X-ray Polarization as a Probe of Strong Magnetic Fields in X-ray
Binaries
Shane Davis (IAS)
Chandra Fellows Symposium, Oct. 17, 2008
Magnetic Fields in Accretion Disks
Big Question: What is the source of angular
momentum transport in accretion disks?
Prad ~ Pgas < Pmag
Probable Answer: Turbulence/Magnetic
Fields (MRI?)
This implies near equipartition field strengths:
R~ BRB~ B2 ~ P
Prad ~ Pgas > Pmag
Thus far, there no direct observational
evidence for strong (equipartition) magnetic
fields.
Indirect evidence in the form of magnetized
wind from GRO J1655-40 (Miller et al. 2006,
2008)?
Prad ~ Pgas < Pmag
Hirose et al. 2007
Polarization: Estimating Spin & Inclination
Future X-ray polarimeters may be able to directly constrain the black hole spin and/or disk
inclination in X-ray binaries using the thermal disk spectra (see e.g. Dovciak et al. 2008; Li et
al. 2008 for recent work). Most work assumes Chandrasekhar polarization in scattering
dominated limit.
a*=0
a*=0.99
Agol 1997 -- KERRTRANS
Electron Scattering of Polarized Light
After scattering the polarization vector p’ is
perpendicular to the photon momentum k’
and in the plane of the original polarization.
k’
p
k
p’
Q>0
Stokes Parameters: P2 = Q2 + U2 + V2
Q & U = linear polarization (differ by 45o)
V = circular polarization = 0
Q<0
Consider an observer viewing a scattering
dominated atmosphere (disk) edge on:
If photons are mostly upward moving (limb
darkened), polarization is parallel to surface
(Q > 0). If photons are mostly horizontal
(limb brightened), polarization is normal to
surface (Q < 0). In both cases U = 0 by
symmetry.
Faraday Rotation of Polarized Light
Faraday Rotation: In the presence of a magnetized plasma, the left and right circularly
polarized EM waves have different phase
velocities, causing the polarization of
linearly polarized light to rotate.
The last scattering dominates the effect so T ~ 1. If B is sufficiently
large (>106 G), we can have F ~ 1 even for  ~ 10 ang.
For radiation pressure dominated,
thin accretion disks we have:
For sufficiently large B and/or , F >> . In
the presence of tangled fields or when the
photon trajectories differ due to scattering,
light rays arriving at the same observer will
have different polarization angles, even if
they were initially identical. This leads to
depolarization rather than a net rotation.
Spectra: The Effects of Faraday Rotation
Monte Carlo spectra from simulations (patch
of disk) show depolarization from low
energies all the way up to the spectral peak.
Green dotted curve shows a simple where:
P = Pch (1 + 2 F(B0,)/)-1
We consider three simulations with varying
ratios of Pgas & Prad. All show depolarization
at low energies and the rise in polarization
scales roughly with the peak energy of the
spectra (indicated by red arrows).
Spectra: The Effects of Compton Scattering
Full treatment of Compton scattering
yields different results at high energy end
than in Thomson scattering limit.
Spectra: The Effects of Compton Scattering
Spectra: Full Disk Models
Full disk spectra generated assuming
blackbody emission, w/ limb darkening, and
assuming surface field B0 = 1/40 Beq.
i ~ 72o
a*=0.99
a*=0
At and below the peak, Faraday rotation
reduces polarization; at high energy Compton
effects rotate polarization angle by 90o.
Effect of changing B field assumptions:
curves (from top to bottom) correspond to no
Faraday rotation, 1/10 B0, 1/3 B0, B0, and
3 B0. Declining polarization near spectral
peak is a sign of strong (near equipartition)
magnetic fields.
Conclusions and Future Prospects
Conclusions
The Bad: Faraday rotation and Compton Scattering will likely complicate efforts to
use the thermal emission of X-ray binaries to estimate spin and inclination.
The Good: Faraday rotation effects are a feasible means of measuring magnetic
fields (albeit crudely) in X-ray binaries as long as detectors have some sensitivity
at softer energies (~1 keV or lower).
Prospects for Observations and Future Work
Work thus far has neglected effects of bound-free absorption opacity. This should be
included since there may be significant effects at or below 1 keV. This could cause a
downturn which might mimic the effects of Faraday rotation, although ionization is
probably high enough that this will be a small effect.
Last X-ray polarization measurements taken before I was born. Several polarimeter
missions are in development stages: IXO(?), NASA small explorer missions using
Bragg crystals or angular distribution of photoelectrons.