The large-scale structure of the Galactic magnetic field & Faraday tomography --desh Raman Research Institute, Bangalore

Large-scale structure of Magnetic field Measurements of Faraday rotation against Galactic and extra-Galactic radio sources  modeling of the magneto-ionic properties of the intervening medium ** correlation between magnetic and optical arms: apparent anti-correlation ? e.g. NGC 6946 (Beck & Hoernes 1996; Beck 2000) Milky-way (Indrani &desh, 1999)

BBS model: arrows=> model field, contours=> TC93 n_e model e.g. Indrani, desh (1999)

Non-thermal emission would imply relatively stronger field in the arm regions. but we see that the “net” large-scale component is stronger in the inter-arm region….. … tangled fields in the spiral arm regions => a lower average value & more scatter ….need to sample the details, particularly in the arm regions.

The background sources of polarized emission against which Faraday rotation can be studied...…is not limited only to discrete objects include also the extended emission from the entire Galaxy. Faraday Tomography ! Is it possible ?

Several extensive surveys have mapped the band- averaged polarized intensity from the extended emission... at various frequencies using single-dish or synthesis imaging. e.g. Spoelstra 1984; Wieringa et al Duncan et al. 1999; Uyanikar et al. 1999, Gaensler et al. 2001

I Q U V The rich structure in Q,U does not relate with that in the Stokes I Wieringa et al. 1993

Derived images of net polarization, position angle and the apparent Rotation Measure.... reveal rich structure over the range of angular scales probed..... show reasonable correspondence between the Faraday-induced structures apparent at both, high & low radio freq.s Uyanikar et al. 1999

As would be expected,.... the net degree of polarization decreases with frequency,.... the apparent mean RMs are rather small in comparison with those against compact sources. (reliability? of the RM values )

A Quick Recap: Such studies so far (till very recently), seek only a single RM value per image pixel, (which would closely correspond to a RM in the foreground of the most dominant polarized emission along the relevant sight-line). However, we expect the extended polarized emission to be well spread in depth along each sight-line (in principle, over the entire extent of the Galaxy).

If so, then at each image-pixel location... different regions, or slabs, of polarized emission at different depth would contribute with their respective foreground Faraday rotation signature. What is this signature ?.... the spectral modulation in the Stokes Q & U

This spectral modulation period is inversely proportional to RM, its depth relates to the percentage linear polarization, and its phase to the apparent position angle. The modulation is not limited to Q & U, but is also in XX & YY…… (and in any linear vector combinations of these). Even a single linearly polarized feed is adequate to probe the modulation details. e.g. psr polarization with the Ooty telescope system (Ramkumar & desh, 1998)

So, each thin slab would contribute spectral modulation... that is almost pure sinusoidal along wavelength-square ordinate. The sum total, in general, would show lower % linear polarization than that is “intrinsic” to the slabs themselves.

The so called "intrinsic" % polarization for a slab itself may already be less than the theoretical maximum for synchrotron radiation, because of contribution from thermal components.... possible random field components.... any "front-back" depolarization internal to the slab. What is said above is far from new, and has long been well appreciated ! e.g., see Burn (1966), for general discussion and for estimates of the above effects. Also, Haverkorn et al (2004), Brentjens & de Bruyn (2005)

Burn (1966) : Faraday dispersion function of the Crab nebula

Nonetheless, the existing surveys had too inadequate spectral resolution and/or bandwidth at the survey frequency to relate to the above picture in sufficient detail.

We argue..... that, with an appropriate combination of observing freq., bandwidth and spectral resolution, it should be possible to perform Faraday Tomography by transforming the spectral modulations to a set of (lin) polarized intensities as a function of Faraday depth (i.e. RM) at each image pixel. =====> polarized intensity data cubes (2-d sky coordinates & RM)... quite like the spectral-line data cubes

CHOICES Considerations..... RM axis is closely related to the "delay" or lag axis in the context of, say, the cross- correlation between the two orthogonal circular polarization signals. And the usual inverse relations apply. 1/( )

Spectral resolution width (un-aliased) RM range Spectral span resolution width in RM. Both these, i.e. RM-span & resolution, share a common and a rather steep (f^-3) dependence on the center frequency f. Angular beam and RM resolutions define the volume over which depolarization would be unavoidable. **Need for calibrators to relate RM to distance

Attractive possibilities with Arecibo receivers: Use of 327 MHz system (25 MHz BW, 1024 ch.s) =====> delta_RM ~ 15 rad/sq.m; RM_limit ~ rad/sq.m 400 MHz BW, 128 channels at L-band can also be used in combination with 327 MHz ======> delta_RM ~ 5 rad/sq.m (desh, Chris Salter, Tapasi Ghosh 2002)

However, beam sizes for the two bands differ The 7 ALFA-beams together would help speed up and match the coverage/resolution. But then.... beam depolarization could be large ? Recent spatial spectral analysis (Tucci et al, 2002) of the continuum polarized emission shows increase in Q & U intensity variation with increasing spatial scale size.... ======> we expect to see a substantial fraction of the polarization structure in the extended component.

So our missing details at arc-min resolutions, may not hurt so much. On the other hand, Arecibo single-dish would sample the crucial low spatial freq.s that are otherwise missed in the existing synthesis surveys. Expected RM resolution based on 300 MHz BW of the ALFA system: about 140 rad/sq.m Need for a corresponding data set at 327 MHz to combine with the GALFACTS data

A sample result from AO observations at 327 MHz Tomographic analysis of data from a 1-d cut : linearly polarized intensity as a function of RM and angular distance Angular distance > (desh, Salter, Ghosh, 2004) +500 RM -500

Thank you. And many thanks to Chris.