Antilensing: The Bright Side of Voids

More than half of the volume of our Universe is occupied by cosmic voids. The lensing magnification effect from those underdense regions is generally thought to give a small dimming contribution: objects on the far side of a void are supposed to be observed as slightly smaller than if the void were not there, which together with conservation of surface brightness implies net reduction in photons received. This is predicted by the usual weak lensing integral of the density contrast along the line of sight. We show that this standard effect is swamped at low redshifts by a relativistic Doppler term that is typically neglected. Contrary to the usual expectation, objects on the far side of a void are brighter than they would be otherwise. Thus the local dynamics of matter in and near the void is crucial and is only captured by the full relativistic lensing convergence. There are also significant nonlinear corrections to the relativistic linear theory, which we show actually underpredicts the effect. We use exact solutions to estimate that these can be more than 20% for deep voids. This remains an important source of systematic errors for weak lensing density reconstruction in galaxy surveys and for supernovae observations, and may be the cause of the reported extra scatter of field supernovae located on the edge of voids compared to those in clusters.

Figure 1

Change in distance modulus due to a 50 Mpc radius void versus observed redshift, based on relativistic convergence (3) (solid line), usual weak lensing formula (2) (dotted line), Doppler term (7) (dot-dashed line), exact model (dashed line) (top panels). There is a brightening for objects on the far side of the void, whereas the usual weak lensing predicts a dimming of much smaller magnitude (see insets). The left-hand panel shows the effect for a small void well in the linear regime, and the right-hand panel shows a very deep void where nonlinear contributions increase the effect. The bottom panels show the void density contrasts. (Asterisk marks the far edge of the void.)

Figure 2

Difference in magnitude (top panels) and density contrast (bottom panels) between the background $\Lambda \mathrm{CDM}$ model and the exact void models. We show results for an observer looking through spherical compensated (top), quasispherical (middle, shown for both horizontal—blue dashed—and vertical—red dotted—lines of sight), and cylindrical (bottom) voids. The insets show the equatorial density contrast, with each square 160 Mpc across. In the spherical case we also show the uncompensated case (red dotted line) discussed in Fig. 1. The standard weak lensing prediction is shown by the solid green line in each case, which predicts the wrong sign and amplitude of the effect.

Figure 3

(Left) Accuracy of the relativistic lensing approximation compared to the exact LTB solution for the magnification near the far edge of a spherical compensated void ($\delta <0$) and a unvirialized overdense lump ($\delta >0$). (Right) Comparison of the full linear approximation to the exact result: maximum differences of $>20\%$ are seen for deep—but nevertheless realistic—voids. Voids or lumps of radius 100, 50, 25, and 10 Mpc are used.