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Quark in stars: where do we stand?

Mark Alford Washington University in St. Louis

Alford, Han, Schwenzer, arXiv:1904.05471 Outline

I What is quark matter? Phase diagram of dense matter Does quark matter have distinguishing characteristics ? II Quark matter in neutron stars Astrophysics and microphysics: I Equation of state I Spindown I Cooling I Merger dynamics III Summary Manifestations of quark matter in neutron stars Looking to the future I. What is quark matter? Conjectured QCD phase diagram T

heavy ion collider

QGP non−CFL hadronic = color− superconducting neutron CFL quark matter star merger

nuclear µ superfluid supercond heavy ion collisions: deconfinement crossover and chiral critical point neutron stars: color superconducting quark matter core? mergers: dynamics of warm matter, heavy remnant Phases of (cool) quark matter

I Quark matter is “Unconfined” Spatially localized baryonic “bags” are not the relevant degrees of freedom, But confinement is not an observable. E.g., excited states are still created by gauge-invariant baryonic operators

I In the ultra-high density limit, we expect the ground state to be a condensate of Cooper pairs of quarks. Many pairing patterns I Color-Flavor-Locked (CFL): all 3 colors and flavors pair I 2SC: only u,d,u,d undergo pairing I LOFF: spatially modulated condensate, forming a “crystal” I Color--Locked (CSL): pairing of all 3 colors of a single flavor I ... Phases of quark matter

Prediction of an NJL model, uniform phases only

60

t NQ 50

uSC 40 guSC → 2SC CFL

(MeV) 30 t gCFL T p2SC ←t χSB g2SC −→ 20 t CFL-K0 10 NQ 0 350 400 450 500 550

µB/3 (MeV) Warringa, hep-ph/0606063 Summary

I There are observables that would point to quark matter in neutron stars I There is no hard evidence for quark matter in neutron stars I There is no hard evidence ruling out quark matter in neutron stars I There is evidence against matter made of quasi-free quarks I There is one mystery that quark matter could solve. How do we distinguish forms of matter?

I Landau classification : qualitative observables (order parameters) signalling spontaneous breaking of exact symmetries. I number superfluidity → I Electromagnetic gauge sym superconductivity → I Spacetime translation and rotation crystallization → I Large quantitative differences I spontaneous breaking of approximate symmetries e.g. chiral breaking light → I Quantitative transitions (gas/, metal/insulator); properties of Fermi surface Is quark matter distinguishable?

Landau classification:

Matter type superfluid supercond crystalline (unpaired) nucleons (paired) - (inner crust) unpaired quarks 2SC CFL LOFF

No exact symmetry breaking pattern distinguishes quark matter Beyond the Landau classification Quantitative transitions hadronic matter: low fermionic degrees of freedom are non-relativistic (low Fermi velocity) E quark matter: low energy fermionic degrees of freedom are relativistic (high Fermi velocity) Manifestation: affects transport properties, e.g. beta equilibration bulk viscosity p ν emission cooling→ →

Approximate symmetry breaking e.g., hadronic matter: chiral sym breaking, light pions. quark matter (unpaired or 2SC): chiral sym restored Manifestation: not clear. play subleading role. II. Quark matter in neutron stars

Conventional scenario Hypothesis Bodmer 1971; Witten 1984; Farhi, Jaffe 1984 Neutron/hybrid star Strange star

nuclear nuclear crust crust neutron NM SQM SQM star

crust NM hybrid star SQM SQM spindown bulk viscosity Depends on Depends on (spin freq, age) shear viscosity phase: phase: heat capacity cooling n p e unpaired emissivity (temp, age) n p e CFL thermal cond. , µ n p e, Λ, Σ− CFL-K 0 glitches shear modulus n superfluid 2SC (superfluid, vortex pinning p supercond CSL crystal) energy π condensate LOFF 1SC merger dynamics eqn of state K condensate (grav waves) bulk viscosity ...

Signatures of quark matter in compact stars Microphysical properties Observable Phases of dense matter ← (and neutron star structure) ← Property Nuclear phase Quark phase distribution known unknown; eqn of state ε(p) (mass, radius, Λ) up to nsat many models ∼ Signatures of quark matter in compact stars Microphysical properties Observable Phases of dense matter ← (and neutron star structure) ← Property Nuclear phase Quark phase mass distribution known unknown; eqn of state ε(p) (mass, radius, Λ) up to nsat many models ∼ spindown bulk viscosity Depends on Depends on (spin freq, age) shear viscosity phase: phase: heat capacity cooling n p e unpaired neutrino emissivity (temp, age) n p e CFL thermal cond. , µ n p e, Λ, Σ− CFL-K 0 glitches shear modulus n superfluid 2SC (superfluid, vortex pinning p supercond CSL crystal) energy π condensate LOFF 1SC merger dynamics eqn of state K condensate (grav waves) bulk viscosity ... Quark Matter and the Equation of State “Masquerade effect” EoS may be very similar in different phases (e.g. in metals: superconducting vs. “normal”). Uncertainty about quark matter EoS allows tuning its parameters to match hadronic EoS.

Sharp 1st-order phase transition This could indicate nuclear to quark matter transition

How would a strong first-order transition in the EoS be manifest in observations?

Conformal speed of sound 2 Quark matter: massless weakly-interacting have cs 1/3 Hadronic matter: relativistic mean field models can give c2 ≈1 s ≈ Manifestation of 1stOPT: twin stars c2 1 2 c2 1 2 equation of state s . / s & / no twin Twin Branch M M energy Hybrid density Quark weakly ∆ ε first-order transition Hadronic Hadronic pressure R

M M energy Quark density strongly ∆ ε first-order transition Hadronic pressure R R

Alford, Han, Prakash, arXiv:1302.4732; Montana, Tolos, Hanauske, Rezzolla, arXiv:1811.10929 st Constraints on 1 OPT from Mmax

2 M observation allows two scenarios:

high ptrans: very small connected• branch

low ptrans: no• twin stars!

Alford, Han, arXiv:1508.01261; see also Tews et al, arXiv:1801.01923, etc.

2 1 With cQM . 3 you can just barely get a 2M star. 1stOPT: grav waves from mergers

22 10− 4 × 12 M = 2.8 M hadronic M = 2.9 M 10 2 with quarks 8 0 [kHz] 22 6 1.5 10− aligned ringdown at 100 Mpc 2 × GW

− f

22 + 4

h 0.0 4 − 2 1.5 − 0.00 0.25 0.50 0.75 1.00 6 0 −3.0

[rad] 1.5 φ

∆ 0.0 10 5 0 5 10 15 20 5 0 5 10 15 20 − − t t [ms] − t t [ms] − mer − mer Most et. al., arXiv:1807.03684 solid lines: gravitational wave strain translucent lines: instantaneous frequency

For EoS with a 1st-order transition to quark matter, the GW signal develops a phase difference of order π. 1stOPT: grav waves from mergers

20 10− fpeak

21 10− (20 Mpc) , 22 eff 10− h DD2F-SF-1 DD2F 23 10− 1 2 3 4 5 Bauswein et. al., f [kHz] arXiv:1809.01116

For EoS with a sharp 1st-order phase transition, GW spectrum shows a shifted f2 peak. Quark matter and spin-down Spindown via grav. waves depends on properties of the star’s interior.

Polar view Side view An r-mode is a quadrupole flow that emits gravitational radiation. It becomes unstable (i.e. arises spontaneously) when a star spins star fast 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) if neutron star some interior physics spins quickly ⇒ damps the r-modes Typical r-mode instability region

Shear viscosity grows at low temperature r−modes (long mean free paths). Spin unstable freq bulk Bulk viscosity has a viscosity resonant peak when beta Ω stabilizes shear r−modes equilibration rate matches viscosity r-mode frequency 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. r-modes and pulsars There are stars in the “forbidden zone” for nuclear matter

1000 viscous Data for accreting pulsars in damping binary systems (LMXBs) vs 800 hadronic matter instability curves for: nuclear stars Ekman • 600 layer hybrid stars with unpaired

D • ¬ quark matter (possible Hz @

f ¬ tension with cooling data) ¬ 400 ¬ ¬ interacting ¬ Another Possibility: quark ¬ ¬¬ ¬ 200 matter ¬ ¬ “tiny r-mode” (small αsat) •r-mode spindown very slow J0437-4715 0 104 105 106 107 108 109 1010 T @KD (Alford, Schwenzer, arXiv:1310.3524; Haskell, Degenaar, Ho, arXiv:1201.2101) R-modes Summary

I r-modes are sensitive to viscosity and other damping characteristics of interior of star I Mystery: There are stars inside the instability region for standard “nuclear matter with viscous damping” model. I Possible explanations: I Microphysical extra damping (e.g. unpaired quark matter) I Astrophysical extra damping (some currently unknown mechanism in a nuclear matter star) I “tiny r-mode” : very low saturation amplitude −8 Need αsat . 10 : what mechanism can do this? Hybrid star: nuclear quark phase conversion dissipation Alford, Han, Schwenzer, arXiv:1404.5279 Quark Matter and Cooling We can understand cooling in terms of hadronic models with slow (modified Urca) or intermediate (pair breaking) cooling.

1 0 7

F S U 2 R ( n u c ) For isolated neutron stars, we do not 1 . 4 0 M / M s u n

) 1 . 8 0 M / M s u n know their mass. K (

S 6 1 . 8 5 M / M s u n

T 1 0 1 . 9 0 M / M s u n If we knew the 1 . 9 5 M / M s u n

2 . 0 4 M / M s u n , the cooling O b s . D a t a C a s A data would provide a 1 0 5 1 0 - 1 1 0 0 1 0 1 1 0 2 1 0 3 1 0 4 1 0 5 1 0 6 1 0 7 more demanding A g e ( y e a r s ) constraint. (Negreiros, Tolos, et al, arXiv:1804.00334) See also, e.g., Wei, Burgio, Schulze, arXiv:1812.07306, Beloin et al, arXiv:1812.00494, etc Cooling of a star with quark matter core

1.000 1.100 1.214 critical 6.4 1.248 Crab 1.323 1.420 RX J0822-43 1.496 1.597 1.641 Unpaired quark matter 6.2 1E 1207-52 1.706 1.793 would cool very fast: is RX J0002+62 [K]) s PSR J0205+64 in 3C58 6 PSR 0656+14 it ruled out? log(T PSR 1055-52 Vela

Geminga CFL quark matter: little 5.8 CTA 1 impact on cooling. RX J1865-3754 5.6 1 2 3 4 5 6 7

log(t[yr]) (Grigorian, Blaschke, Voskresensky, astro-ph/0411619)

This model has quark matter with 2-flavor “2SC” quark pairing and weak pairing of the blue quarks. It can accomodate data with masses ranging from 1.1 M to 1.7 M . III. Manifestations of quark matter in neutron stars

Fast pulsar mystery : suppression of r-modes • r-modes stabilized by bulk viscosity in quark matter r-mode amplitude kept low by quark- conversion Sharp first-order transition to denser phase • separate branch of twin stars (different radii) effect on grav waves from mergers effect on tidal deformability 2 Phase with cs 1/3 (weakly-interacting light quarks) • close to being≈ ruled out by max mass measurement Phase with more/lighter fermions • fast cooling of unpaired quark matter shifted bulk viscosity peak in unpaired quark matter Superfluid insulating phase (probably CFL quark matter) • very low specific heat affects cooling after bursts Very rigid crystalline phase at high density (LOFF phase) • high ellipticity grav waves from pulsar ⇒ Looking to the Future What do we need to detect quark matter in neutron star cores?? I More data on observable properties of neutron stars I mass and radius I spindown (spin and age) I cooling (temperature, age, mass) I grav waves from “mountains” and mergers I Better modelling of neutron stars and mergers: I astrophysical damping and saturation mechanisms for r-modes I mechanism of glitches I effects of magnetic fields I mergers: finer resolution; turbulence? magnetic fields; dissipation; I Understand high-density matter I understand nuclear matter better: EoS, paired phases I better models of quark matter: Functional RG, Schwinger-Dyson quark matter EoS and phases (crystalline (LOFF) or...?) I solve the sign problem and do lattice QCD at high density.