Searching for Planets During Predicted Mesolensing Events: I. Theory, and the Case of VB 10

The first predicted mesolensing event is likely to occur during the winter or spring of 2011/2012. The lens is the nearby, low-mass high-proper-motion star VB 10, and the source a distant field star much bluer than VB 10 and 1.5 magnitudes dimmer in B band. If VB 10 has planets, they could produce lensing signatures that enhance the detectability of the stellar-lens event and/or produce distinct planet-lens signatures. Here, we study the lensing signatures associated with planets orbiting nearby high-proper-motion stars to provide a guide for observers for this event and future predicted ones. We illustrate our case by considering hypothetical planets orbiting VB 10 with separations ranging from 2 R⊙ to tens of AU. We find the following. (1) Wide-orbit planets can be detected for all distances of closest approach between the foreground and background stars, potentially producing independent events long before and/or after the closest approach. (2) Close-orbit planets can be detected for intermediate distances of closest approach (. 50 mas for VB 10), producing quasiperiodic signatures that may occur days or weeks before and after the stellar-lens event. (3) Planets in the so-called “zone for resonant lensing” can significantly increase the magnification when the distance of closest approach is small (. 20 mas for VB 10), making the stellar-lens event easier to detect while simultaneously providing evidence for planets. We show that an observing plan in which VB 10 is targeted several times per night at each of several longitudes will either detect planets, or else place weak limits on possible parameters. We expect VB 10 to be the first of a continuing line of predicted events. An observing program for this event can pave the way for future programs and discoveries. This is discussed in more detail in Paper II.