Metal Pollution of Low-Mass Population III Stars through Accretion of Interstellar Objects like `Oumuamua

We calculate accretion mass of interstellar objects (ISOs) like Oumuamua onto low-mass population III stars (Pop.~III survivors), and estimate surface pollution of Pop.~III survivors. An ISO number density estimated from the discovery of Oumuamua is so high ($\sim 0.2$~au${}^{-3}$) that Pop.~III survivors have chances at colliding with ISOs $\gtrsim {10}^5$ times per $1$~Gyr. `Oumuamua itself would be sublimated near Pop.~III survivors, since it has small size, $\sim 100$~m. However, ISOs with size $\gtrsim 3$~km would reach the Pop.~III survivor surfaces. Supposing an ISO cumulative number density with size larger than $D$ is $n\propto D^{-\alpha }$, Pop.~III survivors can accrete ISO mass $\gtrsim {10}^{-16}{M}_{\odot }$, or ISO iron mass $\gtrsim {10}^{-17}{M}_{\odot }$, if $\alpha <4$. This iron mass is larger than the accretion mass of interstellar medium (ISM) by several orders of magnitude. Taking into account material mixing in a convection zone of Pop.~III survivors, we obtain their surface pollution is typically [Fe/H] $\lesssim -8$ in most cases, however the surface pollution of Pop.~III survivors with $0.8M_{\odot }$ can be [Fe/H] $\gtrsim -6$ because of the very shallow convective layer. If we apply to Pop.III survivors located at the Galactocentric distance of 8 kpc, the dependence of the metal pollustion is as follows. If $\alpha >4$, Pop.~III survivors have no chance at colliding with ISOs with $D\gtrsim 3$~km, and keep metal-free. If $3<\alpha <4$, Pop.~III survivors would be most polluted by ISOs up to [Fe/H] $\sim -7$. If $\alpha <3$ up to $D\sim 10$~km, Pop.~III survivors could hide in metal-poor stars so far discovered. Pop.~III survivors would be more polluted with decreasing the Galactocentric distance. Although the metal pollution depends on $\alpha$ and the Galactocentric distance, we first show the importance of ISOs for the metal pollution of Pop.~III survivors.