Systematic Analysis of 22 Microlensing Parallax Candidates

We attempt to identify all microlensing parallax events for which the parallax fit improves (delta)(chi)^2 > 100 relative to a standard microlensing model. We outline a procedure to identify three types of discrete degeneracies (including a new one that we dub the "ecliptic degeneracy") and find many new degenerate solutions in 16 previously published and six unpublished events. Only four events have one unique solution, and the other 18 events have a total of 44 solutions. Our sample includes three previously identified black hole (BH) candidates. We consider the newly discovered degenerate solutions and determine the relative likelihood that each of these is a BH. We find that the lens of event MACHO-99-BLG-22 is a strong BH candidate (78%), event MACHO96-BLG-5 is a marginal BH candidate (37%), and MACHO-98-BLG-6 is a weak BH candidate (2.2%). The lens of event OGLE-2003-BLG-84 may be a Jupiter-mass freefloating planet candidate based on a weak 3 (alpha)detection of finite-source effects. We find that event MACHO-179-A is a brown dwarf candidate within ~100 pc of the Sun, mostly due to its very small projected Einstein radius, ...E = 0.23 +- 0.05 AU. As expected, these microlensing parallax events are biased toward lenses that are heavier and closer than average. These events were examined for xallarap (or binary-source motion), which can mimic parallax. We find that 23% of these events are strongly affected by xallarap.