Orbits Of Globular Clusters Research Articles

THE INFLUENCE OF OBSERVATIONAL ERRORS IN GAIA DR3 ON THE RECONSTRUCTION OF GLOBULAR CLUSTER ORBITS ON A COSMOLOGICAL TIMESCALE

In recent years, the emerging field of astronomy focused on the history of galaxy formation, known as Galactic Archaeology, has been gaining popularity. Globular clusters have been involved in many key processes occurring in the Milky Way, making their study, particularly the reconstruction of their orbits, significantly important. The Gaia DR3 catalog provides parameters for 165 globular clusters, such as proper motions, radial velocity, and heliocentric distance, with certain accuracy. Therefore, it is important to examine the influence of measurement errors in these parameters on the initial data when converting to the Galactocentric coordinate system and, consequently, on the shape of the orbits. We integrated the orbits of globular clusters 10 billion years lookback. For physical justification during the integration, we used the external dynamic potential with the individual number 411321 from the cosmological simulation database IllustrisTNG-100, which best reproduces the potential of the Milky Way. The integration was performed using the parallel N-body code φ-GPU, based on a fourth-order Hermite scheme with hierarchical individual block timesteps. A total of 1,000 randomizations of the initial data were created considering a normal distribution of errors, and the influence of errors on the scatter of initial velocities and on the shape of the orbits was examined. The parameters with the largest relative errors are proper motions and radial velocity, while the smallest errors are in heliocentric distance. It was found that 85% of the globular clusters have relative errors in all parameters of no more than 10%, and 5.4% have errors of no more than 1%. Investigating the influence of measurement errors for clusters with different magnitudes of relative errors, we concluded that for most globular clusters, the influence of measurement errors on the shape of the orbits is not significant. Consequently, it is possible to reconstruct the orbits with high accuracy for these clusters. Since the reconstruction of globular cluster orbits involves cosmological timescales, accounting for measurement errors is an important aspect of the preparatory procedure before the main integration.

Анализ регулярности/хаотичности динамики шаровых скоплений в центральной области Млечного Пути

We analyzed the regularity/chaoticity of the orbits of 45 globular clusters in the central region of the Galaxy with a radius of 3.5 kpc, which are subject to the greatest influence from an elongated rotating bar. Various analysis methods were used, namely, methods for calculating the maximum characteristic Lyapunov exponents, the method of Poincaré sections, the frequency method based on the calculation of fundamental frequencies, as well as the visual assessment method. Bimodality was discovered in the histogram of the distribution of positive Lyapunov exponents, calculated in the classical version, without renormalization of the shadow orbit, which makes it possible to implement a probabilistic method of GC classification. To construct the orbits of globular clusters, we used a gravitational potential model with a bar in the form of a triaxial ellipsoid, described in detail in the work of Bajkova et al., Izvestiya GAO in Pulkovo, 2023, 228, 1. The following bar parameters were adopted: mass 1010M⊙, semimajor axis length 5 kpc, bar viewing angle 25o, rotation speed 40 km s−1 kpc−1. To form the 6D-phase space required for orbit integration, the most accurate astrometric data to date from the Gaia satellite (EDR3) (Vasiliev, Baumgardt, 2021), as well as new refined average distances to globular clusters (Baumgardt, Vasiliev, 2021) were used. A classification is made of globular clusters with regular and chaotic dynamics. As the analysis showed, globular clusters with small pericentric distances and large eccentricities are most susceptible to the influence of the bar and demonstrate the greatest chaos. It is shown that the results of classifying globular clusters by the nature of their orbital dynamics, obtained using the various methods of analysis considered in the work, correlate well with each other.

Шаровые скопления в центральной области Млечного Пути I. Влияние бара на параметры орбит по данным Gaia EDR3

The work is devoted to the analysis of the influence of the galactic bar on the orbital motion of globular clusters in the central region of the Galaxy. For this task, 45 globular clusters were selected, 34 of which belong to the bulge and 11 to the disk. The most accurate astrometric data from the Gaia satellite (Vasiliev and Baumgardt, 2021), as well as new refined average distances (Baumgardt and Vasiliev, 2021), were used to form the 6D phase space required for orbit integration. The orbits of globular clusters are obtained both in an axisymmetric potential and in a potential including a bar. In this case, the mass, rotation speed, shape and scale length of the bar were varied. A comparison is made of such orbital parameters as apocentric and pericentric distances, eccentricity and maximum distance from the galactic plane. It is shown that the mass of the bar exerts the greatest influence on the orbital motion, which is expressed mainly in an increase in both the apocentric and pericentric distances in the vast majority of globular clusters. The eccentricities of the orbits in the overwhelming majority also change significantly, and there is a change both upward and downward, especially in the range of values from 0.2 to 0.8. The greatest changes in parameters are observed in globular clusters with high radial velocities and small pericentric distances. The change in orbital parameters depending on the bar rotation speed is less pronounced. The influence of the geometric parameters of the bar is insignificant in the accepted range of their changes. Several examples show that globular clusters in the bulge are more affected by the bar than those belonging to the disk.

Milky Way globular clusters on cosmological timescales

Context. Recent observational data show that the Milky Way galaxy contains about 170 globular clusters. A fraction of them is likely formed in dwarf galaxies that were accreted onto the Milky Way in the past, while the remaining clusters were formed in situ. Therefore, the different parameters, including the orbits, of the globular clusters are a valuable tool for studying the Milky Way evolution. However, because the evolution of the 3D mass distribution of the Milky Way is poorly constrained, the orbits of the clusters are usually calculated in static potentials. Aims. We study the evolution of the globular clusters in several external potentials, where we aim to quantify the effects of the evolving galaxy potential on the orbits of the globular clusters. Methods. For the orbit calculation, we used five Milky Way-like potentials from the IllustrisTNG-100 simulation. The orbits of 159 globular clusters were integrated using the high-order N-body parallel dynamic code φ-GPU, with initial conditions obtained from the recent Gaia Data Release 3 catalogues. Results. We provide a classification of the globular cluster orbits according to their 3D shapes and association with different components of the Milky Way (disk, halo, and bulge). We also found that the energy – angular momentum of the globular clusters in the external potentials is roughly similarly distributed at the present time. However, neither total energy nor total angular momentum of the globular clusters are conserved due to time-varying nature of the potentials. In some extreme cases, the total energy can change up to 40% (18 objects) over the last 5 Gyr of evolution. We found that the in situ formed globular clusters are less affected by the evolution of the TNG potentials than clusters that were likely formed ex situ. Therefore, our results suggest that time-varying potentials significantly affect the orbits of the globular clusters, thus making them vital for understanding the formation of the Milky Way.

The Global Dynamical Atlas of the Milky Way Mergers: Constraints from Gaia EDR3–based Orbits of Globular Clusters, Stellar Streams, and Satellite Galaxies

Abstract The Milky Way halo was predominantly formed by the merging of numerous progenitor galaxies. However, our knowledge of this process is still incomplete, especially in regard to the total number of mergers, their global dynamical properties and their contribution to the stellar population of the Galactic halo. Here, we uncover the Milky Way mergers by detecting groupings of globular clusters, stellar streams, and satellite galaxies in action ( J ) space. While actions fully characterize the orbits, we additionally use the redundant information on their energy (E) to enhance the contrast between the groupings. For this endeavor, we use Gaia EDR3‒based measurements of 170 globular clusters, 41 streams, and 46 satellites to derive their J and E. To detect groups, we use the ENLINK software, coupled with a statistical procedure that accounts for the observed phase-space uncertainties of these objects. We detect a total of N = 6 groups, including the previously known mergers Sagittarius, Cetus, Gaia‒Sausage/Enceladus, LMS-1/Wukong, Arjuna/Sequoia/I’itoi, and one new merger that we call Pontus. All of these mergers, together, comprise 62 objects (≈25% of our sample). We discuss their members, orbital properties, and metallicity distributions. We find that the three most-metal-poor streams of our galaxy—“C-19” ([Fe/H] = −3.4 dex), “Sylgr” ([Fe/H] = −2.9 dex), and “Phoenix” ([Fe/H] = −2.7 dex)—are associated with LMS-1/Wukong, showing it to be the most-metal-poor merger. The global dynamical atlas of Milky Way mergers that we present here provides a present-day reference for galaxy formation models.

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’.

Assessing the Fornax globular cluster timing problem in different models of dark matter

We investigate what the orbits of globular clusters (GCs) in the Fornax dwarf spheroidal (dSph) galaxy can teach us about dark matter (DM). This problem was recently studied for ultralight dark matter (ULDM). We consider two additional models: (i) fermionic degenerate dark matter (DDM), where Pauli blocking should be taken into account in the dynamical friction computation; and (ii) self-interacting dark matter (SIDM). We give a simple and direct Fokker-Planck derivation of dynamical friction, new in the case of DDM and reproducing previous results in the literature for ULDM and cold DM. ULDM, DDM and SIDM were considered in the past as leading to cores in dSphs, a feature that acts to suppress dynamical friction and prolong GC orbits. For DDM we derive a version of the cosmological free streaming limit that is independent of the DM production mechanism, finding that DDM cannot produce an appreciable core in Fornax without violating Ly-$\ensuremath{\alpha}$ limits. If the Ly-$\ensuremath{\alpha}$ limit is discounted for some reason, then stellar kinematics data does allow a DDM core which could prolong GC orbits. For SIDM we find that significant prolongation of GC orbits could be obtained for values of the self-interaction cross section considered in previous works. In addition to reassessing the inspiral time using updated observational data, we give a new perspective on the so-called GC timing problem, demonstrating that for a cuspy cold DM profile dynamical friction predicts a $z=0$ radial distribution for the innermost GCs that is independent of initial conditions. The observed orbits of Fornax GCs are consistent with this expectation with a mild apparent fine-tuning at the level of $\ensuremath{\sim}25%$.

Study of the Influence of an Evolving Galactic Potential on the Orbital Properties of 152 Globular Clusters with Data from the Gaia EDR3 Catalogue

We have studied the influence of an evolving gravitational potential of the Milky Way Galaxy on the orbital motion of 152 globular clusters with proper motions from the Gaia EDR3 catalogue and mean distances from Baumgardt and Vasiliev (2021). To construct a semicosmological evolving model potential with changing masses and sizes of the Galactic components, we have used the algorithm described in Haghi et al. (2015). The adopted axisymmetric three-component model potential of the Galaxy includes a spherical bulge, a flat Miyamoto--Nagai disk, and a spherical Navarro--Frenk--White dark matter halo.The orbits are integrated backward in time. We compare the orbital parameters of globular clusters derived in static and evolving potentials when integrating the orbits for 5 and 12 Gyr backward. For the first time we have studied the influence of separately a change in the masses and a change in the sizes of the Galactic components. The changes in the masses and sizes of the components are shown to act on the orbital parameters in the opposite way. At small Galactocentric distances this influence is maximally compensated for. The orbits of distant globular clusters and those with a large apocenter distance undergo the biggest changes. We show that on time scales up to $-5$~Gyr the orbits of globular clusters in the case of a potential with both changing masses and changing sizes of the components undergo, on average, minor changes compared to the case of a static potential. These changes fit into the limits of the statistical uncertainties caused by the errors in the data. So, on these time scales the Galactic potential may be deemed static. We provide tables with the orbital parameters of globular clusters derived in both static and evolving potentials.

Predicting accreted satellite galaxy masses and accretion redshifts based on globular cluster orbits in the E-MOSAICS simulations

ABSTRACT The ages and metallicities of globular clusters (GCs) are known to be powerful tracers of the properties of their progenitor galaxies, enabling their use in determining the merger histories of galaxies. However, while useful in separating GCs into individual accretion events, the orbits of GC groups themselves have received less attention as probes of their progenitor galaxy properties. In this work, we use simulations of galaxies and their GC systems from the MOdelling Star cluster population Assembly In Cosmological Simulations within EAGLE project to explore how the present-day orbital properties of GCs are related to the properties of their progenitor galaxies. We find that the orbits of GCs deposited by accretion events are sensitive to the mass and merger redshift of the satellite galaxy. Earlier mergers and larger galaxy masses deposit GCs at smaller median apocentres and lower total orbital energy. The orbital properties of accreted groups of GCs can therefore be used to infer the properties of their progenitor galaxy, though there exists a degeneracy between galaxy mass and accretion time. Combining GC orbits with other tracers (GC ages, metallicities) will help to break the galaxy mass/accretion time degeneracy, enabling stronger constraints on the properties of their progenitor galaxy. In situ GCs generally orbit at lower energies (small apocentres) than accreted GCs, however they exhibit a large tail to high energies and even retrograde orbits (relative to the present-day disc), showing significant overlap with accreted GCs. Applying the results to Milky Way GCs groups suggests a merger redshift z ∼ 1.5 for the Gaia Sausage/Enceladus and z > 2 for the ‘low-energy’/Kraken group, adding further evidence that the Milky Way had two significant mergers in its past.

Discovery of rotation axis alignments in Milky Way globular clusters

There is an increasing number of recent observational results that show that some globular clusters exhibit internal rotation while they travel along their orbital trajectories around the Milky Way center. Based on these findings, we searched for any relationship between the inclination angles of the globular cluster orbits with respect to the Milky Way plane and those of their rotation. We discovered that the relative inclination, in the sense of inclination of the rotation axis to orbit axis, is a function of the orbit inclination of the globular cluster. Rotation and orbit axes are aligned for an inclination of ∼56°, while the rotation axis inclination is far from the orbit inclination between ∼20° and −20° when the latter increases from 0° up to 90°. We further investigated the origin of this linear relationship and found no correlation with the semimajor axes and eccentricities of the globular cluster orbits, nor with the internal rotation strength, the globular cluster sizes, actual and tidally disrupted masses, or half-mass relaxation times, among others. The uncovered relationship will affect the development of numerical simulations of the internal rotation of globular clusters, our understanding of the interaction of globular clusters with the gravitational field of the Milky Way, and the observational campaigns made to increase the number of globular clusters with detected internal rotation.

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.

Constraining the Formation and Mass of the Milky Way Halo using Globular Cluster Orbits from HST Proper Motions

AbstractThe globular cluster (GC) system of the Milky Way (MW) provides important information on the MW’s present structure and past evolution. Full 3d motions, accessed through proper motions (PMs), are required to calculate accurate orbits of GCs in the MW halo. We present our HST program to create a PM database for 20 halo GCs. We demonstrate how the observed PMs of individual GCs can be used to study their origins, and we also describe how the PM measurements of our entire targets can be used to constrain the anisotropy profile. Finally, we describe how our PM results can be used for Gaia as an external check, and discuss prospects of PM measurements with HST and Gaia in the coming years.

Galactic orbits of globular clusters in the region of the Galactic bulge

Galactic orbits have been constructed over long time intervals for ten globular clusters located near the Galactic center. A model with an axially symmetric gravitational potential for the Galaxy was initially applied, after which a non-axially symmetric potential corresponding to the central bar was added. Variations in the trajectories of all these globular clusters in the XY plane due to the influence of the bar were detected. These were greatest for the cluster Terzan 4 in the meridional (RZ) plane. The globular clusters Terzan 1, Terzan 2, Terzan 4, Terzan 9, NGC 6522, and NGC 6558 always remained within the Galactic bulge, no farther than 4 kpc from the Galactic center.

HST Proper Motions of Distant Globular Clusters: Constraining the Formation & Mass of the Milky Way

AbstractProper motions (PMs) are required to calculate accurate orbits of globular clusters (GCs) in the Milky Way (MW) halo. We present our HST program to create a PM database for 20 GCs at distances of RGC = 10–100 kpc. Targets are discussed along with PM measurement methods. We also describe how our PM results can be used for Gaia as an external check, and discuss the synergy between HST and Gaia as astrometric instruments in the coming years.

Clues on the missing sources of reionization from self-consistent modelling of Milky Way and dwarf galaxy globular clusters

Globular clusters are unique tracers of ancient star formation. We determine the formation efficiencies of globular clusters across cosmic time by modelling the formation and dynamical evolution of the globular cluster population of a Milky Way type galaxy in hierarchical cosmology, using the merger tree from the Via Lactea II simulation. All of the models are constrained to reproduce the observed specific frequency and initial mass function of globular clusters in isolated dwarfs. Globular cluster orbits are then computed in a time varying gravitational potential after they are either accreted from a satellite halo or formed in situ, within the Milky Way halo. We find that the Galactocentric distances and metallicity distribution of globular clusters are very sensitive to the formation efficiencies of globular clusters as a function of redshift and halo mass. Our most accurate models reveal two distinct peaks in the globular cluster formation efficiency at z ∼ 2 and 7–12 and prefer a formation efficiency that is mildly increasing with decreasing halo mass, the opposite of what expected for feedback-regulated star formation. This model accurately reproduces the positions, velocities, mass function, metallicity distribution, and age distribution of globular clusters in the Milky Way and predicts that ∼40 per cent formed in situ, within the Milky Way halo, while the other ∼60 per cent were accreted from about 20 satellite dwarf galaxies with vcir > 30 km s−1, and about 29 per cent of all globular clusters formed at redshifts z > 7. These results further strengthen the notion that globular cluster formation was an important mode of star formation in high-redshift galaxies and likely played a significant role in the reionization of the intergalactic medium.

Roche volume filling of star clusters in the Milky Way

We examine the ratios $r_h/r_J$ of projected half-mass and Jacobi radius as well as $r_t/r_J$ of tidal and Jacobi radius for open and globular clusters in the Milky Way using data of both observations and simulations. We applied an improved calculation of $r_J$ for eccentric orbits of globular clusters. A sample of 236 open clusters of Piskunov et al. within the nearest kiloparsec around the Sun has been used. For the Milky Way globular clusters, data are taken from the Harris catalogue. We particularly use the subsample of 38 Milky Way globular clusters for which orbits have been integrated by Dinescu et al. We aim to quantify the differences between open and globular clusters and to understand, why they form two intrinsically distinct populations. We find under certain assumptions, or, in other words, in certain approximations, (i) that globular clusters are presently Roche volume underfilling and (ii) with at least $3\sigma$ confidence that the ratio $r_h/r_J$ of half-mass and Jacobi radius is $3 - 5$ times larger at present for an average open cluster in our sample than for an average globular cluster in our sample and (iii) that a significant fraction of globular clusters may be Roche volume overfilling at pericentre with $r_t > r_J$. Another aim of this paper is to throw light on the underlying theoretical reason for the existence of the van den Bergh correlation between half-mass and galactocentric radius.

Six New Galactic Orbits of Globular Clusters in a Milky Way–Like Galaxy

Absolute proper motions for six new globular clusters have recently been determined. This motivated us to obtain the Galactic orbits of these six clusters both in an axisymmetric Galactic potential and in a barred potential, such as that of our Galaxy. Orbits are also obtained for a Galactic potential that includes spiral arms. The orbital characteristics are compared and discussed for these three cases. Tidal radii and destruction rates are also computed and discussed.

Dynamical friction on globular clusters in core-triaxial galaxies: is it a cause of massive black hole accretion?

The present work extends and deepens previous examinations of the evolution of globular cluster orbits in elliptical galaxies, by means of numerical integrations of a wide set of orbits in five self-consistent triaxial galactic models characterized by a central core and different axial ratios. These models are valid and complete in the representation of regular orbits in elliptical galaxies. Dynamical friction is definitely shown to be an efficient cause of evolution for the globular cluster systems in elliptical galaxies of any mass or axial ratio. Moreover, our statistically significant sample of computed orbits confirms that the globular cluster orbital decay times are, at least for clusters moving on box orbits, much shorter than the age of the galaxies. Consequently, the mass carried into the innermost galactic region in the form of decayed globular clusters may have contributed significantly to feeding and accreting a compact object therein.

Space distribution and orbits of globular clusters of the galaxy

For 29 globular clusters of the Galaxy with integrated spectral type F, we have calculated their orbits from their radial velocity and proper motion data using three different galactic potential models. The results show: (1) Most of the sample clusters are distributed in the region 5 kpc–10 kpc from the Galactic center, in a spherically symmetrical distribution about the center, and their space velocities follow an ellipsoidal distribution; (2) The clusters can be classified by metallicity into the HB and MP subsystems, and their number density peaks at [ Fe H ]=−1.6 ; (3) The clusters follow periodic but not closed orbits with maximum galactocentric distances generally less than 40 kpc. Using the different potential models makes little difference in the orbital morphology. When an orbit passes within about 1 kpc of the galactic centre, “chaotic” behavior may take place. The orbital morphology is not obviously correlated with metallicity. (4) The orbital semi-major axis, apogalactic distance and azimuthal period vary in similar ways with the metallicity, and the correlation between the orbital eccentricity and the metallicity is obvious. About 24% of the sample clusters have orbital eccentricities less than 0.4. The effect of different potential models is not obvious in the perigalactic distance, eccentricity and the uncertainties of the orbital parameters, but is more obvious in the other orbital parameters, including the apogalactic distance, semi-major axis, radial period, and azimuthal period.

Test of the hypothesis of circular motion of interstellar clouds

The study of the motion of interstellar clouds by direct dynamical methods is hindered by the lack of a complete set of initial conditions of the motion. The hypothesis of the circular motion of interstellar matter of various composition is tested on the basis of the catalog of Brand and Blitz. A modification of the method proposed by Edmondson and Hoerner, which was successfully used for a statistical investigation of the shapes of the orbits of globular clusters, is used. It is established that interstellar clouds move in nearly circular orbits with small deviations, so that data on the spiral structure of the Galaxy obtained by radio-astronomical methods should be considered as close to reality.