Kinematic effect in gravitational lensing by clusters of galaxies

TL;DR

This paper examines how the kinematic motion of galaxy clusters, including translation and rotation, affects gravitational lensing measurements, concluding that these effects are generally negligible but could, in principle, be detected with future technology.

Contribution

It provides a detailed analysis of the impact of cluster motion on gravitational lensing, quantifying the effects and discussing potential observational signatures.

Findings

Peculiar motion causes less than 0.3% error in mass estimates.

Spin effects are less than 0.04% for strong lensing and 0.5% for weak lensing in massive clusters.

Total kinematic effect on mass estimates is below 1%, negligible for current studies.

Abstract

Gravitational lensing provides an efficient tool for the investigation of matter structures, independent of the dynamical or hydrostatic equilibrium properties of the deflecting system. However, it depends on the kinematic status. In fact, either a translational motion or a coherent rotation of the mass distribution can affect the lensing properties. Here, light deflection by galaxy clusters in motion is considered. Even if gravitational lensing mass measurements of galaxy clusters are regarded as very reliable estimates, the kinematic effect should be considered. A typical peculiar motion with respect to the Hubble flow brings about a systematic error < 0.3%, independent of the mass of the cluster. On the other hand, the effect of the spin increases with the total mass. For cluster masses ~ 10^{15}M_{sun}, the effect of the gravitomagnetic term is < 0.04% on strong lensing estimates and < 0.5% in the weak lensing analyses. The total kinematic effect on the mass estimate is then < 1%, which is negligible in current statistical studies. In the weak lensing regime, the rotation imprints a typical angular modulation in the tangential shear distortion. This would allow in principle a detection of the gravitomagnetic field and a direct measurement of the angular velocity of the cluster but the required background source densities are well beyond current tecnological capabilities.