Despite its remarkable success on large scales, the standard ΛCDM paradigm faces persistent small-scale challenges that have motivated alternative models for the dark sector. Self-interacting dark matter (SIDM) offers a compelling possibility, in which dark matter particles can scatter off each other. Stellar bars are a ubiquitous feature of disk galaxies across cosmic time. Bars are dynamically coupled to their host galaxy's dark matter halo, and therefore their properties provide a powerful probe of the nature and distribution of dark matter. In this paper, we use idealized, high-resolution N-body simulations and analytic calculations based on kinetic theory to study bar formation and evolution in disk galaxies embedded in SIDM halos. We find that compared with collisionless CDM, SIDM produces bars that form earlier and grow to larger amplitudes, even for modest self-interaction cross sections. In several cases, disks that remain stable in CDM, including kinematically hot and dark-matter-dominated disks, develop strong bars in SIDM. This accelerated bar growth occurs because self-interactions broaden the bar-halo resonances and enhance angular momentum transfer from the stellar disk to the halo. We explicitly show that this phenomenon is not related to core formation in SIDM halos. At late times, gravothermal core collapse can raise the central dark matter density enough to weaken or dissolve the bar. These results suggest that the abundance, strength, and redshift evolution of barred galaxies offer a promising observational route to constraining dark matter self-interactions, particularly in light of the growing sample of high-redshift bars revealed by JWST.

The Milky Way is known to contain a stellar bar, as are a significant fraction of disc galaxies across the universe. Our understanding of bar evolution, both theoretically and through analysis of simulations indicates that bars both grow in amplitude and slow down over time through interaction and angular momentum exchange with the galaxy's dark matter halo. Understanding the physical mechanisms underlying this coupling requires modelling of the structural deformations to the potential that are mutually induced between components. In this work, we use basis function expansion (BFE) in combination with multichannel singular spectral analysis (mSSA) as a non-parametric analysis tool to illustrate the coupling between the bar and the dark halo in a single high-resolution isolated barred disc galaxy simulation. We demonstrate the power of mSSA to extract and quantify explicitly coupled dynamical modes, determining growth rates, pattern speeds and phase lags for different stages of evolution of the stellar bar and the dark matter response. BFE and mSSA together grant us the ability to explore the importance and physical mechanisms of bar-halo coupling, and other dynamically coupled structures across a wide range of dynamical environments.

The vertical phase-space spirals in the Milky Way are clear evidence of disequilibrium. However, they are challenging to study because phase mixing signals evolve under the influence of many different dynamical processes and can be driven by many sources of disequilibrium. We characterize phase spirals in two simulations-one test particle and one N-body-with basis function expansions, using these to derive winding times (Tfit). We find that phase spirals in the test-particle simulation wind up as expected from pure phase mixing theory while those in the self-consistent simulation do not. Specifically, in the N-body simulation we find that (i) the onset of winding is delayed, (ii) the winding rate is slowed, and (iii) the rate of winding oscillates with time. The extent of these effects depends on the azimuthal action J phi of the phase-spiral region. We build some physical intuition for these effects through 1D toy models, which follow a group of comoving stars traveling through several different evolving potentials. We find that phase spiral winding can be delayed until the group no longer moves coherently with the midplane of the (perturbed) potential and oscillates with time as the group experiences (e.g., a breathing mode traveling through the disk). The modifications to winding are strongest in the inner Galaxy where the disk potential dominates. We conclude that in the Milky Way, all calculations of the winding time should be interpreted as lower limits and that the most trustworthy winding times are likely in the outer disk.

The SMC orbits within the LMC's dark matter (DM) halo in a similar to 1:10 mass-ratio encounter. The LMC-Milky Way (MW) interaction is also similar to 1:10, and is expected to perturb the MW's DM distribution. However, no framework exists to quantify the severity of these perturbations over multiple pericenters and longer periods of time, such as the LMC-SMC interaction history. We construct basis function expansions of a high-resolution N-body simulation of the Clouds interacting in isolation and analyze their DM distributions at an epoch approximating the time of their infall to the MW. Our goal is to quantify how the Clouds distort each other's DM distributions without the MW. The LMC halo's response to the SMC includes a similar to 20 kpc long dynamical friction wake and the displacement of the LMC's density center during each SMC pericenter, which produces two overdensities in the LMC halo (at similar to 60 and similar to 100 kpc) at MW infall. The SMC's tidal radius at infall is just similar to 4 kpc, at which point the SMC has lost two-thirds of its initial DM mass to the LMC. The distortions to the Clouds' halos produce a highly asymmetric acceleration field. Accurate orbit integration in the LMC-SMC system must account for the time-dependent shapes of both halos. The SMC-induced perturbations in the LMC DM halo resemble the MW-LMC system, and persist over multiple SMC pericenters. We conclude that 1:10 satellite-host encounters induce characteristic deformations in both DM halos across host-mass scales, with implications for merger rates and tests of DM models.

Dark-matter (DM) models predict that satellite galaxies distort their host's DM halo. As such, both the satellite and the distorted halo can perturb the host's stellar disk. The LMC-SMC system is a nearby ∼1:10 mass-ratio binary with a well-constrained orbit and well-characterized LMC disk perturbations. Hence, the system offers unique opportunities to test DM theory, provided the impact of halo torques on the LMC's disk can be characterized along with the SMC's torques. We use halo Basis Function Expansions (BFEs) of an N-body simulation of an isolated LMC-SMC-like interaction to quantify the time-dependent torques exerted on the LMC's disk by the SMC and the LMC's DM halo. We find that the halo torques arise from the quadrupole halo distortion, and the inner (R<6 kpc) LMC disk warps are the most promising probe of this quadrupole. For the first time, we construct a BFE to quantify the LMC's disk perturbations resulting from the SMC and halo torques. We find that the LMC's disk is significantly perturbed prior to the Clouds' Milky Way infall, possessing warps with a mean vertical extent of ∼1 kpc. Finally, we apply multi-channel singular spectral analysis (mSSA) to the time-series of the disk BFE coefficients, halo quadrupole, and the LMC-SMC orbit. mSSA successfully separates the temporal evolution of the LMC warps into components correlated with the halo versus the SMC. Our framework identifies correlated evolution between the LMC's halo distortions and the LMC's disk perturbations, enabling the Clouds to be a precision laboratory for DM physics.

We explore the stability of isotropic, spherical, self-gravitating systems with a double power-law density profile. Systems with rapid transitions between the inner and outer slopes are shown to have an inflection in their isotropic distribution function (DF), where d f / d E > 0, thereby violating Antonov’s stability criterion. Using high-resolution N -body simulations, we show that the resulting instability causes the growth of a rotating dipole (or l = 1) mode. The inflection feature in the DF responds to the mode by promoting its growth, driving the instability. The growth of the dipole results in a torque that dislodges the original cusp from its central location and sets it in motion throughout the central region. Once the mode goes nonlinear, it saturates, together with the cusp, into a long-lived soliton (the l = 1 equivalent of a bar in a disk galaxy), which maintains its sloshing motion through the center of the halo along a slowly precessing, elliptical orbit. Concurrently, the soliton traps increasingly more particles into libration, and the exchange of energy and angular momentum with these trapped particles works toward eroding the bump in the distribution function. We point out similarities between the dipole mode and the bump-on-tail instability in electrostatic plasmas, and highlight a potential connection with core stalling and dynamical buoyancy in systems with a cored density profile. Finally, we discuss the astrophysical implications in terms of lopsidedness and off-center nuclei in galaxies.

We present the public release of EXP, a basis function expansion C++ library and Python package for running N-body galactic simulations and dynamical discovery. EXP grew out of the need for methodology that seamlessly connects theoretical descriptions of dynamics, N-body simulations, and compact descriptions of observed data. EXP decomposes a galaxy into multiple bases for a variety of scales and geometries and is thus able to represent arbitrarily complex simulations with many components (e.g., disk, bulge, dark matter halo, satellites). pyEXP provides a full Python interface to the EXP C++ libraries. Example workflows based on previously published work are available and distributed as accompanying examples and tutorials. The examples and tutorials flatten the learning curve for adopting basis function expansion tools to generate and analyze the significance of coefficients and discover dynamical relationships using time series analysis. The current release uses a powerful, non-parametric technique for time series analysis that decomposes basis function expansion coefficients into interpretable components without assuming a specific model structure. This enables the automated discovery of dynamical signals from simulations. We provide a full online manual hosted by Read the Docs.

The coupling between the dark matter (DM) halo and the stellar disc is a key factor in galactic evolution. While the interaction between structures like the Galactic bar and DM halos has been explored (e.g. slowing down of the bar due to dynamical friction), the effect of spiral arms on the DM halo distribution has received limited attention. We analyze a suite of simulations featuring strong stellar spiral arms, ranging in complexity from test-particle models to fully cosmological hydrodynamical simulations. Using Fourier transforms, we characterize the phase and amplitude of the stellar spirals at different times and radii. We then apply the same methodology to DM particles near the stellar disc and compare trends in Fourier coefficients and phases between the two components. We detect a clear spiral arm signal in the DM distribution, correlated with the stellar spirals, confirming the reaction of the halo. The strength of the DM spirals consistently measures around 10\% of that of the stellar spiral arms. In the $N$-body simulation, the DM spiral persistently trails the stellar spiral arm by approximately $10^\circ$. A strong spiral signal of a few km\,s$^{-1}$ appears in the radial, azimuthal, and vertical velocities of halo particles, distinct from the stellar kinematic signature. In a test-particle simulation with an analytical spiral potential (omitting self-gravity), we reproduce a similar density and kinematic response, showing that the test-particle halo responds in the same way as the $N$-body halo. Finally, we also find the rest of the simulations, indicating that the dynamical signatures of the forced response in the DM halo are independent of the dynamical origin of the stellar spiral arms. We reveal the ubiquitous presence of DM spiral arms in Milky Way-like galaxies, driven by a forced response to the stellar spiral potential. (ABR)

The large-scale morphology of Milky Way (MW)–mass dark matter halos is shaped by two key processes: filamentary accretion from the cosmic web and interactions with massive satellites. Disentangling their contributions is essential for understanding galaxy evolution and constructing accurate mass models of the MW. We analyze the time-dependent structure of MW-mass halos from zoomed cosmological-hydrodynamical simulations by decomposing their mass distribution into spherical harmonic expansions. We find that the dipole and quadrupole moments dominate the gravitational power spectrum, encoding key information about the halo’s shape and its interaction with the cosmic environment. While the dipole reflects transient perturbations from infalling satellites and damps on dynamical timescales, the quadrupole—linked to the halo’s triaxiality—is a persistent feature. We show that the quadrupole’s orientation aligns with the largest filaments, imprinting a long-lived memory on the halo’s morphology even in its inner regions (∼30 kpc). At the virial radius, the quadrupole distortion can reach 1–2 times the spherical density, highlighting the importance of environment in shaping MW-mass halos. Using multichannel singular spectrum analysis, we successfully disentangle the effects of satellite mergers and filamentary accretion on quadrupole. We find that, compared to isolated MW–LMC simulations that typically use a spherical halo, the LMC-mass satellite induces a quadrupolar response that is an order of magnitude larger in our cosmological halo. This highlights the need for models that incorporate the MW’s asymmetry and time evolution, with direct consequences for observable structures such as disk warps, the LMC-induced wake, and stellar tracers—particularly in the era of precision astrometry.

The distribution of dark matter in the Milky Way (MW) is expected to exhibit a large-scale dynamical response to the recent infall of the LMC. This event produces a dynamical friction wake and shifts the MW's halo density center. The structure of this response encodes information about the LMC- MW mass ratio, the LMC's orbit, the MW halo's pre-infall structure and could provide constraints on dark matter physics. To extract this information, a method to separate these effects and recover the initial shape of the MW's halo is required. Here, we use basis function expansions to analyze the halo response in eighteen simulations of MW-LMC-like interactions from the MWest cosmological, dark-matter-only zoom-in simulations. The results show that mergers similar to the LMC consistently generate a significant dipole and a secondary quadrupole response in the halo. The dipole arises from the host density center displacement and halo distortions, and its amplitude scales as the square of the MW-LMC mass ratio, peaking 0.2-0.7 Gyr after the LMC's pericenter. The quadrupole's strength depends primarily on the original axis ratios of the host halo, though contributions from the dynamical friction wake cause it to peak less than 0.3 Gyr before pericenter. Future measurements of both the dipole and quadrupole imprints of the LMC's passage in the density of the MW's stellar halo should be able to disentangle these effects and provide insight into the initial structure of the MW's halo, the MW's response, and the mass of the LMC.

The dynamics of star forming gas can be affected by many physical processes, such as turbulence, gravity, supernova explosions, and magnetic fields. In this paper, we investigate several nearby star forming regions (Orion, Upper Sco, Taurus, and Perseus) for kinematic imprints of these influences on the newly formed stars. Using Gaia DR3 astrometry and APOGEE DR17 radial velocities, we compute first-order velocity structure functions (VSFs) of young stars in galactic Cartesian coordinates in both 6D (3D positions and 3D velocities) and 4D (3D positions and each 1D velocity) to identify signatures of turbulence and anisotropic motion. We also construct 3D and 1D radial velocity profiles to identify coherent expansion trends, and compare stellar proper motions to plane-of-sky magnetic field orientations in Taurus and Perseus. We find that the VSFs are mildly anisotropic, with slightly different amplitudes, slopes, or features in different directions in several groups, but in general, they are all consistent with Larson's Relation at intermediate length scales, especially in less compact groups. In several cases, the VSFs exhibit features suggestive of local energy injection from supernovae. Radial velocity profiles reveal clear anisotropic expansion in multiple groups, with the most extreme cases corresponding to those with the most anisotropic VSFs. In Perseus, we find that the motions of young stars are preferentially perpendicular to the local magnetic field. We find multiple, overlapping causes in each group for the observed kinematics. Our findings support that young stars remember more than just the turbulent state of their natal clouds.

I selectively review the various dynamical scenarios that have been explored to date, especially those that illustrate the conundrums. In short, although the existence of asymmetries are convincing enough, the interpretation remains ambiguous. A coherent picture for the Milky Way asymmetries is an obvious lack; each mechanism is considered independently of all others. With this motivation, I will present a nonstandard picture which has the potential to explain some of the signatures and a few of the conundrums. Moreover, it illustrates global features are dynamically connected and I believe that it is time to revisit the Milky Way in this context. Finally, I will end with a wish list for future work—both observational and theoretical—designed to help us pin down the Milky Way.

Many disc galaxies host galactic bars, which exert time-dependent, non-axisymmetric forces that can alter the orbits of stars. There should be both angle and radius dependences in the resulting radial rearrangement of stars ('radial mixing') due to a bar; we present here novel results and trends through analysis of the joint impact of these factors. We use an N-body simulation to investigate the changes in the radial locations of star particles in a disc after a bar forms by quantifying the change in orbital radii in a series of annuli at different times post bar formation. We find that the bar induces both azimuth angle- and radius-dependent trends in the median distance that stars have travelled to enter a given annulus. Angle-dependent trends are present at all radii we consider, and the radius-dependent trends roughly divide the disc into three 'zones'. In the inner zone, stars generally originated at larger radii and their orbits evolved inwards. Stars in the outer zone likely originated at smaller radii and their orbits evolved outwards. In the intermediate zone, there is no net inwards or outwards evolution of orbits. We adopt a simple toy model of a radius-dependent initial metallicity gradient and discuss recent observational evidence for angle-dependent stellar metallicity variations in the Milky Way in the context of this model. We briefly comment on the possibility of using observed angle-dependent metallicity trends to learn about the initial metallicity gradient(s) and the radial rearrangement that occurred in the disc.

We develop a linear perturbative formalism to compute the response of an inhomogeneous stellar disk embedded in a nonresponsive dark matter (DM) halo to various perturbations like bars, spiral arms, and encounters with satellite galaxies. Without self-gravity to reinforce it, the response of a Fourier mode phase mixes away due to an intrinsic spread in the vertical (Ω z ), radial (Ω r ), and azimuthal (Ω ϕ ) frequencies, triggering local phase-space spirals. The detailed galactic potential dictates the shape of phase spirals: phase mixing occurs more slowly and thus phase spirals are more loosely wound in the outer disk and in the presence of an ambient DM halo. Collisional diffusion due to scattering of stars by structures like giant molecular clouds causes superexponential damping of the phase spiral amplitude. The z–v z phase spiral is one-armed (two-armed) for vertically antisymmetric (symmetric) bending (breathing) modes. Only transient perturbations with timescales (τ P) comparable to the vertical oscillation period (τ z ∼ 1/Ω z ) can trigger vertical phase spirals. Each (n, l, m) mode of the response to impulsive (τ P < τ = 1/(nΩ z + lΩ r + mΩ ϕ )) perturbations is power-law (∼τ P/τ) suppressed, but that to adiabatic (τ P > τ) perturbations is exponentially weak ( ∼exp−τP/τα ) except for resonant (τ → ∞ ) modes. Slower (τ P > τ z ) perturbations, e.g., distant encounters with satellite galaxies, induce stronger bending modes. Sagittarius (Sgr) dominates the solar neighborhood response of the Milky Way (MW) disk to satellite encounters. Thus, if the Gaia phase spiral was triggered by a MW satellite, Sgr is the leading contender. However, the survival of the phase spiral against collisional damping necessitates an impact ∼0.6–0.7 Gyr ago.

Studying coupling between different galactic components is a challenging problem in galactic dynamics. Using basis function expansions (BFEs) and multichannel singular spectrum analysis (mSSA) as a means of dynamical data mining, we discover evidence for two multi-component disc-halo dipole modes in a Milky-Way-like simulated galaxy. One of the modes grows throughout the simulation, while the other decays throughout the simulation. The multi-component disc-halo modes are driven primarily by the halo, and have implications for the structural evolution of galaxies, including observations of lopsidedness and other non-axisymmetric structure. In our simulation, the modes create surface density features up to 10 per cent relative to the equilibrium model stellar disc. While the simulated galaxy was constructed to be in equilibrium, BFE+mSSA also uncovered evidence of persistent periodic signals incited by aphysical initial conditions disequilibrium, including rings and weak two-armed spirals, both at the 1 per cent level. The method is sensitive to distinct evolutionary features at and even below the 1 per cent level of surface density variation. The use of mSSA produced clean signals for both modes and disequilibrium, efficiently removing variance owing to estimator noise from the input BFE time series. The discovery of multi-component halo-disc modes is strong motivation for application of BFE+mSSA to the rich zoo of dynamics of multi-component interacting galaxies.

We present a novel method for constraining the length of the Galactic bar using 6D phase space information to directly integrate orbits. We define a pseudo-length for the Galactic bar, named $R_{Freq}$, based on the maximal extent of trapped bar orbits. We find the $R_{Freq}$ measured from orbits is consistent with the $R_{Freq}$ of the assumed potential only when the length of the bar and pattern speed of said potential is similar to the model from which the initial phase-space coordinates of the orbits are derived. Therefore, one can measure the model's or the Milky Way's bar length from 6D phase-space coordinates by determining which assumed potential leads to a self-consistent measured $R_{Freq}$. When we apply this method to $\approx$210,000 stars in APOGEE DR17 and $Gaia$ eDR3 data, we find a consistent result only for potential models with a dynamical bar length of $\approx$3.5 kpc. We find the Milky Way's trapped bar orbits extend out to only $\approx$3.5 kpc, but there is also an overdensity of stars at the end of the bar out to 4.8 kpc which could be related to an attached spiral arm. We also find that the measured orbital structure of the bar is strongly dependent on the properties of the assumed potential.

Spherical stellar systems have weakly-damped response modes. The dipole modes are seiche modes. The quadrupole are zero pattern-speed prolate modes, the stable precursors to the radial-orbit instability (ROI). We demonstrate that small wiggles in the distribution function (DF) can destabilise the dipole modes and describe the newly identified instabilities in NFW-like dark-matter (DM) halos and other power-law spherical systems. The modes were identified in N-body simulations using multivariate singular spectrum analysis (MSSA) and corroborated using linear-response theory. The new mode peaks inside the half-mass radius but has a pattern speed typical of an outer-halo orbit. As it grows, the radial angle of the eccentric orbits that make up the mode correlate and lose angular momentum by a resonant couple to outer-halo orbits. This leads to an unsteady pattern with a density enhancement that swings from one side of the halo to another along a diameter, like the orbits that comprise the instability. In this way, the dipole mode is similar to the ROI. Since the DF found in Nature is unlikely to be smooth and isotropic with $df(E)/dE<0$ necessary for Antonov stability, these modes may be ubiquitous albeit slowly growing. Halos that are less extended than NFW, such as the Hernquist model, tend to be stable to this dipole instability. We present the critical stability exponents for one- and two-power models. These different critical outer power-law exponents illustrate that the gravitational coupling between the inner and outer DM halo depends on the global shape of density profile.

The dynamics of the inner Galaxy contain crucial clues for untangling the evolutionary history of the Milky Way. However, the inner Galaxy's gravitational potential is poorly constrained, partly because the length of the Galactic bar is currently under debate with length estimates ranging from 3.5-5 kpc. We present a novel method for constraining the length and pattern speed of the Galactic bar using 6D phase space information to directly integrate orbits. We verify our method with N-body simulations and find that the maximal extent of orbits in the bar is not always consistent with that of the potential used to calculate the orbits. It is only consistent when the length of the bar in said potential is similar to the N-body model from which the initial positions and velocities of the stars are sampled. When we apply the orbit integration method to $\approx$210,000 stars in APOGEE DR17 and $Gaia$ eDR3 data, we find a self-consistent result only for potential models with a dynamical bar length of $\approx$3.5 kpc and pattern speed of 39 km/s/kpc. We find the Milky Way's trapped bar orbits extend out to only $\approx$3.5 kpc, but there is also an overdensity of stars at the end of the bar out to 4.8 kpc which could be related to an attached spiral arm. We also find that the measured orbital structure of the bar is strongly dependent on the properties of the assumed potential.

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 present the N-body simulation techniques in EXP. EXP uses empirically-chosen basis functions to expand the potential field of an ensemble of particles. Unlike other basis function expansions, the derived basis functions are adapted to an input mass distribution, enabling accurate expansion of highly non-spherical objects, such as galactic discs. We measure the force accuracy in three models, one based on a spherical or aspherical halo, one based on an exponential disc, and one based on a bar-based disc model. We find that EXP is as accurate as a direct-summation or tree-based calculation, and in some ways is better, while being considerably less computationally intensive. We discuss optimising the computation of the basis function representation. We also detail numerical improvements for performing orbit integrations, including timesteps.