Transcript Neutron Stars 4: Magnetism - European Southern Observatory

Neutron Stars 4: Magnetism
Andreas Reisenegger
ESO 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 magnetarstrength 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,
ph/0503047: Theoretical
astro-
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!

2
  2 d   B 2 4
Spin-down  I
3
2
(magnetic dipole model)
2
3c
dt
Magnetic field:
|
|
B
3

Spin-down time
(age?):
Lyne 2000,
http://online.kitp.ucsb.edu/online/neustars_c00/lyne/oh/03.html

ts 
|
2|
“Magnetars”
Classical pulsars
Millisecond pulsars
Kaspi et al. 1999
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, Spin-down, LX
IR
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
8-9?
pulsations, others
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
dI
L  RI  0  I  e
dt
r
L~ 2
c
1
R~
r
R
 t
L
L r 2
tdecay  ~ 2
R
c
• 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
Kinship
Upper main
sequence
Radius
Bmax [G]
Flux
[solar units]
R2Bmax
a few
106
3104
(“peculiar” A/B)
White dwarfs
10-2
109
Neutron stars
10-5
1015 (magnetars) 3105
3105
(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: LX , | I
 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)
2



• “Braking index” in young pulsars n     3
 progressive increase of inferred B
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
Origin & evolution of pulsars
“Classical” radio
pulsars
• born in corecollapse
supernovae
• evolve to longer
period
• eventually turn off
Millisecond pulsars
descend from lowmass 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
 
| j  B | B 2 (r ) Bs2 R 6 GM
~
~
~ 2
7
c
4 r 4 r
r
 Equilibrium period: rotation of star
matches Keplerian rotation at Alfvén radius
Pmin  Peq  B
67
“Magnetars”
Classical pulsars
Millisecond pulsars
circled: binary systems
Manchester et al. 2002
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:
GM
jB
B2
~
~
2
R
c
4 R
Mass transport: M ~ f  4 R 2   v ~ f '  4 R 2  2GM
R
Combination:
 GMM 2 

B ~ 
2
5 
2f' R 
1
4
1
2




8 M M Edd
 G
~ 10 

f
'


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
Protons & electrons move through a fixed neutron background, colliding with each
other and with the background (Goldreich & Reisenegger 1992):



 j 
B
c


   v A  B      
 B     
t

 ne e


j

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).
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 drift
Assume that the only mobile charge carriers are
electrons (solid neutron star crust or white dwarf):
“Electron MagnetoHydroDynamics” (EMHD)

 

B
 c
   
(  B)  B    B 
t
 4ne

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.
Vainshtein et al.
(2000):
– Plane-parallel
geometry
– Evolution governed
by Burgers’ eq.
– Sharp current
sheets dissipate
magnetic energy
Cumming et al. (2003):
Exact solutions
–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 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
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?