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  1. Neutron Stars 4: Magnetism Andreas Reisenegger Departamento de Astronomía y Astrofísica Pontificia Universidad Católica de Chile

  2. Bibliography • General books: • Russell M. Kulsrud, Plasma Physics for Astrophysics • Leon Mestel, Stellar Magnetism • Reviews: • Alice Harding & Dong Lai, Physics of strongly magnetized neutron stars, Rep. Prog. Phys., 69, 2631 (2006): includes interesting physics (QED, etc.) that occurs in magnetar-strength fields - not covered in this presentation • A. Reisenegger, conference reviews: • Origin & evolution of neutron star magnetic fields, astro-ph/0307133: General • Magnetic fields in neutron stars: a theoretical perspective, astro-ph/0503047: Theoretical • Magnetic field evolution in neutron stars, arXiv:0710.2839: Theoretical, short • Papers: • Goldreich & Reisenegger 1992, ApJ • Hoyos, Reisenegger, & Valdivia 2008, A&A • Reisenegger 2009, A&A

  3. Outline • Classes of NSs, evidence for B • Magnetohydrodynamics (MHD) & flux freezing • Comparison to other, related stars, origin of B in NSs • Magnetic equilibria • Observational evidence for B evolution • Physical mechanisms for B evolution • External: Accretion • Internal: Ambipolar diffusion, Hall drift, resistive decay Caution: Little is known for sure – many speculations!

  4. Spin-down(magnetic dipole model) Spin-down time (age?): Magnetic field: Lyne 2000,

  5. “Magnetars” Kaspi et al. 1999 Classical pulsars Millisecond pulsars

  6. Note large range of Bs, but few if any non-magnetic NSs

  7. Neutron star magnetic fields • Strongest B in the Universe, up to at least ~1015G. • Persistent • Cause rotational energy loss: accounts for bolometric luminosity of pulsars • Soft gamma-ray repeaters (SGRs) & Anomalous X-ray Pulsars (AXPs): X/gamma-ray luminosity >> rotational energy loss or cooling • Magnetically powered neutron stars or “Magnetars” (Thompson & Duncan 1993, 1995, 1996) Quasi-periodic oscillations (QPOs) may be probing magnetic structure inside the star (Levin 2007) • (Slight) deformation of NS due to B might cause: • Precession (observed?) • Gravitational waves (hope!)

  8. Magnetic field strengths From R. Duncan’s “magnetar” web page,

  9. Flux freezing • tdecay is long in astrophysical contexts (r large), >> Hubble time in NSs (Baym et al. 1969)  “flux freezing” • Alternative: deform the “circuit” in order to move the magnetic field  MHD

  10. MagnetoHydroDynamics Assume 1 fluid moving with Electrons have small mass: neglect their inertia, gravity, etc.: Induction equation (advection of field lines) Current density is secondary, calculated by

  11. Magnetic field origin? • Fossil: flux conservation during core collapse: • Woltjer (1964) predicted NSs with B up to ~1015G. • Dynamo in convective, rapidly (differentially) rotating proto-neutron star (~ minutes) • Scaling from solar dynamo led to prediction of “magnetars” with B~1016G (Thompson & Duncan 1993) • Both?: Some memory of initial conditions, but strongly modified by differential rotation, etc.?

  12. Sun Highly disordered field: (random component~kG) >> (dipole component~50G) Inversion every 11 yrs Probably due to convection + differential rotation (dynamo effect)

  13. A&A, 358, 929 (2000) Upper main sequence (Ap, Bp stars) Only small fraction detectably magnetic (Ap, Bp or CP=“Chemically Peculiar”) Ordered field: low-order multipoles ~ kG Convective core + stable, radiative envelope

  14. A&A, 358, 929 (2000)

  15. Magnetic white dwarfs Small fraction of all WDs (Statistically) more massive than non-magnetic WDs Ordered field, low multipoles ~ MG

  16. Stars with long-lived, ordered B-fields In all cases, (magnetic pressure) < 10-6 (fluid pressure).  Weak B!! All are stably stratified.

  17. NS energies • EG ~ GM2/R ~ Nn ~ 1054 erg • E= I2/2~ 1053 Pms-2erg • ET ~ N(kT)2/ n~ 1046 T82erg • EB ~ (B2/8)(4R3/3)~ 1048 B152erg Generally E, ET , EB << EG: small perturbations

  18. Stable stratification Barotropic fluid: density  = (P) [P = pressure] Non-barotropic fluid: density  = (P,Y), where Y = another, independent variable: • Specific entropy in radiative zones of stars (upper MS & WDs) • Composition (e.g., proton fraction) in neutron stars (Pethick 1992; Reisenegger & Goldreich 1992; Reisenegger 2009) • Like water with non-uniform temperature or salinity: • Colder or saltier water stays at the bottom • Weak B can’t force substantial, non-radial motions

  19. cross section Equilibrium only in non-barotropic fluid

  20. Magnetic equilibria • Force balance: • B as small perturbation: • Background • Perturbation (fluid perturbation described by 2 independent scalars)

  21. Stable magnetic field configurations Braithwaite & Spruit 2004: simulation of ideal MHD in fluid, stably stratified star. B quickly reaches an equilibrium configuration with poloidal & toroidal components.

  22. Equilibria & stability • Poloidal-toroidal decomposition: • Pure poloidal & pure toroidal field are unstable (Flowers & Ruderman 1977; Tayler 1973) • Our current (semi-)analytic work • Calculation of Flowers-Ruderman instability (P. Marchant) • Construction of non-barotropic, poloidal + toroidal equilibria (A. Mastrano, T. Akgün) • Find unstable modes of toroidal fields, study stabilizing effect of poloidal component (T. Akgün) Braithwaite 2007

  23. Evidence for B-field evolution • Magnetars: • B decay as main energy source? requires internal field ~10x inferred dipole • Young NSs have strongB (classical pulsars, HMXBs), old NSs have weakB (MSPs, LMXBs). Result of accretion? • (Classical) Pulsar population statistics: no decay? - contradictory claims (Narayan & Ostriker 1990; Bhattacharya 1992; Regimbau & de Freitas Pacheco 2001) • “Braking index” in young pulsars  progressive increase of inferred B

  24. Diamagnetic screening Material accreted in the LMXB stage is highly ionized  conducting  magnetic flux is advected Accreted material could screen the original B, which remains inside the star, but is not detectable outside (Bisnovatyi-Kogan & Komberg 1975, Romani 1993, Payne & Melatos 2004, 2007) Questions: • Do instabilities prevent this? • Why 108-9 G, but not 0?

  25. Speculation: Magnetic accretion? Can the field of MSPs have been transported onto them by the accreted flow? Force balance: Mass transport: Combination:

  26. Preliminary conclusions on magnetic accretion The strongest magnetic field that might be forced onto a neutron star by an LMXB accretion flow is close to that observed in MSPs. More serious exploration is required (S. Flores, PhD thesis in progress): • Hydrodynamic model: transport through “turbulent viscosity” or wind • Is the magn. flux transported from the companion star? • Is it generated in the disk (“magneto-rotational inst.”)? • Is it coherent enough?

  27. B evolution inside NS Protons & electrons move through a fixed neutron background, colliding with each other and with the background (Goldreich & Reisenegger 1992): Terms: • Ambipolar diffusion: Driven by magnetic stresses (Lorentz force), protons & electrons move together, carrying the magnetic flux and dissipating magnetic energy. • Hall drift: Magnetic flux carried by the electric current; non-dissipative, may cause “Hall turbulence” to smaller scales. • Ohmic or resistive diffusion: very small on large scales; important for ending “Hall cascade”. May be important in the crust (uncertain conductivity!). Time scales depend on B (nonlinear!), lengthscales, microscopic interactions. Cooper pairing (n superfluidity, p superconductivity) is not included (not well understood, but see Ruderman, astro-ph/0410607).

  28. Model conclusions • Spontaneous field decay is unlikely for parameters characteristic of pulsars, unless the field is confined to a thin surface layer (Goldreich & Reisenegger 1992) • Spontaneous field decay could happen for magnetar parameters (Thompson & Duncan 1996) • Simulations (include moving neutrons): • 1-d: Hoyos, Reisenegger, & Valdivia 2008 • 2-d: in progress

  29. Conclusions Magnetic fields have: • Very small effect on structure of stars • Strong effect on NS appearance & evolution (pulsar braking, magnetars) • Source currents due to moving p, e, or other charged particles • Uncertain origin: fossil – dynamo – both ? • (possibly) Stable equilibrium configurations with linked toroidal & poloidal components, thanks to stable stratification • Non-trivial evolution, even in the most “prosaic” NS models (no need for ferromagnetism, quarks, Cooper pairs, etc. ...): • Internal (ambipolar diffusion, weak interactions) in magnetars • External (diamagnetic screening, flux accretion) in LMXBs  MSPs