We present the results of a study aimed at exploring the evolution towards energy equipartition in star cluster models with different initial degrees of anisotropy in the velocity distribution. Our study reveals a number of novel aspects of the cluster dynamics and shows that the rate of evolution towards energy equipartition (1) depends on the initial degree of radial velocity anisotropy -- it is more rapid for more radially anisotropic systems; and (2) differs for the radial and the tangential components of the velocity dispersion. (3) The outermost regions of the initially isotropic system evolve towards a state of `inverted' energy equipartition in which high-mass stars have a larger velocity dispersion than low-mass stars -- this inversion originates from the mass-dependence of the tangential velocity dispersion whereas the radial velocity dispersion shows no anomaly. Our results add new fundamental elements to the theoretical framework needed to interpret the wealth of recent and upcoming observational studies of stellar kinematics in globular clusters, and shed further light on the link between the clusters' internal kinematics, their formation and evolutionary history.
We examine the degree of energy equipartition in 9 Galactic globular clusters using proper motions measured with the Hubble Space Telescope. For most clusters in the sample, this is the first energy equipartition study ever performed. This study is also the largest of its kind, albeit with only 9 clusters. We begin by rigorously cleaning the catalogues to remove poor-quality measurements and to ensure high signal-to-noise for the study. Using the cleaned catalogues, we investigate how velocity dispersion $σ$ changes with stellar mass $m$. We fit two functional forms: the first, a classic power…
We investigate the long-term dynamical evolution of the internal kinematics of multimass rotating star clusters. We have performed a set of N-body simulations to follow the internal evolution of clusters with different degrees of initial rotation and have explored the evolution of the rotational velocity, the degree of energy equipartition, and anisotropy in the velocity distribution. Our simulations show that: 1) as the cluster evolves, the rotational velocity develops a dependence on the stellar mass with more massive stars characterised by a more rapid rotation and a peak in the rotation cu…
In weakly collisional stellar systems such as some globular clusters, partial energy equipartition and mass segregation are expected to develop as a result of the cumulative effect of stellar encounters even in systems initially characterized by star-mass independent density and energy distributions. In parallel, numerical simulations have demonstrated that radially-biased pressure anisotropy slowly builds up in realistic models of globular clusters from initial isotropic conditions, leading to anisotropy profiles that, to some extent, mimic those resulting from incomplete violent relaxation k…
This paper is the second in a series investigating the evolution of star clusters towards energy equipartition (EEP). Here, we focus on the effects of the external tidal field of the host galaxy, initial anisotropy in the velocity distribution, and primordial binary star population. The results of our $N$-body simulations show that regardless of the strength of the tidal field or the fraction of primordial binaries: (i) the evolution towards EEP in the intermediate and outer regions of initially anisotropic systems is more rapid than for isotropic systems; (ii) this evolution also proceeds at …
oMEGACat. VI. Analysis of the overall kinematics of Omega Centauri in 3D: velocity dispersion, kinematic distance, anisotropy, and energy equipartition
Globular clusters are collisional systems, meaning that the stars inside them interact on timescales much shorter than the age of the Universe. These frequent interactions transfer energy between stars and set up observable trends that tell the story of a cluster's evolution. This contribution focuses on what we can learn by studying velocity anisotropy and energy equipartition in globular clusters with Hubble Space Telescope proper motions.
The effect of unresolved binaries on globular cluster proper-motion dispersion profiles
对球状星团进行高精度的运动学研究需要对所有可能的污染源有准确的了解。在其他来源中，双星可以在运动学中引入系统偏差。使用一组Monte Carlo集群模拟不同的浓度和二进制分数，我们调查未解决的二进制自行运动色散曲线的影响，处理模拟像HST自行运动样本。由于球状星团朝着部分能量均分的状态演化，更多的大质量恒星会失去能量，降低它们的速度色散。因此，平均而言，双星有较低的速度色散，因为它们是更大质量的运动示踪剂。我们表明，在具有高二元分数（初始二元分数为50%）和高浓度（即，接近能量均分），未分辨的双星会在主序星的速度色散中引入一个依赖于颜色的偏差，其量级为0.1-0.3 km s $^{-1}$（相当于速度色散的$1-6$ %），最红的恒星具有较低的速度色散，这是由于污染双星的比例较高。这种偏差取决于区分双星和单星的能力，颜色-星等图的细节和光度误差。我们将我们的分析应用于NGC 7078（M15）的HSTPROMO数据集，并表明没有观察到归因于双星的影响，与星团的低双星比例一致。我们的工作表明，双星不显着偏置自行速度色散配置文件，但应考虑到运动学分析的误差预算。
As a result of the slow action of two-body encounters, globular clusters develop mass segregation and attain a condition of only partial energy equipartition even in their central, most relaxed regions. Realistic numerical simulations show that, during the process, a radially-biased anisotropy profile slowly builds up, mimicking that resulting from incomplete violent relaxation. Commonly used dynamical models, such as the one-component King models, cannot describe these properties. Here we show that simple two-component models based on a distribution function originally conceived to describe e…
Stellar binaries are the most important energy reservoir of star clusters. Via three-body encounters, binaries can reverse the core collapse and prevent a star cluster from reaching equipartition. Moreover, binaries are essential for the formation of stellar exotica, such as blue straggler stars, intermediate-mass black holes and massive ($\gtrsim{}30$ M$_\odot$) black hole binaries.
Hubble Space Telescope proper motion (HSTPROMO) catalogs of Galactic globular clusters. IV. Kinematic profiles and average masses of blue straggler stars
Stars form in spatially and temporarily correlated star formation events (CSFEs) and the dynamical processes within these "embedded clusters" leave imprints in the stellar populations in galactic fields. Such imprints are correlations in phase space (e.g. gravitationally bound star clusters, tidal streams), in the binary properties of stars and in the present-day stellar mass functions in the surviving clusters. The dynamical processes include expulsion of massive stars from cluster cores, disruption of CSFEs due to residual gas expulsion and energy-equipartition driven evaporation of stars fr…
We present the results of a study aimed at exploring, by means of N-body simulations, the evolution of rotating multi-mass star clusters during the violent relaxation phase, in the presence of a weak external tidal field. We study the implications of the initial rotation and the presence of a mass spectrum for the violent relaxation dynamics and the final properties of the equilibria emerging at the end of this stage. Our simulations show a clear manifestation of the evolution towards spatial mass segregation and evolution towards energy equipartition during and at the end of the violent relax…
Through a suite of direct N-body simulations, we explore how the structural and kinematic evolution of a star cluster located at the center of a dwarf galaxy is affected by the shape of its host's dark matter density profile. The stronger central tidal fields of cuspier halos minimize the cluster's ability to expand in response to mass loss due to stellar evolution during its early evolutionary stages and during its subsequent long-term evolution driven by two-body relaxation. Hence clusters evolving in cuspier dark matter halos are characterized by more compact sizes, higher velocity dispersi…
Using the Gaia colour-magnitude diagram, we assign masses to a catalogue of 979 confirmed members of the Hyades cluster and tails. By fitting the cumulative mass profile, stars within the tidal radius have a Plummer-like profile with half-mass radius $r_{\rm h}$ of 5.75 pc. The tails are extended with $r_{\rm h} = 69.35$ pc and fall off more slowly than Plummer with density proportional to distance$^{-1.36}$. The cluster stars are separated into two groups at BP-RP $=2$ or $0.56 M_\odot$ to give a high mass (${\bar M} = 0.95 M_\odot$) and a low mass (${\bar M} = 0.32 M_\odot$) population. We s…
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…
This paper aims at studying the reliability of a few frequently raised but not proven arguments for the modeling of cold gas clouds embedded in or moving through a hot plasma and at sensitizing modelers to a more careful consideration of unavoidable acting physical processes and their relevance. At first, by numerical simulations we demonstrate the growing effect of self-gravity on interstellar clouds and, by this, moreover argue against their initial setup as homogeneous. We apply the adaptive-mesh refinement code {\sc Flash} with extensions to metal-dependent radiative cooling and external h…
The parameter A+, defined as the area enclosed between the cumulative radial distribution of blue straggler stars (BSSs) and that of a reference population, is a powerful indicator of the level of BSS central segregation. As part of the Hubble Space Telescope UV Legacy Survey of Galactic globular clusters (GCs), here we present the BSS population and the determination of A+ in 27 GCs observed out to about one half-mass radius. In combination with 21 additional clusters discussed in a previous paper this provides us with a global sample of 48 systems (corresponding to \sim 32\% of the Milky Way…
We examine the mass-dependence of the velocity dispersion of stars in the young cluster NGC 6530 to better understand how it formed. Using a large sample of members we find that the proper motion velocity dispersion increases with stellar mass. While this trend is the opposite to that predicted if the cluster were developing energy equipartition, it is in agreement with recent N-body simulations that find such a trend develops because of the Spitzer instability. In these simulations the massive stars sink to the centre of the cluster and form a self-gravitating system with a higher velocity di…
We present an improved data-reduction technique to obtain high-precision proper motions (PMs) of globular clusters using Hubble Space Telescope data. The new reduction is superior to the one presented in the first paper of this series for the faintest sources in very crowded fields. We choose the globular cluster NGC 362 as a benchmark to test our new procedures. We measure PMs of 117 450 sources in the field, showing that we are able to obtain a PM precision better than 10 $μ$as yr$^{-1}$ for bright stars. We make use of this new PM catalog of NGC 362 to study the cluster's internal kinematic…
We present the analysis of the radial distributions and kinematic properties of the multiple stellar populations (mPOPs) hosted in the globular cluster (GC) NGC 6352 as part of the Hubble Space Telescope (HST) "UV Legacy Survey of Galactic Globular Clusters" program. NGC 6352 is one of the few GCs for which the mPOP tagging in appropriate color-magnitude diagrams is clear in all evolutionary sequences. We computed high-precision stellar proper motions for the stars from the cluster's core out to 75 arcsec ($\sim$1.5 core radii, or $\sim$0.6 half-light radii). We find that, in the region explor…
We assess how much unused strong lensing information is available in the deep \emph{Hubble Space Telescope} imaging and VLT/MUSE spectroscopy of the \emph{Frontier Field} clusters. As a pilot study, we analyse galaxy cluster MACS\,J0416.1-2403 ($z$$=$$0.397$, $M(R<200\,{\rm kpc})$$=$$1.6$$\times$$10^{14}\msun$), which has 141 multiple images with spectroscopic redshifts. We find that many additional parameters in a cluster mass model can be constrained, and that adding even small amounts of extra freedom to a model can dramatically improve its figures of merit. We use this information to const…
Up to now, the largest sample of galaxy clusters selected in X-rays comes from the ROSAT All-Sky Survey (RASS). Although there have been many interesting clusters discovered with the RASS data, the broad point spread function (PSF) of the ROSAT satellite limits the amount of spatial information of the detected objects. This leads to the discovery of new cluster features when a re-observation is performed with higher resolution X-ray satellites. Here we present the results from XMM-Newton observations of three clusters: RXCJ2306.6-1319, ZwCl1665 and RXCJ0034.6-0208, for which the observations r…
With the help of Gaia data, it is noted that in addition to the core components, there are low-density outer halo components in the extended region of open clusters. To study the extended structure beyond the core radius of the cluster ($\sim$ 10 pc), based on Gaia EDR3 data, taking up to 50 pc as the searching radius, we use the pyUPMASK algorithm to re-determine the member stars of the open cluster within 1-2 kpc. We obtain the member stars of 256 open clusters, especially those located in the outer halo region of open clusters. Furthermore, we find that most open clusters' radial density pr…
We present the results of the analysis of deep photometric data of 32 Galactic globular clusters. We analysed 69 parallel field images observed with the Wide Field Channel of the Advanced Camera for Surveys of the Hubble Space Telescope which complemented the already available photometry from the globular cluster treasury project covering the central regions of these clusters. This unprecedented data set has been used to calculate the relative fraction of stars at different masses (i.e. the present-day mass function) in these clusters by comparing the observed distribution of stars along the c…
We investigate archival Hubble Space Telescope ACS/SBC F140LP observations of NGC~1399 to search for evidence of multiple stellar populations in extragalactic globular clusters. Enhanced FUV populations are thought to be indicators of He-enhanced second generation populations in globular clusters, specifically extreme/blue horizontal branch stars. Out of 149 globular clusters in the field of view, 58 have far ultraviolet (FUV) counterparts with magnitudes brighter than 28.5. Six of these FUV-deteced globular clusters are also detected in X-rays, including one ultraluminous X-ray source ($L_X >…
Population Parameters of Intermediate-Age Star Clusters in the Large Magellanic Cloud. II. New Insights from Extended Main Sequence Turnoffs in 7 Star Clusters
