Magneto-Thermal Evolution of Isolated Neutron Stars

Transcription

1 Magneto-Thermal Evolution of Isolated Neutron Stars Ulrich R.M.E. Geppert J. Gil Institute of Astronomy Zielona Gòra 1

2 B t = c2 4πσ B + c 4πen e B B Ԧv hyd + Ԧv amb B Q T Ohmic decay: σ = σ(t) Ԧv hyd ~ dynamo ~ T Ԧv amb ~ τ pn = τ pn (T) Q T: thermoelectric field, Q = Q(T, B) tensor of thermopower battery & thermal drift of B c V T t κ Ƹ T = Q ν + Q h c V = c V (T) κ Ƹ = κƹ T, B tensor of heat conductivity neutrino losses: Q ν (T, B), heating by Joule, ambipolar diffusion, crust cracking: Q h = Q h (T, B) 2

3 1. Dynamo at NS birth 2. Ambipolar diffusion 3. Magnetic field effects on the heat flux 4. Magneto-thermal processes at the polar cap of radio pulsars 3

4 immediately after birth, Proto-NS - Proto-NS dynamo, convection driven by lepton and temperature gradients ds dr < 0 dlnt dz > dlnt dz ad Andresen etal overshooting convective unstable 1 ρv 2 con 2 ~ B 2 sat 8π B sat~10 16 G 4

5 Thompson & Duncan 1993: high Ro P/τ con mean field dynamo (P~10 ms, τ con ~1 ms) - diff. rotation in first 30 s: α ω dynamo loops of l loop ~1km and B loop ~10 15 G B sat? - flux per loop: Φ loop 1 B 2 2 loopl loop - NS dipole field: B dip = 3 2 π Φ loop R B loop NS G l loop 1km 2 G B dip is derived from smaller scale structures 5

6 recent Proto-NS dynamo studies: Andresen etal. 2017: 3D Proto-NS neutrino HD + convection GW signals Obergaulinger & Aloy 2017: 2D, MHD + neutrino transport t < 2s B tor B pol - accretion more important than convection? - computational extremely costly! 6

7 Ambipolar diffusion - joint transport of magnetic flux and charged particles (p, e) relative to neutral background (n) - driven by magnetic forces Ԧf B = Ԧj B c and chemical imbalances μ μ p + μ e μ n Ԧf B n c μ - opposed by collisions = m p + m e τ pn τ en Ԧv amb strongly T dependent 7

8 GR92: n fixed, p, e move relative to n E amb t = dv m p + m e τ pn τ en Ԧv 2 dvn c Ԧv μ, Ԧv: ambipolar drift velocity losses by frictional drag losses by ν, νҧ during inverse and direct β decays that smooth departures from chemical equilibrium Ԧv sol = n c sol Ԧf B m p + m, Ԧvirr = e τ pn τ en Ԧf B irr n c μ n c m p + m e τ pn τ en 8

9 t amb = L v amb normal npe matter GR92: t sol ~ T 8 2 L yr B 12 t sol decreases with cooling, for magnetar fields ~1000yr t irr ~ T T B 8 L t irr increases with cooling, 5 1/4 12 provided T 8 6L 5 - high temperatures: t irr t sol - low temperatures: t irr t sol solenoidal flow dominates flow almost incompressible Gusakov etal. 2017: not fixed n irrotational regime does not appear 9

10 transition from normal to superfluid matter: Baym, Pethick,Pines 1969 Haensel etal. 2000, 2001, Passamonti etal. 2016: τ 1 pn R pn τ 1 pn, R pn < 1 R pn : superfluid supression factor 1 if T T c t sol ~ 4πm p n c L 2 τ pn B 2 t sol ~ 4πm p n c L 2 R pn H c1 B τ pn H c G at ρ nuc type II SC critical field 10

11 Passamonti etal. 2016: t npe amb ~ SF t amb SF - t amb ~ magnetar livetime magnetars with fast ν reactions (rapid cooling!) advection velocities ~ km/kyr substantial re-organization of core magnetic field? 11

12 temperature magnetic field: τ pn = τ pn (T) would explain observed L surf erg/s at ages ~1 10kyr Beloborodov & Li 2016 magnetic field temperature: Heating by ambipolar diffusion may contribute to observed magnetar luminosities but does not explain it completely. no heating by ambipolar diffusion Problem: huge ν emissivity, murca ~10 20 T 9 8, durca~10 27 T

13 magnetic field effects on heat flux - Greenstein & Hartke 1983: X-ray observations of radio pulsars - B: transport coefficients tensors κ, σ, Q ρ, T, Q imp, cc, κ, Ƹ σ, Q(ρ, T, Q imp, cc,, B) Hall magnetization parameter ω B τ ω B τ(ρ, T(t), A, Z, Q imp,, B(t)) perp. to B parallel to B 13

14 F = κ T, F = κ T F F Heat flows not along T but along B! 14

15 spectral fit for cooling NS B (Mineo et al.2002) variation of fit parameters until χ 2 is minimum BB 1 ~ K BB 2 ~ K PL (magnetospheric) A 2 /A 1 =(6.8±3.7)

16 2D, coupled magneto-thermal evolution: Gourgouliatos etal. 2016, Gourgouliatos & Hollerbach 2017: 3D 16

17 magneto-thermal effects at the polar cap of radio pulsars 17

18 Ruderman & Sutherland 1975: avalanche of positrons γ + B: pair creation finally: spark-breakdown CR of the gap seed photon, E γ > 2m e c 2 heating by bombardment 18

19 conditions for creation of radio emission: - charges have to be accelerated to ultrarelativistic velocities ε coh B > k B T s Medin & Lai 2007: for T B s s ~10 6 K G > B dip pole - a sufficient large number of electron-positron pairs has to be created R cur B s R cur (B dip )~10 8 cm 19

20 balance of heating by bombardment and cooling by radiation: - heat flux input: e Vcn GJ - radiative energy flux: σ SB T s 4 T s 4 = ηω2 B 2 h 2 2πcσ SB - potential drop : ΔV = ηωbh 2 /c X-rays! PSG-model: η ~ 0.1, P 1s, B~ G, h 10 4 cm T s K Significantly hotter then cooling calculations predict! 10/10/2017 B-T Evolution of NSs 20

21 simultaneous radio and X-ray observations:? 21

22 flux conservation within the open field lines that connect-light cylinder with surface: e.g. B : P 1.2 s, ሶ P B dip G, R dip pc 133m R BB pc 14m B s = B dip dipa pc BB A pc B s G 22

23 R cur B s R cur (B dip )~10 8 cm small scale structures: created by crustal Hall drift +? 23

24 - understand quite good combined X- and radio observations + drifting subpulses but no paradise without snake - millisecond pulsars - if on MSP the same emission processes work as on standard pulsars: B MSP MSP s B dip - combined radio and X-ray observations J (Bogdanov 2013): P s, Pሶ B d G, R dip pc cm XMM: R pc cm, T s K B s G for MSP ε coh B < k B T s 24

25 suggestion: collaboration of Hall drift and thermoelectric field modifications r T ~10 7 K/cm last closed field line polar cap surface is hold on a few MK over the whole lifetime of radiopulsars, ~10 7 yr bombarded polar cap Geben Sie T hier s 3 10 eine 6 K Formel ein. after ~10 5 yr: T s ~ K the rest of the NS surface cools down according to cooling scenario 25

26 Ohm Hall battery thermal drift (dimensionless) 26

27 rough estimates η E, η T, ω B τ, ξ: public routines, Potekhin & Chabier and 27

28 1. thermopower has dominating radial gradient, meridional temperature gradient azimuthal magnetic field component will be created 2. thermo-electric field generation has to dominate Ohmic decay (Hall drift may dominate Ohmic decay but is not dissipative!) B t ~ η E B η T T B~ B L B, T~ T L T thermo-electric field creation dominates Ohmic decay if B φ η E 2 L + η E ρ B φ < η T ρ B ρ r L B ρ r T L T L B ~ curvature radius of toroidal field ~ radius of polar cap ~ cm L T ~ scale of meridional temperature gradient ~ a few meter for B~1 28

29 - B φ created in a shallow ring around the polar cap - it certainly enforces the thermal insulation there, maintaining big grad θ T situation looks a bit promising but caveats: - can grad θ T~10 4 K/cm be maintained over lifetime of PSR? - which role plays the non-linear thermal drift? - condensation density depends on local field strength - solid-liquid, partly ionized, partly degenerated: state depends very much on local magnetic field strength and temperature state of matter may vary within the polar cap 29