Do Primordial Black Hole Clusters Survive the Galaxy? Collisional Disruption and Microlensing Implications
We study the collisional disruption of primordial black hole (PBH) clusters in the Milky Way halo. Encounters between clusters strip PBHs into a diffuse component, and the fraction of PBH mass in this smooth component along a sightline determines how microlensing constraints divide between isolated compact objects and extended cluster lenses. We combine an analytic NFW-based collision-rate model, $72$ direct N-body binary collision simulations that calibrate the escaped-mass fraction as a universal function $\tilde f(\tilde v,\tilde b)$ of the relative velocity and impact parameter in units of the cluster velocity scale and half-mass radius, and cosmological N-body simulations of a Milky Way-like halo ($M_{200}\simeq 8\times10^{11}\,M_\odot$, $c_{200}\simeq 11$) that record the encounter history of every cluster from $z=9$ to $z=0$. For $10^6$ and $10^7\,M_\odot$ clusters -- bracketing the maximum mass in the Carr et al.\ formation scenario -- the local encounter rate at the Solar circle is $2.9\times10^{-3}$ and $1.2\times10^{-2}\,\rm Myr^{-1}$, consistent with the simulations to within ${\sim}40\%$. Because the peak-disruption velocity of Carr-radius clusters ($12$--$20\,\rm km\,s^{-1}$) lies far below typical halo encounter velocities, disruption accumulates through many weak encounters, most effectively during the early, cold phases of halo assembly: half of the total mass loss is inflicted before $z\approx2$, a channel that $z=0$ analytic estimates miss entirely. The surviving mass fraction at the Solar circle is $S\simeq0.50$ ($10^6\,M_\odot$) and $0.04$ ($10^7\,M_\odot$), and the DM-mass-weighted smooth fraction toward the LMC and SMC is $0.49$ and $0.92$, respectively. Cluster-cluster disruption is thus substantial over the Galaxy's lifetime, and reanalyses of microlensing surveys must account for the radially varying smooth fraction $f_{\rm sm}(r)$ derived here.