Thermal States of Transiently Accreting Neutron Stars in Quiescence - - PowerPoint PPT Presentation

Thermal States of Transiently Accreting Neutron Stars in Quiescence

Sophia Han University of Tennessee, Knoxville collaboration with Andrew Steiner, UTK/ORNL

ICNT Program at FRIB Wednesday Apr. 5th, 2017

arXiv:1702.08452

Thermal States of

Dense matter in neutron stars

Properties Observables

equations of state mass, radius, moment of inertia… thermal & transport properties, vortex pinning cooling, spin-down, glitches, neutrinos, GW, magnetic field…

• Cooling isolated neutron stars
• Transiently accreting neutron stars

A class of low-mass X-ray binaries (LMXBs)

• outburst state: weeks to months of high accretion; bright in X-rays &
• ptical
• quiescent state: decades or longer; very faint or even unobservable
• Eventually a thermal steady-state for the system is reached
• regulator: deep crustal heating; Brown, Bildsten & Rutledge (1998)
• heat per one accreted nucleon deposited in the crust ~1-2 MeV:

Haensel & Zdunik (1990), Haensel & Zdunik (2003)

• L < 1034erg · s−1

Soft X-ray transients

L ∼ 1036 − 1039erg · s−1

• X-ray luminosity in quiescence (after reaching a stationary state,

heating = cooling) depends on the time-averaged accretion rate

• Exception: quasi-persistent X-ray transients e.g. KS 1731-260 with

accretion period ~ years to decades instead of weeks to months

during accretion stellar interiors are heated out of thermal equilibrium significant late crust cooling observed after outburst

Global thermal balance

→

˙ M ≡ ta ˙ Ma/(ta + tq) ˙ Ma

L∞

dh( ˙

M) = L∞

γ (Ts) + L∞ ν (Ti), Ts = Ts(Ti)

Ldh = Q × ˙ M mN ≈ 6.03 × 1033

• ˙

M 10−10 M yr−1

• Q

MeV erg s−1

Heat-blanketing envelope

• NS interior assumed isothermal

insulating envelope extends to the density

• temperature gradient near surface
• light-element (H/He) amount

thicker light-element layer higher

surface temperature and emitted flux

• this work: NSCool code (Page 2009)

applying standard PCY envelope (Potekhin et al. 1997)

Yakovlev et al. (2004)

Ti = T(r)eΦ(r) = Tb

Ts ≃ 106K × Tb 108K 0.5+α

⇔

ρb ≃ 1010−11 g cm−3

η = g 2

14 ∆Mle/M

g14 ≡ 1014 cm2 s−1

Ts Tb

logη

• if neutrino luminosity is negligible
• when neutrino luminosity takes over
• Simple approximation

→

L∞

dh( ˙

M) = L∞

γ (Ts) + L∞ ν (Ti)

L∞

dh ∝ ˙

M

L∞

γ ∝ (Ts)4

Ts ∝ (Ti)1/2 L∞

dh ≈ L∞ γ ∝ ˙

M L∞

dh ≈ L∞ ν ∝ ˙

M

L∞

ν (Ti) =

Lslow

ν

≈ 3 4πR3 · QslowT 8

9 ≡ NslowT 8 9

Lfast

ν

= 3 4πR3

p · QfastT 6 9 ≡ NfastT 6 9

L∞

γ ∝ (Ti)2

(L∞

γ )4 ∝ ˙

M (L∞

γ )3 ∝ ˙

M

• if neutrino luminosity is negligible
• when neutrino luminosity takes over
• Simple approximation

→

L∞

dh( ˙

M) = L∞

γ (Ts) + L∞ ν (Ti)

L∞

dh ∝ ˙

M

L∞

γ ∝ (Ts)4

Ts ∝ (Ti)1/2 L∞

dh ≈ L∞ γ ∝ ˙

M L∞

dh ≈ L∞ ν ∝ ˙

M

L∞

ν (Ti) =

Lslow

ν

≈ 3 4πR3 · QslowT 8

9 ≡ NslowT 8 9

Lfast

ν

= 3 4πR3

p · QfastT 6 9 ≡ NfastT 6 9

L∞

γ ∝ (Ti)2

(L∞

γ )4 ∝ ˙

M (L∞

γ )3 ∝ ˙

M

On the diagram, two limiting cases

i) linear behavior ii) power law; sensitive to neutrino emissivity

L∞

γ − ˙

M

• Theoretical prediction

specify EoS, composition, light element amount, superfluidity gaps and NS mass

• Observation

lower surface luminosity at the same accretion rate heavy stars cool more efficiently Heinke et al. (2010)

Heating curves

• Thermal equilibrium
• bservables

⇔

L∞

dh( ˙

M) = L∞

γ (Ts) + L∞ ν (Ti)

• photon emission

regime: faint NSs, ind.

• f internal structure
• neutrino emission

regime: warmer NSs

• 1) slow neutrino

emission in low- and intermediate-mass NSs 2) fast emission mechanisms dominate in high-mass NSs

Lν ≈ Ldh Lγ

Photon vs. neutrino cooling

Wijnands et al. (2012)

Kaon DUrca Slow: Neutrino cooling Fast: MMUrca PBF MUrca Brems. Pion

nuc u

Heating: H = (Q /m ) M Photon cooling VFXTs 2 ( 1 )

• t

h

4 ( 3 ) 5 ( 4 ) 3 ( 2 ) Log (yrs) = 1(0)

1

L (erg s )

1 q

M (M yr )

• if heat deposited as 1~2 MeV/

nucleon, most SXRTs are at the neutrino stage: probe interior

(erg cm−3 s−1)

• Hadronic matter
• Pairing in nucleonic SF: suppresses Urca processes but trigger PBF

c Tmin

(optimum)

c

max

T MUrca

(unsuppressed)

PBF

Page et al. (2009)

∼ 1019 − 1021 T 7

9

∼ 1027 T 6

9

∼ 1019 − 1020 T 8

9

∼ 1021 T 8

9

Process mUrca brems. dUrca pair-breaking formation Neutrino Emissivity

Neutrino emission mechanism

Equations of state

• Within nucleons-only model
• Given EoS, specifying the mass designates possible cooling channels

Property APR HHJ SLy4 NL3 symmetry energy

32.6 32.0 32.0 37.3 60 67.2 45.9 118.2

dUrca threshold

0.77 0.57 1.42 0.21

maximum density

1.12 1.02 1.21 0.68

dUrca onset mass

2.01 1.87 2.03 0.82

maximum mass

2.18 2.17 2.05 2.77

radius of heaviest star (km)

10.18 10.98 9.96 13.65

S0 (MeV) L = 3n0 [dS0/dn]n0 (MeV) ndU

B (fm−3)

nmax (fm−3)

(M) (M)

Stellar superfluids

Page et al. (2009)

T GIPSF GC SFB CCDK WAP Core Crust

T NS BCLL a b c AO

Proton S

1

Neutron P

3 2

CCY T

• density/radial profiles of the SF critical temperature remain uncertain

inside the star, regions where undergo pairing-induced suppression of Urca neutrinos PBF neutrino emissions: most noticeable at Ti ≤ Tcrit(r) Ti ≈ Tcrit(r)

→

presence of SF alters the dominant neutrino emission mechanism

• uter core

inner core neutron 1S0

Theoretical prediction

• dichotomy of thermal states of SXRTs: separated by dUrca onset mass
• PBF: test between mild and vanishing neutron triplet superfluidity

3P2

Light-element residue

• APR/HHJ EoS; vanishing neutron gap; dUrca in massive stars (cold)
• tune light-element layer thickness i) cover more luminosity range

ii) help explain hottest Aquila X-1

3P2

Stringent constraints

• need early dUrca onset + small SF gaps to explain extremely cold sources

in SAX J1808.4-3658 (arrow) and 1H 1905+000 (double arrows)

• dUrca: phenomenological shifting

and broadening effects

ndU

B → βndU B

dU

ν

→ RdU dU

ν

Statistical analysis

• Fit to luminosity data of the hottest and coldest source
• Input parameters

two NS masses dUrca onset characterization EoS: nuclear model + polytropes above twice saturation density

• light-element layer thickness

(for Aql X-1, set to zero for SAX J1808) energy release per nucleon in deep crustal heating Gaussian functions

• P(ε) = PNM(ε) + Θ(ε − 2ε0)K
• εΓ − (2ε0)Γ

(L1808, LAql)

(M1808, MAql)

ndU

B (1 − α) ≥ nsat

(K, Γ) (ηAql, Q) n 3P2 : [T max

cnt , kpeak Fn , ∆kFn]

p 1S0 : [T max

cps , kpeak Fp , ∆kFp]

Results & connections to…

0.0 0.5 1.0 1.5 2.0

ndUrca

(fm−3)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

αdUrca

30 60 90 120 150 180 210 240 270

• Example: SLy4 EoS + polytropes; fit to data

−5 −4 −3 −2 −1 1 2

K

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Γ

15 30 45 60 75 90 105

nuclear physics dUrca threshold , anti-correlated with derivative of Esym deep crustal heating energy , can vary with multicomponent softening at higher densities lower L, or other degrees of freedom?

(L1808, LAql)

−18 −16 −14 −12 −10 −8 −6

log η

1.0 1.1 1.2 1.3 1.4 1.5

Q

30 60 90 120 150 180 210 240 270

ndU

B (1 − α) ∼ 3nsat

Q = 1 ∼ 1.3 MeV

⇔

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

M1808 (M)

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

MAqX1 (M)

6 12 18 24 30 36 42 48 54 7.0 7.5 8.0 8.5 9.0 9.5 10.0

log T n3P2

(K)

7.0 7.5 8.0 8.5 9.0 9.5 10.0

log T p1S0

(K)

30 60 90 120 150 180 210 240 270

Results & connections to…

• Example: SLy4 EoS + polytropes; fit to data
• bservation

jointly test SF from cooling isolated neutron stars constraints from mass estimate, in particular 1808 update surface luminosity and mean accretion rate

(L1808, LAql)

• ther studies

pion condensation (Matsuo et al. 2016)

analytical approx.

(Ofengeim et al. 2016)

NS mass distribution

(Beznogov et al. 2015) …future work

Probe properties of dense matter

• surface luminosity at given accretion rate; same physics tested as in

isolated stars

• observational constraint: hottest/coldest star; possible mass & radius

measurement

Thermal states of accreting NSs in SXRTs

• nuclear matter EoSs; direct Urca threshold
• neutron star crust composition and heating
• light-element accreted envelope
• proton and neutron superfluidity
• exotic matter (future work)

Summary

arXiv:1702.08452

THANK YOU! Q & A