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? Probable Answer: Turbulence/Magnetic Fields (MRI?) This implies near equipartition field strengths:  R  ~  B R B  ~ B 2 ~  P Hirose et al P rad ~ P gas > P mag P rad ~ P gas < P mag Thus far, there no direct observational evidence for strong (equipartition) magnetic fields. Indirect evidence in the form of magnetized wind from GRO J (Miller et al. 2006, 2008)?

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 for recent work). Most work assumes Chandrasekhar polarization in scattering dominated limit. a * =0a * =0.99 Agol 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 k’ p p’ Stokes Parameters: P 2 = Q 2 + U 2 + V 2 Q & U = linear polarization (differ by 45 o ) V = circular polarization = 0 Q > 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. 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. The last scattering dominates the effect so  T ~ 1. If B is sufficiently large (>10 6 G), we can have  F ~ 1 even for ~ 10 ang. For radiation pressure dominated, thin accretion disks we have:

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 = P ch (1 + 2  F (B 0, )/  ) -1 We consider three simulations with varying ratios of P gas & P rad. 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 i ~ 72 o a * =0 a * =0.99 Full disk spectra generated assuming blackbody emission, w/ limb darkening, and assuming surface field B 0 = 1/40 B eq. At and below the peak, Faraday rotation reduces polarization; at high energy Compton effects rotate polarization angle by 90 o. Effect of changing B field assumptions: curves (from top to bottom) correspond to no Faraday rotation, 1/10 B 0, 1/3 B 0, B 0, and 3 B 0. 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.