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waynehu

Professor, Department of Astronomy and Astrophysics
University of Chicago

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Temperature-Polarization Correlation

 

As we have seen in §2, the polarization pattern reflects the local quadrupole anisotropy at last scattering. Hence the temperature and polarization anisotropy patterns are correlated in a way that can distinguish between the scalar, vector and tensor sources.

There are two subtleties involved in establishing the correlation. First, the quadrupole moment of the temperature anisotropy at last scattering is not generally the dominant source of anisotropies on the sky, so the correlation is neither 100% nor necessarily directly visible as patterns in the map.

The second subtlety is that the correlation occurs through the E-mode unless the polarization has been Faraday or otherwise rotated between the last scattering surface and the present. As we have seen an E-mode is modulated in the direction of, or perpendicular to, its polarization axis. To be correlated with the temperature, this modulation must also correspond to the modulation of the temperature perturbation. The two options are that E is parallel or perpendicular to crests in the temperature perturbation. As modes of different direction tex2html_wrap_inline1086 are superimposed, this translates into a radial or tangential polarization pattern around hot spots (see Fig. 12a).

On the other hand B-modes do not correlate with the temperature. In other words, the rotation of the pattern in Fig. 12a by 45 tex2html_wrap_inline1160 into those of Fig. 12b (solid and dashed lines) cannot be generated by Thomson scattering. The temperature field that generates the polarization has no way to distinguish between points reflected across the symmetric hot spot and so has no way to choose between the tex2html_wrap_inline1572 rotations. This does not however imply that B vanishes. For example, for a single plane wave fluctuation B can change signs across a hot spot and hence preserve reflection symmetry (e.g. Fig. 6 around the hot spot tex2html_wrap_inline1578 , tex2html_wrap_inline1580 ). However superposition of oppositely directed waves as in Fig. 12b would destroy the correlation with the hot spot.

The problem of understanding the correlation thus breaks down into two steps: (1) determine how the quadrupole moment of the temperature at last scattering correlates with the dominant source of anisotropies; (2) isolate the E-component (Q-component in tex2html_wrap_inline1086 coordinates) and determine whether it represents polarization parallel or perpendicular to crests and so radial or tangential to hot spots.


Next: Large Angle Correlation Pattern