Weak lensing correlation function errors

 Posts: 24
 Joined: February 05 2005
 Affiliation: University of Portsmouth
Weak lensing correlation function errors
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
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

 Posts: 144
 Joined: September 24 2004
 Affiliation: University College London (UCL)
 Contact:
Weak lensing correlation function errors
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 astroph/0309032, in case that helps.
There is some discussion of errors on the correlation function in Simon, King & Schneider astroph/0309032, in case that helps.

 Posts: 24
 Joined: February 05 2005
 Affiliation: University of Portsmouth
Weak lensing correlation function errors
That's unfortunate! From what I've managed to scribble down, I guess I'm not surprised. Thanks for the tip.
Chaz
Chaz

 Posts: 1
 Joined: August 14 2006
 Affiliation: ArgelanderInstitut fuer Astronomie, Bonn
 Contact:
Weak lensing correlation function errors
Hi everyone,
you should also have a look at Schneider et al. (2002), astroph/0206182,
where an estimate of the covariance for twopoint shearshear 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 realspace correlation functions, while power spectra (of Gaussian random fields without gaps, at least?) have uncorrelated errors for different modes.
Patrick
you should also have a look at Schneider et al. (2002), astroph/0206182,
where an estimate of the covariance for twopoint shearshear 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 realspace correlation functions, while power spectra (of Gaussian random fields without gaps, at least?) have uncorrelated errors for different modes.
Patrick

 Posts: 24
 Joined: February 05 2005
 Affiliation: University of Portsmouth
Weak lensing correlation function errors
The Schneider et al. paper is useful  thank you.
Chaz
Chaz