arXiv:1702.08452 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
Dense matter in neutron stars Properties Observables equations of mass, radius, � state moment of inertia… thermal & cooling, spin-down, transport glitches, neutrinos, GW, properties, magnetic field… vortex pinning Thermal States of -Cooling isolated neutron stars � -Transiently accreting neutron stars
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 � L ∼ 10 36 − 10 39 erg · s − 1 -quiescent state: decades or longer; very faint or even unobservable � L < 10 34 erg · s − 1 � 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) � �
Global thermal balance -X-ray luminosity in quiescence (after reaching a stationary state, heating = cooling) depends on the time-averaged accretion rate � � dh ( ˙ M ) = L ∞ γ ( T s ) + L ∞ ν ( T i ), T s = T s ( T i ) L ∞ M ≡ t a ˙ ˙ M a / ( t a + t q ) � ˙ � M a � � ˙ ˙ M M Q � ≈ 6.03 × 10 33 MeV erg s − 1 L dh = Q × 10 − 10 M � yr − 1 m N � � -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
Heat-blanketing envelope T i = T ( r )e Φ ( r ) = T b -NS interior assumed isothermal � insulating envelope extends to the density � T b ρ b ≃ 10 10 − 11 g cm − 3 � log η -temperature gradient near surface � � T b � 0.5+ α T s ≃ 10 6 K × � 10 8 K -light-element (H/He) amount � ⇔ thicker light-element layer higher η = g 2 surface temperature and emitted flux � 14 ∆ M le / M T s g 14 ≡ 10 14 cm 2 s − 1 -this work: NSCool code (Page 2009) applying standard PCY envelope (Potekhin et al. 1997) Yakovlev et al. (2004)
Simple approximation dh ( ˙ M ) = L ∞ γ ( T s ) + L ∞ ν ( T i ) L ∞ dh ∝ ˙ γ ∝ ( T s ) 4 T s ∝ ( T i ) 1 / 2 L ∞ L ∞ M γ ∝ ( T i ) 2 L ∞ γ ∝ ˙ -if neutrino luminosity is negligible � L ∞ dh ≈ L ∞ M -when neutrino luminosity takes over � ν ∝ ˙ L ∞ dh ≈ L ∞ M ≈ 3 γ ) 4 ∝ ˙ � L slow 4 π R 3 · Q slow T 8 9 ≡ N slow T 8 ( L ∞ M 9 ν → � ν ( T i ) = L ∞ = 3 γ ) 3 ∝ ˙ L fast 4 π R 3 p · Q fast T 6 9 ≡ N fast T 6 � ( L ∞ M 9 ν
Simple approximation On the diagram, γ − ˙ L ∞ M dh ( ˙ M ) = L ∞ γ ( T s ) + L ∞ ν ( T i ) L ∞ two limiting cases � dh ∝ ˙ γ ∝ ( T s ) 4 T s ∝ ( T i ) 1 / 2 L ∞ L ∞ M i) linear behavior � ii) power law; sensitive to γ ∝ ( T i ) 2 L ∞ neutrino emissivity γ ∝ ˙ -if neutrino luminosity is negligible � L ∞ dh ≈ L ∞ M -when neutrino luminosity takes over � ν ∝ ˙ L ∞ dh ≈ L ∞ M ≈ 3 γ ) 4 ∝ ˙ � L slow 4 π R 3 · Q slow T 8 9 ≡ N slow T 8 ( L ∞ M 9 ν → � ν ( T i ) = L ∞ = 3 γ ) 3 ∝ ˙ L fast 4 π R 3 p · Q fast T 6 9 ≡ N fast T 6 � ( L ∞ M 9 ν
Heating curves Heinke et al. (2010) -Thermal equilibrium dh ( ˙ M ) = L ∞ γ ( T s ) + L ∞ ν ( T i ) L ∞ 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
Photon vs. neutrino cooling -photon emission Wijnands et al. (2012) Heating: H = (Q /m ) M Neutrino nuc u regime: faint NSs, ind. cooling of internal structure � Slow: VFXTs Brems. -neutrino emission regime: warmer NSs � MUrca PBF MMUrca L ν ≈ L dh � L γ L (erg s ) � � 1 Photon cooling Fast: 1) slow neutrino Kaon emission in low- and q Pion intermediate-mass NSs � DUrca ) 3 2) fast emission Log (yrs) = 1(0) ) ( 4 4 ( 5 mechanisms dominate in high-mass NSs ) h 1 � t ) ( 2 -if heat deposited as 1~2 MeV/ 2 ( 3 nucleon, most SXRTs are at the neutrino stage: probe interior � 1 M (M yr )
Neutrino emission mechanism -Hadronic matter Page et al. (2009) Neutrino Emissivity � Process (erg cm − 3 s − 1 ) (optimum) (unsuppressed) MUrca mUrca ∼ 10 21 T 8 PBF 9 ∼ 10 19 − 10 20 T 8 brems. 9 ∼ 10 27 T 6 dUrca 9 pair-breaking ∼ 10 19 − 10 21 T 7 max formation T min T 9 c c -Pairing in nucleonic SF: suppresses Urca processes but trigger PBF
Equations of state -Within nucleons-only model Property APR HHJ SLy4 NL3 symmetry energy 32.6 32.0 32.0 37.3 S 0 (MeV) L = 3 n 0 [ dS 0 / dn ] n 0 (MeV) 60 67.2 45.9 118.2 dUrca threshold n dU B (fm − 3 ) 0.77 0.57 1.42 0.21 maximum density n max (fm − 3 ) 1.12 1.02 1.21 0.68 dUrca onset mass (M � ) 2.01 1.87 2.03 0.82 maximum mass (M � ) 2.18 2.17 2.05 2.77 radius of heaviest star (km) 10.18 10.98 9.96 13.65 -Given EoS, specifying the mass designates possible cooling channels
Stellar superfluids outer core inner core Page et al. (2009) neutron 1 S 0 3 2 1 Neutron P T Proton S 0 Crust Core c GIPSF BCLL GC CCY NS WAP CCDK b T SFB a AO T -density/radial profiles of the SF critical temperature remain uncertain � inside the star, regions where undergo pairing-induced T i ≤ T crit ( r ) suppression of Urca neutrinos � PBF neutrino emissions: most noticeable at T i ≈ T crit ( r ) → presence of SF alters the dominant neutrino emission mechanism
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
Light-element residue -APR/HHJ EoS; vanishing neutron gap; dUrca in massive stars (cold) � 3 P 2 -tune light-element layer thickness i) cover more luminosity range � ii) help explain hottest Aquila X-1
Stringent constraints -dUrca: phenomenological shifting � and broadening � n dU B → β n dU � dU → R dU � dU B ν ν effects -need early dUrca onset + small SF gaps to explain extremely cold sources in SAX J1808.4-3658 (arrow) and 1H 1905+000 (double arrows)
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 � ( K , Γ ) ε Γ − (2 ε 0 ) Γ � � P ( ε ) = P NM ( ε ) + Θ ( ε − 2 ε 0 ) K � light-element layer thickness � ( η Aql , Q ) (for Aql X-1, set to zero for SAX J1808) � energy release per nucleon in deep crustal heating � cps , k peak cnt , k peak p 1 S 0 : [ T max Gaussian functions � n 3 P 2 : [ T max F p , ∆ k F p ] F n , ∆ k F n ] �
Results & connections to… -Example: SLy4 EoS + polytropes; fit to data ( L 1808 , L Aql ) nuclear physics � dUrca threshold , anti-correlated with derivative of Esym � n dU B (1 − α ) ∼ 3 n sat deep crustal heating energy , can vary with multicomponent � Q = 1 ∼ 1.3 MeV ⇔ softening at higher densities lower L, or other degrees of freedom? 0 . 8 1 . 5 0 . 6 105 270 270 0 . 7 0 . 5 240 240 90 1 . 4 0 . 6 210 210 75 0 . 4 0 . 5 180 180 1 . 3 α dUrca 60 150 150 0 . 4 Q Γ 0 . 3 120 120 45 1 . 2 0 . 3 0 . 2 90 90 30 0 . 2 60 1 . 1 60 0 . 1 15 0 . 1 30 30 0 . 0 0 1 . 0 0 0 . 0 0 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 − 18 − 16 − 14 − 12 − 10 − 8 − 6 − 5 − 4 − 3 − 2 − 1 0 1 2 (fm − 3 ) n dUrca log η K B
Results & connections to… -Example: SLy4 EoS + polytropes; fit to data ( L 1808 , L Aql ) observation � jointly test SF from cooling isolated neutron stars � constraints from mass estimate, in particular 1808 � update surface luminosity and mean accretion rate other studies � 10 . 0 2 . 6 pion condensation � 54 270 2 . 4 9 . 5 48 240 (Matsuo et al. 2016) � 2 . 2 42 210 9 . 0 analytical approx. � 2 . 0 36 180 ( K ) M AqX1 (M � ) log T p 1 S 0 30 150 8 . 5 1 . 8 (Ofengeim et al. 2016) � c 24 120 1 . 6 NS mass distribution � 8 . 0 90 18 1 . 4 60 12 (Beznogov et al. 2015) � 7 . 5 1 . 2 30 6 …future work 7 . 0 0 1 . 0 0 7 . 0 7 . 5 8 . 0 8 . 5 9 . 0 9 . 5 10 . 0 1 . 0 1 . 2 1 . 4 1 . 6 1 . 8 2 . 0 2 . 2 2 . 4 log T n 3 P 2 M 1808 (M � ) ( K ) c
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:1702.08452 -proton and neutron superfluidity � -exotic matter (future work)
THANK YOU! Q & A
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