In a series of three papers, we introduced a novel cluster formation model that describes the formation, growth, and disruption of star clusters in high-resolution cosmological simulations. We tested this model on a Milky Way-sized galaxy and found that various properties of young massive clusters, such as the mass function and formation efficiency, are consistent with observations in the local universe. Interestingly, most massive clusters -- globular cluster candidates -- are preferentially formed during major merger events. We follow the dynamical evolution of clusters in the galactic tidal field. Due to tidal disruption, the cluster mass function evolves from initial power law to a peaked shape. The surviving clusters at $z=0$ show a broad range of metallicity [Fe/H] from -3 to -0.5. A robust prediction of the model is the age--metallicity relation, in which metal-rich clusters are systematically younger than metal-poor clusters by up to 3 Gyr.
We investigate the properties of globular clusters in a galaxy cluster, using the particle tagging method with a semi-analytical approach in a cosmological context. We assume globular clusters form from dark matter halo mergers and their metallicity is assigned based on the stellar mass of the host dark matter halos and the formation redshift of GCs. Dynamical evolution and disruption of globular clusters are considered using semi-analytical approaches, controlled by several free parameters. In this paper, we investigate how our results are changed by the choice of free parameters. We compare …
Observational and theoretical arguments support the idea that violent events connected with $AGN$ activity and/or intense star forming episodes have played a significant role in the early phases of galaxy formation at high red shifts. Being old stellar systems, globular clusters seem adequate candidates to search for the eventual signatures that might have been left by those energetic phenomena. The analysis of the colour distributions of several thousands of globular clusters in the Virgo and Fornax galaxy clusters reveals the existence of some interesting and previously undetected features. …
We very briefly discuss proposed in the literature possible scenarios for intermediate mass black holes (IMBH) formation in globular clusters. We also discuss the results of the MOCCA simulations of about 2000 models (BigSurvey) regarding the distribution of events connected with electromagnetic and gravitational radiations, namely: mass transfer on IMBH, collisions and mergers with IMBH and mergers with IMBH due to gravitational radiation. The rates of these events are very small, so their observation is very improbable.
We performed the photometric analysis of M2 and M92 globular clusters in g and r bands of SLOAN photometric system. We transformed these g and r bands into BV bands of Johnson-Cousins photometric system and built the color magnitude diagram (CMD). We estimated the age, and metallicity of both the clusters, by fitting Padova isochrones of different age and metallicities onto the CMD. We studied Einstein and de Sitter model, bench mark model, the cosmological parameters by WMAP and Planck surveys. Finally, we compared estimated age of globular clusters to the ages from the cosmological models an…
We discuss some of the key open questions regarding the formation and evolution of globular clusters (GCs) during galaxy formation and assembly within a cosmological framework. The current state-of-the-art for both observations and simulations is described, and we briefly mention directions for future research. The oldest GCs have ages $\ge$ 12.5 Gyr and formed around the time of reionisation. Resolved colour-magnitude diagrams of Milky Way GCs and direct imaging of lensed proto-GCs at z $\sim$ 6 with JWST promise further insight. Globular clusters are known to host multiple populations of sta…
This paper is aimed at emphasizing some of the main hints, constraints and difficulties we currently have in trying to understand how globular clusters formed, along with their multiple stellar generations, an issue that must be regarded as intimately connected to the formation process itself. Thus, the topics that are addressed include i) the required mass of the progenitor, ii) how to form new stars in an environment already crowded by a previous stellar generation, iii) how photometry and spectroscopy appear to suggest different formation processes for second generation stars, iv) whether d…
We apply the idea that dense stellar systems in the central region of galaxies are formed via globular cluster mergers to the formation of the nuclear star cluster of the Milky Way, where a massive black hole is present. Our high precision N-body simulations show a good fit to the observational characteristics of the Milky Way nuclear cluster, giving further reliability to the so called migratory model for the formation of compact systems in the inner galaxy regions keywords galaxies: nuclei - galaxies: black holes - galaxies: globular clusters - galaxies: Milky Way - N-body: simulations
Many observed globular clusters (GCs) seem to show a central overabundance of mass whose nature has not yet fully understood. Indeed, it is not clear whether it is due to a central intermediate mass black hole (IMBH) or to a massive stellar system (MSS) composed of mass segregated stars. In this contribution we present a semi-analytic approach to the problem complemented by 12 $N$-body simulations in which we followed the formation of MSSs in GCs with masses up to $3\times 10^5$ \Ms. Some implications for the formation of IMBHs and gravitational waves emission are discussed in perspective of a…
Driven by recent observational findings, we select massive interactive binaries as the most suitable among the existing candidates for producing the chemical patterns typical of multiple populations of Galactic globular clusters. Still, to avoid supernova contamination we are further driven to endorse the notion that above a critical mass stars fail to produce supernova events, but rather eventually sink into black holes without ejecting much energy and heavy metals. This assumption has the attractive implication of suppressing star formation feedback for some 5--10 million years, in practice …
Globular cluster ages provide both an important test of models of globular cluster formation and a powerful method to constrain the assembly history of galaxies. Unfortunately, measuring the ages of unresolved old stellar populations has proven challenging. Here, we present a novel technique that combines optical photometry with metallicity constraints from near-infrared spectroscopy in order to measure ages. After testing the method on globular clusters in the Milky Way and its satellite galaxies, we apply our technique to three massive early-type galaxies using data from the SLUGGS Survey. T…
The Aquarius project is the first simulation that can resolve the full mass range of potential globular cluster formation sites. With a particle mass $m_\mathrm{p}=1.4 \times 10^4$\Msun, Aquarius yields more than 100 million particles within the virial radius of the central halo which has a mass of $1.8 \times 10^{12}$\Msun, similar to that of the Milky Way. With this particle mass, dark matter concentrations (haloes) as small as 10$^6$ M$_\odot$ will contain a minimum of 100 particles.Here, we use this simulation to test a model of metal-poor globular cluster formation based on collapse physi…
Even after decades of research, the origin of multiple stellar populations in globular clusters remains enigmatic. The question as to whether the galaxy environment plays a role in their formation remains unanswered. To that extent, we analysed two classical (> 10 Gyr old) Large Magellanic Cloud globular clusters namely, NGC 1786 and NGC 1898, using imaging data from Hubble Space Telescope to compare and contrast them with ancient Galactic globular clusters to assess systematic differences that might exist between their abundance variations. We calculated their Red Giant Branch width, subtract…
By adopting empirical estimates of the Helium enhancement (Delta Y) between consecutive stellar generations for a sample of Galactic globular clusters (GGC), we uniquely constraint the star formation efficiency of each stellar generation in these stellar systems. In our approach, the star formation efficiency is the central factor that links stellar generations as it defines both their stellar mass and the remaining mass available for further star formation, fixing also the amount of matter required to contaminate the next stellar generation. In this way, the star formation efficiency is here …
The distribution of sites where globular clusters have crossed the Galactic disk during the last 100 million years has been analyzed using the most recent kinematic data for 133 globular clusters (GCs). Three GCs (NGC 6341, NGC 7078, and $ω$ Cen) whose distances between the positions where they crossed the Galactic disk and trajectories of the Gould Belt are less than 20\% of their heliocentric distances at the crossing time (82, 98, and 96 million years ago, respectively) have been identified. For each of the clusters, this was their next to last, rather than their last, crossing of the Galac…
Globular clusters of the Gaia Enceladus/Sausage -- I. Orbital and dynamical evolution on cosmological timescales
Main Astronomical Observatory, National Academy of Sciences of Ukraine（乌克兰国家科学院主天文台）；Nicolaus Copernicus Astronomical Centre Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天文学中心）；Fesenkov Astrophysical Institute（费森科夫天体物理研究所）
We study the impact of Ly$α$ radiation feedback on globular cluster (GC) formation. In this Letter, we analytically derive the relation between star formation efficiency (SFE) and metallicity in spherical clouds with the Ly$α$ radiation feedback. Our models show that the SFE becomes small as the metallicity decreases. In metal-poor gas clouds, Ly$α$ photons are trapped for a long time and exert strong radiation force to the gas, resulting in the suppression of star formation. We find that bound star-clusters (SFE $\gtrsim$ 0.5) form only for the metallicity higher than $\sim 10^{-2.5}~Z_{\odot…
Globular clusters can form inside their host galaxies at high redshift when gas densities were higher and gas-rich mergers were common. They can also form inside lower-mass galaxies that have since been accreted and tidally disrupted, leaving their globular cluster complement bound to higher-mass halos. We argue that the age-metallicity-specific orbital energy relation in a galaxy's globular cluster system can be used to identify its origin. Gas-rich mergers should produce tightly bound systems in which metal-rich clusters are younger than metal-poor clusters. Globular clusters formed in massi…
This is a "biased" review because I will show recent evidence on the contribution of globular clusters (GCs) to the halo of our Galaxy seen through the lens of the new paradigm of multiple populations in GCs. I will show a few examples where the chemistry of multiple populations helps to answer hot questions including whether and how much GCs did contribute to the halo population, if we have evidence of the GCs-halo link, what are the strengths and weak points concerning this contribution.
A cosmological framework for stellar collisions at high redshift in proto-globular clusters, nuclear star clusters, and Little Red Dots
Northwestern University（西北大学）；NSF-Simons AI Institute for the Sky (SkAI)（美国国家科学基金会-西蒙斯天空人工智能研究所）；Rutgers, The State University of New Jersey（新泽西州立罗格斯大学）；Center for Computational Astrophysics, Flatiron Institute（平顿研究所计算天体物理学中心）；The University of Tokyo（东京大学）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), UT Institute for Advanced Study, The University of Tokyo（东京大学UT高等研究院宇宙物理数学研究所（WPI））；Research Center for the Early Universe, School of Science, The University of Tokyo（东京大学理学系早期宇宙研究中心）
Modern hydrodynamic simulations of galaxy formation are able to predict accurately the rates and locations of the assembly of giant molecular clouds in early galaxies. These clouds could host star clusters with the masses and sizes of real globular clusters. I describe current state-of-the-art simulations aimed at understanding the origin of the cluster mass function and metallicity distribution. Metallicity bimodality of globular cluster systems appears to be a natural outcome of hierarchical formation and gradually declining fraction of cold gas in galaxies. Globular cluster formation was mo…
We present a framework that explains the commonly observed variation in light element abundances in globular clusters. If globular clusters form in the centres of dwarf galaxies, they will be pumped onto larger orbits as star formation progresses. The potential well will only retain the moderate velocity AGB ejecta, the expected source of enrichment, but not supernova ejecta. There is no need to increase the initial cluster mass, a requirement of self-enrichment scenarios, as all the stars within the dwarf can contribute. As the clusters move through the dwarf centre they sweep up a mix of AGB…
This work reports the detection of a multi peaked colour pattern in the integrated colours distribution of globular clusters associated to the giant elliptical galaxy NGC 4486, using Next Generation Virgo Survey data. This feature is imprinted on the well known bimodal colour distribution of these clusters. Remarkably, the pattern is similar to that found in previous works based on photometry from the HST Advanced Camera Virgo Survey, in less massive Virgo galaxies. This characteristic can be traced up to to 45 arcmin (217 Kpc) in galactocentric radius. This suggests that globular cluster form…
Preliminary results are presented about a fully self-consistent N-body simulation of a sample of four massive globular clusters in close interaction within the central region of a galaxy. The N-body representation (with N=1.5x10^6 particles in total) of both the clusters and the galaxy allows to include in a natural and self-consistent way dynamical friction and tidal interactions. The results confirm the decay and merging of globulars as a viable scenario for the formation/accretion of compact nuclear clusters. Specifically: i) the frictional orbital decay is about 2 times faster than that pr…
This review summarises the main properties of Young Massive Clusters (YMCs), including their population properties, particularly focusing on extragalactic cluster samples. We discuss potential biases and caveats that can affect the construction of cluster samples and how incompleteness effects can result in erroneous conclusions regarding the long term survival of clusters. In addition to the luminosity, mass and age distributions of the clusters, we discuss the size distribution and profile evolution of the clusters. We also briefly discuss the stellar populations within YMCs. The final part …
One of the leading models for the formation of multiple stellar populations within globular clusters is the "Fast Rotating Massive Star" (FRMS) scenario, where the ejecta of rapidly rotating massive stars is mixed with primordial material left over from the star-formation process, to form a second generation of stars within the decretion discs of the high mass stars. A requirement of this model, at least in its current form, is that young massive (i.e. proto-globular) clusters are not able to eject the unused gas and dust from the star-formation process from the cluster for 20-30 Myr after the…
Globular clusters are compact, gravitationally bound systems of up to a million stars. The GCs in the Milky Way contain some of the oldest stars known, and provide important clues to the early formation and continuing evolution of our Galaxy. More generally, GCs are associated with galaxies of all types and masses, from low-mass dwarf galaxies to the most massive early-type galaxies which lie in the centres of massive galaxy clusters. GC systems show several properties which connect tightly with properties of their host galaxies. For example, the total mass of GCs in a system scales linearly w…
Observations of globular clusters (GCs) and field stars in the halos of the giant elliptical galaxy Cen A and the spiral galaxy M31 show a large range of cluster-to-star number ratios ('specific frequencies'). The cluster-to-star ratio decreases with increasing metallicity by a factor of 100-1000, at all galactocentric radii and with a slope that does not seem to depend on radius. In dwarf galaxies, the GCs are also more metal-poor than the field stars on average. These observations indicate a strong dependence of either the cluster formation efficiency or the cluster destruction rate on metal…
We address the nature and origin of Super Star Clusters (SSCs) discovered by Holtzman et al. (1992) within a radius of $\sim$$5\,\rm kpc$ from the center of NGC 1275, the giant elliptical galaxy at the center of the Perseus Cluster. We show that, in contrast with the much more numerous population of SSCs subsequently discovered up to $\sim$$30\,\rm kpc$ from the center of this galaxy, the central SSC population have maximal masses an order of magnitude higher and a mass function with a shallower power-law slope. Furthermore, whereas the outer SSC population have ages spanning a few $\rm Myr$ t…
The formation of globular clusters (GCs) remains one of the main unsolved problems in star and galaxy formation. The past decades have seen important progress in constraining the physics of GC formation from a variety of directions. In this review, we discuss the latest constraints obtained from studies of present-day GC populations, the formation of young massive clusters (YMCs) in the local Universe, and the observed, large-scale conditions for star and cluster formation in high-redshift galaxies. The main conclusion is that the formation of massive, GC progenitor clusters is restricted to h…
Some formation scenarios that have been put forward to explain multiple populations within Globular Clusters (GCs) require that the young massive cluster have large reservoirs of cold gas within them, which is necessary to form future generations of stars. In this paper we use deep observations taken with Atacama Large Millimeter/sub-millimeter Array (ALMA) to assess the amount of molecular gas within 3 young (50-200 Myr) massive (~10^6 Msun) clusters in the Antennae galaxies. No significant CO(3--2) emission was found associated with any of the three clusters. We place upper limits for the mo…
We explore the possibility of the formation of globular clusters under ultraviolet (UV) background radiation. One-dimensional spherical symmetric radiation hydrodynamics (RHD) simulations by Hasegawa et al. have demonstrated that the collapse of low-mass (10^6-10^7 solar masses) gas clouds exposed to intense UV radiation can lead to the formation of compact star clusters like globular clusters (GCs) if gas clouds contract with supersonic infall velocities. However, three-dimensional effects, such as the anisotropy of background radiation and the inhomogeneity in gas clouds, have not been studi…
Historically, it has been assumed that globular and open clusters never interact. However, recent evidence suggests that: globular clusters passing through the disk may be able to perturb giant molecular clouds (GMCs) triggering formation of open clusters and some old open clusters may be linked to accreted globulars. Here, we further explore the existence of possible dynamical connections between globular and open clusters, and realize that the most obvious link must be in the form of gravitational interactions. If open clusters are born out of GMCs, they have to move in similar orbits. If we…
The paper deals with the conditions required to form at least two stellar generations in globular clusters under the constraints generated by feedback from massive stars as well as radiative cooling and the metallicity of the primordial clouds. Our calculations are based on two main constraints to the star formation efficiency of the first stellar generation (1G) $ε_{1G}$. First, $ε_{1G}$ is restricted to warrant that stellar winds and supernovae do not disrupt the leftover gas out of which a second generation (2G) would form. Second, $ε_{1G}$ is also limited such that the metallicity enhancem…
Globular clusters are unique tracers of ancient star formation. We determine the formation efficiencies of globular clusters across cosmic time by modeling 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…
We confirm that the number of globular clusters (GCs), N$_{GC}$, is an excellent tracer of their host galaxy's halo virial mass M$_{vir}$. The simple linear relation M$_{vir} = 5 \times 10^9$ M$_{\odot} \times$ N$_{GC}$ fits the data perfectly from M$_{vir} = 10^{10}$ M$_{\odot}$ to M$_{vir} = 2 \times 10^{15}$ M$_{\odot}$. This result is independent of galaxy morphology and extends statistically into the dwarf galaxy regime with M$_{vir} = 10^8 - 10^{10}$ M$_{\odot}$, including the extreme ultra diffuse galaxy DF44. As this correlation does not depend on GC mass it is ideally suited for high-…
The formation of globular clusters (GC), with their multiple stellar generations, is still an unsolved puzzle. Thus, interest is rising on the possibility to detect their precursors at high redshift, hence directly witnessing their formation. A simple set of assumptions are empirically justified and then used to predict how many such precursors formed between redshift 3 and 10 could actually be detected by the NIRCam instrument on board of JWST. It is shown that the near power-law shape of the rest-frame UV continuum of young globular cluster precursors (GCP) implies that both colours and lumi…
The formation and evolution of X-ray sources in globular clusters is likely to be affected by the cluster internal dynamics and the stellar interactions in the cluster dense environment.Several observational studies have revealed a correlation between the number of X-ray sources and the stellar encounter rate and provided evidence of the role of dynamics in the formation of X-ray binaries. We have performed a survey of Monte-Carlo simulations aimed at exploring the connection between the dynamics and formation of cataclysmic variables (CVs) and the origin of the observed correlation between th…
We discuss a new scenario for the formation of intermediate mass black holes in dense star clusters. In this scenario, intermediate mass black holes are formed as a result of dynamical interactions of hard binaries containing a stellar mass black hole, with other stars and binaries. We discuss the necessary conditions to initiate the process of intermediate mass black hole formation and the influence of an intermediate mass black hole on the host global globular cluster properties. We discuss two scenarios for intermediate mass black hole formation. The SLOW and FAST scenarios. They occur late…
We have determined the detailed star formation history and total mass of the globular clusters in the Fornax dwarf spheroidal using archival HST WFPC2 data. Colour magnitude diagrams are constructed in the F555W and F814W bands and corrected for the effect of Fornax field star contamination, after which we use the routine Talos to derive the quantitative star formation history as a function of age and metallicity. The star formation history of the Fornax globular clusters shows that Fornax 1, 2, 3 and 5 are all dominated by ancient (>10 Gyr) populations. Cluster Fornax 1,2 and 3 display metall…
We present a hydro-dynamical simulation at sub-parsec and few solar mass resolution of a merger between two gas-rich dwarf galaxies. Our simulation includes a detailed model for the multi-phase interstellar medium (ISM) and is able to follow the entire formation history of spatially resolved star clusters, including feedback from individual massive stars. Shortly after the merger we find a population of $\sim 900$ stellar clusters with masses above $10^{2.5}\; \rm{M_\odot}$ and a cluster mass function (CMF), which is well fitted with a power-law with a slope of $α=-1.70\pm0.08$. We describe he…
We examine whether the super star-forming clumps (R~1-3 kpc; M~10^8-10^9.5 Msun) now known to be a key component of star-forming galaxies at z~2 could be the formation sites of the locally observed old globular cluster population. We find that the stellar populations of these super star-forming clumps are excellent matches to those of local metal-rich globular clusters. Moreover, this globular cluster population is known to be associated with the bulges / thick disks of galaxies, and we show that its spatial distribution and kinematics are consistent with the current understanding of the assem…
The formation of globular clusters and their relation to the distribution of dark matter have long puzzled astronomers. One of the most recently-proposed globular cluster formation channels ties ancient star clusters to the large-scale streaming velocity of baryons relative to dark matter in the early Universe. These streaming velocities affect the global infall of baryons into dark matter halos, the high-redshift halo mass function, and the earliest generations of stars. In some cases, streaming velocities may result in dense regions of dark-matter-free gas that becomes Jeans unstable, potent…
I discuss a search for red giant stars in the Galactic halo with light-element abundances similar to second-generation globular cluster stars, and discuss the implications of such a population for globular cluster formation models and the balance between in situ star formation and accretion for the assembly of the Galactic halo.
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 investigate the possible connection between the most massive globular clusters, such as $ω$ Cen and M54, and nuclear star clusters of dwarf galaxies that exhibit similar spreads in age and metallicity. We examine galactic nuclei in cosmological galaxy formation simulations at $z \approx 1.5$ to explore whether their age and metallicity spreads could explain these massive globular clusters. We derive structural properties of these nuclear regions, including mass, size, rotation, and shape. By using theoretical supernova yields to model the supernova enrichment in the simulations, we obtain i…
We examine the significance of a planar arrangement in the spatial distribution of the Milky Way's globular clusters (GCs). We find that, when separated on the basis of horizontal branch morphology and metallicity, the outer-most canonical young halo GC sample (at galactocentric radii in excess of 10 kpc) exhibit an anisotropic distribution that may be equated to a plane (24 +/- 4) kpc thick (rms) and inclined at 8 degrees +/- 5 degrees to the polar axis of the Milky Way disk. To quantify the significance of this plane we determine the fraction of times that an isotropic distribution replicate…
We review spectroscopic results concerning multiple stellar populations in globularclusters. The cluster initial mass is the most important parameter determining the fraction of second generation stars. The threshold for the onset of the multiple population phenomenon is 1-3x10^5 MSun. Nucleosynthesis is influenced by metallicity: Na/O and Mg/Al anti-correlations are more extended in metal-poor than in metal-rich clusters. Massive clusters are more complex systems than the smaller ones, with several populations characterized by different chemical compositions. The high Li abundance observed in…
We investigate a scenario in which feedback from black-hole X-ray binaries (BHXBs) sometimes begins inside young star clusters before strong supernova feedback. Those BHXBs could reduce the gas fraction inside embedded young clusters whilst maintaining virial equilibrium, which may help globular clusters (GCs) to stay bound when supernova-driven gas ejection subsequently occurs. Adopting a simple toy model with parameters guided by BHXB population models, we produce GC formation efficiencies consistent with empirically-inferred values. The metallicity dependence of BHXB formation could natural…
We analyze Hubble Space Telescope observations of six globular clusters in the Large Magellanic Cloud from program GO-14164 in Cycle 23. These are the deepest available observations of the LMC globular cluster population; their uniformity facilitates a precise comparison with globular clusters in the Milky Way. Measuring the magnitude of the main sequence turnoff point relative to template Galactic globular clusters allows the relative ages of the clusters to be determined with a mean precision of 8.4%, and down to 6% for individual objects. We find that the mean age of our LMC cluster ensembl…
Currently there are two competing scenarios to explain the origin of the stellar population in globular clusters (GCs). The main difference between them is whether or not multiple events of star formation took place within GCs. In this paper we present the star formation history (SFH) of Cluster 1, a massive young cluster in NGC 34 $(\sim10^7\mbox{ M}_\odot)$. We use DynBaS, a spectrum fitting algorithm, to retrieve the SFH and find that Cluster 1 is consistent with a single stellar population of solar metallicity with an age of $100\pm30$ Myr and a mass of $1.9\pm0.4\times10^7\mbox{ M}_\odot$…
We propose that the rotational kinematics of the globular cluster system (GCS) in M31 can result from a past major merger event that could have formed its bulge component. We numerically investigate kinematical properties of globular clusters (GCs) in remnants of galaxy mergers between two disks with GCs in both their disk and halo components. We find that the GCS formed during major merging can show strongly rotational kinematics with the maximum rotational velocities of 140 - 170 km/s for a certain range of orbital parameters of merging. We also find that a rotating stellar bar, which can be…
