  With the recent discoveries of interstellar objects `Oumuamua and Borisov
traversing the solar system, understanding the dynamics of interstellar objects
is more pressing than ever. These detections have highlighted the possibility
that captured interstellar material could be trapped in our solar system. The
first step in rigorously investigating this question is to calculate a capture
cross section for interstellar objects as a function of hyperbolic excess
velocity, which can be convolved with any velocity dispersion to compute a
capture rate (Napier et. al. 2021). Although the cross section provides the
first step toward calculating the mass of alien rocks residing in our solar
system, we also need to know the lifetime of captured objects. We use an
ensemble of N-body simulations to characterize a dynamical lifetime for
captured interstellar objects and determines the fraction of surviving objects
as a function of time (since capture). We also illuminate the primary effects
driving their secular evolution. Finally, we use the resulting dynamical
lifetime function to estimate the current inventory of captured interstellar
material in the solar system. We find that capture from the field yields a
steady state mass of only $\sim 10^{-13} M_{\oplus}$, whereas the mass
remaining from capture events in the birth cluster is roughly $10^{-9}
M_{\oplus}$.
