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