Dynamics Of Globular Clusters Research Articles

Shapes of dark matter haloes with discrete globular cluster dynamics: The example of NGC 5128 (Centaurus A)

Within the Lambda cold dark matter (Lambda CDM) cosmology, dark matter haloes are expected to deviate from spherical symmetry. The particular shape of a galactic halo reflects the environment and mass assembly history of its host, as well as the nature of dark matter. Constraining halo shapes at large galactocentric distances is challenging because of the low density of luminous tracers. The well-studied massive early-type galaxy NGC 5128, also known as Centaurus A (CenA), has a large number of radial velocity measurements for globular clusters (GCs) and planetary nebulae (PNe) extending over a vast area of its extended low-surface-brightness stellar halo. In this work, we aim to determine the deviation from spherical symmetry of the dark matter halo of CenA at 5 using its GCs as kinematic tracers of the gravitational potential. We investigated the largest photometric catalogue of GC candidates in order to accurately characterise the spatial distribution of the relaxed population of GCs. To investigate the presence of non-relaxed structures in the kinematic catalogue of GCs, we used the relaxed point-symmetric velocity field as determined by the host's PNe population. We used anisotropic Jeans modelling under axisymmetric assumptions together with the Gaussian likelihood and GCs as discrete tracers. The gravitational potential is generated by flattened stellar and dark matter distributions. We leveraged the different orbital properties of the blue and red GCs ---such as rotation and velocity anisotropy--- to model both populations separately. By minimising $ we iteratively find the best-fit parameters. We find that the discrete kinematics of the GCs are consistent with being drawn from an underlying relaxed velocity field determined from PNe. The best-fit parameters of the gravitational potential recovered from the blue and red GCs separately agree well and we use them to compute the final results: $M_ $, and the flattening $q_ DM $. Both GC populations show mild rotation, with red having a slightly stronger rotational signature and radially biased orbits, and blue GCs preferring negative velocity anisotropy. An oblate or a spherical dark matter halo of NGC 5128 is strongly disfavoured by our modelling.

Globular clusters and bar: captured or not captured?

ABSTRACT Studies of the dynamics of globular clusters assume different values of bar parameters (mass, velocity, and size) and analyse the results of orbit classifications over the range of the chosen values. It is also a usual thing that a spherical bulge component is converted into the bar to obtain a non-axisymmetric potential from an axisymmetric one. The choice of bar parameters and the way the bar is converted from the bulge introduce systematics into the orbit classifications that we explore in this study. We integrate orbits of 30 bulge globular clusters residing in the inner area of the Galaxy (R ≲ 5 kpc) backwards in time for three different potentials, two of which are obtained by fitting the rotation curve, and one is taken from the surrogate N-body model representing our Galaxy. We analyse each orbit in terms of dominant frequencies obtained from its coordinate spectra. We find that the bar pattern speed is a key factor in orbital classification. With an increase of the bar pattern speed, frequencies deviate more and more from the ‘bar’ frequency ratio 2:1. The bar-to-bulge mass ratio (assuming the total mass of the bar plus the bulge is fixed) and size of the bar play a smaller role. We also find that, in the N-body potential, the fraction of orbits that follow the bar is higher than in those obtained from fitting the rotation curve.

The Influence of the Bar on the Dynamics of Globular Clusters in the Central Region of the Milky Way. Frequency Analysis of Orbits According to Gaia EDR3 Data

The Influence of the Bar on the Dynamics of Globular Clusters in the Central Region of the Milky Way. Frequency Analysis of Orbits According to Gaia EDR3 Data

Шаровые скопления в центральной области Млечного Пути. II. Частотный анализ орбит, построенных по данным Gaia EDR3

This work represents the second stage of research aimed at studying the influence of the bar on the orbital dynamics of globular clusters (Bajkova, Smirnov, and Bobylev, 2023). The orbits of 45 globular clusters in the central galactic region with a radius of 3.5 kpc have been analyzed by spectral dynamics methods in order to identify objects captured by the bar. Since the parameters of the bar of the Milky Way are known with a very large uncertainty, orbits were constructed and their frequency analysis was carried out with varying the mass, length and angular velocity of rotation of the bar in a wide range of values with a fairly dense grid. The orbits were integrated 2.5 billion years backward. As a result, globular clusters supporting the bar were identified for each set of bar parameters. To form the 6D phase space required for orbit integration, we used the most accurate astrometric data from the Gaia satellite (Vasiliev and Baumgardt, 2021), as well as new refined average distances to globular clusters (Baumgardt and Vasiliev, 2021).

The Influence of the Galactic Bar on the Dynamics of Globular Clusters

We make use of recent estimates for the parameters of the Milky Way’s halo globular clusters and study the influence of the galactic bar on the dynamics of these clusters by computing their orbits. We use both an axisymmetric and non-axisymmetric galactic potentials, which include the rotating elongated bar/bulge structure. We account for observational errors both in the positions and in the velocities of the globular clusters and explore the influence of the bar on clusters’ evolution. This is contained in the angular momentum–total energy plane, (Lz,E), which is widely exploited as an indicator of the groups of globular clusters that originated from the same accretion event. Particular attention is devoted to the Gaia-Sausage/Enceladus and Pontus structures identified recently as two independent accretion events. Our study shows that it is not possible to identify GSE and Pontus as different merger events.

Orbits of globular clusters computed with dynamical friction in the Galactic anisotropic velocity dispersion field

ABSTRACT We present a preliminary analysis of the effect of dynamical friction on the orbits of part of the globular clusters in our Galaxy. Our study considers an anisotropic velocity dispersion field approximated using the results of studies in the literature. An axisymmetric Galactic model with mass components consisting of a disc, a bulge, and a dark halo is employed in the computations. We provide a method to compute the dynamical friction acceleration in ellipsoidal, oblate, and prolate velocity distribution functions with similar density in velocity space. Orbital properties, such as mean time-variations of perigalactic and apogalactic distances, energy, and z-component of angular momentum, are obtained for globular clusters lying in the Galactic region R ≲ 10 kpc, |z| ≲ 5 kpc, with R, z cylindrical coordinates. These include clusters in prograde and retrograde orbital motion. Several clusters are strongly affected by dynamical friction, in particular Liller 1, Terzan 4, Terzan 5, NGC 6440, and NGC 6553, which lie in the Galactic inner region. We comment on the more relevant implications of our results on the dynamics of Galactic globular clusters, such as their possible misclassification between the categories ‘halo’, ‘bulge’, and ‘thick disc’, the resulting biasing of globular-cluster samples, the possible incorrect association of the globulars with their parent dwarf galaxies for accretion events, and the possible formation of ‘nuclear star clusters’.

A universal relation between the properties of supermassive black holes, galaxies, and dark matter haloes

ABSTRACT We study the relations between the mass of the central black hole (BH) MBH, the dark matter halo mass Mh, and the stellar-to-halo mass fraction f⋆∝M⋆/Mh in a sample of 55 nearby galaxies with dynamically measured $M_{\rm BH}\gt 10^6\, {\rm M}_\odot$ and $M_{\rm h}\gt 5\times 10^{11}\, {\rm M}_\odot$. The main improvement with respect to previous studies is that we consider both early- and late-type systems for which Mh is determined either from globular cluster dynamics or from spatially resolved rotation curves. Independently of their structural properties, galaxies in our sample build a well defined sequence in the MBH–Mh–f⋆ space. We find that: (i) Mh and MBH strongly correlate with each other and anticorrelate with f⋆; (ii) there is a break in the slope of the MBH–Mh relation at Mh of $10^{12}\, {\rm M}_\odot$, and in the f⋆–MBH relation at MBH of $\sim 10^7\!-\!10^8\, {\rm M}_\odot$; (iii) at a fixed MBH, galaxies with a larger f⋆ tend to occupy lighter haloes and to have later morphological types. We show that the observed trends can be reproduced by a simple equilibrium model in the ΛCDM framework where galaxies smoothly accrete dark and baryonic matter at a cosmological rate, having their stellar and BH build-up regulated both by the cooling of the available gas reservoir and by the negative feedback from star formation and active galactic nuclei (AGNs). Feature (ii) arises as the BH population transits from a rapidly accreting phase to a more gentle and self-regulated growth, while scatter in the AGN feedback efficiency can account for feature (iii).

Milky Way globular cluster dynamics: are they preferentially co-rotating?

The motion of baryonic components of the Milky Way is governed by both luminous and dark matter content of the Galaxy. Thus, the dynamics of Milky Way globular clusters (GCs) can be used as tracers to infer the mass model of the Galaxy up to a large radius. In this work, we apply the directly observable line-of-sight velocities to test if the dynamics of the GC population are consistent with an assumed axisymmetric gravitational potential of the Milky Way. For this, we numerically compute the phase space distribution of the GC population where the orbits are either oriented randomly or co-/counter- rotating with respect to the stellar disk. Then we compare the observed position and line-of-sight velocity distribution of ∼150 GCs with those of the models. We found that, for the adopted mass model, the co-rotating scenario is the favored model based on various statistical tests. We do the analysis with and without the GCs associated with the progenitors of early merger events. This analysis can be extended in the near future to include precise and copious data to better constrain the Galactic potential up to a large radius.

Using Gaia for studying Milky Way star clusters

AbstractWe review the implications of the Gaia Data Release 2 catalogue for studying the dynamics of Milky Way globular clusters, focusing on two separate topics.The first one is the analysis of the full 6-dimensional phase-space distribution of the entire population of Milky Way globular clusters: their mean proper motions (PM) can be measured with an exquisite precision (down to 0.05 mas yr−1, including systematic errors). Using these data, and a suitable ansatz for the steady-state distribution function (DF) of the cluster population, we then determine simultaneously the best-fit parameters of this DF and the total Milky Way potential. We also discuss possible correlated structures in the space of integrals of motion.The second topic addresses the internal dynamics of a few dozen of the closest and richest globular clusters, again using the Gaia PM to measure the velocity dispersion and internal rotation, with a proper treatment of spatially correlated systematic errors. Clear rotation signatures are detected in 10 clusters, and a few more show weaker signatures at a level ∼0.05 mas yr−1. PM dispersion profiles can be reliably measured down to 0.1 mas yr−1, and agree well with the line-of-sight velocity dispersion profiles from the literature.

Phase space complexity of star clusters: Fresh observables for old and new questions

AbstractThe blooming era of precision astrometry for Galactic studies truly brings the rich internal dynamics of globular clusters to the centre stage. But several aspects of our current understanding of fundamental collisional stellar dynamics cannot match such new-generation data and the theoretical ambitions they trigger. This rapidly evolving context offers the stimulus to address a number of old and new questions concerning the phase space properties of this class of stellar systems.

Search for extra-tidal RR Lyrae stars in Milky Way globular clusters fromGaiaDR2

We used extra-tidal RR Lyrae stars to study the dynamics of Galactic globular clusters and know how effects like dynamical friction and tidal disruption affect these clusters. The Gaia DR2 catalog for RR Lyrae stars (Clementini et al. 2018) is used along with the proper motions and tidal radii data for the globular clusters compiled from literature. A sample of 56 Galactic globular clusters is analyzed. Out of these 56 Galactic globular clusters, only 11 have extra-tidal RR Lyrae stars. However, only two clusters, namely, NGC 3201 and NGC 5024, have enough extra-tidal RR Lyrae stars to draw interesting conclusions. NGC 3201 has 13 extra-tidal RR Lyrae stars which are asymmetrically distributed around its center with more number of stars in its trailing zone than its leading part. We conclude that these asymmetrical tidal tails are due to the combined effect of tidal disruption and the stripped debris from the cluster. On the other hand, NGC 5024 has 5 extra-tidal RR Lyrae stars, four of them are concentrated in a region which is at a distance of about 3 times the tidal radius from its center. These may be the stars that are being ripped apart from the cluster due to tidal disruption. The presence of these extra-tidal RR Lyrae stars in the clusters can be an indication that more cluster stars are present outside their tidal radii which may be revealed by deep wide field CMDs of the clusters.

Mass modelling globular clusters in theGaiaera: a method comparison using mock data from anN-body simulation of M 4

As we enter a golden age for studies of internal kinematics and dynamics of Galactic globular clusters (GCs), it is timely to assess the performance of modelling techniques in recovering the mass, mass profile, and other dynamical properties of GCs. Here, we compare different mass-modelling techniques (distribution-function (DF)-based models, Jeans models, and a grid of N-body models) by applying them to mock observations from a star-by-star N-body simulation of the GC M 4 by Heggie. The mocks mimic existing and anticipated data for GCs: surface brightness or number density profiles, local stellar mass functions, line-of-sight velocities, and Hubble Space Telescope- and Gaia-like proper motions. We discuss the successes and limitations of the methods. We find that multimass DF-based models, Jeans, and N-body models provide more accurate mass profiles compared to single-mass DF-based models. We highlight complications in fitting the kinematics in the outskirts due to energetically unbound stars associated with the cluster ("potential escapers", not captured by truncated DF models nor by N-body models of clusters in isolation), which can be avoided with DF-based models including potential escapers, or with Jeans models. We discuss ways to account for mass segregation. For example, three-component DF-based models with freedom in their mass function are a simple alternative to avoid the biases of single-mass models (which systematically underestimate the total mass, half-mass radius, and central density), while more realistic multimass DF-based models with freedom in the remnant content represent a promising avenue to infer the total mass and the mass function of remnants.

The effect of stellar helium abundance on dynamics of multiple populations in globular clusters

We incorporate a semi-analytic formula for the main sequence lifetime of helium-rich stars in N-body simulations of multiple population globular clusters to investigate how the enriched helium stars impact the dynamics of globular clusters. We show that a globular cluster with a helium-rich concentrated population will be slightly smaller than a globular cluster with a normal-helium second generation, with the largest difference seen in the extended normal-helium population. This effect is shown both for a cluster in isolation and one in a realistic Milky Way tidal field. We show that this effect is a result of mass segregation, and the earlier loss of more massive stars in a helium-rich concentrated population due to their decreased main sequence lifetime. The two populations will therefore become dynamically mixed at a slightly earlier time than if they have the same helium abundance. Furthermore, we find that it is possible for the helium-enriched population to become more extended than the normal-helium population if it forms with a low initial concentration or the cluster is able to evolve for a large number of relaxation times. We conclude that the dynamical effects of helium on stellar masses are modest, and that the initial concentration of the two populations and the strength of the Milky Way tidal field are more important in determining the relative radial distributions of multiple populations.

From the top down and back up again: star cluster structure from hierarchical star formation.

Young massive star clusters spanning ~104-108M⊙ in mass have been observed to have similar surface brightness profiles. We show that recent hydrodynamical simulations of star cluster formation have also produced star clusters with this structure. We argue analytically that this type of mass distribution arises naturally in the relaxation from a hierarchically clustered distribution of stars into a monolithic star cluster through hierarchical merging. We show that initial profiles of finite maximum density will tend to produce successively shallower power-law profiles under hierarchical merging, owing to certain conservation constraints on the phase-space distribution. We perform N-body simulations of a pairwise merger of model star clusters and find that mergers readily produce the shallow surface brightness profiles observed in young massive clusters. Finally, we simulate the relaxation of a hierarchically clustered mass distribution constructed from an idealized fragmentation model. Assuming only power-law spatial and kinematic scaling relations, these numerical experiments are able to reproduce the surface density profiles of observed young massive star clusters. Thus, we bolster the physical motivation for the structure of young massive clusters within the paradigm of hierarchical star formation. This could have important implications for the structure and dynamics of nascent globular clusters.

Dating the Tidal Disruption of Globular Clusters with GAIA Data on Their Stellar Streams

Abstract The Gaia mission promises to deliver precision astrometry at an unprecedented level, heralding a new era for discerning the kinematic and spatial coordinates of stars in our Galaxy. Here, we present a new technique for estimating the age of tidally disrupted globular cluster streams using the proper motions and parallaxes of tracer stars. We evolve the collisional dynamics of globular clusters within the evolving potential of a Milky Way-like halo extracted from a cosmological ΛCDM simulation and analyze the resultant streams as they would be observed by Gaia. The simulations sample a variety of globular cluster orbits, and account for stellar evolution and the gravitational influence of the disk of the Milky Way. We show that a characteristic timescale, obtained from the dispersion of the proper motions and parallaxes of stars within the stream, is a good indicator for the time elapsed since the stream has been freely expanding away due to the tidal disruption of the globular cluster. This timescale, in turn, places a lower limit on the age of the cluster. The age can be deduced from astrometry using a modest number of stars, with the error on this estimate depending on the proximity of the stream and the number of tracer stars used.

Testing modified gravity with globular clusters: the case of NGC 2419

Abstract The dynamics of globular clusters has been studied in great detail in the context of general relativity as well as with modifications of gravity that strongly depart from the standard paradigm such as Modified Newtonian Dynamics. However, at present there are no studies that aim to test the impact that less extreme modifications of gravity (e.g. models constructed as alternatives to dark energy) have on the behaviour of globular clusters. This Letter presents fits to the velocity dispersion profile of the cluster NGC 2419 under the symmetron-modified gravity model. The data show an increase in the velocity dispersion towards the centre of the cluster which could be difficult to explain within general relativity. By finding the best-fitting solution associated with the symmetron model, we show that this tension does not exist in modified gravity. However, the best-fitting parameters give a model that is inconsistent with the dynamics of the Solar system. Exploration of different screening mechanisms should give us the chance to understand if it is possible to maintain the appealing properties of the symmetron model when it comes to globular clusters and at the same time recover the Solar system dynamics properly.

Orbital decomposition of CALIFA spiral galaxies

Schwarzschild orbit-based dynamical models are widely used to uncover the internal dynamics of early-type galaxies and globular clusters. Here we present for the first time the Schwarzschild models of late-type galaxies: an SBb galaxy NGC 4210 and an S0 galaxy NGC 6278 from the CALIFA survey. The mass profiles within $2\,R_e$ are constrained well with $1\sigma$ statistical error of $\sim 10\%$. The luminous and dark mass can be disentangled with uncertainties of $\sim 20\%$ and $\sim 50\%$ respectively. From $R_e$ to $2\,R_e$, the dark matter fraction increases from $14\pm10\%$ to $18\pm10\%$ for NGC 4210 and from $15\pm10\%$ to $30\pm20\%$ for NGC 6278. The velocity anisotropy profiles of both $\sigma_r/\sigma_t$ and $\sigma_z/\sigma_R$ are well constrained. The inferred internal orbital distributions reveal clear substructures. The orbits are naturally separated into three components: a cold component with near circular orbits, a hot component with near radial orbits, and a warm component in between. The photometrically-identified exponential disks are predominantly made up of cold orbits only beyond $\sim 1\,R_e$, while they are constructed mainly with the warm orbits inside. Our dynamical hot components are concentrated in the inner regions, similar to the photometrically-identified bulges. The reliability of the results, especially the orbit distribution, are verified by applying the model to mock data.

The relation between the mass-to-light ratio and the relaxation state of globular clusters

The internal dynamics of globular clusters (GCs) is strongly affected by two-body interactions that bring the systems to a state of partial energy equipartition. Using a set of Monte Carlo clusters simulations, we investigate the role of the onset of energy equipartition in shaping the mass-to-light ratio (M/L) in GCs. Our simulations show that the M/L profiles cannot be considered constant and their specific shape strongly depends on the dynamical age of the clusters. Dynamically younger clusters display a central peak up to M/L $\simeq25$ $M_\odot/L_\odot$ caused by the retention of dark remnants; this peak flattens out for dynamically older clusters. Moreover, we find that also the global values of M/L correlate with the dynamical state of a cluster quantified as either the number of relaxation times a system has experienced $n_{rel}$ or the equipartition parameter $m_{eq}$: clusters closer to full equipartition (higher $n_{rel}$ or lower $m_{eq}$) display a lower M/L. We show that the decrease of M/L is primarily driven by the dynamical ejection of dark remnants, rather than by the escape of low-mass stars. The predictions of our models are in good agreement with observations of GCs in the Milky Way and M31, indicating that differences in relaxation state alone can explain variations of M/L up to a factor of $\simeq3$. Our characterization of the M/L as a function of relaxation state is of primary relevance for the application and interpretation of dynamical models.

A Universal Velocity Dispersion Profile for Pressure Supported Systems: Evidence for MONDian Gravity across Seven Orders of Magnitude in Mass

Abstract For any MONDian extended theory of gravity where the rotation curves of spiral galaxies are explained through a change in physics rather than the hypothesis of dark matter, a generic dynamical behavior is expected for pressure supported systems: an outer flattening of the velocity dispersion profile occurring at a characteristic radius, where both the amplitude of this flat velocity dispersion and the radius at which it appears are predicted to show distinct scalings with the total mass of the system. By carefully analyzing the dynamics of globular clusters and elliptical galaxies, we are able to significantly extend the astronomical diversity of objects in which MONDian gravity has been tested, from spiral galaxies to the much larger mass range covered by pressure supported systems. We show that a universal projected velocity dispersion profile accurately describes various classes of pressure supported systems, and further, that the expectations of extended gravity are met across seven orders of magnitude in mass. These observed scalings are not expected under dark matter cosmology, and would require particular explanations tuned at the scales of each distinct astrophysical system.

HUBBLE SPACE TELESCOPEPROPER MOTION (HSTPROMO) CATALOGS OF GALACTIC GLOBULAR CLUSTERS. II. KINEMATIC PROFILES AND MAPS

We present kinematical analyses of 22 Galactic globular clusters using the Hubble Space Telescope proper motion (HSTPROMO) catalogues recently presented in Bellini et al. (2014). For most clusters, this is the first proper-motion study ever performed, and, for many, this is the most detailed kinematic study of any kind. We use cleaned samples of bright stars to determine binned velocity-dispersion and velocity-anisotropy radial profiles and two-dimensional velocity-dispersion spatial maps. Using these profiles, we search for correlations between cluster kinematics and structural properties. We find that: (1) more centrally-concentrated clusters have steeper radial velocity-dispersion profiles; (2) on average, at 1\sigma confidence in two dimensions, the photometric and kinematic centres of globular clusters agree to within ~1", with a cluster-to-cluster rms of 4" (including observational uncertainties); (3) on average, the cores of globular clusters have isotropic velocity distributions to within 1% (\sigma_t/\sigma_r = 0.992 +/- 0.005), with a cluster-to-cluster rms of 2% (including observational uncertainties); (4) clusters generally have mildly radially anisotropic velocity distributions (\sigma_t/\sigma_r ~ 0.8-1.0) near the half-mass radius, with bigger deviations from isotropy for clusters with longer relaxation times; (5) there is a relation between \sigma_minor/\sigma_major and ellipticity, such that the more flattened clusters in the sample tend to be more anisotropic, with \sigma_minor/\sigma_major ~ 0.9-1.0. Aside from these general results and correlations, the profiles and maps presented here can provide a basis for detailed dynamical modelling of individual globular clusters. Given the quality of the data, this is likely to provide new insights into a range of topics concerning globular cluster mass profiles, structure, and dynamics.