Post-Newtonian effects on the stability of the triangular solution in the three-body problem for general masses

Continuing work initiated in earlier publications [Ichita, Yamada and Asada, Phys. Rev. D {bf 83}, 084026 (2011); Yamada and Asada, Phys. Rev. D {bf 86}, 124029 (2012)], we examine the post-Newtonian (PN) effects on the stability of the triangular solution in the relativistic three-body problem for general masses. For three finite masses, a condition for stability of the triangular solution is obtained at the first post-Newtonian (1PN) order, and it recovers previous results for the PN restricted three-body problem when one mass goes to zero. The stability regions still exist even at the 1PN order, though the PN triangular configuration for general masses is less stable than the PN restricted three-body case as well as the Newtonian one.

Improving the Moment Approach for Astrometric Binaries: Possible Application to Cygnus X-1

A moment approach for orbit determinations of astrometric binaries from astrometric observations alone has been recently studied for a low signal-to-noise ratio (Iwama et al. 2013, PASJ, 65, 2). With avoiding a direct use of the time-consuming Kepler equation, temporal information is taken into account to increase the accuracy of statistical moments. As numerical tests, 100 realizations are done and the mean and the standard deviation are also evaluated. For a semi-major axis, the difference between the mean of the recovered values and the true value decreases to less than a tenth in the case of $10000$ observed points. Therefore, the present moment approach works better than the previous one for the orbit determinations when one has a number of the observed points. The present approach is thus applicable to Cyg X-1.

Demagnifying gravitational lenses toward hunting a clue of exotic matter and energy

We examine a gravitational lens model inspired by modified gravity theories and exotic matter and energy. We study an asymptotically flat, static, and spherically symmetric spacetime that is modified in such a way that the spacetime metric depends on the inverse distance to the power of positive $n$ in the weak-field approximation. It is shown analytically and numerically that there is a lower limit on the source angular displacement from the lens object to get demagnification. Demagnifying gravitational lenses could appear, provided the source position $beta$ and the power $n$ satisfy $beta > 2/(n+1)$ in the units of the Einstein ring radius under a large-$n$ approximation. Unusually, the total amplification of the lensed images, though they are caused by the gravitational pull, could be less than unity. Therefore, time-symmetric demagnification parts in numerical light curves by gravitational microlensing (F.Abe, Astrophys. J. 725, 787, 2010) may be evidence of an Ellis wormhole (being an example of traversable wormholes), but they do not always prove it. Such a gravitational demagnification of the light might be used for hunting a clue of exotic matter and energy that are described by an equation of state more general than the Ellis wormhole case. Numerical calculations for the $n=3$ and 10 cases show maximally $sim 10$ and $sim 60$ percent depletion of the light, when the source position is $beta sim 1.1$ and $beta sim 0.7$, respectively.

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

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.