Predictions for the Detection and Characterization of a Population of Free-floating Planets with K2 Campaign 9

K2 Campaign 9 (K2C9) offers the first chance to measure parallaxes and masses of members of the large population of free-floating planets (FFPs) that has previously been inferred from measurements of the rate of short-timescale microlensing events. Using detailed simulations of the nominal campaign (ignoring the loss of events due to Kepler’s emergency mode) and ground-based microlensing surveys, we predict the number of events that can be detected if there is a population of 1 {M}_{Jupiter} FFPs matching current observational constraints. Using a Fisher matrix analysis, we also estimate the number of detections for which it will be possible to measure the microlensing parallax, angular Einstein radius, and FFP mass. We predict that between 1.4 and 7.9 events will be detected in the K2 data, depending on the noise floor that can be reached, but with the optimistic scenario being more likely. For nearly all of these, it will be possible to either measure the parallax or constrain it to be probabilistically consistent with only planetary-mass lenses. We expect that for between 0.42 and 0.98 events it will be possible to gain a complete solution and measure the FFP mass. For the emergency-mode truncated campaign, these numbers are reduced by 20 percent. We argue that when combined with prompt high-resolution imaging of a larger sample of short-timescale events, K2C9 will conclusively determine if the putative FFP population is indeed both planetary and free-floating.