1. Eyes on the Polarized Sky, Feet on the Ground
Jeroen Stil, University of Calgary
On Behalf of the SWG Cosmic Magnetism
NSF

2. How do we turn our dreams into reality?
Far from the Galactic plane: }
Galactic Faraday rotation
Extragalactic Faraday rotation
RM errors (present data)
of order 10 rad m-2 with some exceptions
Several extragalactic applications require error on RRM as small as 1 rad m-2
Outskirts of clusters
(1+z)-2 dependence for internal Faraday rotation
Significant progress to be made by
Improving sampling by > 2 orders of magnitude across the sky
Reducing RM errors by 1 order of magnitude (all-sky)

3. Where Is the Plasma In which Faraday Rotation Occurs?
rad m-2
|f|
300 rad m-2
225 rad m-2
150 rad m-2
75 rad m-2
0 rad m-2
Harvey-Smith et al. (2011), 1 RM per square degree
Association of Faraday rotation with visible sources depends critically on density of the RM grid and RM errors
Much easier if a single “screen” is responsible for most of the Faraday rotation
Or avoid these objects, e.g. X-ray clusters (presentation by T. Akahori this meeting)
Interesting physics in sources that mix synchrotron emission and Faraday rotation
See also Vacca et al. (2014) PoS(AASKA14)114

4. Extragalactic examples of internal Faraday effect from mixed relativistic/thermal plasma
Polarization angle
l2 (m2)
l2 (m2)
Polarized emission in MACS J
Examples of poor 2 fits, indicating that a simple Faraday screen model is not applicable (Bonafede et al. 2009)
Thermal plasma in the radio lobes of Cen A
(O’Sullivan et al. 2013)
Note importance of broad, continuous l2 coverage

5. Resolution in Faraday Depth
Curves mark resolution and sensitivity to extended structure in Faraday depth for surveys with bandwidth indicated. Markers indicate lowest observed frequency 100 MHz, 600 MHz, 1 GHz and 2 GHz.
Depolarization
resolved
unresolved
BW = 1540 MHz
BW = 770 MHz
BW = 50 MHz
Resolved, extended Faraday Depth structure only if source falls under a curve and above the black line.
BW = 100 MHz
resolved
unresolved
RM error is 1 rad m-2 at 10s detection threshold in p
Is 1 GHz bandwidth sufficient?
No: Farnsworth et al. (2011)
Compare O’Sullivan et al. (2012), Anderson et al. (2016), Kim et al. (2016)
See discussion in Haverkorn et al. (2014)

6. Galactic Foreground Estimates in SKA Surveys
Extragalactic RM dispersion (Schnitzeler 2010)
1/sq degr.
25/sq degr.
1000/sq degr.
300/sq degr.
3000/sq degr.
-500 rad m-2
+500 rad m-2
Error in RRM due to statistical error in galactic foreground, averaging sources within annulus with inner radius 10” and outer radius q.
RM structure function with slope 0.7 on scales < 1o.
Curves start at minimum of 5 sources. Must choose inner radius such as not to include extragalactic RM! 20 40
60 rad m-2
Oppermann et al. (2012)
Galactic Faraday rotation and error map

7. Galactic Foreground estimates in SKA Surveys
High-Galactic latitude Faraday rotation of diffuse Galactic emission from GALFACTS.
30 RMs per square degree, errors of individual RMs 1 – 5 rad m-2
Topology of the foreground matters, and isotropic weighting of the data may underestimate the foreground in case of filaments and edges.
Also: structure and variability of the ionosphere for SKA low (Loi et al. 2015)

8. Extended Background Sources
Differential Faraday rotation over
angular size of background radio
galaxy for galaxies more distant than ~ 5 Mpc.
Targets of opportunity from chance alignments.
Observe higher frequency to avoid complete depolarization.
Complex Faraday rotation is the norm.
Confusion about line of sight if foreground galaxy is not observed directly.
Double-lobed radio source behind UGC 10288
Irwin et al. (2013)
NGC 1310 in front of Fornax A (Fomalont et al. 1989)
Radio haloes/relics and radio lobes as
extended polarized screens in galaxy clusters

9. What do we learn if we don’t have a model for ne?
The one application with a well established electron density model based on pulsar dispersion measures is the large-scale magnetic field of the Milky Way.
FRBs can provide large scale dispersion measures possibly rotation measures. Position accuracy, redshift and Faraday rotation by the host provide challenges.
Applications that do not require an electron density model or dispersion measure:
Average direction of magnetic field along line of sight, reversals, geometry
Structure functions (Simonetti et al. 1984)
Physical models and |RM|/sRM, coherence scale (Murgia et al. 2004)
Polarization gradients (Gaensler et al. 2011)
Limit to Alfven speed (Stil & Hryhoriw 2016)
Most likely, we have not exhausted the possibilities.

10. Calibration
Statistical analysis depends on uniform data quality and small, well-understood (systematic) errors.
Polarization purity across the field of view is crucial because
residual instrumental polarization appears as artificial peaks with small |RM|, needed for a lot of extragalactic science.
Need a pipeline that does off-axis polarization calibration and dedicated commissioning work (holography).

11. Conclusions
A dense RM grid connects all aspects of cosmic magnetism science
Wide-band surveys offer more information, not just better information
Can do science without ne model
Uniformity of RM grid and RM variability science limited by quality of wide-field polarization calibration, time-variable ionosphere