  The power spectrum of weak lensing shear caused by large-scale structure is
an emerging tool for precision cosmology, in particular for measuring the
effects of dark energy on the growth of structure at low redshift. One
potential source of systematic error is intrinsic alignments of ellipticities
of neighbouring galaxies (II correlation) that could mimic the correlations due
to lensing. A related possibility pointed out by Hirata and Seljak (2004) is
correlation between the intrinsic ellipticities of galaxies and the density
field responsible for gravitational lensing shear (GI correlation). We present
constraints on both the II and GI correlations using 265 908 spectroscopic
galaxies from the SDSS, and using galaxies as tracers of the mass in the case
of the GI analysis. The availability of redshifts in the SDSS allows us to
select galaxies at small radial separations, which both reduces noise in the
intrinsic alignment measurement and suppresses galaxy- galaxy lensing (which
otherwise swamps the GI correlation). While we find no detection of the II
correlation, our results are nonetheless statistically consistent with recent
detections found using the SuperCOSMOS survey. In contrast, we have a clear
detection of GI correlation in galaxies brighter than L* that persists to the
largest scales probed (60 Mpc/h) and with a sign predicted by theoretical
models. This correlation could cause the existing lensing surveys at z~1 to
underestimate the linear amplitude of fluctuations by as much as 20% depending
on the source sample used, while for surveys at z~0.5 the underestimation may
reach 30%. (Abridged.)
