The microlensing rate and distribution of free-floating planets towards the Galactic bulge

Context. Ground-based optical microlensing surveys have provided tantalising, if inconclusive, evidence for a significant population
of free-floating planets (FFPs). Both ground- and space-based facilities are being used and developed which will be able to probe the
distrubution of FFPs with much better sensitivity. It is also vital to develop a high-precision microlensing simulation framework to
evaluate the completeness of such surveys.
Aims. We present the first signal-to-noise limited calculations of the FFP microlensing rate using the Besançon Galactic model. The
microlensing distribution towards the Galactic centre is simulated for wide-area ground-based optical surveys (I band) such as OGLE
or MOA, a wide-area ground-based near-infrared survey (K band), and a targeted space-based near-infrared survey (H band) which
could be undertaken with Euclid or WFIRST.
Methods.We present a calculation framework for the computation of the optical and near-infrared microlensing rate and optical depth
for simulated stellar catalogues which are signal-to-noise limited, and take account of extinction, unresolved stellar background light,
and finite source size eects, which can be significant for FFPs.
Results.We find that the global ground-based I-band yield over a central 200 deg2 region covering the Galactic centre ranges from 20
Earth-mass FFPs year􀀀1 up to 3,500 year􀀀1 for Jupiter FFPs in the limit of 100% detection eciency, and almost an order of magnitude
larger for a K-band survey. For ground-based surveys we find that the inclusion of finite source and the unresolved background reveals
a mass-dependent variation in the spatial distribution of FFPs. For a targeted space-based H-band covering 2 deg2, the yield depends
on the target field but maximises close to the Galactic centre with around 76 Earth to 1,700 Jupiter FFPs per year. For near-IR
space-based surveys like Euclid or WFIRST the spatial distribution of FFPs is found to be largely insensitive to the FFP mass scale.