Abstract
Free-floating objects (FFOs) in interstellar space$-$rogue planets, brown dwarfs, and large asteroids that are not gravitationally bound to any star$-$are expected to be ubiquitous throughout the Milky Way. Recent microlensing surveys have discovered several free-floating planets that are not bound to any known stellar systems. Additionally, three interstellar objects, namely 1I/'Oumuamua, 2I/Borisov, and 3I/ATLAS, have been detected passing through our solar system on hyperbolic trajectories. In this work, we search for FFOs on hyperbolic orbits that pass near millisecond pulsars (MSPs), where their gravitational influence can induce detectable perturbations in pulse arrival times. Using the NANOGrav 15-year narrowband dataset, which contains high-precision timing data for 68 MSPs, we conduct a search for such hyperbolic scattering events between FFOs and pulsars. Although no statistically significant events were detected, this non-detection enables us to place upper limits on the number density of FFOs as a function of their mass within our local region of the Galaxy. For example, the upper limit on the number density for Jupiter-mass FFOs ($\sim 10^{-2.5} - 10^{-3.5}~M_{\odot}$) obtained from different pulsars ranges from $5.25\times10^{6}~\text{pc}^{-3}$ to $5.37\times10^{9}~\text{pc}^{-3}$, while the upper limit calculated by combining results from all the pulsars is $6.03\times10^{5}~\text{pc}^{-3}$. These results represent the first constraints on FFO population derived from pulsar timing data.