Strange quark matter in neutron stars

Prof. Mark AlfordWashington University in St. Louis

SQM 2013

Schematic QCD phase diagram

superconductingquark matter

= color−

liq

T

µ

gas

QGP

CFL

nuclear

/supercondsuperfluid

compact star

non−CFL

heavy ioncollider

hadronic

M. Alford, K. Rajagopal, T. Schafer, A. Schmitt, arXiv:0709.4635 (RMP review)

A. Schmitt, arXiv:1001.3294 (Springer Lecture Notes)

Quark matter in compact stars

Conventional scenario

Neutron/hybrid star

neutronstar

hybridstar

NM

NM

SQM

crustnuclear

Strange Matter Hypothesis

Bodmer 1971; Witten 1984; Farhi, Jaffe 1984

Strange star

cruststrangelet

SQM SQM

SQM

crustnuclear

Two scenarios for quark matter

Conventional scenario

Vac→NM→QM

p

µ

NM

µcrit

pcrit

310MeV

QM

vac

Nuclear→quark matter transitionat high pressure, (µcrit, pcrit)

Strange Matter Hypothesis

Vac→QM

µsqm

p

µ

NM

vac

QM

MeV310

Vacuum→quark matter transitionat µ = µsqm, p = 0.Strange quark matter (SQM) is thefavored phase down to p = 0.

Stars under the Strange Matter Hypothesis

cruststrangelet

SQM SQM

SQM

crustnuclear

Strangelet crust

At zero pressure, if its surface tension is low enough ,

strange matter, like nuclear matter, will undergo charge separationand evaporation in to charged droplets.

neutral

vacuum

SQM

neutral

neutral SQM

e

e e

e

Jaikumar, Reddy, Steiner, nucl-th/0507055

σcrit . 10 MeVfm−2

Crust thickness∆R . 1 km

Alford, Eby, arXiv:0808.0671

Charge separation: a generic feature

=p

e

poschg

SQM

electrons

vacuumneutralSQM

sepp

neutral

phasecharge−separated

Ω

µ

SQM

charge density ρ =dΩ

dµe

Neutral quark matter andneutral vacuum can coexistat zero pressure.

But if they have differentelectrostatic potentials µe

then psep > 0 and it ispreferable∗ to form acharge-separated phase withintermediate µe .

∗ unless surface costs are too high, e.g. surface tension, electrostatic energy fromE = ∇µe .

Strange quark matter objects

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

1 10 100 1000 10000R (km)

1e-05

0.0001

0.001

0.01

0.1

1

M (

sola

r)

Compactbranch

(strange stars)

Diffusebranch

(strangeletdwarfs)

(strangeletplanets)

stablestability uncertain

Alford, Han arXiv:1111.3937

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.

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 allneutron 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.

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 allneutron stars? (Friedman, Caldwell, 1991)?Depends on SQM params (Bauswein et. al. arXiv:0812.4248).

Conventional hypothesis

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

neutronstar

hybridstar

NM

NM

SQM

crustnuclear

Vac→NM→QM

p

µ

NM

µcrit

pcrit

310MeV

QM

vac

Nuclear→quark matterat high pressure, (µcrit, pcrit)

Signatures of quark matter in compact stars

Observable ← Microphysical properties(and neutron star structure)

← Phases of dense matter

Property Nuclear phase Quark phase

mass, radius eqn of state ε(p)knownup to ∼ nsat

unknown;many models

spindown(spin freq, age)

bulk viscosityshear viscosity

Depends onphase:

n p en p e, µn p e,Λ, Σ−

n superfluidp supercondπ condensateK condensate

Depends onphase:

unpairedCFLCFL-K 0

2SCCSLLOFF1SC. . .

cooling(temp, age)

heat capacityneutrino emissivitythermal cond.

glitches(superfluid,crystal)

shear modulusvortex pinning

energy

Signatures of quark matter in compact stars

Observable ← Microphysical properties(and neutron star structure)

← Phases of dense matter

Property Nuclear phase Quark phase

mass, radius eqn of state ε(p)knownup to ∼ nsat

unknown;many models

spindown(spin freq, age)

bulk viscosityshear viscosity

Depends onphase:

n p en p e, µn p e,Λ, Σ−

n superfluidp supercondπ condensateK condensate

Depends onphase:

unpairedCFLCFL-K 0

2SCCSLLOFF1SC. . .

cooling(temp, age)

heat capacityneutrino emissivitythermal cond.

glitches(superfluid,crystal)

shear modulusvortex pinning

energy

Nucl/Quark EoS ε(p) ⇒ Neutron star M(R)

7 8 9 10 11 12 13 14 15Radius (km)

0.0

0.5

1.0

1.5

2.0

2.5

Mass

(so

lar)

AP4

MS0

MS2

MS1

MPA1

ENG

AP3

GM3PAL6

GS1

PAL1

SQM1

SQM3

FSU

GR

P <

causality

rotation

J1614-2230

J1903+0327

J1909-3744

Double NS Systems

Nucleons Nucleons+ExoticStrange Quark Matter

Recentmeasurement:

M = 1.97± 0.04M

Demorest et al,Nature 467,1081 (2010).

Can quark matter be the favored phase at high density?

A fairly generic QM EoS

Model-independent parameterization based on Classical Ideal Gas (CIG)

ε(p) = εtrans+∆ε + c−2QM(p − pcrit)

ε0,QM

εtrans

ptrans

cQM-2Slope =

MatterQuark

MatterNuclear

Δε

Ener

gy D

ensi

ty

Pressure

Zdunik, Haensel,arXiv:1211.1231

Alford, Han, Prakash,arXiv:1302.4732

QM EoS params: ptrans/εtrans, ∆ε/εtrans, c2QM

Constraints on QM EoS from max mass

QM + Soft Nuclear Matter

2.3M๏

2.1M

๏

2.0M๏

ntrans=2.0n0 (ptrans/εtrans=0.04)ntrans=4.0n0 (ptrans/εtrans=0.2)

2.2M๏

2.0M๏

c QM

2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Δε/εtrans = λ-10 0.2 0.4 0.6 0.8 1

QM + Hard Nuclear Matter

2.4M๏ 2.2M๏

2.0M

๏

ntrans=1.5n0 (ptrans/εtrans=0.1)ntrans=2.0n0 (ptrans/εtrans=0.17)

2.4M

๏

2.2M

๏

2.0M๏

c QM

20.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Δε/εtrans = λ-10 0.25 0.5 0.75 1 1.25 1.5

Alford, Han, Prakash, arXiv:1302.4732; Zdunik, Haensel, arXiv:1211.1231

•Max mass can constrain QM EoS but not rule out generic QM

• For soft NM EoS, need c2QM & 0.4

r-modes and old pulsarsr-modes cause fast-spinning stars to spin down ⇒ exclusion regions

¬

¬

¬¬

¬

¬

¬

¬

¬

¬

¬

¬ ¬

105 106 107 108 109 10100

200

400

600

800

T @KD

f@H

zD

Nuclear, viscous dampingonly

Nuclear with somecore-mantle friction

Nuclear with maximumcore-mantle friction

Free quarks

Quarks with non-Fermicorrections

(Schwenzer, arXiv:1212.5242)

r-modes and young pulsar spindown

Crab

Αsat=1

Αsat=10-4

Vela

J0537-6910

1 5 10 50 100 500 1000

10-11

10-9

10-7

f @HzD

Èdf

dtÈ@

s-2 D

(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 coreI Mass-radius curveI Cooling (e.g. Cas. A)I Spindown (r-mode exclusion regions)I GlitchesI Grav waves? (Spindown, mergers, “mountains”)

I We need to understand quark matter phases and how theirproperties 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 propertiesI r-mode damping mechanismsI Color supercond. crystalline phase (glitches) (gravitational waves?)I CFL phase: superconductor with unstable vortices

I Quark matter properties:I Intermediate density phasesI Role of large magnetic fieldsI Better models of quark matter: PNJL, Schwinger-DysonI Better weak-coupling calculationsI Solve the sign problem and do lattice QCD at high density