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Register a new userA dynamical study of Galactic globular clusters under different relaxation conditions
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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 spherical stellar dynamical models. Systems characterized by shorter relaxation time scales are expected to be better described by isotropic King models, while less relaxed systems might be interpreted by means of non-truncated, radially-biased anisotropic f^( u) models, originally designed to represent stellar systems produced by a violent relaxation formation process and applied here for the first time to the study of globular clusters. The comparison between dynamical models and observations is performed by fitting simultaneously surface brightness and velocity dispersion profiles. For each globular cluster, the best-fit model in each family is identified, along with a full error analysis on the relevant parameters. Detailed structural properties and mass-to-light ratios are also explicitly derived. We find that King models usually offer a good representation of the observed photometric profiles, but often lead to less satisfactory fits to the kinematic profiles, independently of the relaxation condition of the systems. For some less relaxed clusters, f^( u) models provide a good description of both observed profiles. Some derived structural characteristics, such as the total mass or the half-mass radius, turn out to be significantly model-dependent. The analysis confirms that, to answer some important dynamical questions that bear on the formation and evolution of globular clusters, it would be highly desirable to acquire larger numbers of accurate kinematic data-points, well distributed over the cluster field.
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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 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.
We have carried out a set of Monte Carlo simulations to study a number of fundamental aspects of the dynamical evolution of multiple stellar populations in globular clusters with different initial masses, fractions of second generation (2G) stars, and structural properties. Our simulations explore and elucidate: 1) the role of early and long-term dynamical processes and stellar escape in the evolution of the fraction of 2G stars and the link between the evolution of the fraction of 2G stars and various dynamical parameters; 2) the link between the fraction of 2G stars inside the cluster and in the population of escaping stars during a clusters dynamical evolution; 3) the dynamics of the spatial mixing of the first-generation (1G) and 2G stars and the details of the structural properties of the two populations as they evolve toward mixing; 4) the implications of the initial differences between the spatial distribution of 1G and 2G stars for the evolution of the anisotropy in the velocity distribution and the expected radial profile of the 1G and 2G anisotropy for clusters at different stages of their dynamical history; 5) the variation of the degree of energy equipartition of the 1G and the 2G populations as a function of the distance from the clusters centre and the clusters evolutionary phase.
Proper motions (PMs) are crucial to fully understand the internal dynamics of globular clusters (GCs). To that end, the Hubble Space Telescope (HST) Proper Motion (HSTPROMO) collaboration has constructed large, high-quality PM catalogues for 22 Galactic GCs. We highlight some of our exciting recent results: the first directly-measured radial anisotropy profiles for a large sample of GCs; the first dynamical distance and mass-to-light (M/L) ratio estimates for a large sample of GCs; and the first dynamically-determined masses for hundreds of blue-straggler stars (BSSs) across a large GC sample.
We investigate potential correlations between radio source counts (after background corrections) of 22 Galactic globular clusters (GCs) from the MAVERIC survey, and stellar encounter rates ($Gamma$) and masses ($M$) of the GCs. Applying a radio luminosity limit of $L_mathrm{lim}=5.0times 10^{27}~mathrm{erg~s^{-1}}$, we take a census of radio sources in the core and those within the half-light radius. By following a maximum likelihood method and adopting a simplified linear model, we find an unambiguous dependence of core radio source counts on $Gamma$ and/or $M$ at 90% confidence, but no clear dependence of source counts within the half-light radius on either $Gamma$ or $M$. Five of the identified radio sources in cores above our adopted limit are millisecond pulsars or neutron star X-ray binaries (XRBs), the dependence of which on $Gamma$ is well-known, but another is a published black hole (BH) XRB candidate, and ten others are not identified. Accounting for the verified cluster members increases the significance of correlation with $M$ and/or $Gamma$ (to 99% confidence), for fits to core and half-light region source counts, while excluding a dependence on $Gamma$ alone at 90% (core) and 68% (half-light) confidence. This is consistent with published dynamical simulations of GC BH interactions that argue $Gamma$ will be a poor predictor of the distribution of accreting BHs in GCs. Future multiwavelength follow-up to verify cluster membership will enable stronger constraints on the dependence of radio source classes on cluster properties, promising a new view on the dynamics of BHs in GCs.
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