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
l analysis of the photometry and three-dimensional kinematics of omega Cen, 47 Tuc, and M15, by means of a recently introduced family of self-consistent axisymmetric rotating models. The three clusters, characterized by different relaxation conditions, show evidence of differential rotation and deviations from sphericity. The combination of line-of-sight velocities and proper motions allows us to determine their internal dynamics, predict their morphology, and estimate their dynamical distance. The well-relaxed cluster 47 Tuc is very well interpreted by our model; internal rotation is found to explain the observed morphology. For M15, we provide a global model in good agreement with the data, including the central behavior of the rotation profile and the shape of the ellipticity profile. For the partially relaxed cluster omega Cen, the selected model reproduces the complex three-dimensional kinematics; in particular the observed anisotropy profile, characterized by a transition from isotropy, to weakly-radial anisotropy, and then to tangential anisotropy in the outer parts. The discrepancy found for the steep central gradient in the observed line-of-sight velocity dispersion profile and for the ellipticity profile is ascribed to the condition of only partial relaxation of this cluster and the interplay between rotation and radial anisotropy.
A re-investigation of the gravothermal catastrophe is presented. By means of a linear perturbation analysis, we study the dynamical stability of a spherical self-gravitating isothermal fluid of finite volume and find that the conditions for the onset
of the gravothermal catastrophe, under different external conditions, coincide with those obtained from thermodynamical arguments. This suggests that the gravothermal catastrophe may reduce to Jeans instability, rediscovered in an inhomogeneous framework. We find normal modes and frequencies for the fluid system and show that instability develops on the dynamical time scale. We then discuss several related issues. In particular: (1) For perturbations at constant total energy and constant volume, we introduce a simple heuristic term in the energy budget to mimic the role of binaries. (2) We outline the analysis of the two-component case and show how linear perturbation analysis can be carried out also in this more complex context in a relatively straightforward way. (3) We compare the behavior of the fluid model with that of the collisionless sphere. In the collisionless case the instability seems to disappear, which is at variance with the linear Jeans stability analysis in the homogeneous case; we argue that a key ingredient to understand the difference (a spherical stellar system is expected to undergo the gravothermal catastrophe only in the presence of some collisionality, which suggests that the instability is dissipative and not dynamical) lies in the role of the detailed angular momentum in a collisionless system. Finally, we briefly comment on the meaning of the Boltzmann entropy and its applicability to the study of the dynamics of self- gravitating inhomogeneous gaseous systems.
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.
Disk-halo decompositions of galaxy rotation curves are generally performed in a parametric way. We construct self-consistent models of nonspherical isothermal halos embedding a zero-thickness disk, by assuming that the halo distribution function is a
Maxwellian. The method developed here can be used to study other physically-based choices for the halo distribution function and the case of a disk accompanied by a bulge. In a preliminary investigation we note the existence of a fine tuning between the scalelengths R_{Omega} and h, respectively characterizing the rise of the rotation curve and the luminosity profile of the disk, which surprisingly applies to both high surface brightness and low surface brightness galaxies. This empirical correlation identifies a much stronger conspiracy than the one required by the smoothness and flatness of the rotation curve (disk-halo conspiracy). The self-consistent models are characterized by smooth and flat rotation curves for very different disk-to-halo mass ratios, hence suggesting that conspiracy is not as dramatic as often imagined. For a typical rotation curve, with asymptotically flat rotation curve at V_{infty} (the precise value of which can also be treated as a free parameter), and a typical density profile of the disk, self-consistent models are characterized by two dimensionless parameters, which correspond to the dimensional scales (the disk mass-to-light ratio M/L and the halo central density) of standard disk-halo decompositions. We show that if the rotation curve is decomposed by means of our self-consistent models, the disk-halo degeneracy is removed and typical rotation curves are fitted by models that are below the maximum-disk prescription. Similar results are obtained from a study of NGC 3198. Finally, we quantify the flattening of the spheroidal halo, which is significant, especially on the scale of the visible disk.
Context: Several spiral galaxies, as beautifully exhibited by the case of NGC 6946, display a prominent large-scale spiral structure in their gaseous outer disk. Such structure is often thought to pose a dynamical puzzle, because grand-design spiral
structure is traditionally interpreted as the result of density waves carried mostly in the stellar disk. Aims. Here we argue that the outer spiral arms in the cold gas outside the bright optical disk actually have a natural interpretation as the manifestation of the mechanism that excites grand-design spiral structure in the main, star-dominated body of the disk: the excitation is driven by angular momentum transport to the outer regions, through trailing density waves outside the corotation circle that can penetrate beyond the Outer Lindblad Resonance in the gaseous component of the disk. Methods: Because of conservation of the density wave action, these outgoing waves are likely to become more prominent in the outer disk and eventually reach non-linear amplitudes. To calculate the desired amplitude profiles, we make use of the theory of dispersive waves. Results: If the conditions beyond the optical radius allow for an approximate treatment in terms of a linear theory, we show that fitting the observed amplitude profiles leads to a quantitative test on the density of the disk material and thus on the dark matter distribution in the outer parts of the galaxy. Conclusions: This study is thus of interest to the general problem of the disk-halo decomposition of rotation curves.
