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Quark hybrid Stars: how can we identifythem?
Prof. Mark AlfordWashington University in St. Louis
Alford, Han, Prakash, arXiv:1302.4732Alford, Schwenzer, arXiv:1310.3524
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)
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 neutron stars contain quark matter cores?
Constraining QM EoS by observing M(R)
Does a 2M star rule out quark matter cores (hybrid stars)?
Lots of literature on this question, with various models of quark matter
I MIT Bag Model; (Alford, Braby, Paris, Reddy, nucl-th/0411016)
I NJL models; (Paoli, Menezes, arXiv:1009.2906)
I PNJL models (Blaschke et. al, arXiv:1302.6275; Orsaria et. al.;
arXiv:1212.4213)
I hadron-quark NLσ model (Negreiros et. al., arXiv:1006.0380)
I 2-loop perturbation theory (Kurkela et. al., arXiv:1006.4062)
I MIT bag, NJL, CDM, FCM, DSM (Burgio et. al., arXiv:1301.4060)
We need a model-independent parameterization of the quark matterEoS:
I framework for relating different models to each otherI 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) = εtrans + ∆ε + c−2QM(p − ptrans)
ε0,QM
εtrans
ptrans
cQM-2Slope =
MatterQuark
MatterNuclear
Δε
Ener
gy D
ensi
ty
Pressure
QM EoS params:
ptrans/εtrans
∆ε/εtrans
c2QM
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
∆ε < ∆εcritsmall energy density jump atphase transition
“Connected”
R
M
“Both”M
R
∆ε > ∆εcritlarge energy density jump atphase transition
“Absent”
R
M
“Disconnected”M
R
“Phase diagram” of hybrid star M(R)
Soft NM + CSS(c2QM =1)
6.05.03.0ntrans/n0
B
A
2.0 4.0
C
ncausal
D
Δε/ε
tran
s = λ
-1
0
0.2
0.4
0.6
0.8
1
1.2
ptrans/εtrans
0 0.1 0.2 0.3 0.4 0.5
Schematic
transtransεp
∆ε
εtrans
Above the red line (∆ε > ∆εcrit),connected branch disappears
∆εcritεtrans
=1
2+
3
2
ptransεtrans
(Seidov, 1971; Schaeffer, Zdunik, Haensel, 1983; Lindblom, gr-qc/9802072)
Disconnected branch exists in regions D and B.
Sensitivity to NM EoS and c2QM
c2QM =1/3
B
A
NL3
C
HLPS
D
Δε/εtrans
0
0.2
0.4
0.6
0.8
1
1.2
ptrans/εtrans0 0.1 0.2 0.3 0.4 0.5
c2QM =1
B
A
NL3
C
HLPS
D
Δε/εtrans
0
0.2
0.4
0.6
0.8
1
1.2
ptrans/εtrans0 0.1 0.2 0.3 0.4 0.5
• NM EoS (HLPS=soft, NL3=hard) does not make much difference.
• Higher c2QM favors disconnected branch.
Observability of hybrid star branches
Measure length of hybrid branch by
∆M ≡(
mass of heaviesthybrid star
)−Mtrans
Mtrans
∆M
M
R
Soft NM + CSS(c2QM =1)
M = Δ
-2
-3
-4
0.50.3
0.710 M๏
0.1M๏
10 M๏
10 M๏
6.05.03.0ntrans/n0
B
A
2.0 4.0
C
ncausal
D
Δε/ε
tran
s
0
0.2
0.4
0.6
0.8
1
1.2
ptrans/εtrans
0 0.1 0.2 0.3 0.4 0.5
• Connected branch is observable if ptrans is not too highand there is no disconnected branch
• Disconnected branch is always observable
Observability of hybrid star branches
Measure length of hybrid branch by
∆M ≡(
mass of heaviesthybrid star
)−Mtrans
Mtrans
∆M
M
R
Soft NM + CSS(c2QM =1)
M = Δ
-2
-3
-4
0.50.3
0.710 M๏
0.1M๏
10 M๏
10 M๏
6.05.03.0ntrans/n0
B
A
2.0 4.0
C
ncausal
D
Δε/ε
tran
s
0
0.2
0.4
0.6
0.8
1
1.2
ptrans/εtrans
0 0.1 0.2 0.3 0.4 0.5
• Connected branch is observable if ptrans is not too highand there is no disconnected branch
• Disconnected branch is always observable
Constraints on QM EoS from max mass
Soft Nuclear Matter + CSS(c2QM = 1)
2.0M๏
2.3M๏
2.2M๏
B
A
2.1M
๏
C
D
Δε/εtrans
0
0.2
0.4
0.6
0.8
1
1.2
ptrans/εtrans0 0.1 0.2 0.3 0.4 0.5
•Max mass data constrains QM EoS but does not rule out generic QM
Dependence of max mass on c2QM
Soft NM + CSS(c2QM = 1/3)
1.5M๏
1.6M๏1.8M๏ 2.
1M๏
2.0M๏
B
A
C
D
Δε/εtrans
0
0.2
0.4
0.6
0.8
1
1.2
ptrans/εtrans0 0.05 0.1 0.15 0.2 0.25 0.3
Soft NM + CSS(c2QM = 1)
2.0M๏
2.3M๏
2.2M๏
B
A
2.1M
๏
C
D
Δε/εtrans
0
0.2
0.4
0.6
0.8
1
1.2
ptrans/εtrans0 0.1 0.2 0.3 0.4 0.5
• For soft NM EoS, need c2QM & 0.4 to get 2M stars
Quark matter EoS Summary
I CSS (Constant Speed of Sound) is a generic parameterization of theEoS close to a sharp first-order transition to quark matter.
I Any specific model of quark matter with such a transitioncorresponds to particular values of the CSS parameters(ptrans/εtrans, ∆ε/εtrans, c2
QM).Its predictions for hybrid star branches then follow from the genericCSS phase diagram.
I Existence of 2M neutron star → constraint on CSS parameters .
For soft NM we need c2QM & 0.4 (c2
QM = 1/3 for free quarks).
I More measurements of M(R) would tell us more about the EoS ofnuclear/quark matter. If necessary we could enlarge CSS to allowfor density-dependent speed of sound.
r-modes and gravitational spin-down
An r-mode is a quadrupole flowthat emits gravitational radiation. Itbecomes unstable (i.e. arises spon-taneously) when a star spins fastenough, and if the shear and bulkviscosity are low enough.
Side viewPolar view
mode pattern
star
The unstable r -mode can spin the star down very quickly, in a few daysif the amplitude is large enough(Andersson gr-qc/9706075; Friedman and Morsink gr-qc/9706073; Lindblom
astro-ph/0101136).
neutron starspins quickly
⇒ some interior physicsdamps the r -modes
r-mode instability region for nuclear matter
Ω
freqSpin
stabilizes
stabilizes
TTemperature
bulkviscosity
shearviscosity
r−modes
r−modes
unstabler−modes
Shear viscosity grows atlow T (long mean freepaths).
Bulk viscosity has aresonant peak when betaequilibration rate matchesr-mode frequency
• 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
dα
dt= α(|γG | − γV ) γG = 1
τG= grav radiation rate (< 0)
γV = 1τV
= r-mode dissipation rate
dΩ
dt= −2Q γV α
2 Ω Q ≈ 0.1 for typical star
dT
dt= − 1
CV(Lν − PV ) Lν = neutrino emission
PV = power from dissipation
R-mode is unstable when |γG (Ω)| > γV (T ) at infinitesimal α.
R-mode saturates when γV (α) rises with α until
γV (T , αsat) = γG (⇒ PV = PG )
In general, αsat(T ,Ω) is an unknown function determined bymicroscopic and astrophysical damping mechanisms.
R-modes and young neutron stars
Αsat=1Αsat=10-4
107 108 109 1010 10110.0
0.2
0.4
0.6
0.8
1.0
T @KD
WW
K
Young pulsar cools intoinstability region
R-mode quickly saturates
Star spins down along“heating=cooling” line
Star exits instabilityregion at Ω ∼ 50 Hz,indp of cooling model
(Alford, Schwenzer
arXiv:1210.6091)
Could r-modes explain young pulsar’s slowspin?
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
r-modes withαsat ∼ 10−2 to 10−1
could explain slowrotation of youngpulsars (. a fewthousand years old)
J0537-6910 is 4000years old
(Alford, Schwenzer
arXiv:1210.6091)
How quickly r-modes spin down pulsars
Αsat=1 Αsat=10-4
10-10 10-5 1 1050.0
0.2
0.4
0.6
0.8
1.0
t @yD
WW
K
For αsat in the range0.01 to 0.1,spindown is complete in20,000 to 500 years.
(Alford, Schwenzer
arXiv:1210.6091)
GW from r-mode spindown of young pulsars
Known young pulsars.
For given age t, h0 isindp of current freq ν,since if Ω = 2πν ishigher, spindownwould be faster, soαsat must be smallerto ensure we get tofreq Ω in time t.
Several known sourceswould be detected byadvanced LIGO if theyare mainly spinningdown via r-modes.
Gravitational wave emission of young sources• Advanced LIGO will become operational soon …
• Since r-mode emission can quantitively explain the low rotation frequencies of observed pulsars (which spin by now too slow to emit GWs), very young sources are promising targets
SN 1987A
SN 1957D
J0537-6910
G1.9+0.3
Cas A
100 1000500200 300150 150070010-27
10-26
10-25
10-24
10-23
n @HzD
h 0
knowntimingdata
advancedLIGOHNS-opt.L HstandardL
unknowntiming
LIGO
100 1000500200 300150 150070010-27
10-26
10-25
10-24
10-23100
101
102
103
104
105
106
107
n @HzD
h 0 t@yD
Several potential sources in reach of aLigo
r-modes and old pulsarsAbove curves, r-modes go unstable and spin down the star
J0437-4715
¬¬
¬¬
¬
¬
¬
¬¬
¬
¬
¬ ¬
viscousdamping
hadronicmatter
Ekmanlayer
interactingquarkmatter
104 105 106 107 108 109 10100
200
400
600
800
1000
T @KD
f@H
zD
Data for accreting pulsarsin binary systems(LMXBs) vs instabilitycurves for nuclear andhybrid stars.
Possibilities:• additional damping(e.g. quark matter)• r-mode spindown is veryslow (small αsat)
(Alford, Schwenzer,arXiv:1310.3524
Haskell, Degenaar, Ho,arXiv:1201.2101)
Spindown via r-modes of an old neutron star
æ
æ
æ
æ
æ
æ
steady state curve Whc,along which heating
equals cooling
boundary of theinstability region
slow accretionspinup
slow r-modespindown
cooling HrapidL
A
B
CD
E
F
Wmin
W f
logHTL
W
Steady-state spindowncurve is determined byamplitude αsat at whichr-mode saturates.
This determines finalspin frequency Ωf .Stars with Ω < Ωf arenot undergoing r-modespindown.
r-mode spindown trajectories
¬
¬
¬¬
¬
¬
¬
¬
¬¬
¬
¬ ¬
Αsa
t=10
-10
Αsa
t=10
-5
Αsa
t=1
106 107 108 109 10100
100
200
300
400
500
600
700
T @KD
f@H
zD
(Alford, Schwenzer, arXiv:1310.3524)
Explanations:
1) Instability boundary iswrong (additional damping).
2) Many neutron stars (mspulsars and LMXBs) arestuck in the instabilityregion, undergoing r-modespindown with lowsaturation amplitude• αsat ∼ 10−7
• T & 107 K (r-modeheating)• they are emitting gravwaves
Gravitational waves from old ms-pulsars• In addition to the standard
case of deformations r-modes are a promising continuous GW-source
• But, the r-mode saturation mechanism depends weakly on source properties …
novel universal spindown limit for the GW signal
Millisecond pulsars are below the aLigo sensitivity
However they should be detectable with further improvements or 3. generation detectors
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50 100 200 500 1000
10-28
10-26
10-24
Gravitational wave frequency n @HzDStrainsensitivityh 0
standard !spindown!
limits
universal !spindown!
limits
mode!coupling
const!model
Aasi, et. al., arXiv:1309.4027
Alford & Schwenzer, arXiv:1403.7500(universal spindown limit)
“R-mode temperatures“• The connection between the
spindown curves allows todetermine the R-mode temperature of a star with saturated r-mode oscillations (tiny r-mode scenario) for given timing data
• Independent of the saturation mechanism ... but depends on the cooling
• These are only upper bounds since the observed spindown rate can also stem from electromagnetic radiation
Measurements of temperatures of fast pulsars would allow us to test if saturated tiny r-modes can be present!
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105 2â105 3â105 5â105 106 2â1060
100
200
300
400
500
600
700
T• @KD
f@HzDTrm =
I/
3L
1/
hadronic Modified Urca
hadronic direct !Urca
Alford & Schwenzer, arXiv:1310.3524
R-modes Summary
I r-modes are sensitive to viscosity and other damping characteristicsof 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. quark matter)
I Astrophysical extra damping (some currently unknownmechanism in a nuclear matter star)
I “tiny r-mode” = very low saturation amplitude
R-modes prospectsI a-LIGO will tell us whether some young neutron stars are spinning
down via r-modesI Better temperature measurements of ms pulsars will tell us whether
they are inside the simple nuclear-viscous instability region.I If they are inside, this tells us what value of αsat is required for
compatibility with the simple nuclear-viscous model.I If we also know their Ω, we can see if they being heated by
r-modes (T∞ ∼ 105 to 106 K).I If pulsars with f & 300 Hz are outside (too cool) this would require
amazingly low αsat . 10−8 to be compatible with the simplenuclear-viscous model
I Now that we have calculations of r-mode spindown as a function ofgeneral (generic power law) microphysical properties, let’s startsurveying all known phases of dense matter for their spindownpredictions
I Additional astrophysical damping could save simple nuclear-viscousmodel; what other mechanisms could there be?
How will we identify hybrid stars?EoS : density discontinuity at nuclear/quark transition leads to
connected and/or disconnected branches in M(R).We need:
I better measurements of M and RI theoretical constraints on basic properties of QM EoS
(ptrans/εtrans, ∆ε/εtrans, c2QM)
I knowledge of nuclear matter EoS
Spindown : extra damping in some forms of quark matter can explaincurrent observations, but other scenarios (astrophysical extra damping;r-modes with tiny amplitude) have not been ruled out.We need:
I Better theoretical understanding of r-mode damping and saturationmechanisms
I Better temperature measurements (ideally, of ms pulsars too)I Detect grav waves from old pulsars (beyond advanced LIGO) or
very young neutron stars (advanced LIGO)
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
2
0.3
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