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Magnetic Fields around Radio Galaxies

Robert Laing (ESO)

Laing et al. (2006, 2008) MNRAS 368, 48 and 391, 521 Daria Guidetti PhD project


Objectives


Study the magnetic field in the IGM surrounding radio galaxies by observing Faraday rotation and depolarization in sources whose geometry can be (approximately) determined Verify that the correlation between depolarization and jet sidedness observed at low resolution is due to Faraday rotation by a foreground medium Determine the spatial statistics of the rotation measure and therefore those of the magnetic field Understand the spatial distribution of the Faraday-active medium and its relation to the cluster/group scale IGM and the source VLA observations, 1.365 ­ 8.5 GHz, 3 ­ 7 frequencies; no RM synthesis.










3C31 radio ­ optical overlay
Low-power (FRI) radio galaxy NGC383, z = 0.0169 (0.344 kpc/arcsec) Central member of galaxy group

VLA L-band (5.5 arcsec) + DSS Laing et al. (2008)


Negligible depolarization and 2 rotation

Almost all Faraday effects must be due to foreground material


How to fit depolarization caused by foreground Faraday rotation
Complex polarization Rotation measure

Integrate over a beam Observed RM for 0 2 rotation and depolarization


Faraday rotation and depolarization

5.5 arcsec FWHM


Faraday effects at high resolution

FWHM = 1.5 arcsec (0.5 kpc)


RM and depolarization profiles
Mean RM integrated over boxes

rms RM in the same boxes

Burn law k


3C449
Very similar in X-ray properties and RM fluctuation amplitude to 3C31 More depolarization (more power in small-scale RM fluctuations) in 3C449 Very close to the plane of the sky, consistent with symmetrical RM profile High resolution is crucial (1.25 arcsec FWHM = 0.4 kpc)


Range of Environments
3C31 ­ Galaxy + group-scale components

NGC315 ­ Galaxy component only

Croston et al. (2008)


NGC315: polarization at 327MHz on large scales

Total intensity

Degree of polarization (WSRT; Mack et al. 1997)


NGC315: RM in a sparse environment


How to quantify RM statistics in 2D


Structure function S(r) = <[RM(r+x)-RM(x)]2> Power spectrum P(f) ­ Fourier transform of autocorrelation function C(r) = , where f is a spatial frequency vector. We estimate the structure function for regions of the source which appear to be homogeneous (spatial variations come later) Derive model structure functions from power spectrum including the effects of the beam in the short-wavelength approximation. Main problem is poor sampling Next step is clearly to use Bayesian methods (e.g. Vogt & Ensslin 2005)












Structure functions of regions in 3C31
Model structure functions for a power-law RM power spectrum P(f) f-q (f < fb)

P(f) f-11/3 (f > fb) (q = 2.32, 1/fb = 16 arcsec) or P(f) f-q (f < fb) P(f) (f > fb)

(q = 2.39, 1/fb = 7 arcsec) both fit the data (RM and depolarization)


3D modelling


Hot gas distribution from X-ray observations (initially spherically symmetric modes) 3D magnetic field distribution (Gaussian random variable, power spectrum as determined from 2D analysis) Make realizations in Fourier space (start from vector potential to ensure div B = 0; Murgia et al. 2004) Calculate expected RM for radio source given Spherical symmetry Cavity around jet (= lobe emission) with no thermal material Interaction of source with IGM








3D simulations - examples


3D simulations - profiles

B0 = 0.74nT (0.74G); B n0.25, = 52o


X-ray cavities in Hydra A

Chandra X-ray (Wise et al. 2007)

Radio/X-ray superposition


3D simulations of Hydra A
Cavity geometry and hot gas parameters from Wise et al. (2007) Good fit to RM profiles with: = 45o B0 = 1.9nT (0.19G) B n0
.25

Magnetic power spectrum f-2.77


But fields are not always isotropic ....
0206+35 3C353


Implications for LOFAR


LOFAR will be able to explore the low Faraday depth regime ­ needed to give a complete picture Some radio galaxies (e.g. NGC315) are in very sparse environments, with RM fluctuation amplitudes < 5 rad meven close to the core
2





Fluctuations are also small outside the core radius in galaxy groups such as 3C31 and 3C449 Need to think about Galactic RM gradients Should revisit the question of the detectability of internal Faraday rotation with LOFAR in regions where foreground effects are small. Heated and entrained thermal plasma is a prime candidate to provide most of the pressure in plumed FRI sources on large scales: can we detect Faraday rotation/depolarization from it?








Where next


RM bands: more sources, general properties, models. Improved resolution smaller spatial scales Increased sensitivity better sampling on large scales Bayesian ML method (as for CMB) Kolmogorov turbulence ­ what range of scales (if any)? X-ray imaging ­ cavities ­ how do sources affect B in the IGM? More reliable magnetic-field estimates Origin of field in E galaxies, groups and clusters; effects on cooling High Faraday depths EVLA, maybe ALMA Low Faraday depths (external and maybe internal) LOFAR