Math @ Duke

Publications [#244003] of Arlie O. Petters
Papers Published
 Petters, AO, On relativistic corrections to microlensing effects: Applications to the Galactic black hole,
Monthly Notices of the Royal Astronomical Society, vol. 338 no. 2
(2003),
pp. 457464, Oxford University Press (OUP) [0208500], [doi]
(last updated on 2019/04/21)
Abstract: The standard treatment of gravitational lensing by a point mass lens M is based on a weakfield deflection angle α̂ = 2/xo, where X0 = r0c/2GM with r0 being the distance of closest approach to the mass of a lensed light ray. It was shown that for a point mass lens, the total magnification and image centroid shift of a point source remain unchanged by relativistic corrections of second order in 1/X 0. This paper considers these issues analytically, taking into account the relativistic images, under three assumptions A1A3, for a Schwarzschild black hole lens with a background point and extended sources having arbitrary surface brightness profiles. The assumptions are A1, the source is close to the line of sight and lies in the asymptotically flat region outside the black hole lens; A2, the observerlens and lenssource distances are significantly greater than the impact parameters of the lensed light rays; and A3, the distance of closest approach of any light ray that does not wind around the black hole on its travel from the source to the observer, lies in the weakfield regime outside the black hole. We apply our results to the Galactic black hole for lensing scenarios where A1A3 hold. We show that a single factor characterizes the full relativistic correction to the weakfield image centroid and magnification. As the lenssource distance increases, the relativistic correction factor strictly decreases. In particular, we find that for point and extended sources approximately 10 pc behind the black hole, which is a distance significantly outside the tidal disruption radius of a Sunlike source, the relativistic correction factor is minuscule, of the order of 10 14. Therefore, for standard lensing configurations, any detectable relativistic corrections to microlensing by the Galactic black hole will most likely have to come from sources significantly closer to the black hole.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

