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) Spin-down time (age?): Magnetic field: Lyne 2000, http://online.kitp.ucsb.edu/online/neustars_c00/lyne/oh/03.html

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

6. 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 B~1016G (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), >> Hubble time in NSs (Baym et al. 1969)  “flux freezing” • Alternative: deform the “circuit” in order to move the magnetic field  MHD

9. Kinship

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 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

14. 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 http://wwwastro.msfc.nasa.gov/xray/openhouse/ns/ X-ray binaries

15. “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 Origin & evolution of pulsars

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 n’s (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)=2Bat 3 different timesin 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?