Theoretical Estimates of Intrinsic Galaxy Alignment

TL;DR

This paper develops an analytic model linking galaxy ellipticity to angular momentum within the tidal torque framework to predict intrinsic alignment signals. By deriving the ellipticity power spectra as convolutions of the gravitational potential and decomposing into $E$- and $B$-modes, the authors use Limber projection to obtain angular spectra for different source redshift distributions. They find that intrinsic alignments dominate weak-lensing correlations at low redshift and that $E$-mode power is enhanced by about a factor of $\sim 3.5$ over $B$-mode power on small scales, implying intrinsic signals can significantly contaminate cosmic shear in shallow surveys. The work, consistent with CNPT and simulations, provides upper-limit estimates and highlights the importance of intrinsic alignments for interpreting current and future weak-lensing measurements, especially in narrow or shallow redshift bins.

Abstract

It has recently been argued that the observed ellipticities of galaxies may be determined at least in part by the primordial tidal gravitational field in which the galaxy formed. Long-range correlations in the tidal field could thus lead to an ellipticity-ellipticity correlation for widely separated galaxies. We present a new model relating ellipticity to angular momentum, which can be calculated in linear theory. We use this model to calculate the angular power spectrum of intrinsic galaxy shape correlations. We show that for low redshift galaxy surveys, our model predicts that intrinsic correlations will dominate correlations induced by weak lensing, in good agreement with previous theoretical work and observations. We find that our model produces `E-mode' correlations enhanced by a factor of 3.5 over B-modes on small scales, making it harder to disentangle intrinsic correlations from those induced by weak gravitational lensing.

Figures (2)

• Figure 1: The various angular power spectra discussed in the text for our flat $\Lambda$CDM model. The solid line is the predicted weak lensing signal , the dashed line the "intrinsic" ellipticity $EE$ power spectrum and the dot-dashed line the intrinsic $BB$ power spectrum. The first panel is for a low redshift source galaxy distribution of mean redshift $\langle z \rangle = 0.1$ using the redshift distribution described in the text. The second and third panels are for $\langle z \rangle =0.3$ and 1.0 respectively.
• Figure 2: Correlation functions and comparison with other work, all for the low redshift $\langle z \rangle =0.1$ source distribution. Note that different quantities are plotted on each panel, with a different y-axis scale on the first one. Left panel: Comparison of the correlation functions for intrinsic ellipticity correlations (in our model) and lensing induced correlations, as calculated from the power spectra in Fig. 1. Middle panel: Comparison with the theoretical results of CNPT. Plotted is the sum of the two correlation functions in each case. Curve is from Fig. 5 of CNPT for $a=0.24$. Note the similarity of our results, although the amplitude of our result is slightly larger. Right panel: Comparison with the observations of Brown et al. (2000). Plotted is the ellipticity variance as described in the text. The vertical line at $10'$ corresponds to a linear scale of roughly $1h^{-1}$Mpc at the mean source redshift, below which we do not expect our calculation to be relevant.