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We provide a purely dynamical global map of the non-axisymmetric structure of the Milky Way disk. For this, we exploit the information contained within the in-plane motions of disk stars from Gaia DR3 to adjust a model of the Galactic potential, including a detailed parametric form for the bar and spiral arms. We explore the parameter space of the non-axisymmetric components with the backward integration method, first adjusting the bar model to selected peaks of the stellar velocity distribution in the Solar neighbourhood, and then adjusting the amplitude, phase, pitch angle and pattern speed of spiral arms to the median radial velocity as a function of position within the disk. We check a posteriori that our solution also qualitatively reproduces various other features of the global non-axisymmetric phase-space distribution, including most of the moving groups and phase-space ridges despite those not being primarily used in the adjustment. This fiducial model has a bar with pattern speed $37~{\rm kms}^{-1}{\rm kpc}^{-1}$ and two spiral modes that are two-armed and three-armed respectively. The two-armed spiral mode has a $\sim 25~\%$ local contrast surface density, a low pattern speed of $13.1~{\rm kms}^{-1}{\rm kpc}^{-1}$, and matches the location of the Crux-Scutum, Local and Outer arm segments. The three-armed spiral mode has a $\sim 9~\%$ local contrast density, a slightly higher pattern speed of $16.4~{\rm kms}^{-1}{\rm kpc}^{-1}$, and matches the location of the Carina-Sagittarius and Perseus arm segments. The Galactic bar, with a higher pattern speed than both spiral modes, has recently disconnected from those two arms. The fiducial non-axisymmetric potential presented in this paper, reproducing most non-axisymmetric signatures detected in the stellar kinematics of the Milky Way disk, can henceforth be used to confidently integrate orbits within the Galactic plane., Comment: 18 pages, 13 figures, submitted to Astronomy and Astrophysics, comments welcome! Code available at https://github.com/yrkhalil/SPIBACK

It is well established that black holes reside in the central regions of virtually all types of known galaxies. Recent observational and numerical studies however challenge this picture, suggesting that intermediate-mass black holes in dwarf galaxies may be found on orbits far from the center. In particular, constant-density cores minimize orbital energy losses due to dynamical friction, and allow black holes to settle on stable off-center orbits. Using controlled simulations, we study the dynamics of off-center black holes in dwarf galaxies with such cores. We propose a new scenario to describe off-center mergers of massive black holes, starting with a Jacobi capture. We focus on initially circular and co-planar black hole orbits and explore a large parameter space of black hole masses and orbital parameters. We find that Jacobi captures are a complex and chaotic phenomenon that occurs in about 13% of cases in this simplified setup, and we quantify how the likelihood of capture depends on the simulation parameters. We note that this percentage is likely an upper limit of the general case. Nevertheless, we show that Jacobi captures in cored dwarf galaxies can facilitate the formation of off-center black hole binaries, and that this process is sufficiently common to have a substantial effect on black hole growth. While our setup only allows for temporary captures, we expect dissipative forces from baryons and post-Newtonian corrections to maintain the captures over time and to lead to the formation of stable binary systems. This motivates future studies of the effectiveness of such dissipative forces, within stripped nuclei or globular clusters, in forming stable bound systems., Comment: 16 pages, 17 figures and 2 tables. Accepted for publication in A&A

Placed slightly out of dynamical equilibrium, an isolated stellar system quickly returns towards a steady virialized state. We study this process of collisionless relaxation using the matrix method of linear response theory. We show that the full phase space distribution of the final virialized state can be recovered directly from the disequilibrium initial conditions, without the need to compute the time evolution of the system. This shortcut allows us to determine the final virialized configuration with minimal computational effort. Complementing this result, we develop tools to model the system's full time evolution in the linear approximation. In particular, we show that moments of the velocity distribution can be efficiently computed using a generalized moment matrix. We apply our linear methods to study the relaxation of energy-truncated Hernquist spheres, mimicking the tidal stripping of a cuspy dark matter subhalo. Comparison of our linear predictions against controlled, isolated $N$-body simulations shows agreement at per cent level for the parts of the system where a linear response to the perturbation is expected. We find that relaxation generates a tangential velocity anisotropy in the intermediate regions, despite the initial disequilibrium state having isotropic kinematics. Our results also strengthen the case for relaxation depleting the amplitude of the density cusp, without affecting its asymptotic slope. Finally, we compare the linear theory against $N$-body simulation of tidal stripping on a radial orbit, confirming that the theory still accurately predicts density and velocity dispersion profiles for most of the system., Comment: 19 pages, 5 figures. Published in ApJ (updated version after referee review)

Disc stars from the Gaia DR3 RVS catalogue are selected to explore the phase spiral as a function of position in the Galaxy. The data reveal a two-armed phase spiral pattern in the local $z-v_z$ plane inside the solar radius, which appears clearly when colour-coded by $\langle v_R \rangle (z,v_z)$: this is characteristic of a breathing mode that can in principle be produced by in-plane non-axisymmetric perturbations. We note the phase spiral pattern becomes single armed outside the solar radius. When a realistic analytic model with an axisymmetric background potential plus a steadily rotating bar and 2-armed spiral arms as perturbation is used to perform particle test integrations, the pseudo stars get a prominent spiral pattern in the $\langle v_R \rangle$ map in the $x-y$ plane. Additionally, clear breathing mode evidence at a few $\rm{kms}^{-1}$ level can be seen in the $\langle v_z \rangle$ map on the $x-z$ plane, confirming that such breathing modes are non-negligible in the joint presence of a bar and spiral arms. However, no phase-spiral is perceptible in the $(z, v_z)$ plane. When an initial vertical perturbation is added to all pseudo stars to carry out the simulation, the one-armed phase spirals can clearly be seen 500~Myr after the perturbation and gradually disappear inside-out. Finally, we show as a proof of concept how a toy model of a time-varying non-axisymmetric in-plane perturbation with varying amplitude and pattern speed can produce a strong two-armed phase-spiral. We conclude a time-varying strong internal perturbation together with an external vertical perturbation could perhaps explain the transition between the two-armed and one-armed phase-spirals around the Solar radius., Comment: 14 pages, 15 figures, accepted by MNRAS

We model the response of spherical, non-rotating Milky Way (MW) dark matter and stellar halos to the Large Magellanic Cloud (LMC) using the matrix method of linear response theory. Our computations reproduce the main features of the dark halo response from simulations. We show that these features can be well separated by a harmonic decomposition: the large scale over/underdensity in the halo (associated with its reflex motion) corresponds to the $\ell=1$ terms, and the local overdensity to the $\ell\geq2$ multipoles. Moreover, the dark halo response is largely dominated by the first order 'forcing' term, with little influence from self-gravity. This makes it difficult to constrain the underlying velocity distribution of the dark halo using the observed response of the stellar halo, but it allows us to investigate the response of stellar halo models with various velocity anisotropies: a tangential (respectively radial) halo produces a shallower (respectively stronger) response. We also show that only the local wake is responsible for these variations, the reflex motion being solely dependent on the MW potential. Therefore, we identify the structure (orientation and winding) of the in-plane quadrupolar ($m=2$) response as a potentially good probe of the stellar halo anisotropy. Finally, our method allows us to tentatively relate the wake strength and shape to resonant effects: the strong radial response could be associated with the inner Lindblad resonance, and the weak tangential one with corotation., Comment: 24 pages, 13 figures. Submitted to ApJ

Globular clusters contain a finite number of stars. As a result, they inevitably undergo secular evolution (`relaxation') causing their mean distribution function (DF) to evolve on long timescales. On one hand, this long-term evolution may be interpreted as driven by the accumulation of local deflections along each star's mean field trajectory -- so-called `non-resonant relaxation'. On the other hand, it can be thought of as driven by non-local, collectively dressed and resonant couplings between stellar orbits, a process termed `resonant relaxation'. In this paper we consider a model globular cluster represented by a spherical, isotropic isochrone DF, and compare in detail the predictions of both resonant and non-resonant relaxation theories against tailored direct $N$-body simulations. In the space of orbital actions (namely the radial action and total angular momentum), we find that both resonant and non-resonant theories predict the correct morphology for the secular evolution of the cluster's DF, although non-resonant theory over-estimates the amplitude of the relaxation rate by a factor ${\sim 2}$. We conclude that the secular relaxation of hot isotropic spherical clusters is not dominated by collectively amplified large-scale potential fluctuations, despite the existence of a strong ${\ell = 1}$ damped mode. Instead, collective amplification affects relaxation only marginally even on the largest scales. The predicted contributions to relaxation from smaller scale fluctuations are essentially the same from resonant and non-resonant theories., Comment: 26 pages, 14 figures, submitted to MNRAS

We study the bar instability in collisionless, rotating, anisotropic, stellar systems, using N-body simulations and also the matrix technique for calculation of modes with the perturbed collisionless Boltzmann equation. These methods are applied to spherical systems with an initial Plummer density distribution, but modified kinematically in two ways: the velocity distribution is tangentially anisotropic, using results of Dejonghe, and the system is set in rotation by reversing the velocities of a fraction of stars in various regions of phase space, a la Lynden-Bell. The aim of the N-body simulations is first to survey the parameter space, and, using those results, to identify regions of phase space (by radius and orbital inclination) which have the most important influence on the bar instability. The matrix method is then used to identify the resonant interactions in the system which have the greatest effect on the growth rate of a bar. Complementary series of N-body simulations examine these processes in relation to the evolving frequency distribution and the pattern speed. Finally, the results are synthesised with an existing theoretical framework, and used to consider the old question of constructing a stability criterion., Comment: 17 pages, 18 figures, accepted for publication in MNRAS

In the Gaia era, understanding the effects of the perturbations of the Galactic disc is of major importance in the context of dynamical modelling. In this theoretical paper we extend previous work in which, making use of the epicyclic approximation, the linearized Boltzmann equation had been used to explicitly compute, away from resonances, the perturbed distribution function of a Galactic thin-disc population in the presence of a non-axisymmetric perturbation of constant amplitude. Here we improve this theoretical framework in two distinct ways in the new code that we present. First, we use better estimates for the action-angle variables away from quasi-circular orbits, computed from the AGAMA software, and we present an efficient routine to numerically re-express any perturbing potential in these coordinates with a typical accuracy at the per cent level. The use of more accurate action estimates allows us to identify resonances such as the outer 1:1 bar resonance at higher azimuthal velocities than the outer Lindblad resonance (OLR), and to extend our previous theoretical results well above the Galactic plane, where we explicitly show how they differ from the epicyclic approximation. In particular, the displacement of resonances in velocity space as a function of height can in principle constrain the 3D structure of the Galactic potential. Second, we allow the perturbation to be time dependent, thereby allowing us to model the effect of transient spiral arms or a growing bar. The theoretical framework and tools presented here will be useful for a thorough analytical dynamical modelling of the complex velocity distribution of disc stars as measured by past and upcoming Gaia data releases., Comment: 16 pages, 15 figures, conclusions qualitatively unchanged, accepted for publication in Astronomy and Astrophysics

Rotation is ubiquitous in the Universe, and recent kinematic surveys have shown that early type galaxies and globular clusters are no exception. Yet the linear response of spheroidal rotating stellar systems has seldom been studied. This paper takes a step in this direction by considering the behaviour of spherically symmetric systems with differential rotation. Specifically, the stability of several sequences of Plummer spheres is investigated, in which the total angular momentum, as well as the degree and flavour of anisotropy in the velocity space are varied. To that end, the response matrix method is customised to spherical rotating equilibria. The shapes, pattern speeds and growth rates of the systems' unstable modes are computed. Detailed comparisons to appropriate N-body measurements are also presented. The marginal stability boundary is charted in the parameter space of velocity anisotropy and rotation rate. When rotation is introduced, two sequences of growing modes are identified corresponding to radially and tangentially-biased anisotropic spheres respectively. For radially anisotropic spheres, growing modes occur on two intersecting surfaces (in the parameter space of anisotropy and rotation), which correspond to fast and slow modes, depending on the net rotation rate. Generalised, approximate stability criteria are finally presented., Comment: 18 pages, 20 figures. Submitted to MNRAS

If the symmetry breaking responsible for axion dark matter production occurs during the radiation-dominated epoch in the early Universe, then this produces large amplitude perturbations that collapse into dense objects known as axion miniclusters. The characteristic minicluster mass, $M_0$, is set by the mass inside the horizon when axion oscillations begin. For the QCD axion $M_0\sim 10^{-10}M_\odot$, however for an axion-like particle $M_0$ can approach $M_\odot$ or higher. Using the Press-Schechter formalism we compute the mass function of halos formed by hierarchical structure formation from these seeds. We compute the concentrations and collapse times of these halos and show that they can grow to be as massive as $10^6M_0$. Within the halos, miniclusters likely remain tightly bound, and we compute their gravitational microlensing signal taking the fraction of axion dark matter collapsed into miniclusters, $f_{\rm MC}$, as a free parameter. A large value of $f_{\rm MC}$ severely weakens constraints on axion scenarios from direct detection experiments. We take into account the non-Gaussian distribution of sizes of miniclusters and determine how this effects the number of microlensing events. We develop the tools to consider microlensing by an extended mass function of non-point-like objects, and use microlensing data to place the first observational constraints on $f_{\rm MC}$. This opens a new window for the potential discovery of the axion., Comment: 27 pages, 23 figures, follow up paper to 1701.04787. v2 matches published version. Appendix added on non-Gaussian effects, discussion extended