Where Have All the Little Red Dots Gone? Supermassive Black Hole Binary Dynamics and its Impact on Galaxy Properties

Recent James Webb Space Telescope observations have revealed a peculiar class of galaxies at redshifts $z \gtrsim 6$, characterized by extremely high central stellar densities and overmassive central supermassive black holes (SMBHs), "little red dots" (LRDs). A critical question remains: If LRDs were common at high redshifts, how would they evolve into local elliptical galaxies with significantly lower central densities? To address this, we performed direct $N$-body simulations of LRD mergers, focusing on the coevolution of host galaxies and central SMBHs. We track the complete evolution of SMBH binaries into the three-body hardening and gravitational-wave (GW) emission phase. Our results demonstrate that during galaxy mergers, the central SMBHs can eject a substantial amount of mass from the galactic core via the three-body slingshot effect, leading to a decrease in central stellar surface density by an order of magnitude. Additionally, GW recoil can further contribute in making the galaxy centers less dense and more in alignment with low-redshift quiescent galaxies. This transformation occurs on a relatively short timescale of a few $\sim$100 Myr, implying that LRDs can evolve into lower-redshift elliptical galaxies by $z<4$. The timescales for our SMBH mergers vary between 100 Myr and 800 Myr, depending on the initial orbital parameters of the merging galaxies and the mass ratio of the SMBHs. Our findings provide a plausible mechanism for the transformation of LRDs into elliptical galaxies while highlighting the efficiency of SMBH mergers in such high-density environments, which plays a crucial role in SMBH growth.