Intrinsic/Extrinsic Density-Ellipticity Correlations and Galaxy-Galaxy Lensing

TL;DR

This paper analyzes the density-ellipticity cross-correlation to disentangle intrinsic galaxy alignments from gravitational lensing (extrinsic) signals. Under Gaussian tidal-field assumptions, the intrinsic contribution to $\langle \delta_g \epsilon_t \rangle$ vanishes for both MWK and CNPT formalisms, while the extrinsic lensing signal yields two components: magnification bias and galaxy-galaxy lensing within the same selection. The authors further show that non-Gaussian fluctuations from gravitational instability generate nonzero intrinsic correlations, with a linear scaling in the matter power spectrum on large scales, and quantify how this non-Gaussianity affects both density-ellipticity and ellipticity-ellipticity correlations, as well as its impact on SDSS-like galaxy-galaxy lensing contamination (roughly $10$–$30\%$ at $10$ arcmin for overlapping samples). These results suggest the density-ellipticity cross-correlation can serve as a diagnostic for lensing claims and underscore the need to account for non-Gaussianity and nonlinear bias in interpreting weak-lensing signals. They also advocate empirical measurements and simulations to test these predictions and calibrate the model normalization.

Abstract

We compute both extrinsic (lensing) and intrinsic contributions to the (galaxy-)density-ellipticity correlation function, the latter done using current analytic theories of tidal alignment. The gravitational lensing contribution has two components: one is analogous to galaxy-galaxy lensing and the other arises from magnification bias -- that gravitational lensing induces a modulation of the galaxy density as well as ellipticity. On the other hand, the intrinsic alignment contribution vanishes, even after taking into account source clustering corrections, which suggests the density-ellipticity correlation might be an interesting diagnostic in differentiating between intrinsic and extrinsic alignments. {\it However}, an important assumption, commonly adopted by current analytic alignment theories, is the Gaussianity of the tidal field. Inevitable non-Gaussian fluctuations from gravitational instability induces a non-zero intrinsic density-ellipticity correlation, which we estimate. We also argue that non-Gaussian contributions to the intrinsic {\it ellipticity-ellipticity} correlation are often non-negligible. This leads to a linear rather than, as is commonly assumed, quadratic scaling with the power spectrum on sufficiently large scales. Finally, we estimate the contribution of intrinsic alignment to low redshift galaxy-galaxy lensing measurements (e.g. SDSS), due to the partial overlap between foreground and background galaxies: the intrinsic contamination is about 10 - 30 % at 10'. Uncertainties in this estimate are discussed.

Figures (5)

• Figure 1: The lensing density-ellipticity correlation ($A$ and $B$, the magnification bias term and the 'galaxy-galaxy lensing' term respectively, see eq. [\ref{['exdeltagepsilon']}]), and the lensing ellipticity-ellipticity correlations (eq. [\ref{['epep']}]), for a high redshift sample of source galaxies (see eq. [\ref{['Wg1']}] for the selection function).
• Figure 2: Same as Fig. \ref{['DE.paper']} except that the selection function is that of a shallower survey (eq. [\ref{['Wg2']}]).
• Figure 3: Same as Fig. \ref{['DE.paper']} except that the selection function is chosen to be much more narrow (eq. [\ref{['Wg3']}]).
• Figure 4: Ratio of the full expression (including non-Gaussian terms; eq. [\ref{['nonGstart2']}]) for the intrinsic ellipticity-ellipticity correlation to its Gaussian version (i.e. setting $Q_4 = 0$ in both eq. [\ref{['nonGstart2']}] and [\ref{['Afact']}]). The upper panel assumes a selection function appropriate for a deep survey (eq. [\ref{['Wg1']}]), while the lower panel uses that for a shallow survey (eq. [\ref{['Wg2']}]). Dotted lines denote the ratio when using $z_{\rm T} = 3$, while solid lines use $z_{\rm T} = 50$.
• Figure 5: Ratio of intrinsic signal to extrinsic signal. Upper panel: the ratio of eq. (\ref{['nongaussDEin']}) to eq. (\ref{['DEex']}) for the density-ellipticity correlation, for two different selection functions. The short-dashed and solid lines correspond to a shallow survey ($W_g$ given by eq. [\ref{['Wg2']}]), with the short-dashed line using $z_{\rm T} = 3$, and the solid line using $z_{\rm T} = 50$. The long-dashed and dotted lines correspond to a deep survey ($W_g$ given by eq. [\ref{['Wg1']}]), with the long-dashed line using $z_{\rm T} = 3$, and the dotted line using $z_{\rm T} = 50$. Lower panel: the level of contamination from intrinsic alignment to a galaxy-galaxy lensing measurement of density-ellipticity correlation (ratio of eq. [\ref{['nongaussDEin2']}] to [\ref{['DEex2']}]), using two different prescriptions for $z_{\rm T}$. The dashed line uses $z_{\rm T} = 3$ and the solid line uses $z_{\rm T} = 50$. The foreground and background selection functions here are chosen to mimic the SDSS galaxy-galaxy lensing survey of Fischer et al. (2000).