[0708.0387] Analysis of two-point statistics of cosmic shea
Posted: August 03 2007
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.
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.