Dr Eugene Vasiliev

We use stellar proper motions (PM) from Gaia Data Release 2 for studying the internal kinematics of Milky Way globular clusters. In addition to statistical measurement errors, there are significant spatially correlated systematic errors, which cannot be ignored when studying the internal kinematics. We develop a mathematically consistent procedure for incorporating the spatial correlations in any model-fitting approach, and use it to determine rotation and velocity dispersion profiles of a few dozen clusters. We confirm detection of rotation in the sky plane for similar to 10 clusters reported in previous studies, and discover a few more clusters with rotation amplitudes exceeding similar to 0.05 mas yr(-1). However, in more than half of these cases the significance of this rotation signature is rather low when taking into account the systematic errors. We find that the PM dispersion is not sensitive to systematic errors in PM, however, it is quite sensitive to the selection criteria on the input sample, most importantly, in crowded central regions. When using the cleanest possible samples, PM dispersion can be reliably measured down to 0.1 mas yr(-1) for similar to 60 clusters.

We have derived accurate distances to Galactic globular clusters by combining data from the Gaia Early Data Release 3 (EDR3) with distances based on Hubble Space Telescope (HST) data and literature-based distances. We determine distances either directly from the Gaia EDR3 parallaxes, or kinematically by combining line-of-sight velocity dispersion profiles with Gaia EDR3 and HST-based proper motion velocity dispersion profiles. We furthermore calculate cluster distances from fitting nearby subdwarfs, whose absolute luminosities we determine from their Gaia EDR3 parallaxes, to globular cluster main sequences. We finally use HST-based stellar number counts to determine distances. We find good agreement in the average distances derived from the different methods down to a level of about 2 per cent. Combining all available data, we are able to derive distances to 162 Galactic globular clusters, with the distances to about 20 nearby globular clusters determined with an accuracy of 1 per cent or better. We finally discuss the implications of our distances for the value of the local Hubble constant.

In a galaxy merger, the stars tidally stripped from the satellite and accreted onto the host galaxy undergo phase-mixing and form finely grained structures in the phase space. However, these fragile structures may be destroyed in the subsequent galaxy evolution, in particular, by a rotating bar that appears well after the merger is completed. In this work, we investigate the survivability of phase-space structures in the presence of a bar. We find that a bar with amplitude and pattern speed similar to those of the Milky Way would blur and destroy a substantial amount of the substructure that consists of particles with pericentre radii comparable to the bar length. While this appears to be in tension with the recent discovery of phase-space chevrons in Gaia DR3 data, the most prominent chevrons in our simulations can still be recovered when applying the same analysis procedure as in observations. Moreover, the smoothing effect is less pronounced in the population of stars whose angular momenta have the opposite sign to the bar pattern speed.

The mass of a supermassive black hole (M (BH)) is a fundamental property that can be obtained through observational methods. Constraining M (BH) through multiple methods for an individual galaxy is important for verifying the accuracy of different techniques and for investigating the assumptions inherent in each method. However, there exist only a few galaxies where multiple M (BH) measurement techniques can be applied. NGC 4151 is one of these rare galaxies for which multiple methods can be used: stellar and gas dynamical modeling because of its proximity (D = 15.8 +/- 0.4 Mpc from Cepheids), and reverberation mapping because of its active accretion. In this work, we reanalyzed H-band integral field spectroscopy of the nucleus of NGC 4151 from Gemini NIFS, improving the analysis at several key steps. We then constructed a wide range of axisymmetric dynamical models with the new orbit-superposition code Forstand. One of our primary goals is to quantify the systematic uncertainties in M (BH) arising from different combinations of the deprojected density profile, inclination, intrinsic flattening, and mass-to-light ratio. As a consequence of uncertainties on the stellar luminosity profile arising from the presence of the active galactic nucleus, our constraints on M (BH) are rather weak. Models with a steep central cusp are consistent with no black hole; however, in models with more moderate cusps, the black hole mass lies within the range of 0.25 x 10(7) M (circle dot) less than or similar to M (BH) less than or similar to 3 x 10(7) M (circle dot). This measurement is somewhat smaller than the earlier analysis presented by Onken et al. but agrees with previous M (BH) values from gas dynamical modeling and reverberation mapping. Future dynamical modeling of reverberation data, as well as IFU observations with JWST, will aid in further constraining the mass of the central supermassive black hole in NGC 4151.

The presence of supermassive black holes (SMBHs) with masses up to M. similar to 10(9)M(circle dot) at redshifts z similar or equal to 7.5 suggests that their seeds may have started to grow long before the reionization in ambient medium with pristine chemical composition. During their latest 500 Myr episode of growing from z >= 10 to z similar to 7, the black holes shone as luminous as 10(11)-10(12) L-circle dot, with a cumulative spectrum consisting of the intrinsic continuum from the hot accretion disk, nebular hydrogen, and helium spectral lines, and the free-free continuum from the gas of host halos. Here we address the question of whether such a plain spectrum would allow us to trace the evolution of these growing SMBHs. In our calculations we assume that host galaxies have stellar populations with masses smaller than the masses of their central black holes-the so-called obese black hole galaxies. Within this model we show that for a sufficiently high mass of gas in a host galaxy-not smaller than the mass of a growing black hole, the cumulative spectrum in the far-infrared reveals a sharp transition from a quasi-blackbody Rayleigh-Jeans spectrum of the black hole proportional to lambda(-2) to a flat free-free nebular continuum lambda(0.118) on a longer wavelength limit. Once such a transition in the spectrum is resolved, the black hole mass can be inferred as a combination of the observed wavelength at the transition lambda(k) and the corresponding spectral luminosity. The possible observability of this effect in spectra of growing high-z SMBHs and determination of their mass with the upcoming James Webb Space Telescope and the planned space project Spektr-M is briefly discussed.

We present a new constraint on the mass of the black hole in the active S0 galaxy NGC 5273. Due to the proximity of the galaxy at 16.6 +/- 2.1 Mpc, we were able to resolve and extract the bulk motions of stars near the central black hole using adaptive-optics-assisted observations with the Gemini Near-infrared Integral Field Spectrograph, as well as constrain the large-scale kinematics using archival Spectroscopic Areal Unit for Research and Optical Nebulae spectroscopy. High-resolution Hubble Space Telescope imaging allowed us to generate a surface-brightness decomposition, determine approximate mass-to-light ratios for the bulge and disk, and obtain an estimate for the disk inclination. We constructed an extensive library of dynamical models using the Schwarzschild orbit-superposition code FORSTAND, exploring a range of disk and bulge shapes, halo masses, etc. We determined a black hole mass of M (center dot) = [0.5-2] x 10(7) M (circle dot), where the low side of the range is in agreement with the reverberation mapping measurement of M (center dot) = [4.7 +/- 1.6] x 10(6) M (circle dot). NGC 5273 is one of the few nearby galaxies that hosts a broad-lined active galactic nucleus, allowing a crucial comparison of black hole masses derived from independent mass-measurement techniques.

We review the recent theoretical and observational developments concerning the interaction of the Large Magellanic Cloud (LMC) with the Milky Way and its neighbourhood. An emerging picture is that the LMC is a fairly massive companion (10-20% of the Milky Way mass) and just passed the pericentre of its orbit, likely for the first time. The gravitational perturbation caused by the LMC is manifested at different levels. The most immediate effect is the deflection of orbits of stars, stellar streams, or satellite galaxies passing in the vicinity of the LMC. Less well known but equally important is the displacement (reflex motion) of central regions of the Milky Way about the centre of mass of both galaxies. Since the Milky Way is not a rigid body, this displacement varies with the distance from the LMC, and as a result, the Galaxy is deformed and its outer regions (beyond a few tens kpc) acquire a net velocity with respect to its centre. These phenomena need to be taken into account at the level of precision warranted by current and future observational data, and improvements on the modelling side are also necessary for an adequate interpretation of these data.

Abstract We review the Schwarzschild orbit-superposition approach and present a new implementation of this method, which can deal with a large class of systems, including rotating barred disk galaxies. We discuss two conceptual problems in this field: the intrinsic degeneracy of determining the potential from line-of-sight kinematics, and the non-uniqueness of deprojection and related biases in potential inference, especially acute for triaxial bars. When applied to mock datasets with known 3d shape, our method correctly recovers the pattern speed and other potential parameters. However, more work is needed to systematically address these two problems for real observational datasets.

A chemodynamical model of our Galaxy is fitted to data from DR17 of the APOGEE survey supplemented with data from the StarHorse catalogue and Gaia DR3. Dynamically, the model is defined by action-based distribution functions for dark matter and six stellar components plus a gas disc. The gravitational potential jointly generated by the model's components is used to examine the Galaxy's chemical composition within action space. The observational data probably cover all parts of action space that are populated by stars. The overwhelming majority of stars have angular momentum J(phi) > 0 implying that they were born in the Galactic disc. High-alpha stars dominate in a region that is sharply bounded by J(phi) less than or similar to J(phi)(solar). Chemically the model is defined by giving each stellar component a Gaussian distribution in ([Fe/H],[Mg/Fe]) space about a mean that is a linear function of the actions. The model's 47 dynamical parameters are chosen to maximize the likelihood of the data given the model in 72 three-dimensional velocity spaces while its 70 chemical parameters are similarly chosen in five-dimensional chemodynamical space. The circular speed falls steadily from 237 km s(-1) at R = 4 kpc to 218 km s(-1) at R = 20 kpc. Dark matter contributes half the radial force on the Sun and has local density 0.011 M-circle dot pc(-3), there being 24.5 M-circle dot pc(-2) in dark matter and 26.5 M-circle dot pc(-2) in stars within 1.1 kpc of the plane.

A new class of models of stellar discs is introduced and used to build a self-consistent model of our Galaxy. The model is defined by the parameters that specify the action-based distribution functions (DFs) f(J) of four stellar discs (three thin-disc age cohorts and a thick disc), spheroidal bulge and spheroidal stellar and dark haloes. From these DFs plus a specified distribution of gas, we solve for the densities of stars and dark matter and the potential they generate. The principal observational constraints are the kinematics of stars with Gaia Radial Velocity Spectrometer (RVS) data and the density of stars in the column above the Sun. The model predicts the density and kinematics of stars and dark matter throughout the Galaxy, and suggests the structure of the dark halo prior to the infall of baryons. The code used to create the model is available on github.

The Gaia Sausage is the major accretion event that built the stellar halo of the Milky Way galaxy. Here, we provide dynamical and chemical evidence for a second substantial accretion episode, distinct from the Gaia Sausage. The Sequoia Event provided the bulk of the high-energy retrograde stars in the stellar halo, as well as the recently discovered globular cluster FSR 1758. There are up to six further globular clusters, including omega Centauri, as well as many of the retrograde substructures in Myeong et al., associated with the progenitor dwarf galaxy, named the Sequoia. The stellar mass in the Sequoia galaxy is similar to 5 x 10 M-circle dot, whilst the total mass is similar to 10(10)M(circle dot), as judged from abundance matching or from the total sum of the globular cluster mass. Although clearly less massive than the Sausage, the Sequoia has a distinct chemodynamical signature. The strongly retrograde Sequoia stars have a typical eccentricity of similar to 0.6, whereas the Sausage stars have no clear net rotation and move on predominantly radial orbits. On average, the Sequoia stars have lower metallicity by similar to 0.3 dex and higher abundance ratios as compared to the Sausage. We conjecture that the Sausage and the Sequoia galaxies may have been associated and accreted at a comparable epoch.

We present Forstand, a new code for constructing dynamical models of galaxies with the Schwarzschild orbit-superposition method. These models are constrained by line-of-sight kinematic observations and applicable to galaxies of all morphological types, including disks and triaxial rotating bars. Our implementation has several novel and improved features, is computationally efficient, and has been made publicly available. Using mock data sets taken from N-body simulations, we demonstrate that the pattern speed of a bar can be recovered with an accuracy of 10-20%, regardless of orientation, if the 3D shape of the galaxy is known or inferred correctly.

High-accuracy proper motions (PMs) of M31 and other Local Group (LG) satellites have now been provided by the Gaia satellite. We revisit the timing argument to compute the total mass M of the LG from the orbit of the Milky Way and M31, allowing for the cosmological constant. We rectify a systematic effect caused by the presence of the Large Magellanic Cloud (LMC). The interaction of the LMC with the Milky Way induces a motion toward the LMC. This contribution to the measured velocity of approach of the Milky Way and M31 must be removed. We allow for cosmic bias and scatter by extracting correction factors tailored to the accretion history of the LG. The distribution of correction factors is centered around 0.63 with a scatter of +/- 0.2, indicating that the timing argument significantly overestimates the true mass. Adjusting for all these effects, the estimated mass of the LG is M=3.4(-1.1)(+1.4) x 10(12) M-circle dot (68% CL) when using the M31 tangential velocity, v(tan)=82(-35)(+38)kms(-1) v(tan)=59(-38)(+42)kms(-1) (derived from the same PM data with a flat prior on the tangential velocity) lead to an estimated mass of M=3.1(-1.0)(+1.3) x 10(12)M circle dot (68% CL). By making an inventory of the total mass associated with the four most substantial LG members (the Milky Way, M31, M33, and the LMC), we estimate the known mass to be in the range 3.7(-0.5)(+0.5) x 10(12) M-circle dot

We estimate the 3D density profile of the Galactic dark matter (DM) halo within r less than or similar to 30kpc from the Galactic centre by using the astrometric data for halo RR Lyrae stars from Gaia DR2. We model both the stellar halo distribution function and the Galactic potential, fully taking into account the survey selection function, the observational errors, and the missing line-of-sight velocity data for RR Lyrae stars. With a Bayesian method, we infer the model parameters, including the density flattening of the DM halo q, which is assumed to be constant as a function of radius. We find that 99 per cent of the posterior distribution of q is located at q > 0.963, which strongly disfavours a flattened DM halo. We cannot draw any conclusions as to whether the Galactic DM halo at is prolate, because we restrict ourselves to axisymmetric oblate halo models with q

AGAMA is a publicly available software library for a broad range of applications in the field of stellar dynamics. It provides methods for computing the gravitational potential of arbitrary analytic density profiles or N-body models, orbit integration and analysis, transformations between position/velocity and action/angle variables, distribution functions expressed in terms of actions and their moments, and iterative construction of self-consistent multicomponent galaxy models. Applications include the inference about the structure of Milky Way or other galaxies from observations of stellar kinematics, preparation of equilibrium initial conditions for N-body simulations, and analysis of snapshots from simulations. The library is written in C++, provides a PYTHON interface, and can be coupled to other stellar-dynamical software: AMUSE, GALPY, and NEMO. It is hosted at http://github.com/GalacticDynamics-Oxford/Agama.

Spherical Jeans modelling is widely used to estimate mass profiles of systems from star clusters to galactic stellar haloes to clusters of galaxies. It derives the cumulative mass profile, M(

We present an approach for simulating the collisional evolution of spherical isotropic stellar systems based on the one-dimensional Fokker-Planck equation. A novel aspect is that we use the phase volume as the argument of the distribution function instead of the traditionally used energy, which facilitates the solution. The publicly available code PhaseFlow implements a high-accuracy finite-element method for the Fokker-Planck equation, and can handle multiple-component systems, optionally with the central black hole and taking into account loss-cone effects and star formation. We discuss the energy balance in the general setting, and in application to the Bahcall-Wolf cusp around a central black hole, for which we derive a perturbative solution. We stress that the cusp is not a steady-state structure, but rather evolves in amplitude while retaining an approximately density profile. Finally, we apply the method to the nuclear star cluster of the milky Way, and illustrate a possible evolutionary scenario in which a two-component system of lighter main-sequence stars and stellar-mass black holes develops a Bahcall-Wolf cusp in the heavier component and a weaker cusp in the lighter, visible component, over the period of several Gyr. The present-day density profile is consistent with the recently detected mild cusp inside the central parsec, and is weakly sensitive to initial conditions.

Relying on the dramatic increase in the number of stars with full 6D phase-space information provided by the Gaia Data Release 3, we resolve the distribution of the stellar halo around the Sun to uncover signatures of incomplete phase-mixing. We show that, for the stars likely belonging to the last massive merger, the (v(r), r) distribution contains a series of long and thin chevron-like overdensities. These phase-space substructures have been predicted to emerge following the dissolution of a satellite, when its tidal debris is given time to wind up, thin out, and fold. Such chevrons have been spotted in external galaxies before; here, we report the first detection in our own Milky Way. We also show that the observed angular momentum L-z distribution appears more prograde at high energies, possibly revealing the original orbital angular momentum of the in-falling galaxy. The energy distribution of the debris is strongly asymmetric with a peak at low E - which, we surmise, may be evidence of the dwarf's rapid sinking - and riddled with wrinkles and bumps. We demonstrate that similar phase-space and (E, L-z) substructures are present in numerical simulations of galaxy interactions, both in bespoke N-body runs and in cosmological hydrodynamical zoom-in suites. The remnant traces of the progenitor's disruption and the signatures of the on-going phase-mixing discovered here will not only help to constrain the properties of our Galaxy's most important interaction, but also can be used as a novel tool to map out the Milky Way's current gravitational potential and its perturbations.

Stellar shells are low surface brightness features, created during nearly head-on galaxy mergers from the debris of the tidally disrupted satellite. Here, we investigate the formation and evolution mechanism of shells in six dimensions (3D positions and velocities). We propose a new description in action-angle coordinates which condenses the seemingly complex behaviour of an expanding shell system into a simple picture, and stresses the crucial role of the existence of different stripping episodes in the properties of shells. Based on our findings, we construct a method for constraining the potential of the host galaxy and the average epoch of stripping. The method is applicable even if the shells cannot be identified or isolated from the data, or if the data are heavily contaminated with additional foreground stars. These results open up a new possibility to study the ancient merger that built the Milky Way Galaxy's stellar halo.

Due to observational challenges, the mass function of black holes (BH) at lower masses is poorly constrained in the local universe. Understanding the occupation fraction of BHs in low-mass galaxies is crucial for constraining the origins of supermassive BH seeds. Compact stellar systems (CSSs), including ultracompact dwarf galaxies (UCDs) and compact elliptical galaxies (cEs), are potential intermediate-mass BH hosts. Despite the difficulties posed by their limited spheres of influence, stellar dynamical modeling has been effective in estimating central BH masses in CSSs. Some CSSs may harbor a BH constituting up to 20% of their host stellar mass, while others might not have a central BH. In support of our ongoing efforts to determine the BH masses in select CSSs in the Virgo cluster using JWST/NIRSpec IFU observations and orbit-superposition dynamical models, we create mock kinematic data mimicking the characteristics of observed cEs/UCDs in the Virgo cluster with different BH masses. We then construct a series of dynamical models using the orbit-superposition code FORSTAND and explore the accuracy of recovering the BH mass. We find that the mass of BHs comprising 1% or more of the total host stellar mass can be accurately determined through kinematic maps featuring higher-order velocity moments. We also assess how BH mass measurement is affected by deprojection methods, regularization factors, anisotropy parameters, orbit initial conditions, the absence of higher-order velocity moments, the spatial resolution, and the signal-to-noise ratio.

ABSTRACT We use the data from Gaia  Early Data Release 3 (EDR3) to study the kinematic properties of Milky Way globular clusters. We measure the mean parallaxes and proper motions (PM) for 170 clusters, determine the PM dispersion profiles for more than 100 clusters, uncover rotation signatures in more than 20 objects, and find evidence for radial or tangential PM anisotropy in a dozen richest clusters. At the same time, we use the selection of cluster members to explore the reliability and limitations of the Gaia catalogue itself. We find that the formal uncertainties on parallax and PM are underestimated by $10{-}20{{\ \rm per\ cent}}$ in dense central regions even for stars that pass numerous quality filters. We explore the spatial covariance function of systematic errors, and determine a lower limit on the uncertainty of average parallaxes and PM at the level 0.01 mas and 0.025 mas yr$^{-1}$ , respectively. Finally, a comparison of mean parallaxes of clusters with distances from various literature sources suggests that the parallaxes for stars with $G>13$ (after applying the zero-point correction suggested by Lindegren et al.) are overestimated by $\sim 0.01\pm 0.003$ mas. Despite these caveats, the quality of Gaia  astrometry has been significantly improved in EDR3 and provides valuable insights into the properties of star clusters.

Abstract We review the implications of the Gaia Data Release 2 catalogue for studying the dynamics of Milky Way globular clusters, focusing on two separate topics. The first one is the analysis of the full 6-dimensional phase-space distribution of the entire population of Milky Way globular clusters: their mean proper motions (PM) can be measured with an exquisite precision (down to 0.05 mas yr −1 , including systematic errors). Using these data, and a suitable ansatz for the steady-state distribution function (DF) of the cluster population, we then determine simultaneously the best-fit parameters of this DF and the total Milky Way potential. We also discuss possible correlated structures in the space of integrals of motion. The second topic addresses the internal dynamics of a few dozen of the closest and richest globular clusters, again using the Gaia PM to measure the velocity dispersion and internal rotation, with a proper treatment of spatially correlated systematic errors. Clear rotation signatures are detected in 10 clusters, and a few more show weaker signatures at a level ∼0.05 mas yr −1 . PM dispersion profiles can be reliably measured down to 0.1 mas yr −1 , and agree well with the line-of-sight velocity dispersion profiles from the literature.

Binary supermassive black holes (SMBHs) are expected to form naturally during galaxy mergers. After the dynamical friction phase, when the two SMBHs become gravitationally bound to each other, and a brief stage of initial rapid hardening, the orbit gradually continues to shrink due to three-body interactions with stars that enter the loss cone of the binary. Using the stellar-dynamical Monte Carlo code RAGA, we explore the co-evolution of the binary SMBH and the nuclear star cluster in this slow stage, for various combinations of parameters (geometry of the star cluster, primary/secondary SMBH mass, initial eccentricity, inclusion of stellar captures/tidal disruptions). We compare the rates of stellar captures in galactic nuclei containing a binary SMBH to those of galaxies with a single SMBH. At early times, the rates are substantially higher in the case of a binary SMBH, but subsequently they drop to lower levels. Only in triaxial systems both the binary hardening rates and the capture rates remain sufficiently high during the entire evolution. We find that the hardening rate is not influenced by star captures, nor does it depend on eccentricity; however, it is higher when the difference between the black hole masses is greater. We confirm that the eccentricity of the binary tends to grow, which may significantly shorten the coalescence time due to earlier onset of gravitational-wave emission. We also explore the properties of the orbits entering the loss cone, and demonstrate that it remains partially full throughout the evolution in the triaxial case, but significantly depleted in the axisymmetric case. Finally, we study the distribution of ejected hypervelocity stars and the corresponding mass deficits in the central parts of the galaxies hosting a binary, and argue that the missing mass is difficult to quantify observationally.

Recent work uncovered features in the phase space of the Milky Way's stellar halo which may be attributed to the last major merger. When stellar material from a satellite is accreted onto its host, it phase mixes and appears finely substructured in phase space. For a high-eccentricity merger, this substructure most clearly manifests as numerous wrapping chevrons in (v(r), r) space, corresponding to stripes in (E, theta(r)) space. We introduce the idea of using this substructure as an alternative subhalo detector to cold stellar streams. We simulate an N-body merger akin to the GSE and assess the impact of subhaloes on these chevrons. We examine how their deformation depends on the mass, pericentre, and number of subhaloes. To quantify the impact of perturbers in our simulations, we utilize the appearance of chevrons in (E, theta(r)) space to introduce a new quantity - the ironing parameter. We show that: (1) a single flyby of a massive (similar to 10(10) M-circle dot) subhalo with pericentre comparable to, or within, the shell's apocentre smooths out the substructure, (2) a single flyby of a low mass (less than or similar to 10(8) M-circle dot) has negligible effect, (3) multiple flybys of subhalos derived from a subhalo mass function between 10(7) and 10(10) M-circle dot cause significant damage if deep within the potential, (4) the effects of known perturbers (e.g. Sagittarius) should be detectable and offer constraints on their initial mass. The sensitivity to the populations of subhaloes suggests that we should be able to place an upper limit on the Milky Way's subhalo mass function.

We present a new method to infer the 3D luminosity distributions of edge-on barred galaxies with boxy-peanut/X (BP/X) shaped structures from their 2D surface brightness distributions. Our method relies on forward modelling of newly introduced parametric 3D density distributions for the BP/X bar, disc and other components using an existing image fitting software package (imfit). We validate our method using an N-body simulation of a barred disc galaxy with a moderately strong BP/X shape. For fixed orientation angles, the derived 3D BP/X-shaped density distribution is shown to yield a gravitational potential that is accurate to at least 5 per cent and forces that are accurate to at least 15 per cent, with average errors being similar to 1.5 per cent for both. When additional quantities of interest, such as the orientation of the bar to the line of sight, its pattern speed, and the stellar mass-to-light ratio are unknown they can be recovered to high accuracy by providing the parametric density distribution to the Schwarzschild modelling code FORSTAND. We also explore the ability of our models to recover the mass of the central supermassive black hole. This method is the first to be able to accurately recover both the orientation of the bar to the line of sight and its pattern speed when the disc is perfectly edge-on.

We propose a scenario in which the Large Magellanic Cloud (LMC) is on its second passage around the Milky Way. Using a series of tailored N-body simulations, we demonstrate that such orbits are consistent with current observational constraints on the mass distribution and relative velocity of both galaxies. The previous pericentre passage of the LMC could have occurred 5-10Gyr ago at a distance greater than or similar to 100kpc, large enough to retain its current population of satellites. The perturbations of the Milky Way halo induced by the LMC look nearly identical to the first-passage scenario, however, the distribution of LMC debris is considerably broader in the second-passage model. We examine the likelihood of current and past association with the Magellanic system for dwarf galaxies in the Local Group, and find that in addition to 10-11 current LMC satellites, it could have brought a further four to six galaxies that have been lost after the first pericentre passage. In particular, four of the classical dwarfs - Carina, Draco, Fornax, and Ursa Minor - each have an similar to 50 percent probability of once belonging to the Magellanic system, thus providing a possible explanation for the 'plane of satellites' conundrum.

We use the proper motions (PM) of half a million red giant stars in the Large Magellanic Cloud measured by Gaia to construct a 2D kinematic map of mean PM and its dispersion across the galaxy, out to 7 kpc from its centre. We then explore a range of dynamical models and measure the rotation curve, mean azimuthal velocity, velocity dispersion profiles, and the orientation of the galaxy. We find that the circular velocity reaches similar to 90 km s(-1) at 5 kpc, and that the velocity dispersion ranges from similar to 30-40 km s(-1) in the galaxy centre to similar to 15-20 km s(-1) at 7 kpc.

The ongoing interaction between the Milky Way (MW) and its largest satellite - the Large Magellanic Cloud (LMC) - creates a significant perturbation in the distribution and kinematics of distant halo stars, globular clusters and satellite galaxies, and leads to biases in MW mass estimates from these tracer populations. We present a method for compensating these perturbations for any choice of MW potential by computing the past trajectory of LMC and MW and then integrating the orbits of tracer objects back in time until the influence of the LMC is negligible, at which point the equilibrium approximation can be used with any standard dynamical modelling approach. We add this orbit-rewinding step to the mass estimation approach based on simultaneous fitting of the potential and the distribution function of tracers, and apply it to two data sets with the latest Gaia EDR3 measurements of 6D phase-space coordinates: globular clusters and satellite galaxies. We find that models with LMC mass in the range (1-2) x 10(11) M-circle dot better fit the observed distribution of tracers, and measure MW mass within 100 kpc to be (0.75 +/- 0.1) x 10(12) M-circle dot, while neglecting the LMC perturbation increases it by similar to 15 per cent.

We use Gala Data Release 2 to determine the mean proper motions for 150 Milky Way globular clusters (almost the entire known population), with a typical uncertainty of 0.05 mas yr(-1) limited mainly by systematic errors. Combining them with distance and line-of-sight velocity measurements from the literature, we analyse the distribution of globular clusters in the 6D phase space, using both position/velocity and action/angle coordinates. The population of clusters in the central 10 kpc has a mean rotational velocity reaching 50-80 km s(-1), and a nearly isotropic velocity dispersion 100-120 km s(-1), while in the outer galaxy, the cluster orbits are strongly radially anisotropic. We confirm a concentration of clusters at high radial action in the outer region of the Galaxy. Finally, we explore a range of equilibrium distribution function-based models for the entire globular cluster system, and the information they provide about the potential of the Milky Way. The dynamics of clusters is best described by models with the circular velocity between 10 and 50 kpc staying in the range 210-240 km s(-1).

We consider the orbital evolution of satellites in galaxy mergers, focusing on the evolution of eccentricity. Using a large suite of N-body simulations, we study the phenomenon of satellite orbital radialization-a profound increase in the eccentricity of its orbit as it decays under dynamical friction. While radialization is detected in a variety of different setups, it is most efficient in cases of high satellite mass, not very steep host density profiles, and high initial eccentricity. To understand the origin of this phenomenon, we run additional simulations with various physical factors selectively turned off: satellite mass loss, reflex motion and distortion of the host, etc. We find that all these factors are important for radialization because it does not occur for point-mass satellites or when the host potential is replaced with an unperturbed initial profile. The analysis of forces and torques acting on both galaxies confirms the major role of self-gravity of both host and satellite in the reduction of orbital angular momentum. The classical Chandrasekhar dynamical friction formula, which accounts only for the forces between the host and the satellite, but not for internal distortions of both galaxies, does not match the evolution of eccentricity observed in N-body simulations.

We use the astrometric and photometric data from Gaia Data Release 2 and line-of-sight velocities from various other surveys to study the 3D structure and kinematics of the Sagittarius dwarf galaxy. The combination of photometric and astrometric data makes it possible to obtain a very clean separation of Sgr member stars from the Milky Way foreground; our final catalogue contains 2.6 x 10(5) candidate members with magnitudes G < 18, more than half of them being red clump stars. We construct and analyse maps of the mean proper motion and its dispersion over the region similar to 30 x 12 deg, which show a number of interesting features. The intrinsic 3D density distribution (orientation, thickness) is strongly constrained by kinematics; we find that the remnant is a prolate structure with the major axis pointing at similar to 45. from the orbital velocity and extending up to similar to 5 kpc, where it transitions into the stream. We perform a large suite of N-body simulations of a disrupting Sgr galaxy as it orbits the Milky Way over the past 2.5 Gyr, which are tailored to reproduce the observed properties of the remnant (not the stream). The richness of available constraints means that only a narrow range of parameters produce a final state consistent with observations. The total mass of the remnant is similar to 4 x 10(8) M-circle dot, of which roughly a quarter resides in stars. The galaxy is significantly out of equilibrium, and even its central density is below the limit required to withstand tidal forces. We conclude that the Sgr galaxy will likely be disrupted over the next Gyr.