Astrometric Image Centroid Displacements due to Gravitational Microlensing by the Ellis Wormhole

Abstract

Continuing work initiated in an earlier publication (Abe, ApJ, 725 (2010) 787), we study the gravitational microlensing effects of the Ellis wormhole in the weak-field limit. First, we find a suitable coordinate transformation, such that the lens equation and analytic expressions of the lensed image positions can become much simpler than the previous ones. Second, we prove that two images always appear for the weak-field lens by the Ellis wormhole. By using these analytic results, we discuss astrometric image centroid displacements due to gravitational microlensing by the Ellis wormhole. The astrometric image centroid trajectory by the Ellis wormhole is different from the standard one by a spherical lensing object that is expressed by the Schwarzschild metric. The anomalous shift of the image centroid by the Ellis wormhole lens is smaller than that by the Schwarzschild lens, provided that the impact parameter and the Einstein ring radius are the same. Therefore, the lensed image centroid by the Ellis wormhole moves slower. Such a difference, though it is very small, will be in principle applicable for detecting or constraining the Ellis wormhole by using future high-precision astrometry observations. In particular, the image centroid position gives us an additional information, so that the parameter degeneracy existing in photometric microlensing can be partially broken. The anomalous shift reaches the order of a few micro arcsec. if our galaxy hosts a wormhole with throat radius larger than $10^5$ km. When the source moves tangentially to the Einstein ring for instance, the maximum position shift of the image centroid by the Ellis wormhole is 0.18 normalized by the Einstein ring radius. For the same source trajectory, the maximum difference between the centroid displacement by the Ellis wormhole lens and that by the Schwarzschild one is -0.16 in the units of the Einstein radius.