Thermal States of Transiently Accreting Neutron Stars in Quiescence

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1 arxiv: 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

2 Dense matter in neutron stars Properties equations of state thermal & transport properties, vortex pinning Observables mass, radius, moment of inertia cooling, spin-down, glitches, neutrinos, GW, magnetic field Thermal States of -Cooling isolated neutron stars -Transiently accreting neutron stars

3 Soft X-ray transients A class of low-mass X-ray binaries (LMXBs) -outburst state: weeks to months of high accretion; bright in X-rays & optical -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 erg s 1 L < erg s 1

4 Global thermal balance -X-ray luminosity in quiescence (after reaching a stationary state, heating = cooling) depends on the time-averaged accretion rate L dh(ṁ) =L γ (T s )+L ν (T i ), T s = T s (T i ) Ṁ t a M a /(t a + t q ) L dh = Q Ṁ m N ( M a Ṁ M yr 1 ) Q MeV erg s 1 -Exception: quasi-persistent X-ray transients e.g. KS 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

5 Heat-blanketing envelope -NS interior assumed isothermal T i = T (r)e Φ(r) = T b insulating envelope extends to the density -temperature gradient near surface ρ b gcm 3 T s 10 6 K ( Tb 10 8 K ) 0.5+α -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) T s logη T b η = g14 2 M le /M g cm 2 s 1 Yakovlev et al. (2004)

6 Simple approximation L dh(ṁ) =L γ (T s )+L ν (T i ) L dh Ṁ L γ (T s ) 4 T s (T i ) 1/2 L γ (T i ) 2 -if neutrino luminosity is negligible L dh L γ Ṁ -when neutrino luminosity takes over L dh L ν Ṁ L ν (T i )= L slow ν 3 4 πr 3 Q slow T 8 9 N slow T 8 9 L fast ν = 3 4 πr 3 p Q fast T 6 9 N fast T 6 9 (L γ ) 4 Ṁ (L γ ) 3 Ṁ

7 Simple approximation L dh(ṁ) =L γ (T s )+L ν (T i ) L dh Ṁ L γ (T s ) 4 T s (T i ) 1/2 L γ (T i ) 2 -if neutrino luminosity is negligible L dh L γ Ṁ L γ Ṁ On the diagram, two limiting cases i) linear behavior ii) power law; sensitive to neutrino emissivity -when neutrino luminosity takes over L dh L ν Ṁ L ν (T i )= L slow ν 3 4 πr 3 Q slow T 8 9 N slow T 8 9 L fast ν = 3 4 πr 3 p Q fast T 6 9 N fast T 6 9 (L γ ) 4 Ṁ (L γ ) 3 Ṁ

8 Heating curves Heinke et al. (2010) -Thermal equilibrium L dh(ṁ) =L γ (T s )+L ν (T i ) observables -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

9 Photon vs. neutrino cooling Wijnands et al. (2012) 1 L (erg s ) q VFXTs Photon cooling 5(4) 3(2) 4(3) Heating: H = (Q 2(1) M (M yr 1 ) th nuc /m ) M u Log (yrs) = 1(0) Neutrino cooling Slow: Brems. MUrca PBF MMUrca Fast: Kaon Pion DUrca -photon emission regime: faint NSs, ind. of internal structure -neutrino emission regime: warmer NSs L ν L dh L γ 1) slow neutrino emission in low- and intermediate-mass NSs 2) fast emission mechanisms dominate in high-mass NSs -if heat deposited as 1~2 MeV/ nucleon, most SXRTs are at the neutrino stage: probe interior

10 Neutrino emission mechanism -Hadronic matter Process murca brems. Neutrino Emissivity (erg cm 3 s 1 ) T T9 8 Page et al. (2009) PBF (optimum) MUrca (unsuppressed) durca T 6 9 pair-breaking formation T 7 9 Tc min Tc max -Pairing in nucleonic SF: suppresses Urca processes but trigger PBF

11 Equations of state -Within nucleons-only model Property APR HHJ SLy4 NL3 symmetry energy S 0 (MeV) L =3n 0 [ds 0 /dn] n0 (MeV) n du durca threshold B (fm 3 ) maximum density n max (fm 3 ) durca onset mass (M ) (M ) maximum mass radius of heaviest star (km) Given EoS, specifying the mass designates possible cooling channels

12 Stellar superfluids outer core inner core Page et al. (2009) Proton 1 S 0 Neutron 3 P2 c neutron 1 S 0 GIPSF T Crust Core BCLL CCY GC NS T b CCDK WAP SFB AO T a -density/radial profiles of the SF critical temperature remain uncertain inside the star, regions where T i T crit (r) undergo pairing-induced suppression of Urca neutrinos PBF neutrino emissions: most noticeable at T i T crit (r) presence of SF alters the dominant neutrino emission mechanism

13 Theoretical prediction -dichotomy of thermal states of SXRTs: separated by durca onset mass -PBF: test between mild and vanishing neutron triplet superfluidity 3 P 2

14 Light-element residue -APR/HHJ EoS; vanishing neutron -tune light-element layer thickness 3 P 2 gap; durca in massive stars (cold) i) cover more luminosity range ii) help explain hottest Aquila X-1

15 Stringent constraints -durca: phenomenological shifting nb du βnb du and broadening ϵ du ν R du ϵ du ν effects -need early durca onset + small SF gaps to explain extremely cold sources in SAX J (arrow) and 1H (double arrows)

16 Statistical analysis -Fit to luminosity data of the hottest and coldest source (L 1808, L Aql ) -Input parameters two NS masses (M 1808, M Aql ) durca onset characterization n du B (1 α) n sat EoS: nuclear model + polytropes above twice saturation density P(ε) =P NM (ε)+θ(ε 2ε 0 )K [ ε Γ (2ε 0 ) Γ] (K,Γ) light-element layer thickness (for Aql X-1, set to zero for SAX J1808) (η Aql, Q) energy release per nucleon in deep crustal heating Gaussian functions n 3 P 2 :[T max cnt, k peak F n, k F n] p 1 S 0 :[T max cps, k peak F p, k F p]

17 Results & connections to -Example: SLy4 EoS + polytropes; fit to data (L 1808, L Aql ) nuclear physics n du durca threshold B (1 α) 3n sat, anti-correlated with derivative of Esym deep crustal heating energy Q =1 1.3 MeV, can vary with multicomponent softening at higher densities lower L, or other degrees of freedom? durca Q n durca B (fm 3 ) log K 0

18 Results & connections to -Example: SLy4 EoS + polytropes; fit to data (L 1808, L Aql ) log T p1 S0 c (K) observation jointly test SF from cooling isolated neutron stars constraints from mass estimate, in particular 1808 update surface luminosity and mean accretion rate log T n3 P 2 c (K) MAqX1 (M ) M 1808 (M ) other studies pion condensation (Matsuo et al. 2016) analytical approx. (Ofengeim et al. 2016) NS mass distribution (Beznogov et al. 2015) future work

19 Summary Thermal states of accreting NSs in SXRTs -surface luminosity at given accretion rate; same physics tested as in isolated stars -observational constraint: hottest/coldest star; possible mass & radius measurement Probe properties of dense matter -nuclear matter EoSs; direct Urca threshold -neutron star crust composition and heating -light-element accreted envelope arxiv: proton and neutron superfluidity -exotic matter (future work)

20 THANK YOU Q & A