This paper suggests some estimators for the shear E and B power spectrum. The first section considers a very idealized case of uniform full-sky geometry, but later they consider more realistic cases.
The problem is essentially identical to the analysis of CMB polarization, which seems to be much more advanced - it is striking that there are no references at all to this well-developed literature. As far as I can see the estimators in this paper are basically what are called Pseudo-Cl estimators in CMB analysis. References include astro-ph/0008111, astro-ph/0105302 (for CMB temperature), astro-ph/0410394, astro-ph/0601107 and many others. The relation to correlation functions is analysed in detail in astro-ph/0303414, along with detailed analysis of the covariances in astro-ph/0410097. Not only does the CMB literature have the generalization to the curved sky, but includes general methods for constructing de-biased estimators and their covariances in realistic cases, as well as a detailed understanding of the E/B mixing effects.
Furthermore quadratic estimators are available that cleanly separate E and B modes even in complicated geometries, eg. astro-ph/0610059.
The noise properties in galaxy lensing are obviously somewhat different from the CMB, but I think there is scope for a lot more overlap between fields.
[0708.0387] Analysis of two-point statistics of cosmic shear: III. Covariances of shear measures made easy
|Authors:||B. Joachimi, P. Schneider, T. Eifler (Argelander-Institut für Astronomie, Universität Bonn)|
|Abstract:||In recent years cosmic shear, the weak gravitational lensing effect by the large-scale structure of the Universe, has proven to be one of the observational pillars on which the cosmological concordance model is founded. Several cosmic shear statistics have been developed in order to analyze data from surveys. For the covariances of the prevalent second-order measures we present simple and handy formulae, valid under the assumptions of Gaussian density fluctuations and a simple survey geometry. We also formulate these results in the context of shear tomography, i.e. the inclusion of redshift information, and generalize them to arbitrary data field geometries. We define estimators for the E- and B-mode projected power spectra and show them to be unbiased in the case of Gaussianity and a simple survey geometry. From the covariance of these estimators we demonstrate how to derive covariances of arbitrary combinations of second-order cosmic shear measures. We then recalculate the power spectrum covariance for general survey geometries and examine the bias thereby introduced on the estimators for exemplary configurations. Our results for the covariances are considerably simpler than and analytically shown to be equivalent to the real-space approach presented in the first paper of this series. We find good agreement with other numerical evaluations and confirm the general properties of the covariance matrices. The studies of the specific survey configurations suggest that our simplified covariances may be employed for realistic survey geometries to good approximation.|
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