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Neutron Stars 4: Magnetism

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Neutron Stars 4: Magnetism Andreas Reisenegger ESO Visiting Scientist Associate Professor, Pontificia Universidad Cat lica de Chile – PowerPoint PPT presentation

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Title: Neutron Stars 4: Magnetism


1
Neutron Stars 4 Magnetism
  • Andreas Reisenegger
  • ESO Visiting Scientist
  • Associate Professor,
  • Pontificia Universidad Católica de Chile

2
Bibliography
  • 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

3
Outline
  • Classes of NSs, evidence for B
  • Comparison to other, related stars, origin of B
    in NSs
  • 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)
Magnetic field
  • Spin-down time (age?)

Lyne 2000, http//online.kitp.ucsb.edu/online/neu
stars_c00/lyne/oh/03.html
5
Magnetars
Classical pulsars
Millisecond pulsars
  • Kaspi et al. 1999

6
Objects Emission B determination log B G log age yr
Classical pulsars Radio to gamma Spin-down 11-13 3-8
Millisecond pulsars Radio to gamma Spin-down 8-9 8-10
Magnetars gamma, X, IR Spin-down, LX 14-15 (-16?) 3-5
RRATs Radio, X Spin-down 12-14 5-7
Isolated thermal X, optical Spin-down, cyclotron lines 13-14 4-6
Thermal CCOs in SNRs X Spin-down 12.5??? 2.5-4.5
HMXBs X Cyclotron lines 12 young
LMXBs X Absence of pulsations, others 8-9? old
Note large range of Bs, but few if any
non-magnetic NSs
7
Magnetic field origin?
  • Fossil flux conservation during core collapse
  • Woltjer (1964) predicted NSs with B up to 1015G.
  • Dynamo in convective, rapidly rotating
    proto-neutron star?
  • Scaling from solar dynamo led to prediction of
    magnetars with B1016G (Thompson Duncan
    1993).
  • Thermoelectric instability due to heat flow
    through the crust of the star (Urpin Yakovlev
    1980 Blandford et al. 1983)
  • Field ?1012G confined to outer crust (easier to
    modify)
  • Does not generate magnetar-strength fields

8
Flux freezing
  • tdecay is long in astrophysical contexts (r
    large), gtgt Hubble time in NSs (Baym et al.
    1969) ? flux freezing
  • Alternative deform the circuit in order to
    move the magnetic field ? MHD

9
Kinship
Radius solar units Bmax G Flux ?R2Bmax
Upper main sequence a few 3?104 (peculiar A/B) 106
White dwarfs 10-2 109 3?105
Neutron stars 10-5 1015 (magnetars) 3?105
10
(2006)
11
  • Speculation Magnetic strip-tease
  • Upper main sequence stars produce B fields in
    their convective cores, not their radiative
    envelopes. Later they lose most of the envelope,
    leaving a WD or NS.
  • At very high masses, the WD or NS forms only of
    magnetized material, so it is fully magnetic.
  • At lower masses, the magnetized material is
    confined to the core of the WD not visible on
    the surface.

12
Stable magnetic configurations
Pure toroidal pure poloidal field
configurations are unstable, but in combination
they can stabilize each other. (Simulations
Braithwaite Spruit 2004)
13
Evidence for B-field evolution
  • Magnetars
  • B decay as main energy source?
  • requires internal field 10x inferred dipole
  • Young NSs have strong B (classical pulsars,
    HMXBs), old NSs have weak B (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

14
X-ray binaries
http//wwwastro.msfc.nasa.gov/xray/openhouse/ns/
  • High-mass companion (HMXB)
  • Young
  • X-ray pulsars magnetic chanelling of accretion
    flow
  • Cyclotron resonance features ? B(1-4)1012G
  • Low-mass companion (LMXB)
  • Likely old (low-mass companions, globular cluster
    environment)
  • Mostly non-pulsating (but QPOs, ms pulsations)
    weak magnetic field

15
Origin evolution of pulsars
  • Classical radio pulsars
  • born in core-collapse supernovae
  • evolve to longer period
  • eventually turn off
  • Millisecond pulsars descend from low-mass X-ray
    binaries.
  • Mass transfer in LMXBs produces
  • spin-up
  • (possibly) magnetic field decay

16
Spin-up line
  • Alfvén radius Balance of magnetic vs.
    gravitational force on accretion flow
  • Equilibrium period rotation of star matches
    Keplerian rotation at Alfvén radius

17
Magnetars
Classical pulsars
Millisecond pulsars
circled binary systems
Manchester et al. 2002
18
Diamagnetic screening
  • Material accreted in the LMXB stage is highly
    ionized ? conducting ? magnetic flux is frozen
  • Accreted material could screen the original
    field, which remains inside the star, but is not
    detectable outside (Bisnovatyi-Kogan Komberg
    1975, Romani 1993, Cumming et al. 2001)
  • Questions
  • Are there instabilities that prevent this?
  • Why is the field reduced to 108-9 G, but not to
    0?

19
Another speculation Magnetic accretion?
  • Can the field of MSPs have been transported onto
    them by the accreted flow?
  • Force balance
  • Mass transport
  • Combination

20
Conclusions
  • The strongest magnetic field that can be forced
    onto a neutron star by an LMXB accretion flow is
    close to that observed in MSPs.
  • More serious exploration appears warranted
  • Hydrodynamic model
  • Is the magn. flux transported from the companion
    star?
  • Is it generated in the disk (magneto-rotational
    inst.)?
  • Is it coherent enough?

21
Chemistry and stratification
  • (Goldreich R. 1992)
  • NS core is a fluid mix of degenerate fermions
    neutral (n) and charged (p, e-)
  • Chemical equilibrium through weak interactions,
    e.g., p e- ? n ?e ? density-dependent mix.
  • Stable chemical stratification (Ledoux
    criterion), stronger than magnetic buoyancy up
    to B 1017 G.
  • To advect magnetic flux, need one of
  • Real-time adjustment of chemical equilibrium
  • Ambipolar diffusion of charged particles w. r.
    to ns (as in star formation).

22
Model
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).

23
Model conclusions
  • Spontaneous field decay is unlikely for
    parameters characteristic of pulsars, unless the
    field is confined to a thin surface layer.
  • Spontaneous field decay could happen for magnetar
    parameters (Thompson Duncan 1996).
  • Simulations underway (Hoyos, Valdivia, R.)

24
Hall drift
  • Assume that the only mobile charge carriers are
    electrons (solid neutron star crust or white
    dwarf)
  • Electron MagnetoHydroDynamics (EMHD)
  • 1st term Hall drift
  • field lines transported by electron flow (? ? ?
    B)
  • purely kinematic, non-dissipative, non-linear
  • turbulent cascade to smaller scales?
  • (Goldreich Reisenegger 1992)
  • 2nd term Resistive dissipation

25
Simulations
  • Biskamp et al. 1999 w(x,y)?2B at 3 different
    times in 2-D simulation.
  • Turbulence clearly develops.
  • Properties (power spectrum) not quite the same as
    predicted by Goldreich Reisenegger (1992).
  • Models of Hall drift in neutron stars
  • Geppert, Rheinhardt, et al. 2001-04
  • Hollerbach Rüdiger 2002, 2004
  • others.

26
Exact solutions
  • Vainshtein et al. (2000)
  • Plane-parallel geometry
  • Evolution governed by Burgers eq.
  • Sharp current sheets dissipate magnetic energy
  • Cumming et al. (2003)
  • Axisymmetric geometry
  • Stable equilibrium solution rigidly rotating
    electron fluid constant, poloidal field
  • R. et al., in preparation
  • Toroidal equilibrium field, unstable to poloidal
    perturbations

27
Exact solutions
  • Our recent work
  • (paper in preparation)
  • Evolution of a toroidal field in axisymmetric
    geometry
  • Also obtain Burgers eq., current sheets
  • Toroidal equilibrium solution is unstable

28
Hall drift many open questions
  • Are all realistic B-configurations unstable to
    Hall drift and evolve by the Hall cascade?
  • Can the field get trapped in a stable
    configuration for a resistive time scale, as in
    ordinary MHD (Braithwaite Spruit 2004) ?
  • What happens in the fluid interior of the star?
  • How is the evolution if all particles are allowed
    to move?
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