Roman FFP Revolution: Two, Three, Many Plutos

Abstract: Roman microlensing stands at a crossroads between its originally charted path of cataloging a population of cool planets that has subsequently become well-measured down to super-Earths, and the path of free-floating planets (FFPs), which did not exist when Roman was chosen in 2010, but by now promises revolutionary insights into planet formation and evolution via their possible connection to a spectrum of objects spanning 18 decades in mass. Until now, it was not even realized that the 2 paths are in conflict: Roman strategy was optimized for bound-planet detections, and FFPs were considered only in the context of what could be learned about them given this strategy. We derive a simple equation that mathematically expresses this conflict and explains why the current approach severely depresses detection of 2 of the 5 decades of potential FFP masses, i.e., exactly the two decades, $M_{\rm Pluto}< M <2\,M_{\rm Mars}$, that would tie terrestrial planets to the proto-planetary material out of which they formed. FFPs can be either truly free floating or can be bound in "Wide", "Kuiper", and "Oort" orbits, whose separate identification will allow further insight into planet formation. In the (low-mass) limit that the source radius is much bigger than the Einstein radius, $\theta_\gg\theta_{\rm E}$, the number of significantly magnified points on the FFP light curve is $N=2\Gamma\theta_\sqrt{1-z^2}/\mu$ --> 3.0, when normalized to the adopted Roman cadence $\Gamma=4/$hr, and to source radius $\theta_=0.3\,\mu$as, lens-source proper motion $\mu=6\,$mas/yr, and source impact parameter $z=0.5$, which are all typical values. By contrast $N=6$ are needed for an FFP detection. Thus, unless $\Gamma$ is doubled, FFP detection will be driven into the (large-$\theta_$, small-$\mu$) corner of parameter space, reducing the detections by a net factor of 2 and cutting off the lowest-mass FFPs.