Velocity Dispersion Profiles Research Articles

The surface mass density of the Milky Way: does the traditional KZ approach work in the context of new surveys?

ABSTRACT We revisit the classical KZ problem – determination of the vertical force and implied total mass density distribution of the Milky Way disc – for a wide range of Galactocentric radius and vertical height using chemically selected thin and thick disc samples based on Apache Point Observatory Galactic Evolution Experiment spectroscopy combined with the Gaia astrometry. We derived the velocity dispersion profiles in Galactic cylindrical coordinates, and solved the Jeans equation for the two samples separately. The result is surprising that the total surface mass density as a function of vertical height as derived for these two chemically distinguished populations is different. The discrepancies are larger in the inner compared to the outer Galaxy, with the density calculated from thick disc being larger, independent of the Galactic radius. Furthermore, while there is an overall good agreement between the total mass density derived for the thick disc population and the standard halo model for vertical heights larger than 1 kpc, close to the mid-plane the mass density observed using the thick disc population is larger than that predicted from the standard halo model. We explore various implications of these discrepancies, and speculate their sources, including problems associated with the assumed density laws, velocity dispersion profiles, and the Galactic rotation curve, potential non-equilibrium of the Galactic disc, or a failure of the Navarro-Frenk-White (NFW) dark matter halo profile for the Milky Way. We conclude that the growing detail in hand on the chemodynamical distributions of Milky Way stars challenges traditional analytical treatments of the KZ problem.

Unraveling the Complexity of Dwarf Galaxy Dynamics: A Study of Binary Orbital Motions

We investigate the impact of binary orbital motions on the dynamical modeling of dwarf galaxies with intrinsic line-of-sight velocity dispersions () of 1–9 km s−1. Using dwarf galaxies from the auriga level-2 and level-3 simulations, we apply the Jeans Anisotropic Multi-Gaussian Expansion modeling to tracer stars before and after including binaries to recover the dynamical masses. The recovered total masses within the half-mass radius of tracers, M(< r half), are always inflated due to binary motions, with greater inflations occurring for smaller . However, many dwarf galaxies experience central density deflated due to binary motions, with little dependence on . This is due to the negative radial gradients in the velocity dispersion profiles, with the fractional inflation in due to binaries more significant in outskirts. An extreme binary fraction of 70% can lead to central density deflation of up to 10%–20% at 3 km s−1 < < 8 km s−1, with M( < r half) inflated by 4% at 9 km s−1 and up to 15% at 3 km s−1. A lower binary fraction of 36% leads to similar deflations, with the inflations decreasing to approximately 10% at 3 km s−1 and becoming statistically insignificant. The choice of binary orbit distribution models does not result in significant differences, and observational errors tend to slightly weaken the deflations in the recovered central density. Two observations separated by 1 yr to exclude binaries lead to almost zero inflations/deflations for a binary fraction of 36% over 3 km s−1 < km s−1. For km s−1 to 3 km s−1, a binary fraction of 70% (36%) still results in 60% (30%) to 10% (1%) of inflations in M( < r half), even with two-epoch observation.

Multiple stellar populations found outside the tidal radius of NGC 1851 via Gaia DR3 XP spectra

Aims. Ancient galactic globular clusters (GCs) have long fascinated astronomers due to their intriguing multiple stellar populations (MPs), which are characterized by variations in light element abundances. Among these clusters, type II GCs stand out as they exhibit stars with large differences in heavy-element chemical abundances. These enigmatic clusters, comprising approximately 17% of analyzed GCs with MPs, have been hypothesized to be the remnants of accreted dwarf galaxies. Methods. We focus on one of the most debated type II GCs, namely, NGC 1851, to investigate its MPs across a wide spatial range of up to 50 arcmin from the cluster center. By using Gaia Data Release 3 low-resolution XP spectra, we generated synthetic photometry to perform a comprehensive analysis of the spatial distribution and kinematics of the canonical and anomalous populations within this GC. By using appropriate color-magnitude diagrams from the synthetic photometry in the BVI bands and in the f41525 band introduced in this work, we identified distinct stellar sequences associated with different heavy-element chemical compositions. Results. Our results suggest that the canonical and the anomalous populations reside both inside and outside the tidal radius of NGC 1851, up to a distance that exceeds its tidal radius 3.5 times. However, about 80% of stars outside the tidal radius are consistent with characteristics that class them among the canonical population, emphasizing its dominance in the cluster’s outer regions. Remarkably, canonical stars exhibit a more circular on-sky morphology, while the anomalous population displays an elliptical shape. Furthermore, we delve into the kinematics of the multiple populations, examining velocity dispersions, rotation patterns, and potential substructures. Our results reveal a flat or increasing velocity dispersion profile in the outer regions. Additionally, we observe hints of a tangentially anisotropic motion in the outer regions, indicating a preference for stars to escape on radial orbits. Our work demonstrates the capability of synthetic photometry, based on Gaia spectra, to explore multiple populations across the entire cluster field.

Resolving the physics of quasar Ly α nebulae (RePhyNe): I. Constraining quasar host halo masses through circumgalactic medium kinematics

ABSTRACT Ly α nebulae ubiquitously found around z &amp;gt; 2 quasars can supply unique constraints on the properties of the circumgalactic medium, such as its density distribution, provided the quasar halo mass is known. We present a new method to constrain quasar halo masses based on the line-of-sight velocity dispersion maps of Ly α nebulae. By using MUSE-like mock observations obtained from cosmological hydrodynamic simulations under the assumption of maximal quasar fluorescence, we show that the velocity dispersion radial profiles of Ly α emitting gas are strongly determined by gravity and that they are thus self-similar with respect to halo mass when rescaled by the virial radius. Through simple analytical arguments and by exploiting the kinematics of He ii1640 Å emission for a set of observed nebulae, we show that Ly α radiative transfer effects plausibly do not change the shape of the velocity dispersion profiles but only their normalization without breaking their self-similarity. Taking advantage of these results, we define the variable $\eta ^{140-200}_{40-100}$ as the ratio of the median velocity dispersion in two specifically selected annuli and derive an analytical relation between $\eta ^{140-200}_{40-100}$ and the halo mass which can be directly applied to observations. We apply our method to 37 observed quasar Ly α nebulae at 3 &amp;lt; z &amp;lt; 4.7 and find that their associated quasars are typically hosted by ∼1012.16 ± 0.14M⊙ haloes independent of redshift within the explored range. This measurement, which is completely independent of clustering methods, is consistent with the lowest mass estimates based on quasar autocorrelation clustering at z∼3 and with quasar-galaxies cross-correlation results.

Star cluster progenitors are dynamically decoupled from their parent molecular clouds

ABSTRACT The formation of stellar clusters dictates the pace at which galaxies evolve, and solving the question of their formation will undoubtedly lead to a better understanding of the Universe as a whole. While it is well known that star clusters form within parsec-scale overdensities of interstellar molecular gas called clumps, it is, however, unclear whether these clumps represent the high-density tip of a continuous gaseous flow that gradually leads towards the formation of stars, or a transition within the gas physical properties. Here, we present a unique analysis of a sample of 27 infrared dark clouds embedded within 24 individual molecular clouds that combine a large set of observations, allowing us to compute the mass and velocity dispersion profiles of each, from the scale of tens of parsecs down to the scale of tenths of a parsec. These profiles reveal that the vast majority of the clouds, if not all, are consistent with being self-gravitating on all scales, and that the clumps, on parsec-scale, are often dynamically decoupled from their surrounding molecular clouds, exhibiting steeper density profiles (ρ∝r−2) and flat velocity dispersion profiles (σ∝r0), clearly departing from Larson’s relations. These findings suggest that the formation of star clusters correspond to a transition regime within the properties of the self-gravitating molecular gas. We propose that this transition regime is one that corresponds to the gravitational collapse of parsec-scale clumps within otherwise stable molecular clouds.

Self-consistent dynamical models with a finite extent – III. Truncated power-law spheres

ABSTRACT Fully analytical dynamical models usually have an infinite extent, while real star clusters, galaxies, and dark matter haloes have a finite extent. The standard method for generating dynamical models with a finite extent consists of taking a model with an infinite extent and applying a truncation in binding energy. This method, however, cannot be used to generate models with a preset analytical mass density profile. We investigate the self-consistency and dynamical properties of a family of power-law spheres with a general tangential Cuddeford (TC) orbital structure. By varying the density power-law slope γ and the central anisotropy β0, these models cover a wide parameter space in density and anisotropy profiles. We explicitly calculate the phase–space distribution function for various parameter combinations, and interpret our results in terms of the energy distribution of bound orbits. We find that truncated power-law spheres can be supported by a TC orbital structure if, and only if, γ ≥ 2β0, which means that the central density slope–anisotropy inequality is both a sufficient and a necessary condition for this family. We provide closed expressions for structural and dynamical properties such as the radial and tangential velocity dispersion profiles, which can be compared against more complex numerical modelling results. This work significantly adds to the available suite of self-consistent dynamical models with a finite extent and an analytical description.

Characteristic evaluation of passive seismic ellipticity method in urban shield tunnel

In recent years, engineering examples have shown that traditional surface-wave detection methods are easily limited in areas with small space and heavy traffic. The horizontal-to-vertical spectral ratio survey method has become increasingly prevalent in site measurements and is favored by geophysicists for its ability to detect near-surface velocity structures with greater sensitivity than phase velocities. Based on the phase difference method and polarization filtering, we proposed a passive seismic ellipticity method. The objective of this method is to extract the Rayleigh waves from ambient noise recordings and the analysis of ellipticity dispersion characteristic. This method was applied to an actual case study. Specifically, the velocity dispersion profile of the site is obtained using the active-source surface-wave method. Then, we compared the results obtained by the passive seismic ellipticity method with those obtained by the active-source surface-wave method and the field data, to evaluate the accuracy of results. The results demonstrate that the proposed method can effectively detect the location of subsurface shield tunnels and has the characteristics of simple data processing steps, less interference, and high stability of results. This demonstrates the necessity of using the phase difference method to select segments dominated by Rayleigh waves in ambient noise recordings and applying polarization filtering before calculating ellipticity. The paper provides an actual case study for the application and promotion of the passive seismic ellipticity method and has significant practical value and reference significance.

Testing quasi-linear modified Newtonian dynamics theory with Galactic globular clusters in a weak external field

ABSTRACT We developed self-consistent dynamical models of stellar systems in the framework of quasi-linear modified Newtonian dynamics (QUMOND). The models are constructed from the anisotropic distribution function of Gunn and Griffin, combined with the modified Poisson equation defining this gravitation theory and take into account the external field effect. We have used these models, and their Newtonian analogues, to fit the projected density and the velocity dispersion profiles of a sample of 18 Galactic globular clusters, using the most updated data sets of radial velocities and Gaia proper motions. We have thus obtained, for each cluster, estimates of the dynamical mass-to-light ratio (M/L) for each theory of gravity. The selected clusters have accurate proper motions and a well-sampled mass function down to the very low-mass regime. This allows us to constrain the degree of anisotropy and to provide, from comparison with stellar evolution isochrones, a dynamics-independent estimate of the minimum mass-to-light ratio (M/L)min. Comparing the best-fitting dynamical M/L with (M/L)min, we find that for none of the analysed clusters the two gravity theories are significantly incompatible with the observational data, although for one of them (NGC 5024) the dynamical M/L predicted by QUMOND lies at 2.8σ below (M/L)min. Though the proposed approach suffers from some limitations (in particular the lack of a treatment of mass segregation), the obtained results suggest that the kinematics of globular clusters in a relatively weak external field can be a powerful tool to prove alternative theories of gravitation.

Internal Kinematics and Structure of the Bulge Globular Cluster NGC 6569 ∗ ∗ Based on observations collected at the European Southern Observatory, Cerro Paranal (Chile), in the context of the ESO-VLT Multi-Instrument Kinematic Survey (MIKiS survey) under Large Programmes 106.21N5 (PI: Ferraro), 195.D-0750 (PI: Ferraro), 193.D-0232 (PI: Ferraro). This publication makes use of data products from the Two Micron All

In the context of a project aimed at characterizing the properties of star clusters in the Galactic bulge, here we present the determination of the internal kinematics and structure of the massive globular cluster NGC 6569. The kinematics has been studied by means of an unprecedented spectroscopic data set acquired in the context of the ESO-VLT Multi-Instrument Kinematic Survey of Galactic globular clusters, combining the observations from four different spectrographs. We measured the line-of-sight velocity of a sample of almost 1300 stars distributed between ∼0.″8 and 770″ from the cluster center. From a subsample of high-quality measures, we determined the velocity dispersion profile of the system over its entire radial extension (from ∼5″ to ∼200″ from the center), finding the characteristic behavior usually observed in globular clusters, with a constant inner plateau and a declining trend at larger radii. The projected density profile of the cluster has been obtained from resolved star counts, by combining high-resolution photometric data in the center, and the Gaia EDR3 catalog radially extended out to for a proper sampling of the Galactic field background. The two profiles are properly reproduced by the same King model, from which we estimated updated values of the central velocity dispersion, main structural parameters (such as the King concentration, the core, half mass, and tidal radii), total mass, and relaxation times. Our analysis also reveals a hint of ordered rotation in an intermediate region of the cluster (40″ < r < 90″, corresponding to 2r c < r < 4.5r c ), but additional data are required to properly assess this possibility.

Ongoing hierarchical massive cluster assembly: The LISCA II structure in the Perseus complex

We report on the identification of a massive (∼105 M⊙) substructured stellar system in the Galactic Perseus complex likely undergoing hierarchical cluster assembly. This system comprises nine star clusters (including the well-known clusters NGC 654 and NGC 663) and an extended and low-density stellar halo. Gaia-DR3 and available spectroscopic data show that all its components are physically consistent in 6D phase-space (position, parallax, and 3D motion), and homogeneous in age (14–44 Myr) and chemical content (half-solar metallicity). In addition, the system’s global stellar density distribution is that of typical star clusters and shows clear evidence of mass segregation. We find that the hierarchical structure is mostly contracting toward the center with a speed of up to ≃4 − 5 km s−1, while the innermost regions expand at a lower rate (about ≃1 km s−1) and are dominated by random motions. Interestingly, this pattern is dominated by the kinematics of massive stars, while low-mass stars (M &lt; 2 M⊙) are characterized by contraction across the entire cluster. Finally, the nine star clusters in the system are all characterized by a relatively flat velocity dispersion profile possibly resulting from ongoing interactions and tidal heating. We show that the observational results are generally consistent with those found in N-body simulations following the cluster violent relaxation phase, strongly suggesting that the system is a massive cluster in the early assembly stages. This is the second structure with these properties identified in our Galaxy and, following the nomenclature of our previous work, we named it LISCA II.

Clustertools: A Python Package for Analyzing Star Cluster Simulations

$clustertools$ is a Python package for analyzing star cluster simulations. The package is built around the $StarCluster$ class, which stores all data read in from the snapshot of a given model star cluster. The package contains functions for loading data from commonly used $N$-body codes, generic snapshots, and software for generating initial conditions. All operations and functions within $clustertools$ are then designed to act on a $StarCluster$. $clustertools$ can be used for unit and coordinate transformations, the calculation of key structural and kinematic parameters, analysis of the cluster's orbit and tidal tails, and measuring common cluster properties like its mass function, density profile, and velocity dispersion profile (among others). While originally designed with star clusters in mind, $clustertools$ can be used to study other types of $N$-body systems, including stellar streams and dark matter sub-halos.

The Initial Mass Function and Other Stellar Properties Across the Core of the Hydra I Cluster* * This paper includes data gathered with the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile.

The Hydra I cluster offers an excellent opportunity to study and compare the relic old stellar populations in the core of its two brightest galaxies. In addition, the differing kinematics of the two galaxies allows a test of the local validity of general scaling relations. In this work, we present a direct comparison employing full spectral fitting of new high-quality long-slit optical and near-infrared spectroscopic data. We retrieve age, metallicity, and 19 elemental abundances out to ∼12 kpc within each galaxy, as well as the Initial Mass Function (IMF) in their central regions. Our results suggest that the inner ∼5 kpc regions of both galaxies, despite their different masses, formed at the same time and evolved with a similar star formation timescale and chemical enrichment, confirming their early formation in the cluster buildup. Only the overall metallicity and IMF radial profiles show differences connected with their different velocity dispersion profiles. The radial trends of the IMF positively correlate with both [Z/H] and σ. While the trends of the IMF slope values with metallicity agree with a global trend for both galaxies, the trends with the velocity dispersion exhibit differences. The outer regions show signs of mixed stellar populations with large differences in chemical content compared to the centers, but with similarly old ages.

Accurate model of the projected velocity distribution of galaxies in dark matter haloes

ABSTRACT We present a per cent-level accurate model of the line-of-sight velocity distribution of galaxies around dark matter haloes as a function of projected radius and halo mass. The model is developed and tested using synthetic galaxy catalogues generated with the UniverseMachine run on the Multi-Dark Planck 2 N-body simulations. The model decomposes the galaxies around a cluster into three kinematically distinct classes: orbiting, infalling, and interloping galaxies. We demonstrate that: (1) we can statistically distinguish between these three types of galaxies using only projected line-of-sight velocity information; (2) the halo edge radius inferred from the line-of-sight velocity dispersion is an excellent proxy for the three-dimensional halo edge radius; and (3) we can accurately recover the full velocity dispersion profile for each of the three populations of galaxies. Importantly, the velocity dispersion profiles of the orbiting and infalling galaxies contain five independent parameters – three distinct radial scales and two velocity dispersion amplitudes – each of which is correlated with mass. Thus, the velocity dispersion profile of galaxy clusters has inherent redundancies that allow us to perform non-trivial systematics checks from a single data set. We discuss several potential applications of our new model for detecting the edge radius and constraining cosmology and astrophysics using upcoming spectroscopic surveys.

The ESO-VLT MIKiS Survey Reloaded: Exploring the Internal Kinematics of NGC 6440* * Based on observations collected at the European Southern Observatory, Cerro Paranal (Chile), under proposal 193.D-0232 (PI: Ferraro), 195.D-0750 (PI: Ferraro), 60.A-9489 (PI: Ferraro), and 093.D-0319 (PI: Lanzoni).

In the context of the ESO-VLT Multi-Instrument Kinematic Survey of Galactic globular clusters, here we present the line-of-sight velocity dispersion profile of NGC 6440, a massive globular cluster located in the Galactic bulge. By combining the data acquired with four different spectrographs, we obtained the radial velocity of a sample of ∼1800 individual stars distributed over the entire cluster extension, from ∼0.″1 to 778″ from the center. Using a properly selected sample of member stars with the most reliable radial velocity measures, we derived the velocity dispersion profile up to 250″ from the center. The profile is well described by the same King model that best fits the projected star density distribution, with a constant inner plateau (at σ 0 ∼ 12 km s−1) and no evidence of a central cusp or other significant deviations. Our data allowed us to study the presence of rotation only in the innermost regions of the cluster (r < 5″), revealing a well-defined pattern of ordered rotation with a position angle of the rotation axis of ∼132° ± 2° and an amplitude of ∼3 km s−1 (corresponding to V rot/σ 0 ∼ 0.3). In addition, a flattening of the system qualitatively consistent with the rotation signal has been detected in the central region.

Classifying MaNGA velocity dispersion profiles by machine learning

Abstract We present a machine-learning (ML) approach for classifying kinematic profiles of elliptical galaxies in the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey. Previous studies employing ML to classify spectral data of galaxies have provided valuable insights into morphological galaxy classification. This study aims to enhance the understanding of galaxy kinematics by leveraging ML. The kinematics of 2624 MaNGA elliptical galaxies are investigated using integral field spectroscopy by classifying their one-dimensional velocity dispersion (VD) profiles. We utilized a total of 1266 MaNGA VD profiles and employed a combination of unsupervised and supervised learning techniques. The unsupervised K-means algorithm classifies VD profiles into four categories: flat, decline, ascend, and irregular. A bagged decision trees classifier (TreeBagger)-supervised ensemble is trained using visual tags, achieving 100 ${{\ \rm per\ cent}}$ accuracy on the training set and 88 ${{\ \rm per\ cent}}$ accuracy on the test set. Our analysis identifies the majority (68 ${{\ \rm per\ cent}}$) of MaNGA elliptical galaxies presenting flat VD profiles, which requires further investigation into the implications of the dark matter problem.

Catching a Milky Way open cluster in its last breath

ABSTRACT Theoretical models have suggested peculiar velocity dispersion profiles of star clusters facing dissolution. They predicted that, besides bound stars that still belong to the star cluster, and unbound ones already stripped off, there is an intermediate population of stars that having acquired the enough energy to escape the cluster are still within the cluster Jacobi radius. Both, potential escapers and unbound stars, show hot kinematics, not observed along tidal tails of star clusters. We report on the first evidence of an open cluster with stars crossing such a transitional scenario, namely: ASCC 92. The open cluster gathers nearly 10 per cent of its initial total mass, and is moving towards Galactic regions affected by higher interstellar absorption. Precisely, the obscured appearance of the cluster could have hampered disentangling its true internal dynamical evolutionary stage, previously.

Dynamics of dwarf galaxies in f(R) gravity

ABSTRACT We use the kinematic data of the stars in eight dwarf spheroidal galaxies to assess whether f(R) gravity can fit the observed profiles of the line-of-sight velocity dispersion of these systems without resorting to dark matter. Our model assumes that each galaxy is spherically symmetric and has a constant velocity anisotropy parameter β and constant mass-to-light ratio consistent with stellar population synthesis models. We solve the spherical Jeans equation that includes the Yukawa-like gravitational potential appearing in the weak field limit of f(R) gravity, and a Plummer density profile for the stellar distribution. The f(R) velocity dispersion profiles depends on two parameters: the scale length ξ−1, below which the Yukawa term is negligible, and the boost of the gravitational field δ &amp;gt; −1. δ and ξ are not universal parameters, but their variation within the same class of objects is expected to be limited. The f(R) velocity dispersion profiles fit the data with a value $\xi ^{-1}= 1.2^{+18.6}_{-0.9}$ Mpc for the entire galaxy sample. On the contrary, the values of δ show a bimodal distribution that picks at $\overline{\delta }=-0.986\pm 0.002$ and $\overline{\delta }=-0.92\pm 0.01$. These two values disagree at 6σ and suggest a severe tension for f(R) gravity. It remains to be seen whether an improved model of the dwarf galaxies or additional constraints provided by the proper motions of stars measured by future astrometric space missions can return consistent δ’s for the entire sample and remove this tension.

A halo of trapped interstellar matter surrounding the Solar system

ABSTRACT This paper shows that gravitating bodies travelling through the Galaxy can trap lighter interstellar particles that pass nearby with small relative velocities onto temporarily bound orbits. The capture mechanism is driven by the Galactic tidal field, which can decelerate infalling objects to a degree where their binding energy becomes negative. Over time, trapped particles build a local overdensity – or ‘halo’– that reaches a steady state as the number of particles being captured equals that being tidally stripped. This paper uses classical stochastic techniques to calculate the capture rate and the phase-space distribution of particles trapped by a point-mass. In a steady state, bound particles generate a density enhancement that scales as δ(r) ∼ r−3/2 (a.k.a ‘density spike’) and follow a velocity dispersion profile σh(r) ∼ r−1/2. Collision-less N-body experiments show excellent agreement with these theoretical predictions within a distance range r ≳ rϵ, where $r_\epsilon \simeq 0.8\, \exp [-V_\star ^2/(2\sigma ^2)]\, Gm_\star /\sigma ^2$ is the thermal critical radius of a point-mass m⋆ moving with a speed V⋆ through a sea of particles with a velocity dispersion σ. Preliminary estimates that ignore collisions with planets and Galactic substructures suggest that the Solar system may be surrounded by a halo that contains the order of $N^{\rm ISO}(\lt 0.1\, {\rm pc})\sim 10^7$ energetically bound ‘Oumuamua-like objects, and a dark matter mass of $M^{\rm DM}(\lt 0.1\, {\rm pc})\sim 10^{-13}M_\odot$. The presence of trapped interstellar matter in the Solar system can affect current estimates on the size of the Oort Cloud, and leave a distinct signal in direct dark matter detection experiments.

Investigating dynamical properties of globular clusters through a family of lowered isothermal models

ABSTRACT To investigate the dynamical properties of globular clusters, surface brightness and kinematic data were collected and fitted to a family of lowered isothermal models called limepy models. For the 18 globular clusters studied, the amounts of concentration, truncation, and anisotropy were determined. In addition, the cluster mass, half-mass radius, distance, and mass-to-light ratio were also obtained. In general, limepy models can describe these clusters well. Among these 18 clusters, NGC 5139, 6388, and 7078 have been claimed to be candidates for hosting intermediate-mass black holes in the literature. The models could not appropriately fit the central proper-motion velocity dispersion of NGC 5139, nor the slope of the proper-motion velocity dispersion profile of NGC 6388. Thus, more dedicated models with intermediate-mass black holes or a group of stellar-mass black holes at cluster centres may need to be considered. Regarding NGC 7078, our model with some degree of anisotropy can fit the data. Finally, a strong concentration–truncation anticorrelation and a truncation–semimajor-axis correlation were revealed, which could be the observational imprint of the dynamical evolution of globular clusters.

Dynamics in the outskirts of four Milky Way globular clusters: it’s the tides that dominate

ABSTRACT We present the results of a spectroscopic survey of the outskirts of four globular – 1261, NGC 4590, NGC 1904, and NGC 1851 – covering targets within 1° from the cluster centres, with 2dF/AAOmega on the Anglo-Australian Telescope (AAT) and FLAMES on the very large telescope (VLT). We extracted chemo-dynamical information for individual stars, from which we estimated the velocity dispersion profile and the rotation of each cluster. The observations are compared to direct N-body simulations and appropriate limepy/spes models for each cluster to interpret the results. In NGC 1851, the detected internal rotation agrees with existing literature, and NGC 1261 shows some rotation signal beyond the truncation radius, likely coming from the escaped stars. We find that the dispersion profiles for both the observations and the simulations for NGC 1261, NGC 1851, and NGC 1904 do not decrease as the limepy/spes models predict beyond the truncation radius, where the N-body simulations show that escaped stars dominate; the dispersion profile of NGC 4590 follows the predictions of the limepy/spes models, though the data do not effectively extend beyond the truncation radius. The increasing/flat dispersion profiles in the outskirts of NGC 1261, NGC 1851, and NGC 1904, are reproduced by the simulations. Hence, the increasing/flat dispersion profiles of the clusters in question can be explained by the tidal interaction with the galaxy without introducing dark matter.