Reich (2006)

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Personal summary of the paper: Galactic polarization surveys by Wolfgang Reich

Starts with a historical sketch of the galactic polarization surveys. First galactic polarized diffuse emission was detected in 1962. In the 80s and 90s some high resolution surveys showed a large variety of polarization structures including Faraday screens and canals that have no counterparts in the total intensity. It meant Faraday rotation in the magneto-ionic medium (MIM) varies largely at small scales.

Galactic synchrotron emission

Caused by cosmic ray electrons gyrating around magnetic field lines. For power law energy distribution of cosmic ray electrons observed synchrotron intensity is,

<math>I(\nu) \sim N_e\ B_\perp^{(\gamma+1)/2} \nu^{-(\gamma-1)/2}</math>

where gamma is the power law index of the cosmic ray electrons energy distribution which is related to the spectral index of the intensity as,

<math>\alpha = -\frac{\gamma-1}{2}</math>

A brightness temperature can be defined from the intensity which is,

<math>T_b \sim \nu^\beta \text{ where } \beta=\alpha-2</math>

The degree of polarization (p) is directly determined by the spectral index,

<math>p = \frac{\gamma+1}{\gamma+7/3}</math>

In this equation putting gamma = 2 or 3 gives a polarization fraction of 69% or 75% respectively. But observed polarization fraction is much lower than this. Because,

  1. Depolarization due to Faraday rotation and other effects
  2. It also depends on the degree of regularity of the magnetic field

Magnetic field has a random and a regular component,

<math>B_{tot} = \sqrt{B_{ran}^2+B_{reg}^2}</math>

And the observed degree of polarization depends on regularity as,

<math>p_{obs} = p_{int} \frac{B_{reg}^2}{B_{tot}^2}</math>

So the more is the regular fraction of magnetic field the more is the observed degree of polarization.

Surveys: All-sky survey of total intensity available upto 1.4 GHz, large-scale survey available at 2.3 GHz. At higher frequencies ground based telescope restricted to the galactic plane as higher resolution is needed to resolve complex emission structures. All-sky survey at higher frequencies (above 22.8 GHz) available from space telescopes (WMAP).

Calibration: At high frequencies absolute calibration done by comparing the data obtained usually with parabolic antennas with the lower resolution survey maps obtained by sky-horn measurements. At low frequencies Galactic sky temperature is so high that absolute calibration is possible through temperature standards.

Spectrum: At low frequencies synchrotron dominates, but as frequency increases thermal emission becomes more dominant and thus spectrum flattens. At lower frequencies synchrotron spectra also varies depending on electron energies and magnetic field strengths as we know electron energy spectra steepens towards high energies. In general synchrotron spectra are flatter at lower frequencies.

Galactic magnetic field

Sadly we live inside our galaxy. So it is useful to observe neighboring galaxies and guess our own situation. A galaxy observed face-on will provide information about its disk magnetic field while one observed edge-on will provide information about halo field.

  • Beuermann et al. 1985 deconvolved the Haslam et al. 1982 408 MHz survey to model the Galaxy.
  • Strong et al. 2000 compared gamma ray and synchrotron emission to get the magnetic field strength as a function of Galacto-centric radius.
  • Berkhuijsen used emissivities from Beuermann and assumed equipartition between magnetic field energy and cosmic ray energy densities to model.

Direction of local magnetic field determined by rotation measures (RM) of pulsars. The direction points towards Cygnus region in the northern hemisphere and towards Vela complex in the southern: there is a general orientation of the magnetic field along the spiral arms.

  • Regular component of the local magnetic field = 1.4 muG
  • Total local field = 6 muG

Magnetic field reversals: prediction of dynamo theory (Shukurov 2004). For nearby spiral galaxies evidence is rare. But there is a common agreement on a field reversal between the local Orion arm and the Sagittarius arms at a distance of few hundred parsec. More reversals could be there, need more RM data.

Interstellar Magneto-ionic Medium (MIM)

Thermal emission: from the gas clouds ionized by photons from OB-stars. There are discrete gas complexes (HII regions) and huge amount of diffuse low density gas. They have a smaller scale height than synchrotron emission, but new H-alpha surveys suggest they can exist also in the halo. Optically thin emission spectra from these gas (at few hundred MHz) are flatter than synchrotron spectra. So fraction of thermal emission increases towards higher frequencies.

Dispersion measure (DM) of pulsars is used to derive the thermal electron densities. We must know the distances to the pulsars independently as usual which can be done by HI absorption measurements. One model of thermal electrons done by Taylor & Cordes 1993.

This is called warm ionized gas: with typical temperature of few thousands kelvin. But also cool low density thermal gas exists as suggested by low-frequency absorption measurements. Gas temperature increases with distance from galactic plane.

Faraday rotation

Go to: Faraday rotation

If there is magnetic field and thermal gas there will be Faraday rotation. Amount of rotation is called Faraday depth which is equivalent to rotation measure. Detail discussion of Faraday rotation and depth: Brentjens & Bruyn 2005

Galactic polarization survey

Galactic synchrotron emission is linearly polarized. If we know Stokes U and Q we can easily get,

<math>PI = \sqrt{U^2+Q^2}</math>

<math>\phi = \frac{1}{2} \tan^{-1} \frac{U}{Q}</math>

Early polarization measurement: single dish with rotating cross dipoles as feeds. Power difference between the dipoles was measured.

Another method: to measure cross-correlation between two feed dipoles. A set of Stokes parameters can be obtained from cross-correlation in two ways:

  1. If feeds couple out linear polarization I, Q and V are obtained after correlation and a 90 degree phase shift of one of the signals.
  2. If they couple out two circular polarization components I, Q and U are obtained. This is preferred.

Low frequency: use dipoles, higher frequencies: use corrugated waveguide feeds. Various methods used to change linear into circular polarization.

Instrumental effects

Cross talk: between the polarization channels, losses. The polarimeter response may not be circular. U, Q depends on the polarization angle or in case of altazimuth telescopes on parallactic angle. Instrumental influences may also vary with time.