Hubble Space Telescope Proper Motion Research Articles

Energy equipartition in globular clusters through the eyes of dynamical models

Context. Following their birth, globular clusters (GCs) experience a very peculiar dynamical evolution. Gravitational encounters drive these systems toward energy equipartition, mass segregation, and evaporation, which alter structural, spatial, and kinematic features. Aims. We determine the dynamical state of a few GCs by means of a multi-mass King-like dynamical model. Our work focuses on the prediction of the energy equipartition degree and its relationship with model parameters. Methods. We adjusted the dynamical model parameters in order to reproduce the observed velocity dispersion – as derived from Hubble Space Telescope proper motion data – as a function of the stellar mass. By doing so, we estimated Φ0, a measure of the gravitational potential well. We repeated the same fit by means of the Bianchini relation, a function obtained by interpolating on N-body simulation results. We studied the relationship between Φ0 and the Bianchini equipartition mass meq and discuss the structural properties, such as concentration c, the number of core relaxation timescales Ncore, and core radius rc. To obtain an independent estimate of Φ0, we also fitted observed surface brightness profiles using the predicted surface density and a mass-luminosity relation from isochrones. Results. The quality of the fits of the velocity dispersion–mass relationship obtained by means of our dynamical model is comparable to those obtained with the Bianchini function. Nonetheless, when the Bianchini function is used to fit the projected velocity dispersion, the resulting degree of equipartition is underestimated. On the contrary, our approach provides the equipartition degree at any radial or projected distance by means of Φ0. As a result, a cluster in a more advanced dynamical state shows a larger Φ0, as well as larger Ncore and c, while rc decreases. We find the estimates of Φ0 obtained by fitting surface brightness profiles to be compatible at 2σ confidence level with those from internal kinematics, although further investigation of statistical and systematic errors is required. Conclusions. Our work illustrates the predicting power of dynamical models to determine the energy equipartition degree of GCs. These models are a unique tool for determining structural and kinematic properties, and can be used where observational data are poor, as is the case for the most crowded regions of a cluster, where stars are barely resolved.

Hubble Space Telescope proper motions of Large Magellanic Cloud star clusters

We present proper motion (PM) measurements for a sample of 23 massive star clusters within the Large Magellanic Cloud using multi-epoch data from the Hubble Space Telescope (HST). We combined archival data from the ACS/WFC and WFC3/UVIS instruments with observations from a dedicated HST programme, resulting in time baselines between 4.7 and 18.2 yr available for PM determinations. For bright well-measured stars, we achieved nominal PM precisions of 55 μas yr−1 down to 11 μas yr−1. To demonstrate the potential and limitations of our PM data set, we analysed the cluster NGC 1850 and showcase a selection of different science applications. The precision of the PM measurements allows us to disentangle the kinematics of the various stellar populations that are present in the HST field. The cluster has a centre-of-mass motion that is different from the surrounding old field stars and also differs from the mean motion of a close-by group of very young stars. We determined the velocity dispersion of field stars to be 0.128 ± 0.003 mas yr−1 (corresponding to 30.3 ± 0.7 km s−1). The velocity dispersion of the cluster inferred from the PM data set most probably overestimates the true value, suggesting that the precision of the measurements at this stage is not sufficient for a reliable analysis of the internal kinematics of extra-galactic star clusters. Finally, we exploit the PM-cleaned catalogue of likely cluster members to determine any radial segregation between fast and slowly-rotating stars, finding that the former are more centrally concentrated. With this paper, we also release the astro-photometric catalogues for each cluster.

Detailed chemical abundances of the globular cluster Terzan 6 in the inner bulge

We used near-infrared spectroscopy at medium-high resolution (R = 8000 − 25 000) to perform the first comprehensive chemical study of the intermediate luminosity bulge globular cluster Terzan 6. We derived detailed abundances and abundance patterns of 27 giant stars, likely members of Terzan 6, based on their accurate Hubble Space Telescope proper motions and line-of-sight radial velocities. From the spectral analysis of these stars, we determined an average heliocentric radial velocity of 143.3 ± 1.0 km s−1 with a velocity dispersion of 5.1 ± 0.7 km s−1 and an average [Fe/H] = −0.65 ± 0.01 and a low 1σ dispersion of 0.03 dex. We also measured some depletion of [Mn/Fe] with respect to the solar-scaled values and enhancement of for [Ca/Fe], [Si/Fe], [Mg/Fe], [Ti/Fe], [O/Fe], [Al/Fe], [Na/Fe], and, to a lower extent, for [K/Fe], consistent with previous measurements of other bulge globular clusters and favoring the scenario of a rapid bulge formation and chemical enrichment. Some spread in the light element abundances suggest the presence of first- and second-generation stars, typical of genuine globulars. Finally, we measured some depletion of carbon and low 12C/13C isotopic ratios, as in previous studies of field and cluster bulge giants, indicating that extra-mixing mechanisms should be at work during the post main sequence evolution in the high metallicity regime as well.

Satellite group infall into the Milky Way: Exploring the Crater-Leo case with new HST proper motions

Context. Within Λ cold dark matter (ΛCDM) simulations, Milky Way-like galaxies accrete some of their satellite galaxies in groups of 3–5 members rather than individually, and this has been suggested as a possible mechanism driving the formation of satellite planes. Objects accreted in groups are expected to share similar specific total energy and angular momentum, and to also have identical orbital planes and directions. Aims. Looking at observatio ns of Milky Way satellites, the dwarf galaxies Leo II, IV, V, and Crater II, and the star cluster Crater 1 were proposed to be a vestige of group infall. The suggested ‘Crater-Leo group’ shows a coherent distance gradient and all these objects align along a great circle on the sky. We used proper motion data to investigate whether the phase-space distribution of the members of the proposed group are indeed consistent with group infall. Methods. To further investigate this possibility, we used Gaia Data Release 3 (DR3) and new Hubble Space Telescope (HST) proper motions – namely, (μα*, μδ) = (−0.1921 ± 0.0514, −0.0686 ± 0.0523) mas yr−1 for Leo IV and (μα*, μδ) = (0.1186 ± 0.1943, −0.1183 ± 0.1704) mas yr−1 for Leo V – to derive accurate orbital properties for the proposed group objects. In addition, we explored other possible members of this putative association. Results. Leo II, Leo IV, and Crater 1 show orbital properties consistent with those we predict from assuming group infall. However, our results suggest that Crater II was not accreted with the rest of the objects. If confirmed with increasingly accurate proper motions in the future, the Crater-Leo objects would appear to constitute the first identified case of a cosmologically expected, typical group infall event, as opposed to the highly hierarchical Magellanic Cloud system.

Astrometry in crowded fields towards the Galactic bulge

Context. The astrometry towards the Galactic bulge is hampered by high stellar crowding and patchy extinction. This effect is particularly severe for optical surveys such as the European Space Agency satellite Gala. Aims. In this study, we assess the consistency of proper motion measurements between optical (Gaia DR3) and near-infrared (VIRAC2) catalogues in comparison with proper motions measured with the Hubble Space Telescope (HST) observations in several crowded fields towards the Galactic bulge and in Galactic globular clusters. Methods. Assuming that the proper motion measurements are well characterised, the uncertainty-normalised proper motion differences between pairs of catalogues are expected to follow a normal distribution. A deviation from a normal distribution defines the inflation factor r. By multiplying the proper motion uncertainties with the appropriate inflation factor values, the Gaia (VIRAC2) proper motion measurements are brought into a 1σ agreement with the HST proper motions. Results. The inflation factor (r) depends on stellar surface density. For the brightest stars in our sample (G < 18), the dependence on G-band magnitude is strong, corresponding to the most precise Gaia DR3 proper motions. We used the number of observed Gaia DR3 sources as a proxy for the stellar surface density. Assuming that the HST proper motion measurements are well determined and free from systematic errors, we find that Gaia DR3 proper motion uncertainties are better characterised, having r < 1.5 in fields with a stellar number density with fewer than 200 Gaia DR3 sources per arcmin2, and are underestimated by up to a factor of 4 in fields with stellar densities higher than 300 sources per arcmin2. For the most crowded fields in VIRAC2, the proper motion uncertainties are underestimated by a factor of 1.1 up to 1.5, with a dependence on J-band magnitude. In all fields, the brighter sources have the higher r value. At the faint end (G > 19), the inflation factor is close to 1, meaning that the proper motions already fully agree with the HST measurements within 1σ. Conclusions. In the crowded fields common to both catalogues, VIRAC2 proper motions agree with HST proper motions and do not need an inflation factor for their uncertainties. Because of the depth and completeness of VIRAC2 in these fields, it is an ideal complement to Gaia DR3 for proper motion studies towards the Galactic bulge.

HST proper motions on the far side of the Galactic bar—data

ABSTRACT This is the third paper in a series that attempts to observe a clear signature of the Galactic bar/bulge using kinematic observations of the bulge stellar populations in low foreground extinction windows. We report on the detection of ∼100 000 new proper motions in four fields covering the far side of the Galactic bar/bulge, at negative longitudes. Our proper motions have been obtained using observations from the Advance Camera for Surveys (ACS), on board of the Hubble Space Telescope (HST), with a time-baseline of 8–9 years, which has produced accuracies better than 0.5 mas yr−1 for a significant fraction of the stellar populations with F814W < 23 mag. Interestingly, as shown in previous works, the Hess diagrams show a strikingly similar proper motion distribution to fields closer to the Galactic center and consistent with an old stellar population. The observed kinematics point to a significant bulge rotation, which seems to predominate even in fields as far as l ≃ −8°, and is also reflected in the changes of the velocity ellipsoid in the l, b plane as a function of distance.

Hubble Space Telescope Proper Motion Measurements of Supernova Remnant N132D: Center of Expansion and Age

We present proper motion measurements of the oxygen-rich ejecta of the LMC supernova remnant N132D using two epochs of Hubble Space Telescope Advanced Camera for Surveys data spanning 16 years. The proper motions of 120 individual knots of oxygen-rich gas were measured and used to calculate a center of expansion (CoE) of α = 5h25m01.ˢ71 and δ = −69°38′41.″64 (J2000) with a 1σ uncertainty of 2.″90. This new CoE measurement is 9.″2 and 10.″8 from two previous CoE estimates based on the geometry of the optically emitting ejecta. We also derive an explosion age of 2770 ± 500 yr, which is consistent with recent age estimates of ≈2500 yr made from 3D ejecta reconstructions. We verified our estimates of the CoE and age using a new automated procedure that detected and tracked the proper motions of 137 knots, with 73 knots that overlap with the visually identified knots. We find that the proper motions of the ejecta are still ballistic, despite the remnant’s age, and are consistent with the notion that the ejecta are expanding into an interstellar medium cavity. Evidence for explosion asymmetry from the parent supernova is also observed. Using the visually measured proper motion measurements and corresponding CoE and age, we compare N132D to other supernova remnants with proper motion ejecta studies.

Kinematic Structure of the Large Magellanic Cloud Globular Cluster System from Gaia eDR3 and Hubble Space Telescope Proper Motions

We have determined bulk proper motions (PMs) for 31 LMC GCs from Gaia eDR3 and Hubble Space Telescope data using multiple independent analysis techniques. Combined with literature values for distances, line-of-sight velocities, and existing bulk PMs, we extract full 6D phase-space information for 32 clusters, allowing us to examine the kinematics of the LMC GC system in detail. Except for two GCs (NGC 2159 and NGC 2210) whose high velocities suggest they are not long-term members of the LMC system, the data are consistent with a flattened configuration that rotates like the stellar disk. The one-dimensional velocity dispersions are on the order of 30 km s−1, similar to that of old stellar populations in the LMC disk. Similarly to the case for Milky Way disk clusters, the velocity anisotropy is such that the dispersion is smallest in the azimuthal direction; however, alternative anisotropies cannot be ruled out, due to distance uncertainties. The data are consistent with a single multidimensional Gaussian velocity distribution. Given the non-collisional nature of the LMC disk, this suggests that most, if not all, of the LMC GCs are formed by a single formation mechanism in the stellar disk, despite a significant spread in age and metallicity. Any accreted halo GC population is absent or far smaller in the LMC compared to the Milky Way.

3D core kinematics of NGC 6362: central rotation in a dynamically evolved globular cluster

ABSTRACT We present a detailed 3D kinematic analysis of the central regions (R < 30 arcsec) of the low mass and dynamically evolved galactic globular cluster (GC) NGC 6362. The study is based on data obtained with ESO-VLT/MUSE used in combination with the adaptive optics module and providing ∼3000 line-of-sight radial velocities, which have been complemented with Hubble Space Telescope proper motions. The quality of the data and the number of available radial velocities allowed us to detect for the first time a significant rotation signal along the line of sight in the cluster core with amplitude of ∼1 km s−1 and with a peak located at only ∼20 arcsec from the cluster centre, corresponding to only ${\sim}10{{\ \rm per\ cent}}$ of the cluster half-light radius. This result is further supported by the detection of a central and significant tangential anisotropy in the cluster innermost regions. This is one of the most central rotation signals ever observed in a GC to date. We also explore the rotational properties of the multiple populations hosted by this cluster and find that Na-rich stars rotate about two times more rapidly than the Na-poor sub-population thus suggesting that the interpretation of the present-day GC properties require a multicomponent chemo-dynamical approach. Both the rotation amplitude and peak position would fit qualitatively the theoretical expectations for a system that lost a significant fraction of its original mass because of the long-term dynamical evolution and interaction with the Galaxy. However, to match the observations more quantitatively further theoretical studies to explore the initial dynamical properties of the cluster are needed.

Kinematic complexity around NGC 419: resolving the proper motion of the cluster, the Small Magellanic Cloud, and the Magellanic bridge

ABSTRACT We present Hubble Space Telescope proper motions in the direction of the star cluster NGC 419 in the Small Magellanic Cloud. Because of the high precision of our measurements, for the first time it is possible to resolve the complex kinematics of the stellar populations located in the field, even along the tangential direction. In fact, the proper motions we measured allow us to separate cluster stars, which move on average with ($\mu _{\alpha }\cos \delta ^{\rm NGC\, 419}, \mu _{\delta }^{\rm NGC\, 419}$) = (+0.878 ± 0.055, −1.246 ± 0.048) mas yr−1, from those of the Small Magellanic Cloud and those belonging to a third kinematic feature that we recognize as part of the Magellanic Bridge. Resolving such a kinematic complexity enables the construction of decontaminated colour–magnitude diagrams, as well as the measurement of the absolute proper motion of the three separate components. Our study therefore sets the first steps towards the possibility of dynamically investigating the Magellanic system by exploiting the resolved kinematics of its stellar clusters.

HST Proper Motions of NGC 147 and NGC 185: Orbital Histories and Tests of a Dynamically Coherent Andromeda Satellite Plane

Abstract We present the first proper-motion (PM) measurements for the dwarf elliptical galaxies NGC 147 and NGC 185, two satellite galaxies of M31, using multiepoch Hubble Space Telescope (HST) imaging data with time baselines of ∼8 yr. For each galaxy, we take an error-weighted average of measurements from HST Advanced Camera for Surveys/WFC and Wide Field Camera 3/UVIS to determine the PMs. Our final results for the PMs are (μ W, μ N)N147 = (−0.0232, 0.0378) ± (0.0143, 0.0146) mas yr−1 for NGC 147 and (μ W, μ N)N185 = (−0.0242, 0.0058) ± (0.0141, 0.0147) mas yr−1 for NGC 185. The 2D direction of motion for NGC 147 about M31 is found to be aligned with its tidal tails. The 3D positions and velocities of both galaxies are transformed into a common M31-centric coordinate system to study the detailed orbital histories of the combined M31+NGC 147+NGC 185 system via numerical orbit integration. We find that NGC 147 (NGC 185) had its closest passage to M31 0.3–0.5 Gyr (≳1.6 Gyr) within the past 6 Gyr at distances of ∼70 kpc (70–260 kpc). The pericentric times of NGC 147/NGC 185 correlate qualitatively well with the presence/absence of tidal tails seen around the galaxies. Our PMs show that the orbital poles of NGC 147, as well as NGC 185, albeit to a lesser degree, agree within the uncertainties with the normal of the Great Plane of Andromeda (GPoA). These are the first measurements of the 3D angular momentum vector of any satellite identified as original GPoA members. Our results strengthen the hypothesis that the GPoA may be a dynamically coherent entity. We revisit previous claims that NGC 147 and NGC 185 are binary galaxies and conclude that it is very unlikely that the two galaxies were ever gravitationally bound to each other.

Imprints of evolution on the internal kinematics of Globular Clusters

AbstractGlobular 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 Sausage Globular Clusters

Abstract The Gaia Sausage is an elongated structure in velocity space discovered by Belokurov et al. using the kinematics of metal-rich halo stars. They showed that it could be created by a massive dwarf galaxy (∼5 × 1010 ) on a strongly radial orbit that merged with the Milky Way at a redshift z ≲ 3. This merger would also have brought in globular clusters (GCs). We seek evidence for the associated Sausage Globular Clusters (GCs) by analyzing the structure of 91 Milky Way GCs in action space using the Gaia Data Release 2 catalog, complemented with Hubble Space Telescope proper motions. There is a characteristic energy that separates the in situ objects, such as the bulge/disk clusters, from the accreted objects, such as the young halo clusters. There are 15 old halo GCs that have E > . Eight of the high-energy, old halo GCs are strongly clumped in azimuthal and vertical action, yet strung out like beads on a chain at extreme radial action. They are very radially anisotropic (β ∼ 0.95) and move on orbits that are all highly eccentric (e ≳ 0.80). They also form a track in the age–metallicity plane compatible with a dwarf galaxy origin. These properties are consistent with GCs associated with the merger event that gave rise to the Gaia Sausage.

Hubble Space Telescope Proper Motion (HSTPROMO) Catalogs of Galactic Globular Cluster. VI. Improved Data Reduction and Internal-kinematic Analysis of NGC 362

Abstract We present an improved data-reduction technique to obtain high-precision proper motions (PMs) of globular clusters (GCs) 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 GC 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 μas yr−1 for bright stars. We make use of this new PM catalog of NGC 362 to study the cluster’s internal kinematics. We investigate the velocity dispersion profiles of the multiple stellar populations hosted by NGC 362 and find new pieces of information on the kinematics of first- and second-generation stars. We analyze the level of energy equipartition of the cluster and find direct evidence for its post-core-collapsed state from kinematic arguments alone. We refine the dynamical mass of the blue stragglers (BSs) and study possible kinematic differences between BSs formed by collisions and mass transfer. We also measure no significant cluster rotation in the plane of the sky. Finally, we measure the absolute PM of NGC 362 and of the background stars belonging to the Small Magellanic Cloud, finding a good agreement with previous estimates in the literature. We make the PM catalog publicly available.

Radial anisotropy in ω Cen limiting the room for an intermediate-mass black hole

Finding an intermediate-mass black hole (IMBH) in a globular cluster (or proving its absence) would provide valuable insights into our understanding of galaxy formation and evolution. However, it is challenging to identify a unique signature of an IMBH that cannot be accounted for by other processes. Observational claims of IMBH detection are indeed often based on analyses of the kinematics of stars in the cluster core, the most common signature being a rise in the velocity dispersion profile towards the centre of the system. Unfortunately, this IMBH signal is degenerate with the presence of radially-biased pressure anisotropy in the globular cluster. To explore the role of anisotropy in shaping the observational kinematics of clusters, we analyse the case of omega Cen by comparing the observed profiles to those calculated from the family of LIMEPY models, that account for the presence of anisotropy in the system in a physically motivated way. The best-fit radially anisotropic models reproduce the observational profiles well, and describe the central kinematics as derived from Hubble Space Telescope proper motions without the need for an IMBH.

Is The Vast Polar Structure Of Dwarf Galaxies A Serious Problem For ΛCDM?

The dwarf galaxies around the Milky Way are distributed in a so-called vast polar structure (VPOS) that may be in conflict with Lambda CDM simulations. Here, we seek to determine if the VPOS poses a serious challenge to the Lambda cold dark matter paradigm on galactic scales. Specifically, we investigate if the VPOS remains coherent as a function of time. Using the measured Hubble Space Telescope (HST) proper motions and associated uncertainties, we integrate the orbits of the classical Milky Way satellites backwards in time and find that the structure disperses well before a dynamical time. We also examine in particular Leo I and Leo II using their most recent proper motion data, both of which have extreme kinematic properties, but these satellites do not appear to drive the polar fit that is seen at the present day. We have studied the effect of the uncertainties on the HST proper motions on the coherence of the VPOS as a function of time. We find that 8 of the 11 classical dwarfs have reliable proper motions; for these 8, the VPOS also loses significance in less than a dynamical time, indicating that the VPOS is not a dynamically stable structure. Obtaining more accurate proper motion measurements of Ursa Minor, Sculptor, and Carina would bolster these conclusions.

Orbits of massive satellite galaxies – I. A close look at the Large Magellanic Cloud and a new orbital history for M33

The Milky Way (MW) and M31 both harbour massive satellite galaxies, the Large Magellanic Cloud (LMC) and M33, which may comprise up to 10 per cent of their host's total mass. Massive satellites can change the orbital barycentre of the host–satellite system by tens of kiloparsec and are cosmologically expected to harbour dwarf satellite galaxies of their own. Assessing the impact of these effects crucially depends on the orbital histories of the LMC and M33. Here, we revisit the dynamics of the MW–LMC system and present the first detailed analysis of the M31–M33 system utilizing high-precision proper motions and statistics from the dark-matter-only Illustris cosmological simulation. With the latest Hubble Space Telescope proper motion measurements of M31, we reliably constrain M33's interaction history with its host. In particular, like the LMC, M33 is either on its first passage (tinf < 2 Gyr ago) or if M31 is massive (≥2 × 1012 M⊙), it is on a long-period orbit of about 6 Gyr. Cosmological analogues of the LMC and M33 identified in Illustris support this picture and provide further insight about their host masses. We conclude that, cosmologically, massive satellites such as the LMC and M33 are likely completing their first orbits about their hosts. We also find that the orbital energies of such analogues prefer an MW halo mass ∼1.5 × 1012 M⊙ and an M31 halo mass ≥1.5 × 1012 M⊙. Despite conventional wisdom, we conclude it is highly improbable that M33 made a close (<100 kpc) approach to M31 recently (tperi < 3 Gyr ago). Such orbits are rare (<1 per cent) within the 4σ error space allowed by observations. This conclusion cannot be explained by perturbative effects through four-body encounters amongst the MW, M31, M33, and the LMC. This surprising result implies that we must search for a new explanation for M33's strongly warped gas and stellar discs.

HUBBLE SPACE TELESCOPE PROPER MOTION (HSTPROMO) CATALOGS OF GALACTIC GLOBULAR CLUSTERS. IV. KINEMATIC PROFILES AND AVERAGE MASSES OF BLUE STRAGGLER STARS∗

ABSTRACT We make use of the Hubble Space Telescope proper-motion catalogs derived by Bellini et al. to produce the first radial velocity dispersion profiles for blue straggler stars (BSSs) in Galactic globular clusters (GCs), as well as the first dynamical estimates for the average mass of the entire BSS population. We show that BSSs typically have lower velocity dispersions than stars with mass equal to the main-sequence turnoff mass, as one would expect for a more massive population of stars. Since GCs are expected to experience some degree of energy equipartition, we use the relation , where η is related to the degree of energy equipartition, along with our velocity dispersion profiles to estimate BSS masses. We estimate η as a function of cluster relaxation from recent Monte Carlo cluster simulations by Bianchini et al. and then derive an average mass ratio and an average mass M ⊙ from 598 BSSs across 19 GCs. The final error bars include any systematic errors that are random between different clusters, but not any potential biases inherent to our methodology. Our results are in good agreement with the average mass of M ⊙ for the 35 BSSs in Galactic GCs in the literature with properties that have allowed individual mass determination.

THE EFFECT OF UNRESOLVED BINARIES ON GLOBULAR CLUSTER PROPER-MOTION DISPERSION PROFILES

ABSTRACT High-precision kinematic studies of globular clusters (GCs) require an accurate knowledge of all possible sources of contamination. Among other sources, binary stars can introduce systematic biases in the kinematics. Using a set of Monte Carlo cluster simulations with different concentrations and binary fractions, we investigate the effect of unresolved binaries on proper-motion dispersion profiles, treating the simulations like Hubble Space Telescope proper-motion samples. Since GCs evolve toward a state of partial energy equipartition, more-massive stars lose energy and decrease their velocity dispersion. As a consequence, on average, binaries have a lower velocity dispersion, since they are more-massive kinematic tracers. We show that, in the case of clusters with high binary fractions (initial binary fractions of 50%) and high concentrations (i.e., closer to energy equipartition), unresolved binaries introduce a color-dependent bias in the velocity dispersion of main-sequence stars of the order of 0.1–0.3 km s−1 (corresponding to 1%−6% of the velocity dispersion), with the reddest stars having a lower velocity dispersion, due to the higher fraction of contaminating binaries. This bias depends on the ability to distinguish binaries from single stars, on the details of the color–magnitude diagram and the photometric errors. We apply our analysis to the HSTPROMO data set of NGC 7078 (M15) and show that no effect ascribable to binaries is observed, consistent with the low binary fraction of the cluster. Our work indicates that binaries do not significantly bias proper-motion velocity-dispersion profiles, but should be taken into account in the error budget of kinematic analyses.

A novel look at energy equipartition in globular clusters

Two-body interactions play a major role in shaping the structural and dynamical properties of globular clusters (GCs) over their long-term evolution. In particular, GCs evolve toward a state of partial energy equipartition that induces a mass-dependence in their kinematics. By using a set of Monte Carlo cluster simulations evolved in quasi-isolation, we show that the stellar mass dependence of the velocity dispersion $\sigma(m)$ can be described by an exponential function $\sigma^2\propto \exp(-m/m_\mathrm{eq})$, with the parameter $m_\mathrm{eq}$ quantifying the degree of partial energy equipartition of the systems. This simple parametrization successfully captures the behaviour of the velocity dispersion at lower as well as higher stellar masses, that is, the regime where the system is expected to approach full equipartition. We find a tight correlation between the degree of equipartition reached by a GC and its dynamical state, indicating that clusters that are more than about 20 core relaxation times old, have reached a maximum degree of equipartition. This equipartition$-$dynamical state relation can be used as a tool to characterize the relaxation condition of a cluster with a kinematic measure of the $m_\mathrm{eq}$ parameter. Vice versa, the mass-dependence of the kinematics can be predicted knowing the relaxation time solely on the basis of photometric measurements. Moreover, any deviations from this tight relation could be used as a probe of a peculiar dynamical history of a cluster. Finally, our novel approach is important for the interpretation of state-of-the-art Hubble Space Telescope proper motion data, for which the mass dependence of kinematics can now be measured, and for the application of modeling techniques which take into consideration multi-mass components and mass segregation.