Related papers: Integrals of motion for non-axisymmetric potential…
Rotational speed is an important physical parameter of stars and knowing the distribution of stellar rotational velocities is essential for the understanding stellar evolution. However, it cannot be measured directly but the convolution of…
We address an issue that arises when self-consistently flattened dynamical stellar systems are constructed by adopting a distribution function (DF) that depends on the action integrals. The velocity distribution at points on the symmetry…
The stellar velocity fields of elliptical galaxies hold clues to their dynamical structure and origin. The construction of velocity field models is greatly simplified by assuming an approximate geometrical form for the streamlines of the…
We describe a method for parameterizing two-integral distribution functions, based on triangular tesselations of the integral plane. We apply the method to the axisymmetric isotropic rotator model for the Galactic bulge of Kent~(1992), and…
We recently derived, using the density-of-states approximation, analytic distribution functions for the outcomes of direct single-binary scatterings (Stone & Leigh 2019). Using these outcome distribution functions, we present in this paper…
Action-angle coordinates are an essential tool for understanding the properties of the six dimensional phase space involved in orbits of stars in galactic potentials. A new method, which does not require specific knowledge of a generating…
The observed stellar kinematics of dispersion-supported galaxies are often used to measure dynamical masses. Recently, several analytical relationships between the stellar line-of-sight velocity dispersion, the projected (2D) or deprojected…
Since the early 1970s, stellar population modelling has been one of the basic tools for understanding the physics of unresolved systems from observation of their integrated light. Models allow us to relate the integrated spectra (or…
We present RoadMapping, a full-likelihood dynamical modelling machinery that aims to recover the Milky Way's (MW) gravitational potential from large samples of stars in the Galactic disk. RoadMapping models the observed positions and…
Along with data on radial velocities, more and more data on proper motions of individual stars in globular clusters are becoming available. Their usage was until now rather limited. It was mostly restricted to determining cluster membership…
Starting from the problem of two fixed centres we find a simple derivation of its third integral in terms of the scalar product of the angular momenta about the two fixed centres. This is then generalised to find the general form of the…
The manner in which probability amplitudes of paths sum up to form wave functions of orbital angular momentum eigenstates is described. Using a generalization of stationary-phase analysis, distributions are derived that provide a measure of…
Steady state distribution functions can be used to calculate stability conditions for modes, radiation energy losses, and particle loss rates. Heuristic analytic approximations to these distributions can capture key behaviors of the true…
We study a class of three-point functions on the de Sitter universe and on the asymptotic cone. A blending of geometrical ideas and analytic methods is used to compute some remarkable integrals, on the basis of a generalized star-triangle…
We propose functional approach to the stochastic inflationary universe dynamics. It is based on path integral representation of the solution to the differential equation for the scalar field probability distribution. In the saddle-point…
The only way to map the Galaxy's gravitational potential $\Phi({\bf x})$ and the distribution of matter that produces it is by modelling the dynamics of stars and gas. Observations of the kinematics of gas provide key information about…
Dynamical evolution of stellar mass distribution in star clusters is analysed by considering simultaneously the effects of dynamical friction, stochastic heating and the gravitational potential due to mass distribution in the clusters. A…
We discuss possible mechanisms underlying the observed features of stellar activity cycles, such as multiple periodicities in very active stars, non-cyclic activity observed in moderately active stars, and spatial distribution of stellar…
We study the equation of motion appropriate to an inspiralling binary star system whose constituent stars have strong internal gravity. We use the post-Newtonian approximation with the strong field point particle limit by which we can…
One of the most efficient and reliable observational technique allowing to probe the internal structure of a star is the determination of the apsidal motion in close eccentric binaries. This secular precession of the binary orbit's major…