arXiv 0809.39002008-09-23astro-phgr-qc

关于引力透镜的像差

On aberration in gravitational lensing

M. Sereno

备注：: 8 pages, 2 figures, in press on PRD
发表信息：: Phys.Rev.D78:083003,2008
DOI：: 10.1103/PhysRevD.78.083003

摘要：

已知偏转器和观察者之间的相对平移运动影响引力透镜。在本文中，得到了一个透镜方程来描述这种影响的实际透镜可观测量。结果可以很容易地用光线的像差来解释。径向和横向运动与相对论速度被认为是。首先考虑光子在透镜的静止坐标系史瓦西时空中的测地线运动，然后考虑在移动观察者坐标系中的光线探测，从而导出透镜方程。由于横向运动，图像在观察者的天球中发生位移和失真，而沿着视线的径向速度导致透镜质量的有效重新缩放。爱因斯坦环被扭曲成椭圆，而源平面中的焦散仍然是点状的。无论是零横向运动还是线性速度级，临界曲线仍是一个半径相对于静态情况作了（1+z_d）倍修正的圆，z_d是偏转器的相对论多普勒频移。从观测的角度来看，地球的轨道运动可能会导致对银河系中心超大质量黑洞的微弧秒量级的透镜效应的潜在可观测修正。在宇宙学尺度上，星系团的切向速度在弱透镜区会导致背景星系像的典型弯曲，但未来的测量似乎太具有挑战性。

英文摘要：

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 spacetime of the lens, and, then, light-ray detection in the moving observer's frame. Due to 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 re-scaling of the lens mass. The Einstein ring is distorted to an ellipse whereas the caustics in the source plane are still point-like. 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+z_d) with respect to the static case, z_d 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 microarcsec in lensing towards the super-massive black hole at the Galactic center. On a cosmological scale, tangential peculiar velocities of 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 much challenging.

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