2D Fokker-Planck models of rotating clusters

Abstract

Globular clusters rotate significantly, and with the increasing amount of detailed morphologicaland kinematical data obtained in recent years on galactic globular clusters many interesting features show up. We show how our theoretical evolutionary models of rotating clusters can be used to obtain fits, which at least properly model the overall rotation and its implied kinematics in full 2D detail (dispersions, rotation velocities). Our simplified equal mass axisymmetric rotatingmodel provides detailed two-dimensional kinematical and morphological data for star clusters. The degree of rotation is not dominant in energy, but also non-negligible for the phase space distribution function, shape and kinematics of clusters. Therefore the models are well applicable for galactic globular clusters. Since previously published papers on that matter by us made it difficult to do detailed comparisons with observations we provide a much more comprehensive and easy-to-use set of data here, which uses as entries dynamical age and flattening of observed cluster andthen offers a limited range of applicable models in full detail. The method, data structure and some exemplary comparison with observations are presented. Future work will improve modelling anddata base to take a central black hole, a mass spectrum and stellar evolution into account

Differences in the rotational properties of multiple stellar populations in M13: a faster rotation for the ‘extreme’ chemical subpopulation

“…Lagoute & Longaretti 1996;Varri & Bertin 2012) as well as in evolutionary models of rotating globular clusters (e.g. Kim et al 2002;Fiestas et al 2006;Hong et al 2013). As we show below, this parametrisation also satisfyingly reproduces the observed rotation curve of the cluster (as well as the rotation curve of the different chemical subsamples considered) obtained from binning the radial velocity data (see Section 3.2).…”

“…They suggested that there may be a weak anticorrelation between A rot /σ 0 and the inter quartile range (IQR) of the Na-O anticorrelation (a parameter defined by Carretta (2006) to measure the extension of the Na-O distribution in clusters and thus directly 8 When comparing our V rot /σ profile with those of Fiestas et al (2006) and Kim et al (2002), note that our V rot /σ values may be underestimated because of the way we define V rot compared to these authors. Our understanding is that they represent V rot as the azimuthal velocity evaluated on the equatorial plane, while we average the rotational velocity over all angles in the meridional plane.…”

A study of rotating globular clusters

“…Additionally, significant amounts of internal rotation (Lane et al 2011;Bellazzini et al 2012;Bianchini et al 2013) have been observed in most Milky Way GCs. This has motivated the development of dynamical models, including the effects of external tides, mass segregation, corecollapse, and binary stars (Gunn & Griffin 1979;Küpper et al 2010;Zocchi et al 2012) as well as a significant degree of rotation (Wilson 1975;Satoh 1980;Davoust 1986;van de Ven et al 2006;Fiestas et al 2006;.…”

Self-consistent models of quasi-relaxed rotating stellar systems

“…Because of the small number of particles, N-body simulations were initially (Aarseth 1969, Wielen 1974, and Akiyama & Sugimoto 1989 unable to clearly describe the complex interplay between relaxation and rotation. Later investigations, primarily based on a Fokker-Planck approach (Goodman 1983, Einsel & Spurzem 1999, Kim et al 2002, and Fiestas et al 2006 have clarified this point, not only by testing the proposed mechanism of angular momentum removal by escaping stars, but also by showing that rotation accelerates the entire dynamical evolution of the system. More recent N-body simulations (Boily 2000, Ernst et al 2007, and Kim et al 2008) confirm these conclusions and show that, when a three-dimensional tidal field is included, such acceleration is enhanced even further.…”

“…In addition, specifically designed 2D Fokker-Planck models (Fiestas et al 2006) have been applied to the study of M5, NGC 2808, and NGC 5286. We recall that the detection of internal rotation in globular clusters is a challenging task, because the typical value of the ratio of mean velocity to velocity dispersion is only of a few tenths, for example V/σ ≈ 0.26, 0.32 for 47 Tuc and ω Cen, respectively (Meylan and Mayor 1986; for a summary of the results for several Galactic objects, see also Table 7.2 in Meylan & Heggie 1997).…”