Intrinsic and Extrinsic Galaxy Alignment

TL;DR

The paper demonstrates that intrinsic alignments of galaxies, driven by tidal fields and halo angular momenta, can generate ellipticity correlations that mimic weak-lensing shear. It develops analytic formalisms for both halo-shape– and tidal-torque–driven alignments, deriving intrinsic ellipticity power spectra and comparing them to the weak-lensing signal, with explicit dependence on redshift distribution and a smoothing scale. The work proposes practical discriminants—redshift information, ellipticity cuts, density cross-correlations, cluster environments, and morphology—to separate intrinsic from extrinsic signals. It concludes that intrinsic alignments are likely subdominant for deep surveys but non-negligible for precision cosmology and a valuable probe of galaxy formation and tidal fields. The findings stress the need to include intrinsic correlations in future weak-lensing analyses and offer a framework to extract information about structure and galaxy formation from these alignments.

Abstract

We show with analytic models that the assumption of uncorrelated intrinsic ellipticities of target sources that is usually made in searches for weak gravitational lensing due to large-scale mass inhomogeneities (``field lensing'') is unwarranted. If the orientation of the galaxy image is determined either by the angular momentum or the shape of the halo in which it forms, then the image should be aligned preferentially with the component of the tidal gravitational field perpendicular to the line of sight. Long-range correlations in the tidal field will thus lead to long-range ellipticity-ellipticity correlations that mimic the shear correlations due to weak gravitational lensing. We calculate the ellipticity-ellipticity correlation expected if halo shapes determine the observed galaxy shape, and we discuss uncertainties (which are still considerable) in the predicted amplitude of this correlation. The ellipticity-ellipticity correlation induced by angular momenta should be smaller. We consider several methods for discriminating between the weak-lensing (extrinsic) and intrinsic correlations, including the use of redshift information. An ellipticity--tidal-field correlation also implies the existence of an alignment of images of galaxies near clusters. Although the intrinsic alignment may complicate the interpretation of field-lensing results, it is inherently interesting as it may shed light on galaxy formation as well as on structure formation.

Figures (3)

• Figure 1: The two panels show how a tidal field can either elongate or compress a galactic halo. The arrows labeled "g" indicate the size and direction of the gravitational field. In (a) the tidal field stretches the halo, and in (b) the tidal field compresses the halo.
• Figure 2: The angular shear power spectra for weak lensing (dashed curves) and for intrinsic alignments (solid curves) for a high-redshift source population with median redshift $z_m\sim1$ (heavier curves) and a lower-redshift source population with $z_m\sim0.3$ (lighter curves). The upper and lower dotted curves show the intrinsic power spectrum that would be obtained (for the high-redshift population) using a smoothing radius of $R=2\,h^{-1}$ Mpc or $R=0.5\,h^{-1}$ Mpc, respectively, instead of the nominal value of $R=1\,h^{-1}$. The mean source ellipticity is assumed here to be $\bar{\epsilon}=0.15$, and the amplitude of the intrinsic power spectrum scales with $\bar{\epsilon}^2$.
• Figure 3: The upper panel shows a distant mass acting upon a prolate halo and causing it to start spinning as shown. The torque vanishes when $\theta=0,\pi/2$, cf., Eq. \ref{['eqn:orientation']}. The lower panel shows that baryons in the potential well will fall in to form a disk lying in the plane of the figure. When this disk is viewed from the direction perpendicular to the figure, there will be no induced ellipticity; when viewed from the plane of the figure, the ellipticity will be $\sim 1$. If the mass is replaced by a void, the sense of rotation is reversed, but the shape remains unchanged. Averaging over all viewing directions gives a non-zero mean elongation of the galaxy image along the projected direction of the distant mass and this will be correlated among neighboring galaxies. More generally, tidal gravitational fields will be induced by the large-scale distribution of mass (rather than by a single large mass), and long-range correlations in these tidal fields will induce long-range correlations in the ellipticities of widely separated galaxies.