Neutron Stars 4: Magnetism

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Neutron Stars 4 Magnetism

• Andreas Reisenegger
• ESO Visiting Scientist
• Associate Professor,
• Pontificia Universidad Católica de Chile

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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

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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!

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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
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Magnetars
Classical pulsars
Millisecond pulsars

• Kaspi et al. 1999

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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
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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

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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

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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
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(2006)
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• 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.

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Stable magnetic configurations
Pure toroidal pure poloidal field
configurations are unstable, but in combination
they can stabilize each other. (Simulations
Braithwaite Spruit 2004)
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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

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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

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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

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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

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Magnetars
Classical pulsars
Millisecond pulsars
circled binary systems
Manchester et al. 2002
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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?

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Another speculation Magnetic accretion?

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

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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?

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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).

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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).

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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.)

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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

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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.

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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

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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

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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?