Neutron Star Magnetic Fields: Genesis & Decay

1. Neutron Star Magnetic Fields:Genesis & Decay Chris Thompson (CITA)

2. Kramer & Stairs 2008 Spinning downNeutron stars(Not accreting) 1010 T 109 T 108 T Magnetars B ~ 1014-1015 G P ~ 5-10 s 107 T 106 T LX ~ 1035-1046 erg/s >> Lspindown B ~ 108-109 G P ~ 1-100 ms `recycled’ pulsars

3.  QED Magnetic Field: Radio pulsars generally B < BQED Soft Gamma Repeaters Anomalous X-ray Pulsars Radio pulsars: 10-12 is small ! Why aren’t all neutron stars magnetars? How strong is internal (e.g. toroidal) magnetic field compared with the dipole - Are some radio pulsars `very transient’ magnetars?

4. (threading one hemisphere) Magnetic Flux Solar-type Magnetic A-B-O stars White Dwarfs Neutron stars

5. Helical equilibria of a magnetic field in a stably stratified star Braithwaite 2009: Braithwaite & Spruit (2004) assumed random initial magnetic field Etoroidal > 30 Epoloidal is possible numerically with mainly toroidal seed field

6. (Some) Magnetar Formation Channels 0. Maybe it’s just conserved `fossil’ magnetic flux (any neutron star formation channel) Wickramasinghe & Ferrario Collapsed stellar core with rapid rotation (+ seed magnetic field above threshold value) T & Duncan, T & Murray, Blackman et al. 2. Merger of neutron star with dense stellar core (and/or white dwarf) Collapse of rapidly rotating white dwarf AIC with moderately strong (106 G) B-field T & Duncan or WD + WD merger King et al; Levan et al.; Metzger et al.

7. Magnetars from Supernova Collapse • Violent convection extends close to -sphere: ms ms Helical dynamo when • Accretion of angular momentum in outermost from shock instabilities Need to make 1016 G r.m.s.! Rgain R Buras et al. 2005 (astro-ph/0507135)

8. (Some) Magnetar Formation Channels 0. Maybe it’s just conserved `fossil’ magnetic flux (any neutron star formation channel) Wickramasinghe & Ferrario Collapsed stellar core with rapid rotation (+ seed magnetic field above threshold value) T & Duncan, T & Murray, Blackman et al. 2. Merger of neutron star with dense stellar core (and/or white dwarf) Collapse of rapidly rotating white dwarf AIC with moderately strong (106 G) B-field T & Duncan or WD + WD merger King et al; Levan et al.; Metzger et al.

9. Some comments: 0. Most of the available energy in convection and differential rotation is post-collapse B > 107 G WD are a much smaller fraction of WD pop (~ 0.01) than magnetars are of NS pop (> 0.1) 1./2./3. Dynamo within proto-neutron star, vs. dynamo within accretion flow onto star 2. Mergers expected in some Be - NS binaries but rate is too low (< 1/10 of magnetar formation) 3. AIC: WD rotates slowly if B > 106 G WD-WD: Stable C burning(?) -> mini Wolf-Rayet star

10. White Dwarf Magnetic Field Distribution Schmidt et al. (2003) Isolated WD Sloan ~ 10% B > 106 G B < 5x108 G Polars (synchronized CVs) ~25% CVs B < 4x107 G Wickramasinghe & Ferrario (2001)

11. Isolated Magnetic White Dwarf Rotation Non-magnetic white dwarfs: Prot ~ hours-days Ultramagnetic white dwarfs (B > 100 MG) with measured spin periods: Prot , B = 130 min, 35 MG 725 s, ~300 MG 1.33 d, ~100 MG 98 min, ~120 MG 3.4 hr, ~200 MG WD-WD mergers

12. Rotation of Isolated White Dwarfs Limiting spin period from AGB envelope collapse: Disk forms if specific ang. mom. Disk transfers ang. mom. outward, so maximum spin ang. mom. H-depleted core Remnant AGB envelope Mass (Spruit)

13. Dynamos in Massive Stars Differential rotation driven by convection Also: Magnetic Energy  Gravitational Binding Energy under an expansion or contraction

14. core carbon burning • base of H-rich envelope • convective H, He, C burning in stellar core [ ] • core collapse / proto-neutron star enforces nearly solid-body rotation

15. Pre-Main Sequence Convection tKelvin ~ M/(dM/dt) Building a massive star by accretion ( ) Convection

16. Averaged magnetic flux  ~ 1012 G x (10 km)2 Stronger B-fields if Magnetic early-type stars form by mergers? Ferrario, Pringle et al. 2009

17. Core Collapse DynamosNeutrino-Aided Magnetic Buoyancy Infall with shear (r) Toroidal B-field amplified by linear winding: Strong shear Convection A magnetic flux tube is cooler than surroundings: and is heated by neutrinos:

18. Competition between buoyancy and down-flow neutrino heating adiabatic cooling Buoyancy speed:

19. Neutrino-aided buoyancy outside -sphere log10 Magnetic field suppresses emission of e/e by decreasing particle densities gain region (Q+ > Q-) shock Fernandez & Thompson

20. Threshold seed magnetic field for a dynamo: (shear concentrated in surface layer) Seed field is lower if angular momentum is concentrated in outer layers of newborn neutron star

21. Late Fallback Neutrino heating is too weak to drive convection: SASI helps to trigger post-shock turbulence shock

22. Origin of Angular Momentum:Fossil Spin or Shock Instability? Spruit & Phinney (generalized random kicks) Thompson 2000 (bernoulli fluctuations) Blondin & Mezzacappa 2007 (m>0 SASI mode) Outer accretes all the angular momentum accreted Effective dynamo for convection

23. Supernova Accretion Shock Instability (2D, Full EOS with electron captures) (Scheck et al. 2008) Linear instability with neutrino flux suppressed at inner computational boundary but boundary moves rapidly inward

24. A linear instability is present in the ideal gas accretion flow, especially for What is its nature? Does it persist when a significant fraction of the flow kinetic energy is lost to nuclear dissociation? Blondin & Mezzacappa Non-spherical shock displacement  Entropy + vortex perturbation  Acoustic perturbation  shock displacement (SASI: Foglizzo & Tagger 2000)

25. Upstream of shock: Downstream of shock: Shock compression:

27. Shock displacements much smaller at finite dissociation energy Expansion driven mainly by turbulent kinetic energy Fernandez & Thompson 2009ab

28. Comparison of Linear Stability Analysisand Direct Hydrodynamical Simulation Fernandez & T 2009

29. Oscillation • amplitudes grow • strongly just below • critical heating rate • for explosion • Asymmetries driven by Bernoulli fluctuations below the shock Fernandez & T 2009b

30. Bubbles of Positive Energy Fluid:

31. crystallization

32. Neutron Stars: Relativistic, degenerate electron gas in outer, inner crust; core Degenerate neutron gas in core, inner crust; proton gas in core inner crust and core

33. Time Evolution of the Magnetic Field Very high electrical conductivity   magnetic field lines `imprinted’ in fluid on a MHD timescale ~ 10-1 sec Induction equation: fluid motions induced by loss of stability Drift of charged particle + field w.r.t neutrons Hall drift: B-field advected by the drift-motion of e- Haensel et al. 1990; Goldreich & Reisenegger 1992

34. Ohmic Transport White Dwarfs: Electrical conductivity: Ohmic decay time: Neutron stars: Ohmic decay in fluid core is very slow Crust: scattering off impurities and lattice vibrations

35. Hall Drift Timescale depends on flux and charged particle densities, not on transport coefficients (White Dwarf) (Neutron Star) Density scale height ~ 0.3 km deep in NS crust Hall drift is fast in outer NS crust, or in presence of small-scale B-field:

36. Mechanism of Hall Drift Twist Ejection into Magnetosphere Turbulent cascade Hall term in induction equation is non-linear Individual wave modes: equivalent to whistlers Goldreich & Reisenegger 1992 T, Lyutikov & Kulkarni 2002

37. Ambipolar Drift in Neutron Star Cores (Yakovlev et al. 1990; Goldreich & Reisenegger 1992; T & Duncan 1996) ~ 95% of mass is in neutral particles (neutrons) Even for magnetars, In degenerate Fermi fluid Chemical equilibrium chemical potential of species k

38. Low ion abundance Adding gives Yakovlev et al. 1990 Drag dominated:

39. Transport of charged particles pushes the e-p-n fluid out of weak-interaction equilibrium if Transport then depends on rate of weak interactions, which are very temperature sensitive: Balancing gives Pethick 1991; Goldreich & Reisenegger 1992 T & Duncan

40. An Old Question: Do the neutrons in the core of a neutron star form a superfluid (V.L. Ginzburg 1964) Superfluidity results from binding of neutrons into pairs near the Fermi surface High neutron density -> pairing through P-wave component of nuclear force Pairing energy is very uncertain (medium effects….) Forming and breaking of Cooper pairs leads to enhanced cooling(Flowers, Ruderman & Sutherland)

41. An interesting observational clue Thermal X-ray output of Anomalous X-ray Pulsars is clustered around 1x1035 erg/s (kTbb ~ 0.5 keV)  buffered by neutrino cooling (Durant & Kerkwijk 2007) Ambipolar heating of non-superfluid NS core + thermal conduction through 1015 G envelope  Lbb = 0.5 x 1034 erg/s (T & Duncan 1996) Lbb (Vela pulsar) = 10-2 Lbb (AXPs) But: factor of 102 is hard to achieve just by core magnetic heating + increased transmissivity of neutron star envelope Neutrino emissivity of Vela needs to be higher

42. Solutions Increase thermal X-ray flux: <Bsurface> is larger than spindown field (1x1015 G) (3-5)x1015 G is needed to power SGR flares Alternative: shallow magnetic heating e.g. magnetospheric currents (T, Lyutikov & Kulkarni 2002) field decay in upper crust (Kaminker et al. 2007) [ ] Pairing temperature of core neutrons is 5-6 x 108 K Magnetic field decay releases enough energy to delay pairing transition from ~ 102 yrs to 104 yrs (Arras, Cumming & Thompson 2004)

43. Delayed Core Superfluid Transition (Tcn < 6x108 K)  emissivities from Yakovlev & collaborators see Arras, Cumming, & T 2004 Page et al. 2009 for non-magnetic NS