weak lensing measurements?
Priyamvada Natarajan , Robert G. Crittenden,
Ue-Li Pen \& Tom Theuns
, PASA, 18 (2), in press.
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Results
The amplitude and shape of the computed ellipticity correlation function can be understood intuitively. The ellipticity is a function of the shear tensor, which is the second derivative of the potential. By virtue of Poisson's equation, the trace of the shear tensor is the density. Therefore, we expect the correlation of the other components of the shear field will drop at the same rate as the density correlation function. Since the ellipticities are quadratic in the shear field, correlations in them will fall as the density correlation function squared, 
(see Fig. 1). Comparing the strength of the intrinsic correlation to that expected for weak lensing, we find that the intrinsic signal grows as the depth of the survey decreases (the projected intrinsic shape correlation function scales as zm-2 whereas the weak lensing correlation function scales as zm1.52), because in that case galaxies close on the sky are also on average physically closer, and are hence more correlated. The weak lensing signal, on the other hand, drops off, since typically there is less matter between us and the lensed objects. For typical weak lensing surveys, however, with a median redshift of zm=1, the intrinsic signal is between 1 - 10 per cent of the weak lensing amplitude. For surveys such as the SDSS the intrinsic signal may dominate the lensing one, on small scales (see Left panel of Fig. 1). Recently, Brown et al. (2000) have measured the intrinsic correlation function measured from the COSMOS survey and find good agreement with our theoretical predictions. The intrinsic ellipticity depends on the square of the tidal field, whereas the lensing distortion is linear in the shear. As a direct consequence, the distortion field is curl-free when induced by lensing, but not when intrinsic correlations are present as well (Crittenden et al. 2000b). Angular momentum couplings produce E and B-modes in comparable amounts and one might expect that noise, telescope distortions and other sources of systematic errors will produce curl modes as well. The detection of such magnetic modes will be an invaluable way of separating lensing from intrinsic correlations. Details on how to unambiguously do so are presented in Crittenden et al. (2001b).
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