Detecting luminous gravitational microlenses using spectroscopy

We propose a new method to detect the gravitational lenses in the ongoing microlensing experiments using medium and high resolution spectroscopy (λ/∆λ > 6000). Since the radial velocity of the lens and lensed source typically differs by ∼ 100 km s−1, the spectral lines from the lens and source will be shifted relative to each other by (1− 2)Å in the optical. We simulate realistic composite spectra assuming different spectral types for the lens and source and study the lens detectability as a function of the signal-to-noise ratio, spectral resolution and lens-to-source light ratio. We show that it is possible to measure the difference in radial velocity from an unequivocal signature in the difference of crossand auto-correlation functions calculated from two spectra obtained at different magnifications. If the lens is brighter than 10% (∆mv ∼ 2.5) of the unmagnified source we find that a spectral resolution of λ/∆λ ∼ 6000 and a signal-to-noise of 50 (at magnification maximum) are sufficient to determine the relative radial velocity of the lens. At λ/∆λ = 40000, the spectral resolution of high resolution spectrographs of 8-10m class telescopes, the lens could even be detected at a brightness of ∼ 3% (∆mv ∼ 4.0) of the source. Radial velocities higher than 50 km s−1 can be measured with an accuracy of a few km s−1. Practical difficulties and observation strategies are also discussed.