Intrinsic alignment-lensing interference as a contaminant of cosmic shear

Cosmic shear surveys have great promise as tools for precision cosmology, but can be subject to systematic errors including intrinsic ellipticity correlations of the source galaxies. The intrinsic alignments are believed to be small for deep surveys, but this is based on intrinsic and lensing distortions being uncorrelated. Here we show that the gravitational lensing shear and intrinsic shear need not be independent: correlations between the tidal field and the intrinsic shear cause the intrinsic shear of nearby galaxies to be correlated with the gravitational shear acting on more distant galaxies. We estimate the magnitude of this effect for two simple intrinsic-alignment models: one in which the galaxy ellipticity is linearly related to the tidal field, and one in which it is quadratic in the tidal field as suggested by tidal torque theory. The first model predicts a gravitational-intrinsic ($GI$) correlation that can be much greater than the intrinsic-intrinsic ($II$) correlation for broad redshift distributions, and that remains when galaxies pairs at similar redshifts are rejected. The second model, in its simplest form, predicts no gravitational-intrinsic correlation. In the first model, and assuming a normalization consistent with recently claimed detections of intrinsic correlations, we find that the $GI$ correlation term can exceed the usual $II$ term by $>1$ order of magnitude and the intrinsic correlation induced $B$-mode by 2 orders of magnitude. These interference effects can suppress the lensing power spectrum for a single broad redshift bin by of order $\sim 10\%$ at $z_s=1$ and $\sim 30\%$ at $z_s=0.5$. We conclude that, depending on the intrinsic-alignment model, the $GI$ correlation may be the dominant contaminant of the lensing signal and can even affect cross spectra between widely separated bins. We describe two ways to constrain this effect, one based on density-shear correlations and one based on scaling of the cross correlation tomography signal with redshift.

Figure 1

The effect of the density-intrinsic shear correlation on the shear power spectrum. Density fluctuations in the nearby plane (gray masses) induce a tidal field (arrows). A source galaxy in a more distant plane (dashed ellipse) is gravitationally sheared tangentially to these masses. If the intrinsic shears of galaxies in the nearby plane (solid ellipse) are aligned with the stretching axis of the tidal field, then this results in an anticorrelation between the shears of galaxies at different redshifts, i.e. $C_{\ell }^{EE,GI}<0$. (The opposite case, $C_{\ell }^{EE,GI}>0$, results if galaxies are preferentially aligned with the compressing axis of the tidal field.)

Figure 2

The gravitational ($GG$), intrinsic alignment ($II$), and gravitational-intrinsic correlation ($GI$) contributions to the shear power spectrum, for the linear alignment model. The $B$-mode shear power spectrum is labeled “B” and has only an intrinsic-intrinsic contribution. The cross term ($GI$) is negative for this model, so we have plotted its absolute values on the log scale. We show results for (a) the shear power spectrum for a survey with redshift distribution of Eq. (25) with $z_m=0.1$; (b) and (c) similar for $z_m=0.5$ and 1.0, respectively; (d) the shear cross-power between redshifts $z=0.5$ and $z=1.0$ (the slices have Gaussian redshift distributions with width ${\sigma }_z=0.1$); (e) the shear cross-power between redshifts $z=0.5$ and $z=2.0$; and (f) the shear cross-power between redshifts $z=1.0$ and $z=2.0$. The intrinsic alignment amplitude $C_1$ is normalized to SuperCOSMOS. Panel (a) is cut off at $\ell =300$, roughly the smoothing scale used for the intrinsic alignment calculation, since the model does not make sense on smaller scales.

Figure 3

The intrinsic shear statistic $\Delta \gamma (r)$ of Eq. (26). The SDSS data points are shown, with the horizontal error bars indicating the range of radii used, the thick vertical error bars indicating $1\sigma$ statistical errors, and the thin vertical error bars representing 99.9% confidence limits including systematics (principally shear calibration and removal of lensing signal) [51].