Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userResonant and non-resonant relaxation of globular clusters
300
0
0.0
(
0
)
Added by
Jean-Baptiste Fouvry
Publication date
2021
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
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 interpreted as driven by the accumulation of local deflections along each stars mean field trajectory -- so-called `non-resonant relaxation. On the other hand, it can be thought of as driven by non-local, collectively dressed and resonant couplings between stellar orbits, a process termed `resonant relaxation. In this paper we consider a model globular cluster represented by a spherical, isotropic isochrone DF, and compare in detail the predictions of both resonant and non-resonant relaxation theories against tailored direct $N$-body simulations. In the space of orbital actions (namely the radial action and total angular momentum), we find that both resonant and non-resonant theories predict the correct morphology for the secular evolution of the clusters DF, although non-resonant theory over-estimates the amplitude of the relaxation rate by a factor ${sim 2}$. We conclude that the secular relaxation of hot isotropic spherical clusters is not dominated by collectively amplified large-scale potential fluctuations, despite the existence of a strong ${ell = 1}$ damped mode. Instead, collective amplification affects relaxation only marginally even on the largest scales. The predicted contributions to relaxation from smaller scale fluctuations are essentially the same from resonant and non-resonant theories.
rate research
Read More
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.
In the vicinity of a massive black hole, stars move on precessing Keplerian orbits. The mutual stochastic gravitational torques between the stellar orbits drive a rapid reorientation of their orbital planes, through a process called vector resonant relaxation. We derive, from first principles, the correlation of the potential fluctuations in such a system, and the statistical properties of random walks undergone by the stellar orbital orientations. We compare this new analytical approach with effective $N$-body simulations. We also provide a simple scheme to generate the random walk of a test stars orbital orientation using a stochastic equation of motion. We finally present quantitative estimations of this process for a nuclear stellar cluster such as the one of the Milky Way.
Supermassive black holes in the centre of galaxies dominate the gravitational potential of their surrounding stellar clusters. In these dense environments, stars follow nearly Keplerian orbits, which get slowly distorted as a result of the potential fluctuations generated by the stellar cluster itself as a whole. In particular, stars undergo a rapid relaxation of their eccentricities through both resonant and non-resonant processes. An efficient implementation of the resonant diffusion coefficients allows for detailed and systematic explorations of the parameter space describing the properties of the stellar cluster. In conjunction with recent observations of the S-cluster orbiting SgrA*, this framework can be used to jointly constrain the distribution of the unresolved, old, background stellar cluster and the characteristics of a putative dark cluster. Specifically, we show how this can be used to estimate the typical mass and cuspide exponent of intermediate-mass black holes consistent with the relaxed state of the distribution of eccentricities in the observed S-cluster. This should prove useful in constraining super massive black hole formation scenarios.
Direct numerical integrations of the Fokker-Planck equation in energy-angular momentum space are carried out for stars orbiting a supermassive black hole (SBH) at the center of a galaxy. The algorithm, which was described in detail in an earlier paper, includes diffusion coefficients that describe the effects of both random (classical) and correlated (resonant) encounters. Steady-state solutions are similar to the Bahcall-Wolf solution but are modified at small radii due to the higher rate of diffusion in angular momentum, which results in a low-density core. The core radius is a few percent of the influence radius of the SBH. The corresponding phase-space density f(E,L) drops nearly to zero at low energies, implying almost no stars on tightly-bound orbits about the SBH. Steady-state rates of stellar disruption are presented, and a simple analytic expression is found that reproduces the numerical feeding rates with good accuracy. The distribution of periapsides of disrupted stars is also computed. Time-dependent solutions are also computed, starting from initial conditions similar to those produced by a binary SBH. In these models, feeding rates evolve on two timescales: rapid evolution during which the region evacuated by the massive binary is refilled by angular-momentum diffusion; and slower evolution as diffusion in energy causes the density profile at large radii to attain the Bahcall-Wolf form.
We discuss the importance of the background in order to understand the scattering in the J^{PC}=0^{++} low and intermediate energy region and in particular regarding the sigma meson. In order to appreciate better its importance we compare with the rho meson in the P-wave pipi scattering. We also point out that in present analyses of three-body heavy meson decays, like those of D^+ and B, the role of this background is still not properly settled although it happens to be considerably smaller.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
