Clustering of cosmic string loops within a Milky-way like halo

Loops of cosmic string experience a recoil from anisotropic gravitational radiation, known as the rocket effect, which influences the extent to which they are captured by galaxies during structure formation. Analytical studies have reached different conclusions regarding loop capture in galaxies: early treatments argued for efficient capture, while later analyses incorporating the loop rocket force throughout halo formation found that capture efficiency is reduced and strongly dependent on loop size. In this work, we employ the N-body simulation code GADGET-4, introducing non-backreacting tracer particles subject to a constant recoil force to model cosmic string loops with the rocket effect. We simulate the formation of a Milky-Way-like halo from redshift $z=127$ to $z=0$, considering loop populations characterized by a range of length parameters $\xi$, inversely proportional to the rocket acceleration. We find that the number of captured loops exhibits a pronounced peak at $\xi_{\textrm{peak}}\simeq 12.5$, arising from the competition between rocket-driven ejection at small $\xi$ and the declining intrinsic loop abundance at large $\xi$. For fiducial string tensions, this corresponds to $\mathcal{O}(10^6)$ loops within the halo. We further find that loops with weak rocket forces closely trace the dark-matter distribution, while those subject to stronger recoil but still captured -- particularly the most abundant loops near $\xi_{\textrm{peak}}$ -- are preferentially concentrated toward the central regions of the halo.