Dynamical friction is typically regarded as a secular process, in which the subject (“perturber”) evolves very slowly (secular approximation) and has been introduced to the host over a long time (adiabatic approximation). These assumptions imply that dynamical friction arises from the LBK torque with nonzero contribution only from purely resonant orbits. However, dynamical friction is only of astrophysical interest if its timescale is shorter than the age of the universe. In this paper we therefore relax the adiabatic and secular approximations. We first derive a generalized LBK torque, which reduces to the LBK torque in the adiabatic limit, and show that it gives rise to transient oscillations due to nonresonant orbits that slowly damp out, giving way to the LBK torque. This is analogous to how a forced, damped oscillator undergoes transients before settling to a steady state, except that here the damping is due to phase mixing rather than dissipation. Next, we present a self-consistent treatment that properly accounts for time dependence of the perturber potential and circular frequency (memory effect), which we use to examine orbital decay in a cored galaxy. We find that the memory effect results in a phase of accelerated, super-Chandrasekhar friction before the perturber stalls at a critical radius, R crit, in the core (core stalling). Inside R crit the torque flips sign, giving rise to dynamical buoyancy, which counteracts friction and causes the perturber to stall. This phenomenology is consistent with N-body simulations, but has thus far eluded proper explanation.

Galactic disks are highly responsive systems that often undergo external perturbations and subsequent collisionless equilibration, predominantly via phase mixing. We use linear perturbation theory to study the response of infinite isothermal slab analogs of disks to perturbations with diverse spatiotemporal characteristics. Without self-gravity of the response, the dominant Fourier modes that get excited in a disk are the bending and breathing modes, which, due to vertical phase mixing, trigger local phase-space spirals that are one- and two-armed, respectively. We demonstrate how the lateral streaming motion of slab stars causes phase spirals to damp out over time. The ratio of the perturbation timescale (τ P) to the local, vertical oscillation time (τ z ) ultimately decides which of the two modes is excited. Faster, more impulsive (τ P < τ z ) and slower, more adiabatic (τ P > τ z ) perturbations excite stronger breathing and bending modes, respectively, although the response to very slow perturbations is exponentially suppressed. For encounters with satellite galaxies, this translates to more distant and more perpendicular encounters triggering stronger bending modes. We compute the direct response of the Milky Way disk to several of its satellite galaxies and find that recent encounters with all of them excite bending modes in the solar neighborhood. The encounter with Sagittarius triggers a response that is at least 1–2 orders of magnitude larger than that due to any other satellite, including the Large Magellanic Cloud. We briefly discuss how ignoring the presence of a dark matter halo and the self-gravity of the response might impact our conclusions.

We study an integrable Hamiltonian reducible to free fermions which is subjected to an imperfect periodic driving with the amplitude of driving (or kicking) randomly chosen from a binary distribution like a coin-toss problem. The randomness present in the driving protocol destabilises the periodic steady state, reached in the limit of perfectly periodic driving, leading to a monotonic rise of the stroboscopic residual energy with the number of periods (N ). We establish that a minimal deviation from the perfectly periodic driving would always result in a bounded heating up of the system with N to an asymptotic finite value. Remarkably, exploiting the completely uncorrelated nature of the randomness and the knowledge of the stroboscopic Floquet operator in the perfectly periodic situation, we provide an exact analytical formalism to derive the disorder averaged expectation value of the residual energy through a disorder operator. This formalism not only leads to an immense numerical simplification, but also enables us to derive an exact analytical form for the residual energy in the asymptotic limit which is universal, i.e, independent of the bias of coin-toss and the protocol chosen. Furthermore, this formalism clearly establishes the nature of the monotonic growth of the residual energy at intermediate N while clearly revealing the possible non-universal behaviour of the same. arXiv:1705.03662v2 [cond-mat.stat-mech]

Strong lensing of active galactic nuclei in the radio can result in razor-thin arcs, with a thickness of less than a milli-arcsecond, if observed at the resolution achievable with very long baseline interferometry (VLBI). Such razor-thin arcs provide a unique window on the coarseness of the matter distribution between source and observer. In this paper, we investigate to what extent such razor-thin arcs can constrain the number density and mass function of 'free-floating' black holes, defined as black holes that do not, or no longer, reside at the centre of a galaxy. These can be either primordial in origin or arise as by-products of the evolution of super-massive black holes in galactic nuclei. When sufficiently close to the line of sight, free-floating black holes cause kink-like distortions in the arcs, which are detectable by eye in the VLBI images as long as the black hole mass exceeds ∼ 1000 Solar masses. Using a crude estimate for the detectability of such distortions, we analytically compute constraints on the matter density of free-floating black holes resulting from null-detections of distortions along a realistic, fiducial arc, and find them to be comparable to those from quasar milli-lensing. We also use predictions from a large hydrodynamical simulation for the demographics of free-floating black holes that are not primordial in origin, and show that their predicted mass density is roughly four orders of magnitude below the constraints achievable with a single razor-thin arc.

Impulsive encounters between astrophysical objects are usually treated using the distant tide approximation (DTA) for which the impact parameter, b, is assumed to be significantly larger than the characteristic radii of the subject, rS, and the perturber, rP. The perturber potential is then expanded as a multipole series and truncated at the quadrupole term. When the perturber is more extended than the subject, this standard approach can be extended to the case where rS ≪ b &lt; rP. However, for encounters with b of order rS or smaller, the DTA typically overpredicts the impulse, Δv, and hence the internal energy change of the subject, ΔEint. This is unfortunate, as these close encounters are the most interesting, potentially leading to tidal capture, mass stripping, or tidal disruption. Another drawback of the DTA is that ΔEint is proportional to the moment of inertia, which diverges unless the subject is truncated or has a density profile that falls off faster than r−5. To overcome these shortcomings, this paper presents a fully general, non-perturbative treatment of impulsive encounters which is valid for any impact parameter, and not hampered by divergence issues, thereby negating the necessity to truncate the subject. We present analytical expressions for Δv for a variety of perturber profiles, apply our formalism to both straight-path encounters and eccentric orbits, and discuss the mass-loss due to tidal shocks in gravitational encounters between equal-mass galaxies.