Neutron Stars 4: Magnetism

Andreas ReiseneggerESO Visiting Scientist

Associate Professor,

Pontificia Universidad Católica de Chile

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

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!

Spin-down(magnetic dipole model)

Spin-down time (age?):

Lyne 2000, http://online.kitp.ucsb.edu/online/neustars_c00/lyne/oh/03.html

42

2

2

2

33

2 B

dt

d

cI

Magnetic field:

3

||

B

||2

st

Kaspi et al. 1999

“Magnetars”

Classical pulsars

Millisecond pulsars

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

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

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

tL

R

eIRIdtdI

L

0

2

2

decay2~

1~~

c

r

R

Lt

rR

c

rL

Kinship

Radius [solar units]

Bmax [G] Flux R2Bmax

Upper main sequence

a few 3104 (“peculiar” A/B)

106

White dwarfs 10-2 109 3105

Neutron stars 10-5 1015 (magnetars) 3105

(2006)

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.

Stable magnetic

configurations

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

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

32 n

||, ILX

X-ray binaries

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/

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

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

27

62s

2

~4

~4

)(~

||

r

GM

r

RB

r

rB

c

Bj

76eqmin BPP

Manchester et al. 2002

“Magnetars”

Classical pulsars

Millisecond pulsarscircled: binary systems

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?

Another speculation: Magnetic accretion?

Can the field of MSPs have been transported onto them by the accreted flow?

Force balance:

Mass transport:

Combination:

R

B

c

Bj

R

GM

4~~

2

2

R

GMRfvRfM

24'~4~ 22

G'

10~'2

~2

1

Edd84

1

52

2

f

MM

Rf

MGMB

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?

“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).

Model

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).

jc

Ben

jBv

tB

eA

Protons & electrons move through a fixed neutron background, colliding with each other and with the background (Goldreich & Reisenegger 1992):

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.)

Hall driftAssume that the only mobile charge carriers are

electrons (solid neutron star crust or white dwarf): “Electron MagnetoHydroDynamics” (EMHD)

BBBne

c

t

B

)(4

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

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.

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

Exact solutionsOur recent work

(paper in preparation):– Evolution of a toroidal field in

axisymmetric geometry– Also obtain Burgers’ eq.,

current sheets– Toroidal equilibrium solution is

unstable

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?