Archive for Faraday Rotation

Circular Polarization in the Cosmic Microwave Background?

Posted in The Universe and Stuff with tags , , , , on November 23, 2018 by telescoper

Some years ago I went to a seminar on the design of an experiment to measure the polarization of the cosmic microwave background. At the end of the talk I asked what seemed to me to be an innocent question. The point of my question was the speaker had focussed entirely on measuring the intensity of the radiation (I) and the two Stokes Parameters that measure linear polarization of the radiation (usually called Q and U). How difficult, I asked, would it be to measure the remaining Stokes parameter V (which quantifies circular polarization)?

There was a sharp intake of breath among the audience as if I had uttered an obscenity, and the speaker responded with a glare and a curt `the cosmic microwave background is not circularly polarized’. It is true that in the standard cosmological theory the microwave background is produced by Thomson scattering in the early Universe which produces partial linear polarization, so that Q and U are non-zero, but not circular polarization, so V=0. However, I had really asked my question because I had an idea that it might be worth measuring V (or at least putting an upper limit on it) in order to assess the level of instrumental systematics (which are a serious issue with polarization measurements).

I was reminded of this episode when I saw a paper on the arXiv by Keisuke Inomata and Marc Kamionkowski which points out that the CMB may well have some level of circular polarization. Here is the abstract of the paper:

(You can click on the image to make it more readable.) It’s an interesting calculation, but it’s hard to see how we will ever be able to measure a value of Stokes V as low as 10-14.

A few years ago there was a paper on the arXiv by Asantha Cooray, Alessandro Melchiorri and Joe Silk which pointed out that the CMB may well have some level of circular polarization. When light travels through a region containing plasma and a magnetic field, circular polarization can be generated from linear polarization via a process called Faraday conversion. For this to happen, the polarization vector of the incident radiation (defined by the direction of its E-field) must have non-zero component along the local magnetic field, i.e. the B-field. Charged particles are free to move only along B, so the component of E parallel to B is absorbed and re-emitted by these charges, thus leading to phase difference between it and the component of E orthogonal to B and hence to the circular polarization. This is related to the perhaps more familiar process of which causes the plane of linear polarization to rotate when polarized radiation travels through a region containing a magnetic field.

Here is the abstract of that paper:

(Also clickable.) This is a somewhat larger effect but differs from the first paper in that it is produced by foreground processes rather than primordial physics. In any case a Stokes V of 10-9 is also unlikely to be measurable at any time in the foreseeable future.

Stokes V – The Lost Parameter

Posted in The Universe and Stuff with tags , , , , , , on August 27, 2014 by telescoper

Some years ago I went to a seminar on the design of an experiment to measure the polarization of the cosmic microwave background. At the end of the talk I asked what seemed to me to be an innocent question. The point of my question was the speaker had focussed entirely on measuring the intensity of the radiation (I) and the two Stokes Parameters that measure linear polarization of the radiation (usually called Q and U). How difficult, I asked, would it be to measure the remaining Stokes parameter V (which quantifies circular polarization)?

There was a sharp intake of breath among the audience and the speaker responded with a curt “the cosmic microwave background is not circularly polarized”. It is true that in the standard cosmological theory the microwave background is produced by Thomson scattering in the early Universe which produces partial linear polarization, so that Q and U are non-zero, but not circular polarization so V=0. However, I had really asked my question because I had an idea that it might be worth measuring V (or at least putting an upper limit on it) in order to assess the level of instrumental systematics (which are a serious issue with polarization measurements).

I was reminded of this episode when I saw a paper on the arXiv today by Asantha Cooray, Alessandro Melchiorri and Joe Silk which points out that the CMB may well have some level of circular polarization. When light travels through a region containing plasma and a magnetic field, circular polarization can be generated from linear polarization via a process called Faraday conversion. For this to happen, the polarization vector of the incident radiation (defined by the direction of its E-field) must have non-zero component along the local magnetic field, i.e. the B-field. Charged particles are free to move only along B, so the component of E parallel to B is absorbed and re-emitted by these charges, thus leading to phase difference between it and the component of E orthogonal to B and hence to the circular polarization. This is related to the perhaps more familiar process of Faraday rotation, which causes the plane of linear polarization to rotate when polarized radiation travels through a region containing a magnetic field.

Anyway, here is the abstract of the paper

The primordial anisotropies of the cosmic microwave background (CMB) are linearly polarized via Compton-scattering. The Faraday conversion process during the propagation of polarized CMB photons through regions of the large-scale structure containing magnetized relativistic plasma, such as galaxy clusters, will lead to a circularly polarized contribution. Though the resulting Stokes-V parameter is of order 10-9 at frequencies of 10 GHz, the contribution can potentially reach the total Stokes-U at low frequencies due to the cubic dependence on the wavelength. In future, the detection of circular polarization of CMB can be used as a potential probe of the physical properties associated with relativistic particle populations in large-scale structures.

It’s an interesting idea, but it’s hard for me to judge the feasibility of measuring a value of Stokes V as low as 10-9. Clearly it would only work at frequencies much lower than those probed by current CMB experiments such as BICEP2 (which operates at 150 GHz). Perhaps if the speaker had answered my question all those years ago I’d be in a better position to decide!

In a Galaxy, Faraday…

Posted in The Universe and Stuff with tags , , , , on July 21, 2009 by telescoper

I was finishing off the draft of a paper the other day and remembered a little paper I did some time ago with a former PhD student of mine, Patrick Dineen. I thought it would be fun to put the pictures up here because it was one of those occasions when a little idea turns out much nicer than you expected…

What we had to start with was a collection of Faraday Rotation measurements of extragalactic radio sources dotted around the sky. Their distribution is fairly uniform but I hasten to add that it was not a controlled sample so it would be not possible to take the sources as representative of anything for statistical purposes.

Faraday rotation occurs because left and right-handed polarizations of electromagnetic radiation travel at different speeds along a magnetic field line. The effect of this is for the polarization vector to be rotated as light waves travel and the net rotation angle (which can be either positive or negative) is related to the line integral of the component of the magnetic field along the line of sight travelled by the waves. The picture below shows the distribution of sources, plotted in Galactic coordinates and coded black for negative and white for positive.

rotation

Some radio galaxies have enormously large Faraday rotation measures because light reaches us through regions of the source that have strong magnetic fields. However, for most sources in our sample the rotation measures are smaller and are thought to be determined largely by the propagation of light not through the emitting galaxy, near the start of its journey towards us, but through our own Galaxy, the Milky Way, which is near the end of its path.

If this is true then the distribution of rotation measures across the sky should contain information about the magnetic field distribution inside our own Galaxy. Looking at the above picture doesn’t give much of a hint of what this structure might be, however.

What Patrick and I decided to do was to try to make a map of the rotation measure distribution across the sky based only on the information given at the positions where we had radio sources. This is like looking at the sky through a mask full of little holes at the source positions. Using a nifty (but actually rather simple) trick of decomposing into spherical harmonics and transforming to a new set of functions that are orthogonal on the masked sky we obtained the following map:

uni_16_rmjoint

(The technical details are in the paper, if you’re interested.) You probably think it looks a bit ropey but, as far as I’m concerned, this turned out stunningly well. The most obvious features are a big blue blob to the left and a big red blob to the right, both in the Galactic plane. What you’re seeing in those regions is almost certainly the local spur (sometimes called the Orion Spur; see below), which is a small piece of spiral arm in which the local Galactic magnetic field is confined. The blobs show the field coming towards the observer on one side and receding on the other. The structure seen is relatively local, i.e. within a kiloparsec or so of the observer.

I was very pleased to see this come out so clearly from an apparently unpromising data set, although we had to confine ourselves to large-scale features because of instabilities in the reconstruction of high-frequency components.