Monitoring lensed starlight emitted close to the Galactic centre

Abstract

We describe the feasibility of detecting the gravitational deflection of light emitted by stars moving around the massive object at the Galactic centre. Light reaching us from an orbiting star can pass closer to the large central mass than the star itself, so the central potential is in principle constrained to a smaller radius by lensing rather than by orbit fitting. A mass of 4.3 × 106M⊙ causes a 0.1-2 mas deflection in the apparent position of orbiting stars in a cone of diameter 10° as seen from the central mass. The distance to the centre of the Galaxy is uniquely constrained from such measurements because lensing deflections depend on the ratio r g/R0 of the Schwarzschild radius to the distance to the black hole, R0, whereas the ratio rg/R03 is obtained by fitting the shapes of the orbits. Deflection measurements are complimentary to observations of radial velocities of stars which constrain the ratio rg/R0 in the framework of Newtonian gravity.