Related papers: Gauss's method for secular dynamics, softened
Long-term evolution of a stellar orbit captured by a massive galactic center via successive interactions with an accretion disc has been examined. An analytical solution describing evolution of the stellar orbital parameters during the…
Axisymmetric accretion disks in vicinity of a central compact body are studied. In the case of non-viscous disk it is proven that all solutions for the midplane circular velocity are unstable. Hence, the pure hydrodynamic turbulence in…
We present the secular theory of coplanar $N$-planet system, in the absence of mean motion resonances between the planets. This theory relies on the averaging of a perturbation to the two-body problem over the mean longitudes. We expand the…
A simple dynamical model is employed to study the possible orbital evolution of scattered planets and phase plane analysis is used to classify the parameter space and solutions. Our results reconfirm that there is always an increase in…
Solutions of the system of evolutionary equations in the short-wavelength approximation are found and studied. A connection is established between the problem of the evolution of short-wavelength gravitational-scalar perturbations and the…
The equation describing the secular diffusion of a self-gravitating collisionless system induced by an exterior perturbation is derived while assuming that the timescale corresponding to secular evolution is much larger than that…
It is found that a previously thought-to-be well established result of density wave theory, that there is no interaction between a quasi-stationary spiral density wave and the basic state (i.e. the axisymmetric part) of the galactic disk,…
The SecularMultiple code, presented in two previous papers of this series, integrates the long-term dynamical evolution of multiple systems with any number of bodies and hierarchical structure, provided that the system is composed of nested…
Traditionally, secular evolution is defined as evolution of systems where the internal growth of structure and instabilities dominates the growth via external drivers (e.g. accretion/mergers). Most study has focused on 'isolated' galaxies,…
We formulate the collisionless Boltzmann equation (CBE) for dense star clusters that lie within the radius of influence of a massive black hole in galactic nuclei. Our approach to these nearly Keplerian systems follows that of Sridhar and…
In this study, we formulate a set of differential equations for a binary system to describe the secular-tidal evolution of orbital elements, rotational dynamics, and deformation (flattening), under the assumption that one body remains…
We obtain from the first principles a general-relativistic Keplerian rotation law for self-gravitating disks around spinning black holes. This is an extension of a former rotation law that was designed mainly for toroids around spin-less…
The dynamics of galaxies in an expanding universe is often determined for gravitational and dark matter in an Einstein-de Sitter universe, or alternatively by modifying the gravitational long-range attractions in the Newtonian dynamics…
The time evolution of initially balanced, rapidly rotating models for an isolated disk of highly flattened galaxies of stars is calculated. The method of direct integration of the Newtonian equations of motion of stars over a time span of…
In this paper we address the issue of the origin of some observational properties of the galactic globular cluster system. After a preliminary study of some general properties of the main evolutionary processes, we investigate the evolution…
We show that the ideal hydrodynamics of an eccentric astrophysical disc can be derived from a variational principle. The nonlinear secular theory describes the slow evolution of a continuous set of nested elliptical orbits as a result of…
Variability in the light curves of spotted, rotating stars is often non-sinusoidal and quasi-periodic --- spots move on the stellar surface and have finite lifetimes, causing stellar flux variations to slowly shift in phase. A strictly…
The accelerated Kepler problem is obtained by adding a constant acceleration to the classical two-body Kepler problem. This setting models the dynamics of a jet-sustaining accretion disk and its content of forming planets as the disk loses…
We introduce a one-dimensional toy model of globular clusters. The model is a version of the well-known gravitational sheets system, where we take additionally into account mass and energy loss by evaporation of stars at the boundaries.…
The secular evolution process which slowly transforms the morphology of a given galaxy over its lifetime through mostly internal dynamical mechanisms could naturally account for most of the observed properties of physical galaxies (Zhang…