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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.
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
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