Spectrophotometric resolution of stellar surfaces with microlensing

Microlensing is a powerful tool for studying stellar atmospheres, because as the source crosses regions of formally infinite magnification (caustics), the surface of the star is resolved, thereby allowing one to measure the radial intensity profile both photometrically and spectroscopically. However, caustic crossing events are relatively rare and monitoring them requires intensive application of telescope resources. It is therefore essential that the observational parameters needed to accurately measure the intensity profile are quantified. We calculate the expected errors in the recovered radial intensity profile as a function of the unlensed flux, source radius, spatial resolution of the recovered intensity profile, and caustic crossing time for the two principle types of caustics: point-mass and binary lenses. We demonstrate that for both cases there exist simple scaling relations between these parameters and the resultant errors. We find that the error as a function of the spatial resolution of the recovered profile, parameterized by the number of radial bins, increases as N-R(3/2), considerably faster than the naive N-R(1/2) expectation. Finally, we discuss the relative advantages of binary caustic-crossing events and point-lens events. Binary events are more common, easier to plan for, and provide more homogeneous information about the stellar atmosphere; however, a subclass of point-mass events with low impact parameters can provide dramatically more information provided that they can be recognized in time to initiate observations.