Strange Quark Matter in Neutron Stars

Prof. Mark Alford Washington University in St. Louis

SQM 2013 Schematic QCD phase diagram T

heavy ion collider

QGP non−CFL hadronic = color− superconducting gas liq CFL quark matter

nuclear compact star µ superfluid /supercond

M. Alford, K. Rajagopal, T. Sch¨afer, A. Schmitt, arXiv:0709.4635 (RMP review) A. Schmitt, arXiv:1001.3294 (Springer Lecture Notes) Quark matter in compact stars

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

nuclear crust nuclear crust neutron NM star SQM SQM

strangelet NM crust hybrid star SQM SQM Two scenarios for quark matter Conventional scenario Strange Matter Hypothesis Vac→NM→QM Vac→QM p QM NM p QM NM

pcrit vac vac µ µcrit µ 310 MeV 310MeV µsqm Nuclear→quark matter transition Vacuum→quark matter transition at high pressure, (µcrit, pcrit) at µ = µsqm, p = 0. Strange quark matter (SQM) is the favored phase down to p = 0. Stars under the Strange Matter Hypothesis

nuclear crust SQM SQM

strangelet crust

SQM Strangelet crust

At zero pressure, if its surface tension is low enough, strange matter, like nuclear matter, will undergo charge separation and evaporation in to charged droplets.

neutral −2 vacuum σcrit . 10 MeVfm e e Crust thickness neutral e e ∆R . 1 km SQM Alford, Eby, arXiv:0808.0671

neutral SQM

Jaikumar, Reddy, Steiner, nucl-th/0507055 Charge separation: a generic feature

charge−separated dΩ phase charge density ρ = Ω = dµe p neutral neutral vacuum SQM Neutral quark matter and µe neutral vacuum can coexist at zero pressure. psep electronsSQM But if they have diﬀerent electrostatic potentials µe chg then psep > 0 and it is preferable∗ to form a pos SQM charge-separated phase with intermediate µe .

∗ unless surface costs are too high, e.g. surface tension, electrostatic energy from E = ∇µe . Strange quark matter objects

Similar to nuclear matter objects, if surface tension is low enough.

1 Compact Diffuse branch branch

0.1 (strangelet dwarfs) (strange stars) 0.01

M (solar) 0.001

stable 0.0001 (strangelet stability uncertain planets)

1e-05 1 10 100 1000 10000 R (km) Alford, Han arXiv:1111.3937 Is SMH ruled out by observations of neutron stars?

I X-ray bursts oscillations indicate ordinary nuclear crust (Watts, Reddy astro-ph/0609364). But... − Maybe nuclear crust can show similar behavior? − Maybe strangelet crust can show similar behavior? I Would cosmic strangelet ﬂux be large enough to convert all neutron stars? (Friedman, Caldwell, 1991)? Depends on SQM params (Bauswein et. al. arXiv:0812.4248).

Strange Matter Hypothesis summary

I Strange matter is the true ground state at zero pressure. I For a compact star, ground state is strange matter, perhaps with a strangelet or nuclear matter crust. I Neutron stars will convert to strange stars if hit by a strangelet. I Regular matter is immune since strangelets are positively charged. I If surface tension of strange matter is low enough, it will form atoms, planets, dwarfs, compact stars, roughly like nuclear matter. Strange Matter Hypothesis summary

Transition from nuclear matter to quark matter occurs at high pressure. Compact stars have nuclear crust/mantle, possible quark matter core.

Vac→NM→QM nuclear crust neutron NM p QM NM star

pcrit vac µ µ NM crit hybrid SQM star 310MeV Nuclear→quark matter at high pressure, (µcrit, pcrit) spindown bulk viscosity Depends on Depends on (spin freq, age) shear viscosity phase: phase: n p e unpaired heat capacity n p e, µ CFL cooling neutrino emissivity n p e, Λ, Σ− CFL-K 0 (temp, age) thermal cond. n superﬂuid 2SC p supercond CSL glitches shear modulus π condensate LOFF (superﬂuid, vortex pinning K condensate 1SC crystal) energy ...

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 ∼ nsat 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 ∼ nsat many models spindown bulk viscosity Depends on Depends on (spin freq, age) shear viscosity phase: phase: n p e unpaired heat capacity n p e, µ CFL cooling neutrino emissivity n p e, Λ, Σ− CFL-K 0 (temp, age) thermal cond. n superﬂuid 2SC p supercond CSL glitches shear modulus π condensate LOFF (superﬂuid, vortex pinning K condensate 1SC crystal) energy ... Nucl/Quark EoS ε(p) ⇒ Neutron star M(R)

GR MS0 MPA1

2.5 AP3 P < PAL1 ENG AP4 MS2 causality Recent 2.0 J1614-2230 SQM3 MS1 measurement: J1903+0327 FSU

SQM1 GM3 1.5 J1909-3744 PAL6 M = 1.97 ± 0.04 M GS1 Double NS Systems Mass (solar) 1.0 Demorest et al, Nature 467, 1081 (2010). 0.5 rotation

Nucleons Nucleons+Exotic Strange Quark Matter 0.0 7 8 9 10 11 12 13 14 15 Radius (km)

Can quark matter be the favored phase at high density? A fairly generic QM EoS Model-independent parameterization based on Classical Ideal Gas (CIG)

−2 ε(p) = εtrans +∆ε + cQM(p − pcrit)

Quark y

t Matter i

s -2

n ε0,QM Slope = cQM e Zdunik, Haensel,

D Δε arXiv:1211.1231 y

g ε

r trans

e Alford, Han, Prakash, n E arXiv:1302.4732 Nuclear Matter

ptrans Pressure 2 QM EoS params: ptrans/εtrans, ∆ε/εtrans, cQM Constraints on QM EoS from max mass

QM + Soft Nuclear Matter QM + Hard Nuclear Matter 1 1 ๏ ๏ ๏ 2.4M๏ 2.2M๏ M M M 4 0 ๏ 3 . . M ๏ . 2 0.9 2 0.9 2 2 . M 2 1 . 2 2.0M๏ 2.2M 0.8 ๏ 0.8

2.0M 0.7 ๏ 0.7 2.0M๏ M M 2 Q 2 Q c c 0.6 0.6

0.5 0.5

0.4 ntrans=2.0n0 (ptrans/εtrans=0.04) 0.4 ntrans=1.5n0 (ptrans/εtrans=0.1)

ntrans=4.0n0 (ptrans/εtrans=0.2) ntrans=2.0n0 (ptrans/εtrans=0.17) 0.3 0.3 0 0.2 0.4 0.6 0.8 1 0 0.25 0.5 0.75 1 1.25 1.5

Δε/εtrans = λ-1 Δε/εtrans = λ-1 Alford, Han, Prakash, arXiv:1302.4732; Zdunik, Haensel, arXiv:1211.1231 • Max mass can constrain QM EoS but not rule out generic QM 2 • For soft NM EoS, need cQM & 0.4 r-modes and old pulsars r-modes cause fast-spinning stars to spin down ⇒ exclusion regions

800

Nuclear, viscous damping only 600

¬ Nuclear with some core-mantle friction

D ¬ ¬ Hz 400

@ ¬ Nuclear with maximum f ¬ core-mantle friction ¬ ¬ Free quarks ¬¬ ¬ 200 ¬ ¬ Quarks with non-Fermi corrections

0 105 106 107 108 109 1010 (Schwenzer, arXiv:1212.5242) T @KD r-modes and young pulsar spindown

Αsat=1 10-7

J0537-6910 D 2 -

s -9 @ 10 È dt df

È Crab

Vela

10-11

-4 Αsat=10

1 5 10 50 100 500 1000 f @HzD (Alford, Schwenzer arXiv:1210.6091) Conventional Scenario summary

I Critical density for nuclear→quark transition is unknown. Neutron stars may have quark matter cores. I We need signatures that are sensitive to properties of the core

I Mass-radius curve

I Cooling (e.g. Cas. A)

I Spindown (r-mode exclusion regions)

I Glitches

I Grav waves? (Spindown, mergers, “mountains”)

I We need to understand quark matter phases and how their properties are manifested in these signature behaviors. The future

I Neutron stars:

I More data on neutron star mass, radius, age, temperature, etc.

I Better understanding of nuclear matter properties

I r-mode damping mechanisms

I Color supercond. crystalline phase (glitches) (gravitational waves?)

I CFL phase: superconductor with unstable vortices

I Quark matter properties:

I Intermediate density phases

I Role of large magnetic ﬁelds

I Better models of quark matter: PNJL, Schwinger-Dyson

I Better weak-coupling calculations

I Solve the sign problem and do lattice QCD at high density