The Magnificent Seven : Strong Toroidal Fields?

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2 Basic Neutron Star Cooling Troubles: Surface Effects and Pairing Minimal Cooling The Magnificent Seven : Strong Toroidal Fields? Conclusions 2

3 Basic Neutron Star Cooling Troubles: Surface Effects and Pairing Minimal Cooling The Magnificent Seven : Strong Toroidal Fields? Conclusions 3

4 Overall View of a Neutron Star homogeneous matter Swiss cheese Lasagna Spaghetti Core: Crust: B nuclei + neutron superfluid Atmosphere Envelope Crust Outer core Inner core A Neutron superfluid Neutron superfluid + proton superconductor Neutron vortex Neutron vortex Nuclei in a lattice Magnetic flux tube C 4

5 Basic Equations Schwarzschild metric: ds 2 = e 2φ c 2 dt 2 dr 2 Proper time: dτ = e φ dt + 1 2Gm/c 2 r + r2 dω 2 dr Proper length: dl = 1 2Gm/c2 r Energy balance: d(le 2Φ ) dr 4πr 2 e Φ = 1 2Gm/c2 r ( ) dɛ dt + eφ (q ν q h ) and L(r = 0) = 0 dɛ dt = dɛ dt dt dt = c dt v dt Energy transport: d(t e Φ ) dr = 1 λ Le Φ 4πr 2 1 2Gm/c 2 r and T (r = r b ) T b = T b (L b ) L(r = r b ) L b = L γ and L γ 4πR 2 σ B T e 5

6 Reduce it to One Simple Equation Energy balance: de th dt = C v dt dt = L γ L ν + H 3 essential ingredients are needed: Cv = total stellar specific heat Lγ = total surface photon luminosity Lν = total stellar neutrino luminosity 6

7 Neutrino Emission Basic mechanism: β and inverse β decays: n p + e + ν e and p + e n + ν e Energy conservation: E Fn = E Fp + E Fe Momentum conservation: Triangle rule : p Fn < p Fp + p Fe n e - p n i = k3 F i 3π 2 n1/3 n n 1/3 p + n 1/3 e = 2n 1/3 p x p n p n n + n p % Direct URCA process in neutron stars, Lattimer, Pethick, Prakash & Haensel, 1991 PRL 66,

8 Fast vs Slow Neutrino Emission Name Process Emissivity (erg cm 3 s 1 ) Modified Urca cycle n + n n + p + e + ν e (neutron branch) n + p + e 2 10 n + n + ν 21 R T9 8 Slow e Modified Urca cycle p + n p + p + e + ν e (proton branch) p + p + e 10 p + n + ν 21 R T9 8 Slow e n + n n + n + ν + ν Bremsstrahlung n + p n + p + ν + ν R T9 8 Slow p + p p + p + ν + ν Cooper pair n + n [nn] + ν + ν R T9 7 formations p + p [pp] + ν + ν R T9 7 Medium n p + e Direct Urca cycle + ν e p + e 10 n + ν 27 R T9 6 Fast e π condensate n+ < π > n + e + ν e R T9 6 Fast K condensate n+ < K > n + e + ν e R T9 6 Fast The Cooling of Compact Stars, Page, Geppert, Weber, Nucl. Phys. A 777, p (2006). [Special issue on Nuclear Astrophysics] 8

9 Direct vs Modified Urca Processes Slow Fast The cooling of neutron stars by the direct URCA process, Page & Applegate, 1992 ApJ 394 L17 9

10 Specific Heat Sum over all degenerate Fermion: C v = i C v i C v i = N i (0) π2 3 k2 BT with N i (0) = m i p F i π

11 Envelope and Photon Emission ( ) 1/2 T e 10 6 Tint 10 8 K L γ = 4πR 2 σt 4 e Structure of neutron star envelopes, Gudmundsson, Pethick, Epstein, 1983 ApJ 272,

12 Some Simple Analytical Solutions de th dt = C v dt dt = L γ L ν C v = CT L ν = NT 8 L γ = ST 2+4α Neutrinos L γ = 4πR 2 σt 4 e with T e T 0.5+α Photons Neutrino Cooling Era: L ν >> L γ dt dt = N C T 7 t t 0 = A T t 1/6 [ 1 T 6 1 T 6 0 ] Photon Cooling Era: L γ >> L ν dt dt = N S T 1+α t t 0 = A [ 1 T α 1 T α 0 ] T t 1/α 12

13 Basic Neutron Star Cooling Troubles: Surface Effects and Pairing Minimal Cooling The Magnificent Seven : Strong Toroidal Fields? Conclusions 13

14 Troubles (1): Envelope Chemical Composition The T e - T b relationship for heavy element envelopes 14

15 Troubles (1): Envelope Chemical Composition The T e - T b relationship for heavy element envelopes ΔM Light 10-7 M Sun... and for light element envelopes Thermal conductivity in the liquid phase λ 1 Z Cooling Neutron Stars with Accreted Envelopes, Chabrier, Potekhin, Yakovlev, 1997 ApJ 477, L99 15

16 Troubles (1): Envelope Chemical Composition Light elements envelope Iron-like envelope 16

17 Troubles (2): Nucleon Pairing Possible Analogy between the Excitation Spectra of Nuclei and Those of the Superconducting Metallic State, Bohr, Mottelson, Pines, 1958 PhRv 110,

18 Suppression of Cv and Qν by Pairing The presence of a pairing gap in the single particple excitation spectrum results in a Boltzmann-like [exp(-δ/k B T)] suppression of C v and Q ν : C v C Paired v Q ν Q Paired ν = R c C Normal v = R ν Q Normal ν See, e.g., Neutrino emission from neutron stars, Yakovlev, Kaminker, Gnedin & Haensel, Phys. Rep. 354, 1 (2001) 18

19 Trouble (2): Pairing Tc Neutron 1 S 0 Proton 1 S 0 Neutron 3 P 2 Enormous uncertainties on the actual values of Tc for pairing in the core (proton 1 S0 and neutron 3 P2) 19

20 Effect of Pairing on the Cooling Slow cooling q ν T 8 9 erg cm 3 s 1 Standard cooling Fast cooling n = and SF N SF Fast cooling q ν 10 n T 6 9 erg cm 3 s 1 N controlled by pairing 20

21 Basic Neutron Star Cooling Troubles: Surface Effects and Pairing Minimal Cooling The Magnificent Seven : Strong Toroidal Fields? Conclusions 21

22 Minimal Cooling Early plateau: controlled by crustal physics (mainly plasma neutrinos) Neutrino Cooling Era Photon Cooling Era Minimal Cooling: exclude anything beyond just nucleons and leptons (i.e., no meson condensates, no hyperons, no deconfined quarks,... no nothing) but include all uncertainties on standard physics. 22

23 Minimal Cooling Minimal Cooling: exclude anything beyond just nucleons and leptons (i.e., no meson condensates, no hyperons, no deconfined quarks,... no nothing) but include all uncertainties on standard physics. 23

24 Minimal Cooling vs Data 1. RX J (in SNR Puppis A) 2. 1E (in SNR PKS ) 3. PSR RX J (in SNR CTB 1) 5. PSR PSR (in SNR ``Vela'') 7. PSR PSR PSR (``Geminga'') 10. RX J RX J A. CXO J (in SNR Cas A) B. PSR J (in SNR 3C58) C. PSR J (in SNR G ) D. RX J (in SNR CTA 1) Heavy elements envelopes Light elements envelopes A B C a b c d D a.? (in SNR G ) b.? (in SNR G ) c.? (in SNR G ) d.? (in SNR G ) Minimal Cooling of Neutron Stars: A New Paradigm, Page, Lattimer, Prakash & Steiner, 2004 ApJS 155,

25 Basic Neutron Star Cooling Troubles: Surface Effects and Pairing Minimal Cooling The Magnificent Seven : Strong Toroidal Fields? Conclusions 25

26 The Magnificent Seven : Strong B The Magnificent Seven: Magnetic fields and surface temperature distributions, F Haberl, 2006 astro.ph/

27 The Composite Spectrum of RX J1856 The puzzles of RX J : Neutron Star or Quark Star?, Truemper, Burwitz, Haberl & Zavlin, 2004 NuPhS 132,

28 Heat Transport with Strong B F = κ T κ = κ κ 0 κ κ κ 5 = Log T B = G κ = κ = κ 0 κ (ω B τ) κ = κ 0 ω B τ 1 + (ω B τ) 2 ω B = eb m ec = electron cyclotron frequency τ = electron relaxation time Temperature distribution in magnetized neutron star crusts, Geppert, Küker & Page, 2004 A&A 426,

29 Crust + Core Poloidal Field Crustal Poloidal Core Poloidal 29

30 Crust + Core Poloidal Field Crustal Poloidal Core Poloidal Magnetic field lines are isothermal! Temperature distribution in magnetized neutron star crusts, Geppert, Küker & Page, 2004 A&A 426,

31 Add a Toroidal Component Core poloidal Crust poloidal Crust toroidal 31

32 Add a Toroidal Component Core poloidal Crust poloidal Crust toroidal Temperature distribution in magnetized neutron star crusts. II. The effect of a strong toroidal component, Geppert, Küker & Page, 2006 A&A 457,

33 Composite BB Fit for RX J1856 Temperature distribution in magnetized neutron star crusts. II. The effect of a strong toroidal component, Geppert, Küker & Page, 2006 A&A 457,

34 Composite BB Fit for RX J1856 Raileigh-Jeans tail of the X-ray observed BB Temperature distribution in magnetized neutron star crusts. II. The effect of a strong toroidal component, Geppert, Küker & Page, 2006 A&A 457,

35 Long Live the Magnificent Seven! B 0 tor = 3x10 3x G G (T2) (T1) G (T1) G (T2) 35

36 Long Live the Magnificent Seven! 3x10 3x10 B 0 tor = G G (T2) (T1) G (T1) G (T2) The Magnificent Seven 36

37 Basic Neutron Star Cooling Troubles: Surface Effects and Pairing Minimal Cooling The Magnificent Seven : Strong Toroidal Fields? Conclusions 37

38 Conclusions Many options for fast cooling, complicated by possible pairing of nucleons (or/and hyperons, quarks). Minimal Cooling: little evidence for fast cooling, but nevertheless we have some conspicuous cases. Still large uncertainties on observed luminosities (and ages). The Magnificent Seven : are they permeated by strong toroidal fields? Is this telling us something? 38

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