The ultra-diffuse galaxy NGC 1052-DF2 has an overabundance of luminous globular clusters (GCs), and its kinematics is consistent with the presence of little to no dark matter. As the velocity dispersion among the GCs is comparable to the expected internal dispersions of the individual GCs, the galaxy might be highly conducive to GC-GC merging. If true, this could explain the puzzling luminosity function of its GCs. Here, we examine this possibility by re-simulating three of our earlier simulations of the GC system (Dutta Chowdhury et al. 2019), where the GCs were modeled as single particles, with live GCs. Somewhat surprisingly, we infer a low merger rate of $\sim 0.03\ \rm Gyr^{-1}$. The main reason is that the GCs are too dense for tidal shock capture, caused by impulsive encounters among them, to operate efficiently (we infer a tidal capture rate of only $\sim 0.002\ \rm Gyr^{-1}$). Therefore, whatever mergers occur are driven by other mechanisms, which we find to be captures induced by dynamical friction and compressive tides from other GCs. The low merger rate inferred here makes it unlikely that the unusually large luminosities of the GCs can be explained as a result of past GC-GC mergers. Our simulations also indicate that, if NGC 1052-DF2 is indeed largely devoid of dark matter, its tidal field is too weak to induce any significant mass loss from the GCs. Therefore, in such a scenario, we predict that it is improbable for the GCs to reveal tidal features, something that can be tested with future deep observations.
We discuss dynamical friction in an $N$-body system in the presence of tidal interactions caused by a distant external source. Using the distant tide approximation, we develop a perturbation scheme for the calculation of dynamical friction that takes tidal effects into account to linear order. In this initial analytic approach to the problem, we neglect the influence of tides on the distribution function of stars in the background stellar system. Our result for the dynamical friction force in the appropriate limit is in agreement with Chandrasekhar's formula in the absence of tides. We provide…
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-v…
We present the results of a spectroscopic survey of the outskirts of 4 globular clusters -- NGC 1261, NGC 4590, NGC 1904, and NGC 1851 -- covering targets within 1 degree 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 {\sc limepy}/{\sc spes} models for each cluster to interpret the resul…
Halo inhabitants are individual stars, stellar streams, star and globular clusters, and dwarf galaxies. Here we compare the two last categories that include objects of similar stellar mass, which are often studied as self-dynamical equilibrium systems. We discover that the half-light radius of globular clusters depends on their orbital pericenter and total energy, and that Milky Way (MW) tides may explain the observed correlation. We also suggest that the accretion epoch of stellar systems in the MW halo can be calibrated by the total orbital energy, and that such a relation is due to both the…
The detections of gravitational waves produced in mergers of binary black holes (BH) and neutron stars (NS) by LIGO/Virgo have stimulated interest in the origin of the progenitor binaries. Dense stellar systems - globular and nuclear star clusters - are natural sites of compact object binary formation and evolution towards merger. Here we explore a new channel for the production of binary mergers in clusters, in which the tidal field of the cluster secularly drives the binary to high eccentricity (even in the absence of a central massive black hole) until gravitational wave emission becomes im…
We study the effect of dynamical friction on globular clusters and on the stars evaporated from the globular clusters (stellar streams) moving in a galactic halo. Due to dynamical friction, the position of a globular cluster (GC) as a stream progenitor starts to shift with respect to its original position in the reference frame of initial GC orbit. Therefore the stars that have evaporated at different times have different mean position with respect to the GC position. This shifting results in a certain asymmetry in stellar density distribution between the leading and trailing arms of the strea…
(Abridged) Dynamical friction can be used to distinguish Newtonian gravity and modified Newtonian dynamics (MOND) because it works differently in these frameworks. This concept, however, has yet to be explored very much with MOND. Previous simulations showed weaker dynamical friction during major mergers for MOND than for Newtonian gravity with dark matter. Analytic arguments suggest the opposite for minor mergers. In this work, we verify the analytic predictions for MOND by high-resolution $N$-body simulations of globular clusters (GCs) moving in isolated ultra-diffuse galaxies (UDGs). We tes…
Blue straggler stars are more massive than the average star in globular clusters, as they originate from the merger of two stars. Consequently, they experience dynamical friction, progressively sinking to the cluster center. Recently, several indicators of the degree of dynamical relaxation of a globular cluster have been proposed, based on the observed radial distribution of blue straggler stars. The most successful is the Alessandrini indicator, or A+ for short, which is the integral of the cumulative distribution of the blue straggler stars minus that of a lighter reference population. A+ c…
Ultra-diffuse galaxies that contain a large sample of globular clusters (GCs) offer an opportunity to test the predictions of galactic dynamics theory. NGC5846-UDG1 is an excellent example, with a high-quality sample of dozens of GC candidates. We show that the observed distribution of GCs in NGC5846-UDG1 is suggestive of mass segregation induced by gravitational dynamical friction. We present simple analytic calculations, backed by a series of numerical simulations, that naturally explain the observed present-day pattern of GC masses and radial positions. Subject to some assumptions on the GC…
Introducing AuriGLOBES: The effects of compressive tides, compact object-induced mass loss, and size evolution on modelling globular clusters
Instituto de Astrofísica de Canarias（加那利天体物理研究所）；Universidad de La Laguna（拉古纳大学）；Liverpool John Moores University（利物浦约翰摩尔斯大学）；Astrophysics Research Institute, Liverpool John Moores University（利物浦约翰摩尔斯大学天体物理研究所）；Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学）；Canadian Institute for Theoretical Astrophysics (CITA), University of Toronto（多伦多大学加拿大理论天体物理研究所）；McMaster University（麦克马斯特大学）
Damping of dynamical friction force in self-interacting ultralight dark matter and Fornax timing problem
Faculty of Physics, Taras Shevchenko National University of Kyiv（基辅塔拉斯舍甫琴科国立大学物理学院）；Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine（乌克兰国家科学院博戈留博夫理论物理研究所）；Institut für Mathematische Physik, Technische Universität Braunschweig（布伦瑞克工业大学数学物理研究所）；Fundamentale Physik für Metrologie FPM, Physikalisch-Technische Bundesanstalt PTB（德国联邦物理技术研究院基础计量物理学部）
Dynamical friction of star clusters against disk field stars in galaxies: Implications on stellar nucleus formation and globular cluster luminosity functions
I summarize our recent results to use the orbits of globular clusters (GCs) in the Fornax dwarf spheroidal (dSph) galaxy to learn more about dark matter (DM) properties. Our focus is on clarifying how dynamical friction (DF) from the DM halo is modified from the different microscopic properties of DM, which may alter $both$ the scattering processes responsible of DF and the DM profiles (in particular generating a core), which also modifies DF. We consider: $(i)$ fermionic degenerate dark matter (DDM), where Pauli blocking should be taken into account in the dynamical friction computation; $(ii…
The dark matter (DM) content of the Fornax dwarf spheroidal galaxy inferred from its kinematics is substantially lower than expected from LCDM cosmological simulations. We use N-body simulations to examine whether this may be the result of Galactic tides. We find that, despite improved proper motions from the Gaia mission, the pericentric distance of Fornax remains poorly constrained, mainly because its largest velocity component is roughly anti-parallel to the solar motion. Translating Fornax's proper motion into a Galactocentric velocity is thus sensitively dependent on Fornax's assumed dist…
Fuzzy dark matter dynamical friction: stalling of globular clusters induced by dynamical heatings
Observatoire de Paris, Université PSL, Sorbonne Université, Université Paris Cité, CY Cergy Paris Université, CNRS（巴黎天文台，巴黎文理研究大学，索邦大学，巴黎西岱大学，塞吉-蓬图瓦兹大学，法国国家科学研究中心）；David A. Dunlap Department of Astronomy and Astrophysics, University of Toronto（多伦多大学戴维·A·邓普尔天文学与天体物理学系）
Vortex State of Ultralight Dark Matter and the Fornax Timing Problem
Faculty of Physics, Taras Shevchenko National University of Kyiv（基辅塔拉斯舍甫琴科国立大学物理系）；Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine（乌克兰国家科学院博戈留博夫理论物理研究所）；Institut für Mathematische Physik, Technische Universität Braunschweig（布伦瑞克工业大学数学物理研究所）；Fundamentale Physik für Metrologie (FPM), Physikalisch-Technische Bundesanstalt (PTB)（德国联邦物理技术研究院计量基础物理部）
Direct observational evidence for the creation of nuclear star clusters (NSCs) is needed to support the proposed scenarios for their formation. We analysed the dwarf galaxy UGC 7346, located in the peripheral regions of the Virgo Cluster, to highlight a series of properties that indicate the formation of a NSC caught in its earlier stages. First, we report on remnants of a past interaction in the form of diffuse streams or shells, suggesting a recent merging of two dwarf galaxies with a 1:5 stellar mass ratio. Second, we identify a number of globular cluster (GC) candidates that are broadly co…
M54 is a prototype of a globular cluster embedded in a dark matter halo. Gaia EDR3 photometry and proper motions separate the old, metal-poor stars from the more metal rich and younger dwarf galaxy stars. The metal poor stars dominate the inner 50 pc, with a velocity dispersion profile that declines to a minimum around 30 pc then rises back to nearly the central velocity dispersion, as expected for a globular cluster at the center of a dark matter halo. The Jeans analysis of the three separate stellar populations give consistent masses that rise approximately linearly with radius to 1 kpc, imp…
The five globular clusters (GCs) of the Fornax dSph are puzzling for two reasons; the mass in GCs is high with respect to the galaxy's old stellar mass, and their survival and large distance (> 1 kpc) is at odds with naive expectations of dynamical friction. We present here a semi-analytic model, simultaneously addressing both problems in a comprehensive evolutionary framework for Fornax. Key to the model is inclusion of: 1) hydrodynamical constraints on the GC formation locations, 2) self-consistent velocity distribution functions in the dynamical friction calculations and 3) expansion of GC …
The dark matter content of the ultra diffuse galaxy NGC1052-DF2, as inferred from globular cluster (GC) and stellar kinematics, carries a considerable amount of uncertainty, with current constraints also allowing for the complete absence of dark matter. We test the viability of such a scenario by examining whether in a `baryon-only' mass model, the observed GC population experiences rapid orbital decay due to dynamical friction. Using a suite of 50 multi-GC N-body simulations that match observational constraints on both the stellar component of NGC1052-DF2 and its GC population but differ in t…
Recently, \cite{vanDokkum2018} have presented an important discovery of an ultra diffuse galaxy, NGC1052-DF2, with a dark matter content significantly less than predicted from its stellar mass alone. The analysis relies on measured radial velocities of 10 Globular Clusters (GCs), of estimated individual masses of a few $ \times 10^6 M_\odot$. This is about $1\%$ of the inferred mass of NGC1052-DF2 of $2\times 10^8 M_\odot$ within a half-light radius, $R_\mathrm{e}=2.2\, \mathrm{kpc}$. The large relative mass and the old age of these objects imply that they might be susceptible to orbital decay…
We have derived the mean proper motions and space velocities of 154 Galactic globular clusters and the velocity dispersion profiles of 141 globular clusters based on a combination of Gaia DR2 proper motions with ground-based line-of-sight velocities. Combining the velocity dispersion profiles derived here with new measurements of the internal mass functions allows us to model the internal kinematics of 144 clusters, more than 90% of the currently known Galactic globular cluster population. We also derive the initial cluster masses by calculating the cluster orbits backwards in time applying su…
We collected radial velocities of more than 50.000 individual stars in 156 Galactic globular clusters (GGC) and matched them with HST photometry and Gaia DR2 proper motions. This allowed us to derive the GGC's mean proper motions and space velocities. By fitting a large set of N-body simulations to their velocity dispersion and surface density profiles, combined with new measurements of their internal radially dependent mass functions, we have determined their present-day masses and structural parameters, and for 144 GGCs their internal kinematics. We also derive the initial cluster masses by …
Dynamical friction vs. subhalo heating in Cold Dark Matter haloes
Institute of Corpuscular Physics (IFIC), CSIC–Universitat de València（核物理研究所（IFIC），西班牙科学研究中心-瓦伦西亚大学）；VALER；Institute for Astronomy, University of Edinburgh（爱丁堡大学天文研究所）；Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche（复杂系统研究所，意大利国家研究委员会）；Osservatorio Astrofisico di Arcetri, Istituto Nazionale di Astrofisica（阿切特里天体物理观测台，意大利国家天体物理研究所）；Istituto nazionale di Fisica Nucleare（意大利国家核物理研究所）；McWilliams centre for Cosmology and Astrophysics, Department of Physics, Carnegie Mellon University（卡内基梅隆大学物理学院麦克威廉斯宇宙学与天体物理学中心）
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,…
We used extra-tidal RR Lyrae stars to study the dynamics of Galactic globular clusters and know how effects like dynamical friction and tidal disruption affect these clusters. The Gaia DR2 catalog for RR Lyrae stars (Clementini et al. 2018) is used along with the proper motions and tidal radii data for the globular clusters compiled from literature. A sample of 56 Galactic globular clusters is analyzed. Out of these 56 Galactic globular clusters, only 11 have extra-tidal RR Lyrae stars. However, only two clusters, namely, NGC 3201 and NGC 5024, have enough extra-tidal RR Lyrae stars to draw in…
Stellar dynamical model globular clusters are introduced into reconstituted versions of the dark matter halos of the Via-Lactea II (VL-2) simulation to follow the star cluster tidal mass loss and stellar stream formation. The clusters initially evolve within their local sub-galactic halo, later being accreted into the main halo. Stars are continually removed from the clusters, but those that emerged in the sub-galactic halos are dispersed in a wide stream when accreted into the main halo. Thin tidal streams that survive to the present can begin to form once a cluster is in the main halo. A hig…
We use N-body simulations to revisit the globular cluster (GC) ``timing problem'' in the Fornax dwarf spheroidal (dSph). In agreement with earlier work, we find that, due to dynamical friction, GCs sink to the center of dark matter halos with a cuspy inner density profile but ``stall'' at roughly 1/3 of the core radius ($r_{\rm core}$) in halos with constant-density cores. The timescales to sink or stall depend strongly on the mass of the GC and on the initial orbital radius, but are essentially the same for either cuspy (NFW) or cored halos normalized to have the same total mass within $r_{\r…
Globular clusters (GCs) and their dynamic interactions with the Galactic components provide an important insight into the structure and formation of the early Milky Way. Here, we present a kinematic study of two outer halo GCs based on a combination of VLT/FORS2, VLT/FLAMES, and Magellan/MIKE low- and high-resolution spectroscopy of 32 and 27 member stars, respectively. Although both clusters are located at Galactocentric distances of 15 kpc, they have otherwise very different properties. M 75 is a luminous and metal-rich system at [Fe/H] = $-1.2$ dex, a value that we confirm from the calcium …
We re-investigate the Fornax cusp-core problem using observational results on the spatial and mass distributions of globular clusters (GCs) in order to put constraints on the dark matter profile. We model Fornax using high-resolution N-body simulations with entirely live systems, i.e. self-gravitating systems composed of stars and dark matter, which account correctly for dynamical friction and tidal effects between Fornax and the globular clusters. We test two alternative hypotheses, which are a cored and a cuspy halo for Fornax by exploring a reasonable range of initial conditions on globular…
Dynamical friction is often modeled with reasonable accuracy by the widely used Chandrasekhar formula. However, in some circumstances, Chandrasekhar's local and uniform approximations can break down severely. An astrophysically important example is the "core stalling" phenomenon seen in N-body simulations of massive perturber inspiralling into the near-harmonic potential of a stellar system's constant-density core (and possibly also in direct observations of dwarf galaxies with globular clusters). In this paper we use the linearized collisionless Boltzmann equation to calculate the global resp…
The dynamical friction timescale of massive globular clusters (GCs) in the inner regions of cuspy dark haloes in dwarf spheroidal (dSph) galaxies can be much shorter than the Hubble time. This implies that a small fraction of the GCs is expected to be caught close to the centre of these galaxies. We compare the radial distribution of GCs predicted in simple Monte Carlo models with that of a sample of $38$ spectroscopically confirmed GCs plus 17 GC candidates, associated mainly to low-luminosity dSph galaxies. If dark matter haloes follow an NFW profile, the observed number of off-center GCs at…
Constraints on the fuzzy dark matter mass using globular clusters in dwarf galaxies from Euclid ERO data
LIRA, Observatoire de Paris, Université PSL, Sorbonne Université, Université Paris Cité, CY Cergy Paris Université, CNRS（巴黎天文台 LIRA 实验室，PSL 大学，索邦大学，巴黎西岱大学，CY 塞吉-蓬图瓦兹大学，法国国家科学研究中心）；Université de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR 7550（斯特拉斯堡大学，法国国家科学研究中心，斯特拉斯堡天文台）；Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学 Kavli 宇宙物理学与数学起源研究所（WPI），UTIAS）；Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona（巴塞罗那大学宇宙科学研究所）
In order to find the possible progenitors of Milky Way globular clusters, we perform orbit integrations to track the orbits of 170 Galactic globular clusters and the eleven classical Milky Way satellite galaxies backwards in time for 11 Gyr in a Milky-Way-plus-satellites potential including the response of the MW to the infall of the Large Magellanic Cloud and the effect of dynamical friction on the satellites. To evaluate possible past associations, we devise a globular-cluster--satellite binding criterion based on the satellite's tidal radius and escape velocity and we test it on globular cl…
