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The classical theory of cluster relaxation is unsatisfactory because it involves the Coulomb logarithm. The Balescu-Lenard (BL) equation provides a rigorous alternative that has no ill-defined parameter. Moreover, the BL equation, unlike classical theory, includes the clusters self-gravity. A heuristic argument is given that indicates that relaxation does not occur predominantly through two-particle scattering and is enhanced by self-gravity. The BL equation is adapted to a spherical system and used to estimate the flux through the action space of isochrone clusters with different velocity anisotropies. A range of fairly different secular behaviours is found depending on the fraction of radial orbits. Classical theory is also used to compute the corresponding classical fluxes. The BL and classical fluxes are very different because (a) the classical theory materially under-estimates the impact of large-scale collectively amplified fluctuations and (b) only the leading terms in an infinite sum for the BL flux are computed. A complete theory of cluster relaxation likely requires that the sum in the BL equation be decomposed into a sum over a finite number of small wavenumbers complemented by an integral over large wavenumbers analogous to classical theory.
Globular clusters contain a finite number of stars. As a result, they inevitably undergo secular evolution (`relaxation) causing their mean distribution function (DF) to evolve on long timescales. On one hand, this long-term evolution may be interpre
We perform a systematic combined photometric and kinematic analysis of a sample of globular clusters under different relaxation conditions, based on their core relaxation time (as listed in available catalogs), by means of two well-known families of
Internal rotation is considered to play a major role in the dynamics of some globular clusters. However, in only few cases it has been studied by quantitative application of realistic and physically justified global models. Here we present a dynamica
Blue hook (BHk) stars are a rare class of horizontal branch stars that so far have been found in only very few Galactic globular clusters (GCs). The dominant mechanism for producing these objects is currently still unclear. In order to test if the pr
It is widely believed that globular clusters evolve over many two-body relaxation times toward a state of energy equipartition, so that velocity dispersion scales with stellar mass as sigma ~ m^{-eta} with eta = 0.5. We show that this is incorrect, u