Weak lensing correlation function errors

[Charles Shapiro]

Hi All,

Most papers will tell you that the uncertainty in the weak lensing power spectrum is (e.g. Hu and Tegmark 1998)
[tex]
\Delta P_{\psi}=\sqrt{\frac{2}{(2l+1)f_{\rm sky}}}(P_{\psi}+\frac{4}{n}<\gamma^2_{\rm int}>)
[/tex]

...but can someone please point me to a derivation of the analogous formula for the correlation function?

Chaz

[Sarah Bridle]

I had the impression that there is no similarly simple formula for the correlation function.
There is some discussion of errors on the correlation function in Simon, King & Schneider astro-ph/0309032, in case that helps.

[Charles Shapiro]

That's unfortunate! From what I've managed to scribble down, I guess I'm not surprised. Thanks for the tip.

Chaz

[Patrick Simon]

Hi everyone,

you should also have a look at Schneider et al. (2002), astro-ph/0206182,
where an estimate of the covariance for two-point shear-shear correlations in the Gaussian limit is given.

But, sadly, sadly, sadly, it is not a nice and handy small formula, as Sarah has already mentioned. The problem is that statistical errors become correlated for different scales, if you work with real-space correlation functions, while power spectra (of Gaussian random fields without gaps, at least?) have uncorrelated errors for different modes.

Patrick

[Charles Shapiro]

The Schneider et al. paper is useful - thank you.

Chaz