Quark matter in neutron stars - Strange Matter Hypothesis summary I Strange matter is the true ground

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  • Quark matter in neutron stars

    Mark Alford Washington University in St. Louis

  • Phases of quark matter

    liq

    T

    µ

    gas

    QGP

    CFL

    nuclear

    /supercond superfluid

    compact star

    non−CFL

    heavy ion collider

    hadronic

    NJL model, uniform phases only

    µB/3 (MeV) T (M

    eV )

    550500450400350

    60

    50

    40

    30

    20

    10

    0

    g2SC

    NQ

    NQ

    2SC

    uSC guSC →

    CFL

    ← gCFL

    CFL-K0

    p2SC−→ χSB

    t

    t tt

    Warringa, hep-ph/0606063

    But there are also non-uniform phases, such as the crystalline (“LOFF”/”FFLO”) phase.

  • Quark matter in compact stars

    Conventional scenario

    Neutron/hybrid star

    neutron star

    hybrid star

    NM

    NM

    SQM

    crust nuclear

    Strange Matter Hypothesis

    Bodmer 1971; Witten 1984; Farhi, Jaffe 1984

    Strange star

    crust strangelet

    SQM SQM

    SQM

    crust nuclear

  • Two scenarios for quark matter

    Conventional scenario

    Vac→NM→QM

    p

    µ

    NM

    µcrit

    p crit

    310MeV

    QM

    vac

    Nuclear→quark matter transition at high pressure, (µcrit, pcrit)

    Strange Matter Hypothesis

    Vac→QM

    µsqm

    p

    µ

    NM

    vac

    QM

    MeV310

    Vacuum→quark matter transition at µ = µsqm, p = 0. Strange quark matter (SQM) is the favored phase down to p = 0.

  • Two scenarios for quark matter

    Conventional scenario

    Vac→NM→QM

    p

    µ

    NM

    µcrit

    p crit

    310MeV

    QM

    vac

    Nuclear→quark matter transition at high pressure, (µcrit, pcrit)

    Strange Matter Hypothesis

    Vac→QM

    µsqm

    p

    µ

    NM

    vac

    QM

    MeV310

    Vacuum→quark matter transition at µ = µsqm, p = 0. Strange quark matter (SQM) is the favored phase down to p = 0.

  • Stars under the Strange Matter Hypothesis

    crust strangelet

    SQM SQM

    SQM

    crust nuclear

  • 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

    vacuum

    SQM

    neutral

    neutral SQM

    e

    e e

    e

    Jaikumar, Reddy, Steiner, nucl-th/0507055

    σcrit . 10 MeV fm −2

    Crust thickness ∆R . 1 km

    Alford, Eby, arXiv:0808.0671

  • Charge separation: a generic feature

    = p

    e

    p o s c h g

    S Q M

    electrons

    vacuum neutral SQM

    sep p

    neutral

    phase charge−separated

    µ

    SQM

    charge density ρ = dΩ

    dµe

    Neutral quark matter and neutral vacuum can coexist at zero pressure.

    But if they have different electrostatic potentials µe then psep > 0 and it is preferable∗ to form a 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 10 100 1000 10000 R (km)

    1e-05

    0.0001

    0.001

    0.01

    0.1

    1

    M (

    so la

    r)

    Compact branch

    (strange stars)

    Diffuse branch

    (strangelet dwarfs)

    (strangelet planets)

    stable stability 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 burst 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.

    Is SMH ruled out by observations of neutron stars?

    I X-ray burst 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).

  • Conventional hypothesis

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

    neutron star

    hybrid star

    NM

    NM

    SQM

    crust nuclear

    Vac→NM→QM

    p

    µ

    NM

    µcrit

    p crit

    310MeV

    QM

    vac

    Nuclear→quark matter at 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) known up to ∼ nsat

    unknown; many models

    spindown (spin freq, age)

    bulk viscosity shear viscosity

    Depends on phase:

    n p e n p e, µ n p e,Λ, Σ−

    n superfluid p supercond π condensate K condensate

    Depends on phase:

    unpaired CFL CFL-K 0

    2SC CSL LOFF 1SC . . .

    cooling (temp, age)

    heat capacity neutrino emissivity thermal cond.

    glitches (superfluid, crystal)

    shear modulus vortex 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) known up to ∼ nsat

    unknown; many models

    spindown (spin freq, age)

    bulk viscosity shear viscosity

    Depends on phase:

    n p e n p e, µ n p e,Λ, Σ−

    n superfluid p supercond π condensate K condensate

    Depends on phase:

    unpaired CFL CFL-K 0

    2SC CSL LOFF 1SC . . .

    cooling (temp, age)

    heat capacity neutrino emissivity thermal cond.

    glitches (superfluid, crystal)

    shear modulus vortex pinning

    energy

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

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

    0.0

    0.5

    1.0

    1.5

    2.0

    2.5

    M a ss

    ( so

    la r)

    AP4

    MS0

    MS2

    MS1

    MPA1

    ENG

    AP3

    GM3PAL6

    GS1

    PAL1

    SQM1

    SQM3

    FSU

    GR

    P < �

    cau sal

    ity

    rota tion

    J1614-2230

    J1903+0327

    J1909-3744

    Double NS Systems

    Nucleons Nucleons+ExoticStrange Quark Matter

    Recent measurement:

    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:

    ε(p) = εtrans+∆ε + c −2 QM(p − pcrit)

    ε0,QM

    εtrans

    ptrans

    cQM-2Slope = Matter Quark

    Matter Nuclear

    Δε

    En er

    gy D

    en si

    ty

    Pressure

    Zdunik, Haensel, arXiv:1211.1231

    Alford, Han, Prakash, arXiv:1302.4732

    QM EoS params: ptrans/εtrans, ∆ε/εtrans, c 2 QM

  • Constraints on QM EoS from max mass ε(p) = εtrans+∆ε + c

    −2 QM(p − pcrit)

    QM + Soft Nuclear Matter

    2.3 M๏

    2. 1M

    2.0M๏

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

    2.2M๏

    2.0M๏

    c Q M

    2

    0.3

    0.4

    0.5

    0.6

    0.7

    0.8

    0.9

    1

    Δε/εtrans = λ-1 0 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๏