Contribution of White Dwarf Formation Kicks to the Free-Floating Planet Population

Free-Floating Planets (FFPs) are a distinct class of exoplanets that do not orbit stars but are nevertheless found to be very common. A variety of formation mechanisms have been proposed as their origin, such as "star-like" direct collapse from gas and dust clouds or ejection from young planetary systems via dynamical instabilities. Here, another possible formation scenario is explored that would instead apply for old planetary systems, in the form of White Dwarf (WD) formation kicks. Observations over recent years have shown that WDs experience a mild recoil kick during their formation from Asymptotic Giant Branch (AGB) stars. Here we show that, while WD formation kicks directly unbind only $\sim1\%$ of the known planet and exoplanet population, they drive dynamical instabilities in $\gtrsim40\%$ of known long-period multi-planet systems, likely leading to planet ejection and FFP generation in roughly half of all such systems. We also show that FFPs generated via WD kicks will additionally have undergone significant and long-lasting heating via their host stars' enhanced AGB luminosities. Given the low ejection velocities due to the weakness of the WD kicks, such warmed FFPs can thus be associated with their former host stars for several Myr after formation. Therefore, WD formation kicks contribute a distinct, observationally identifiable FFP sub-population comprising a few percent of the Galaxy's FFPs, relevant for the results of the upcoming {\it Roman} Galactic Exoplanet Survey.