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Aberration in gravitational lensing


Sereno, M (2008). Aberration in gravitational lensing. Physical Review D, 78(8):083003.

Abstract

It is known that a relative translational motion between the deflector and the observer affects gravitational lensing. In this paper, a lens equation is obtained to describe such effects on actual lensing observables. Results can be easily interpreted in terms of aberration of light rays. Both radial and transverse motions with relativistic velocities are considered. The lens equation is derived by first considering geodesic motion of photons in the rest-frame Schwarzschild space-time of the lens, and, then, light-ray detection in the moving observer's frame. Because of the transverse motion images are displaced and distorted in the observer's celestial sphere, whereas the radial velocity along the line of sight causes an effective rescaling of the lens mass. The Einstein ring is distorted to an ellipse whereas the caustics in the source plane are still pointlike. Either for null transverse motion or up to linear order in velocities, the critical curve is still a circle with its radius corrected by a factor (1+zd) with respect to the static case, zd being the relativistic Doppler shift of the deflector. From the observational point of view, the orbital motion of the Earth can cause potentially observable corrections of the order of the µarcsec in lensing towards the supermassive black hole at the Galactic center. On a cosmological scale, tangential peculiar velocities of a cluster of galaxies bring about a typical flexion in images of background galaxies in the weak lensing regime but future measurements seem to be too challenging.

It is known that a relative translational motion between the deflector and the observer affects gravitational lensing. In this paper, a lens equation is obtained to describe such effects on actual lensing observables. Results can be easily interpreted in terms of aberration of light rays. Both radial and transverse motions with relativistic velocities are considered. The lens equation is derived by first considering geodesic motion of photons in the rest-frame Schwarzschild space-time of the lens, and, then, light-ray detection in the moving observer's frame. Because of the transverse motion images are displaced and distorted in the observer's celestial sphere, whereas the radial velocity along the line of sight causes an effective rescaling of the lens mass. The Einstein ring is distorted to an ellipse whereas the caustics in the source plane are still pointlike. Either for null transverse motion or up to linear order in velocities, the critical curve is still a circle with its radius corrected by a factor (1+zd) with respect to the static case, zd being the relativistic Doppler shift of the deflector. From the observational point of view, the orbital motion of the Earth can cause potentially observable corrections of the order of the µarcsec in lensing towards the supermassive black hole at the Galactic center. On a cosmological scale, tangential peculiar velocities of a cluster of galaxies bring about a typical flexion in images of background galaxies in the weak lensing regime but future measurements seem to be too challenging.

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3 citations in Web of Science®
4 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute for Computational Science
Dewey Decimal Classification:530 Physics
Language:English
Date:October 2008
Deposited On:06 Mar 2009 09:57
Last Modified:05 Apr 2016 13:06
Publisher:American Physical Society
ISSN:1550-2368
Publisher DOI:10.1103/PhysRevD.78.083003
Related URLs:http://arxiv.org/abs/0809.3900
Permanent URL: http://doi.org/10.5167/uzh-16581

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