OSCULATING VERSUS INTERSECTING CIRCLES IN SPACE-BASED MICROLENS PARALLAX DEGENERACIES

I investigate the origin of arc degeneracies in satellite microlens parallax ${\pi}_E$ measurements with only late time data, e.g., t > $t_0+t_E$ as seen from the satellite. I show that these are due to partial overlap of a series of osculating, exactly circular, degeneracies in the ${\pi}_E$ plane, each from a single measurement. In events with somewhat earlier data, these long arcs break up into two arclets, or (with even earlier data) two points, because these earlier measurements give rise to intersecting rather than osculating circles. The two arclets (or points) then constitute one pair of degeneracies in the well-known four-fold degeneracy of space-based microlens parallax. Using this framework of intersecting circles, I show that next-generation microlens satellite experiments could yield good ${\pi}_E$ determinations with only about five measurements per event, i.e., about 30 observations per day to monitor 1500 events per year. This could plausibly be done with a small (hence cheap, in the spirit of Gould & Yee 2012) satellite telescope, e.g., 20 cm.