We analyze the dynamics of small two-dimensional disturbances in stable plane-parallel inviscid shear flows under linear theory. Using a velocity profile Vx=U(y) with an inflection point but stable according to Fjørtoft's theorem, we illustrate that the continuum spectrum of van Kampen modes, possessing real phase velocities c=ω/k, aggregates into Landau damping solutions or “quasi-modes,” which exhibit exponential decay. It was found that the real part of the complex phase velocity cL(k) of these solutions may lie outside the allowable range for van Kampen modes, suggesting a non-resonant damping mechanism for these quasi-modes. This conclusion was reached by solving the eigenvalue problem and observing the evolution of initial perturbations, calculated by directly solving the evolutionary equation for vorticity as well as by decomposing the initial disturbance into van Kampen modes. Landau damping of the total vorticity across the channel emerges as an intermediate stage before transitioning to power-law damping.

An analytical solution for the perturbed equations, applicable to all ergodic models of collisionless spherical stellar systems with a single length parameter, has been derived. This solution corresponds to variations in this parameter, i.e., the expansion or contraction of the sphere while conserving total mass. During this process, the system maintains an equilibrium state. The simplicity of the solution allows for the explicit expression of the distribution function, potential, and density across all orders of perturbation theory. This, in turn, aids in clarifying the concept of perturbation energy, which, being of second order in amplitude, cannot be calculated using linear theory. It is demonstrated that the correct expression for perturbation energy, accounting for second-order perturbations, does not align with the well-known expression for perturbation energy via a quadratic form, derived from first-order perturbations within linear theory. However, both these energies are integrals of motion and differ only by a constant. The derived solution can be utilized to verify the correctness of codes and the precision of calculations in the numerical study of collisionless stellar models.

In a previous paper using Gaia DR2 data, we demonstrated that the two closely situated open clusters Collinder 135 and UBC 7 might have formed together about 50 Myr ago. In this work, we performed star-by-star dynamical modelling of the evolution of the open clusters Collinder 135 and UBC 7 from their supposed initial state to their present-day state, reproducing observational distributions of members. Modelling of the Collinder 135 and UBC 7 dynamical evolution was done using the high-order parallel N-body code \phi-GPU with up-to-date stellar evolution. Membership and characteristics of the clusters were acquired based on Gaia DR3 data. The comparison of the present-day radial cumulative star count obtained from the N-body simulations with the current observational data gave us full consistency of the model with observational data, especially in the central 8 pc, where 80% of the stars reside. The proper motion velocity components obtained from the N-body simulations of the stars are also quite consistent with the observed distributions and error bars. These results show that our numerical modelling is able to reproduce the open clusters' current complex 6D observed phase-space distributions with a high level of confidence. Thus, the model demonstrates that the hypothesis of a common origin of Collinder 135 and UBC 7 complies with present-day observational data.

Aims. We built Galactic open star cluster mass functions (CMFs) for different age sub-samples and spatial locations in the wider solar neighbourhood. Here, we present a simple cluster formation and evolution model to reproduce the main features of the CMFs. Methods. We used an unbiased working sample of 2227 clusters of the Milky Way Star Cluster (MWSC) catalogue, which occupy the heliocentric cylinders with magnitude-dependent completeness radii of 1–5 kpc. The MWSC survey provides an extended set of open star cluster parameters, including tidal radii, distances, and ages. From an analytic three-component Galaxy model, we derived tidal masses of clusters with a typical accuracy of about 70%. Our simple model includes a two-section cluster initial mass function, constant cluster formation rate, supervirial phase after a sudden expulsion of the remaining gas, and cluster mass loss due to stellar evolution and the clusters’ gradual destruction in the Galactic tidal field. The dynamical evolution model is based on previous N-body simulations. Results. The obtained tidal masses have been added to the MWSC catalogue. A general CMF (GCMF), built for all cluster ages around the Sun, has a bell-like shape and extends over four decades in mass. The high-mass slope found for tidal mass log mt/M⊙ ≥ 2.3 is equal to 1.14 ± 0.07. The CMFs for different age groups show the same high-mass slopes, while the low-mass slope is nearly flat for the youngest sub-sample (clusters younger than 20 Myr) and about −0.7 for the others. The inner and outer sub-samples covering Galactocentric radii R = 4.2–8.1 kpc and 8.9–13.5 kpc, respectively, are consistent with the GCMF, once the exponential decline of the Galactic disc density is taken into account. The model suggests star formation with low efficiency of 15–20%, where only 10% of stars remain bound in a cluster after gas expulsion and subsequent violent relaxation. The cluster formation rate required to reproduce the observed distributions in age and mass is about 0.4 M⊙ pc−2 Gyr−1. Conclusions. The obtained high-mass slope of the GCMF for the wide neighbourhood of the Sun is similar to slopes determined earlier in nearby galaxies for more luminous clusters with log m/M⊙ > 3.8. The MWSC catalogue supports models with a low star-formation efficiency, where 90% of stars are lost quickly after gas expulsion. The obtained cluster formation rate corresponds to open clusters’ contribution to the stellar content of the thin disc at the level of 30%.

We built Galactic open star cluster mass functions (CMFs) for different age sub-samples in the wider solar neighbourhood. We present a simple cluster formation and evolution model to reproduce the main features of the CMFs. We used an unbiased sample of 2227 clusters of the Milky Way Star Cluster (MWSC) catalogue, which occupy the heliocentric cylinders with magnitude-dependent completeness radii of 1-5 kpc. We derived tidal masses of clusters with an accuracy of 70%. Our cluster formation and evolution model is based on the cluster initial mass function, the cluster formation rate, cluster mass loss due to stellar evolution and the clusters' dynamical evolution in the Galactic tidal field. The obtained tidal masses have been added to the MWSC catalogue. A general CMF (GCMF), built for all cluster ages around the Sun, extends over four decades in mass. The high-mass slope is +1.14. The CMFs for different age groups show the same high-mass slopes, while the low-mass slope is flat for the youngest sub-sample and about -0.7 for the others. The sub-samples inside and outside the solar Galactocentric radius are consistent with the GCMF, once the exponential decline of the Galactic disc density is taken into account. The model suggests star formation with low efficiency of 15%, where 10% of stars remain bound in a cluster after gas expulsion and violent relaxation. The cluster formation rate required to reproduce the observed age-mass-distribution is 0.4 solar masses per square pc and Gyr. The obtained high-mass slope of the GCMF for the wide solar neighbourhood is similar to slopes determined in nearby galaxies. The MWSC catalogue supports models with low star-formation efficiency, where 90% of stars are lost quickly after gas expulsion. The cluster formation rate corresponds to open clusters' contribution to the stellar content of the thin disc of 30%.

We compare initial value and eigenvalue problems for two-dimensional perturbations of the inviscid shear flow in a channel. Singular solutions, known in plasma physics as van Kampen (vK) modes, are constructed. They form a complete set of eigenfunctions for decomposition of any initial perturbation for stable wavy perturbations. A pair of discrete modes appears to ensure completeness in the unstable case. Expansion coefficients for eigenmodes are found, and equivalence of temporal evolution obtained with the help of the evolutionary equation for vorticity and expansion over eigenmodes is presented. This alternative description of the evolution using vK modes is analogous to ones found earlier in plasma and in stellar dynamics. In particular, for stable wavy perturbations, an initial state decays first exponentially due to Landau damping, then algebraically. It has been established (numerically and analytically) that the final decay law is t−1. Also, we numerically demonstrate that Landau-damped perturbations are not true eigenmodes, but rather a superposition of vK-modes with a real frequency, which does not retain its shape over time. However, solution on contours in the complex plane may exhibit properties of a true eigenmode, that is, decay without changing its spatial form. Energy redistribution between perturbation and the flow, in stable and unstable regimes, is analyzed.

An analytical review of the current state of the problems of stellar astronomy is presented. The review is mainly based on the reports made at the Modern Stellar Astronomy Conference (Sternberg Astronomical Institute, Moscow State University, August 2021).

This research was stimulated by the recent studies of damping solutions in dynamically stable spherical stellar systems. Using the simplest model of the homogeneous stellar medium, we discuss non-trivial features of stellar systems. Taking them into account will make it possible to correctly interpret the results obtained earlier and will help to set up decisive numerical experiments in the future...

We describe the interaction between the qubit and the electromagnetic field in a waveguide in accordance with the Lee model using the fact that photons in the waveguide are quanta of a massive scalar neutral field. We study the case where the energy of the excited state of the qubit is larger than the photon mass. We find the stationary state of the "qubit + electromagnetic field " system. We describe the evolution of nonstationary states under initial conditions of the general form. We present results of numerical calculations under the initial conditions of two types: 1) the qubit is in the excited state, and there is no photon; 2) the qubit is in the ground state, and the photon is present. The study is related to the consistent quantum theory of the qubit control with the goal to force qubits to make transitions from one state to another.

Context. Understanding the formation of bound star clusters with a low star formation e ffi ciency (SFE) is important for improving our knowledge of the star-formation history of galaxies. In N -body models of star-cluster evolution after gas expulsion, the Plummer model with an outer power law density profile has been used in a broad range of studies. Aims. Here, we study the impact of the density profile slopes on the survivability of the low-SFE star clusters after instantaneous gas expulsion. We compare cases when a stellar cluster exhibits a Plummer profile to those with Dehnen profiles, including cuspy ones of di ff erent slopes at the time of formation. Methods. We determined the corresponding density profile of the residual gas for a given global SFE, assuming that our model clusters formed with a constant e ffi ciency per free-fall time and, hence, with a shallower density profile for the gas than that of the stars. We performed direct N -body simulations of evolution of clusters initially in virial equilibrium within the gas potential following gas removal. Results. We find that the violent relaxation lasts no longer than 20 Myr, independently of the density profile power law slopes. Dehnen model clusters survive after violent relaxation with significantly lower SFEs when the global SFE measured within the Jacobi radius or within a half-mass radius. Dehnen γ = 0 model clusters show a similar final bound fraction with the Plummer model clusters if the global SFE is measured within ten scale radii. The final bound fraction increases with the γ values for a given global SFE. Conclusions. We conclude that Dehnen clusters better resist the consequences of the violent relaxation that follows the instantaneous gas expulsion, as compared to the Plummer clusters. Therefore, the shallower the outer density slope of the low-SFE clusters, the better their prospects for survival after gas expulsion. Among the Dehnen clusters, we find that the steeper the inner slope, the higher the bound mass fraction that is retained, following the violent relaxation for a given global SFE.

According to our previous theoretical findings, physical processes in centres of galaxies, star clusters, and the Oort comet cloud can be significantly altered by a new so-called ‘gravitational loss-cone instability’. Using N-body simulations of a spherical stellar model in the dominating Keplerian potential, we confirm the possibility of the instability and go beyond the linear theory. Unlike most other instabilities, the new one shows no notable change in spherical geometry of the cluster, but it significantly accelerates the speed of diffusion of particles in phase space leading to a repopulation of the loss cone and early instability saturation.

One of the possible bar formation mechanisms in the disks of galaxies was proposed by Lynden-Bell (1979). The presumed amplification of a weak seed oval stellar surface density perturbation in the central regions of the galaxy through the alignment of the major axes of precessing elliptical orbits underlies it. According to his qualitative reasoning, the orbits are aligned along the perturbation if the precession rate diminishes with decreasing angular momentum at a constant adiabatic invariant. Using a rigorous approach based on finding the system’s stable stationary points, we show that this condition is not the only one that determines the orbit alignment orientation. The orbit precession direction in the unperturbed potential and the rate of decrease of the bar potential amplitude with radius also turn out to be important. In some cases, the latter can even be more important.

Using the canonical Hamilton-Jacobi approach we study the Lynden-Bell concept of bar formation based on the idea of orbital trapping parallel to the long or short axes of the oval potential distortion. The concept considered a single parameter - a sign of the derivative of the precession rate over angular momentum, determining the orientation of the trapped orbits. We derived a perturbation Hamiltonian which includes two more parameters characterising the background disc and the perturbation, that are just as important as the earlier known one. This allows us to link the concept with the matrix approach in linear perturbation theory, the theory of weak bars, and explain some features of the nonlinear secular evolution observed in N-body simulations.

Context. Given the closeness of the two open clusters Collinder 135 and UBC 7 on the sky, we investigate the possibility that the two clusters are physically related. Aims. We aim to recover the present-day stellar membership in the open clusters Cr 135 and UBC 7 (300 pc from the Sun) in order to constrain their kinematic parameters, ages, and masses and to restore their primordial phase space configuration. Methods. The most reliable cluster members are selected with our traditional method modified for the use of Gaia DR2 data. Numerical simulations use the integration of cluster trajectories backwards in time with our original high-order Hermite4 code φ−GRAPE. Results. We constrain the age, spatial coordinates, velocities, radii, and masses of the clusters. We estimate the actual separation of the cluster centres equal to 24 pc. The orbital integration shows that the clusters were much closer in the past if their current line-of-sight velocities are very similar and the total mass is more than seven times larger than the mass of the most reliable members. Conclusions. We conclude that the two clusters Cr 135 and UBC 7 might very well have formed a physical pair based on the observational evidence as well as numerical simulations. The probability of a chance coincidence is only about 2%.

AbstractBased on cosmological re-simulations we have shown that the impact of satellite galaxies has a minor effect on the thin disc heating. In contrast satellite galaxies can generate long-lived warps of the outer disc and they can advance or delay bar formation significantly.

Interaction of spiral density waves with stars in the vicinity of the inner Lindblad resonance in galactic discs is investigated using the linear perturbation theory and the leading orders in the epicyclic and WKB approximations. In analogy with shear flows in hydrodynamics, we conjecture that a weak non-linearity in a narrow resonance region modifies the standard (Landau - Lin) bypass rule of the singularity to the integration in the principal value sense. This indeed leads to the reflection of the spiral wave instead of absorption, but the detailed picture looks awkward: the intervals of the wave weakening alternate with the intervals of the wave growth, so that the net absorption is absent. Incidentally, we rectify the result concerning leading spiral waves obtained earlier for the standard bypass rule.

We present an analytical review of the current state of the problems of stellar astronomy. We report the results obtained by Russian astronomers by 2017.We show that the studies conducted in Russia cover all major fields of stellar astronomy, use modern observational methods and data analysis techniques, and meet high scientific standards.