε/ε trans 0.6 -3 10 M ๏ C 0.4 -2 10 M ๏ 0.7 0.2 0.5 0.1M ๏ 0.3 0 0 0.1 0.2 0.3 0.4 0.5 p trans /ε trans Observability of hybrid star branches Measure length of hybrid branch by � mass of heaviest � ∆ M ≡ − M trans hybrid star M ∆ M M trans R
Observability of hybrid star branches Soft NM + CSS( c 2 QM =1) Measure length of hybrid branch by n trans /n 0 2.0 3.0 4.0 5.0 n causal 6.0 � mass of heaviest � ∆ M ≡ − M trans 1.2 A hybrid star 1 D -4 M B 0.8 Δ M = 10 M ๏ Δε/ε trans ∆ M 0.6 -3 10 M ๏ C M trans 0.4 -2 10 M ๏ 0.7 0.2 0.5 0.1M ๏ 0.3 R 0 0 0.1 0.2 0.3 0.4 0.5 p trans /ε trans • Connected branch is observable if p trans is not too high and there is no disconnected branch • Disconnected branch is always observable
Constraints on QM EoS from max mass Soft Nuclear Matter + CSS( c 2 QM = 1) 1.2 A D 1 2.0M ๏ 0.8 Δε/ε trans B 2.1M ๏ C 0.6 0.4 2 . 2 M ๏ 0.2 2 . 3 M ๏ 0 0 0.1 0.2 0.3 0.4 0.5 p trans /ε trans • Max mass data constrains QM EoS but does not rule out generic QM
Dependence of max mass on c 2 QM Soft NM + CSS( c 2 Soft NM + CSS( c 2 QM = 1 / 3) QM = 1) 1.2 1.2 A A D 1 D 1 2.0M ๏ 0.8 1.5M ๏ 0.8 Δε/ε trans Δε/ε trans B 2.1M ๏ C B 0.6 0.6 C 1.6M ๏ ๏ 0.4 0.4 M 1 2.2M ๏ 1.8M ๏ . 2 0.2 0.2 2.3M ๏ 2.0M ๏ 0 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.1 0.2 0.3 0.4 0.5 p trans /ε trans p trans /ε trans • For soft NM EoS, need c 2 QM � 0 . 4 to get 2 M ⊙ stars
Quark matter EoS Summary ◮ CSS (Constant Speed of Sound) is a generic parameterization of the EoS close to a sharp first-order transition to quark matter. ◮ Any specific model of quark matter with such a transition corresponds to particular values of the CSS parameters c 2 QM ) . ( p trans /ε trans , ∆ ε/ε trans , Its predictions for hybrid star branches then follow from the generic CSS phase diagram. ◮ Existence of 2 M ⊙ neutron star → constraint on CSS parameters . For soft NM we need c 2 ( c 2 QM � 0 . 4 QM = 1 / 3 for free quarks). ◮ More measurements of M ( R ) would tell us more about the EoS of nuclear/quark matter. If necessary we could enlarge CSS to allow for density-dependent speed of sound.
r-modes and gravitational spin-down Polar view Side view An r-mode is a quadrupole flow that emits gravitational radiation. It becomes unstable (i.e. arises spon- taneously) when a star spins fast star enough, and if the shear and bulk viscosity are low enough. mode pattern The unstable r -mode can spin the star down very quickly, in a few days if the amplitude is large enough (Andersson gr-qc/9706075 ; Friedman and Morsink gr-qc/9706073 ; Lindblom astro-ph/0101136 ) . neutron star ⇒ some interior physics spins quickly damps the r -modes
r-mode instability region for nuclear matter Shear viscosity grows at low T (long mean free paths). r−modes Spin unstable Bulk viscosity has a freq bulk resonant peak when beta viscosity Ω stabilizes equilibration rate matches shear r−modes r-mode frequency viscosity stabilizes r−modes Temperature T • Instability region depends on viscosity of star’s interior. • Behavior of stars inside instability region depends on saturation amplitude of r-mode.
Evolution of r-mode amplitude α d α 1 dt = α ( | γ G | − γ V ) γ G = τ G = grav radiation rate ( < 0) 1 γ V = τ V = r-mode dissipation rate d Ω = − 2 Q γ V α 2 Ω Q ≈ 0 . 1 for typical star dt dT = − 1 C V ( L ν − P V ) L ν = neutrino emission dt P V = power from dissipation R-mode is unstable when | γ G (Ω) | > γ V ( T ) at infinitesimal α . R-mode saturates when γ V ( α ) rises with α until γ V ( T , α sat ) = γ G ( ⇒ P V = P G ) In general, α sat ( T , Ω) is an unknown function determined by microscopic and astrophysical damping mechanisms.
R-modes and young neutron stars 1.0 Young pulsar cools into instability region 0.8 R-mode quickly saturates Star spins down along 0.6 “heating=cooling” line � � � K Α sat � 10 � 4 Α sat � 1 Star exits instability region at Ω ∼ 50 Hz, 0.4 indp of cooling model 0.2 (Alford, Schwenzer 0.0 arXiv:1210.6091 ) 10 7 10 8 10 9 10 10 10 11 T � K �
Could r-modes explain young pulsar’s slow spin? r-modes with Α sat � 1 α sat ∼ 10 − 2 to 10 − 1 10 � 7 could explain slow rotation of young J0537 � 6910 pulsars ( � a few � df � dt � � s � 2 � thousand years old) 10 � 9 Crab J0537-6910 is 4000 years old Vela 10 � 11 Α sat � 10 � 4 (Alford, Schwenzer arXiv:1210.6091 ) 1 5 10 50 100 500 1000 f � Hz �
How quickly r-modes spin down pulsars 1.0 0.8 For α sat in the range 0.01 to 0.1, 0.6 spindown is complete in � � � K 20,000 to 500 years. Α sat � 10 � 4 Α sat � 1 0.4 (Alford, Schwenzer 0.2 arXiv:1210.6091 ) 0.0 1 10 � 10 10 � 5 10 5 t � y �
Recommend
More recommend
