Detection of weak gravitational lensing distortions of distant galaxies by cosmic dark matter at large scales

TL;DR

The detection of cosmic shear on angular scales of up to half a degree is reported using 145,000 galaxies and along three separate lines of sight and it is found that the dark matter is distributed in a manner consistent with either an open universe, or a flat universe that is dominated by a cosmological constant.

Abstract

Most of the matter in the universe is not luminous and can be observed directly only through its gravitational effect. An emerging technique called weak gravitational lensing uses background galaxies to reveal the foreground dark matter distribution on large scales. Light from very distant galaxies travels to us through many intervening overdensities which gravitationally distort their apparent shapes. The observed ellipticity pattern of these distant galaxies thus encodes information about the large-scale structure of the universe, but attempts to measure this effect have been inconclusive due to systematic errors. We report the first detection of this ``cosmic shear'' using 145,000 background galaxies to reveal the dark matter distribution on angular scales up to half a degree in three separate lines of sight. The observed angular dependence of this effect is consistent with that predicted by two leading cosmological models, providing new and independent support for these models.

Figures (5)

• Figure 1: The distorted universe. Light rays from distant galaxies travel a tortuous path through a universe filled with clustering dark mass. Every bend in the path of a bundle of light from a distant galaxy stretches its apparent image. The orientation of the resulting elliptical images of galaxies contains information on the size and mass of the gravitational lenses distributed over the light path. The figure shows a schematic view of weak gravitational lensing by large-scale mass structure: distant galaxy orientation is correlated on scales characteristic of the lensing dark matter structures. Light bundles from two distant galaxies which are projected closely together on the sky follow similar paths and undergo similar gravitational deflections by intervening dark matter concentrations. Apparent orientations of distant galaxies are thus correlated on angular scales of less than a few degrees. The larger the mass in the gravitational deflectors, the larger the faint galaxy ellipticity correlations on a given angular scale. These ellipticity correlations of distant galaxies reveal the statistics of the large-scale dark mater distribution in the intervening universe -- a key diagnostic of the underlying cosmology.
• Figure 2: Making stars round. Foregound stars at many positions in the field of view are used to correct for position-dependent systematic ellipticity error. Convolution with a position-dependent kernel with ellipticity components equal and opposite to those of the stars, reduces this systematic error everywhere in the field. Here we illustrate this technique with one particularly bad frame of raw data from one of the four CCDs in our mosaic. Each panel represents stars at their positions in the field as a line encoding the ellipticity and position angle, or as a point if the ellipticity is less than one percent. The left panel is the raw data; the stars in a more typical frame have only half the ellipticity of those shown here, or about 5%. The middle panel shows the stellar shapes in the same single image after convolution with the rounding kernel. The stars are vastly less out of round, but local correlations still exist. The right panel shows the final shapes of stars in the same region of sky, after combining ten shifted exposures, convolving the combined image, and measuring the shapes in more than one filter. Many of the local correlations in the middle panel have disappeared. The density of stars is greater due to better identification of stars in the combined image. The final field size is roughly ten times larger in area than this patch, and contains about 1000 such stars in most of our mid-latitude fields. This figure is for illustration purposes only; Figure 4 contains a quantitative assessment of the final level of systematic error.
• Figure 3: Lens-induced galaxy orientation correlations. Pairs of background galaxies, separated on the sky by some angle, can have their relative orientations affected by weak lensing. The ellipticity components of any galaxy $i$ with respect to galaxy $j$ can be visualised as $e_1 = \epsilon \cos(2\theta)$ and $e_2 = \epsilon \sin(2\theta)$, where $\epsilon$ is the scalar ellipticity and $\theta$ is the position angle with respect to a line joining the two galaxies. Ellipticity correlation functions are computed from the products of the ellipticity components of millions of such pairs, as a function of angular separation between pairs. A variety of relative orientations are illustrated along with their contributions to the correlations. Gravitational lensing leaves its signature on these correlations in several ways. First, the amplitude of the correlations scales with the amount of foreground mass. Second, the correlations are large at small separations and drop to nearly zero at large separations in a particular way. The bottom (red) case on the left cannot be caused by gravitational lensing, so that $\langle e_1e_1 \rangle$ (averaged over many pairs) is always positive in the absence of systematic error. But lensing can cause the $e_2$ product to have either sign, as shown, and $\langle e_2e_2 \rangle$ should become negative at a separation characteristic of the underlying cosmology. Third, correlations between $e_1$ and $e_2$ (not shown here) are not induced by gravitational lensing, so that any putative measurement of a weak lensing effect should vanish in the cross correlation $\langle e_1 e_2\rangle + \langle e_2 e_1\rangle$.
• Figure 4: Detection of ellipticity correlations. The upper panels show the measured ellipticity correlations as a function of angle for three independent fields covering a total of 1.5 square degrees ($\xi_1$ at left and $\xi_2$ at right). Markers have been slightly offset horizontally for clarity. From left to right in each bin are fields at 11$^h$38$^m$, -12$^\circ$33$^\prime$, 23$^h$48$^m$, +00$^\circ$57$^\prime$, and 04$^h$29$^m$, -36$^\circ$18$^\prime$ (J2000). In each field, roughly 45,000 faint galaxies passed all the filters and significance tests, from an initial catalogue of about 150,000 objects. Errors shown are 68% confidence intervals determined from 200 bootstrap-resamplings of the galaxy catalogues. The lower panels show the mean of the ellipticity correlation functions over the three fields (black), with 1$\sigma$ errors derived from the variance between fields. The behavior as a function of angle matches that expected from weak gravitational lensing by large-scale structure. The lower panels also contain several null tests of systematic error. The cross-correlation of the galaxies $\xi_3$ should vanish in the absence of systematic error, and in fact is everywhere consistent with zero (red). The ellipticity correlations of stars (blue) are everywhere consistent with zero except in the innermost bin of $\xi_1$. The effect of nonzero stellar correlations on the galaxy correlations is illustrated by the star-galaxy correlation (green), which is very close to zero in this bin. An additional test of systematics, a search for preferential alignment of galaxies with the CCD axes, is also null. Though galaxy ellipticity correlations continue to rise at smaller angles, the smaller number of galaxy pairs makes the measurement noisier, there are few closely-spaced stars to assess systematic error, and the theoretical interpretation on small scales is difficult.
• Figure 5: Comparison of ellipticity correlations with predictions. We plot our measurements with 1$\sigma$ errors on a logarithmic scale along with theoretical predictions based on various models for a cold dark matter universe. The top theoretical curve is for the old standard cold dark matter model (blue) and the center and lower curves are for a universe with a cosmological constant ($\Lambda$CDM, solid green) and an open universe (orange), respectively. The dotted green curve shows the effect of decreasing the mode of the background galaxy redshift distribution, $2z_0$, from 1.0 to 0.6 for one model ($\Lambda$CDM). The errors shown are derived from the variance among three fields; the statistical errors in each field are larger than any cosmic variance present. The data from Figure 4 have been multiplied by a correction factor of 20 here, to compensate for the ellipticity dilution factor of 4.5 described in the text, which is squared in the correlation functions. The measurements are consistent with $\Lambda$CDM and an open universe at the $3\sigma$ level despite the visual impression given by $\xi_2$, which is due to the logarithmic axes. Standard cold dark matter is inconsistent with $\xi_1$ at many sigma. This first measurement of ellipticity correlations due to cosmic shear over half-degree angular scales is in agreement with a variety of other evidence in ruling out standard cold dark matter. Weak lens observations of larger fields and more distant galaxies will be able to clearly distinguish between the remaining models, or suggest the need for a new model.