We follow trajectories of recoiling supermassive black holes (SMBHs) in analytical and numerical models of galaxy merger remnants with masses of 10 11 M and 10 12 M . We construct various merger remnant galaxies in order to investigate how the central SMBH mass and the mass ratio of progenitor galaxies influence escape velocities of recoiling SMBHs. Our results show that static analytical models of major merger remnant galaxies overestimate the SMBHs escape velocities. During major mergers violent relaxation leads to the decrease of galaxy mass and lower potential at large remnant radii. This process is not depicted in static analytical potential but clearly seen in our numerical models. Thus, the evolving numerical model is a more realistic description of dynamical processes in galaxies with merging SMBHs. We find that SMBH escape velocities in numerical major merger remnant galaxies can be up to 25 per cent lower compared to those in analytical models. Consequently, SMBHs in numerical models generally reach greater galactocentric distances and spend more time on bound orbits outside of the galactic nuclei. Thus, numerical models predict a greater number of spatially-offset active galactic nuclei (AGNs).Once the separation between SMBHs becomes 10 −3 pc, gravitational wave radiation will efficiently extract angular momentum and energy from the binary system, causing

Galaxy flybys, interactions where two independent halos inter-penetrate but detach at a later time and do not merge, occur frequently at lower redshifts. These interactions can significantly impact the evolution of individual galaxies - from the mass loss and shape transformation to the emergence of tidal features and formation of morphological disc structures. The main focus of this paper is on the dark matter mass loss of the secondary, intruder galaxy, with the goal of determining a functional relationship between the impact parameter and dark matter mass loss. Series of N-body simulations of typical galaxy flybys (10:1 mass ratio) with differing impact parameters show that the dark matter halo leftover mass of the intruder galaxy follows a logarithmic growth law with impact parameter, regard- less of the way the total halo mass is estimated. The lost mass then, clearly, follows the exponential decay law. The stellar component stretches faster as the impact parameter decreases, following the exponential decay law with impact parameter. Functional dependence on impact parameter in all cases seems universal, but the fitting parameters are likely sensitive to the interaction parameters and initial conditions (e.g. the mass ratio of interacting galaxies, initial relative velocity of the intruder galaxy, interaction duration). While typical flybys, investigated here, could not be the sole culprit behind the formation of ultra-diffuse or dark matter deficient galaxies, they can still contribute significantly. Rare, atypical and stronger flybys are worth further exploring.

Close galaxy flybys, interactions during which two galaxies inter-penetrate, are frequent and can significantly affect the evolution of individual galaxies. Equal-mass flybys are extremely rare and almost exclusively distant, while frequent flybys have mass ratios q = 0.1 or lower, with a secondary galaxy penetrating deep into the primary. This can result in comparable strengths of interaction between the two classes of flybys and lead to essentially the same effects. To demonstrate this, emphasise and explore the role of the impact parameter further, we performed a series of N-body simulations of typical flybys with varying relative impact parameters b/Rvir,1 ranging from 0.114 to 0.272 of the virial radius of the primary galaxy. Two-armed spirals form during flybys, with radii of origin correlated with the impact parameter and strengths well approximated with an inverted S-curve. The impact parameter does not affect the shape of induced spirals, and the lifetimes of a distinguished spiral structure appear to be constant, TLF ∼ 2 Gyr. Bars, with strengths anti-correlated with the impact parameter, form after the encounter is over in simulations with b/Rvir,1 ≤ 0.178 and interaction strengths S ≥ 0.076, but they are short-lived except for the stronger interactions with S ≥ 0.129. We showcase an occurrence of multiple structures (ring-like, double bar) that survives for an exceptionally long time in one of the simulations. Effects on the pre-existing bar instability, that develops much later, are diverse: from an acceleration of bar formation, little to no effect, to even bar suppression. There is no uniform correlation between these effects and the impact parameter, as they are secondary effects, happening later in a post-flyby stage. Classical bulges are resilient to flyby interactions, while dark matter halos can significantly spin up in the amount anti-correlated with the impact parameter. There is an offset angle between the angular momentum vector of the dark matter halo and that of a disc, and it correlates linearly with the impact parameter. Thus, flybys remain an important pathway for structural evolution within galaxies in the local Universe.