arXiv subjects

A. Askar

Publications and source records attributed to A. Askar.

15 recordsLinked to original sources

arXiv2026

The evolution of high-z proto-star clusters into local globular clusters

The James Webb Space Telescope (JWST) detected numerous massive and relatively compact stellar clumps around proto-galaxies at high redshift (z>0.5). Their properties suggest that these systems may represent proto-globular clusters (GCs), but their possible connection to local old GCs is poorly understood. In this Letter, we explore the dynamical evolution of proto-star clusters, building the missing evolutionary link between high-z systems observed by JWST and local GCs. Our simulations include the effects of stellar interactions, stellar evolution, and the strong time-dependent cosmological tidal field in which these proto-star clusters evolve. We also explore the role of multiple stellar populations and stellar-mass black holes (BHs), two fundamental ingredients in stellar cluster dynamics. We show that systems hosting multiple populations (as routinely observed in local GCs) are more likely to endure the early strong tidal field than single-population clusters. In addition, after 12 Gyr, such systems have properties consistent with those of Galactic GCs. Our work confirms that the high-z clumps observed by JWST can be the progenitors of the local GCs. Finally, we show that a population of stellar-mass BHs within a proto-star cluster favors its disruption, but that surviving systems can retain a sizable population of BHs.

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arXiv2026

ROLLIN': Rotating globular cluster simulations. I. The kinematic evolution of realistic direct N-body models

Internal rotation has emerged as a fundamental feature of globular clusters (GCs), yet its origin and long-term evolution remain poorly understood. We explore the evolution of rotating GCs over a Hubble time under the combined influence of two-body relaxation, tidal field, and stellar evolution. We introduce the ROLLIN' simulations, a suite of 25 N-body models characterized by a realistic number of stars from 250k to 1.5M, ran with the direct N-body code NBODY6++GPU and evolved for 14 Gyr. With present-day masses of 5 x 10^4 - 5x10^5 M_sun, the models cover the parameter space of low-density MW GCs. Our analysis reveals that rapidly rotating GCs experience earlier and more pronounced core collapse, efficiently segregating massive objects and remnants in their centers within the first few 100 Myr. In the long-term, internal rotation declines and a correlation emerges between rotation and GC mass, in agreement with observations. The primary driver of this evolution is mass loss, capturing both internal (stellar evolution, evaporation) and external processes (tidal stripping). The velocity anisotropy also evolves in response to mass loss: GCs initially near isotropy develop radial anisotropy, peaking around 40% mass loss, before progressing toward isotropy or tangentiality. The GC orbital history also plays a role, as retrograde rotators retain rotation more effectively than prograde rotators. Finally, we quantify the long-term changes of GCs after 12 Gyr: (1) The surface density decreases by up to 2 orders of magnitude. (2) The half-mass radius increases by a factor of 3-5. (3) The rotation decreases by a factor >5 for GCs that have lost >50% of their mass. The ROLLIN' simulations demonstrate that angular momentum is crucial to understand the origin, evolution, and survival of GCs. These models provide a benchmark for interpreting GC observations in the local and high-z Universe.

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arXiv2026

Is the overconcentration of pristine populations in Galactic globular clusters real? An N-body approach to the problem

Recent observations indicate that in some Milky Way globular clusters (GCs) pristine red giant branch (RGB) stars appear more centrally concentrated than enriched ones. This contradicts most multiple stellar population (MSP) formation scenarios, which predict that the enriched (second) population (2P) should initially be more concentrated than the pristine (first) population (1P). Previous MOCCA Monte Carlo simulations suggested that this apparent overconcentration is a transient effect arising in clusters that have lost a large fraction of their initial mass and host an active black hole subsystem (BHS), and is visible only when RGB stars are used as tracers. In this letter, we test this interpretation using tailored NBODY6++GPU models evolved with direct N-body simulations, providing an independent validation that does not rely on a statistical treatment of relaxation. We performed direct N-body simulations with the NBODY6++GPU code, adopting initial conditions designed to reproduce the dynamical regime relevant to the proposed mechanism. The simulations include updated stellar and binary evolution, dynamical interactions, and the Galactic tidal field, enabling a direct comparison with MOCCA results. The simulations confirm that the spatial distributions and kinematics inferred from RGB stars can be strongly affected by stochastic fluctuations and interactions with the BHS. Preferential ejection of 2P RGB and their progenitors from the cluster center leads to a transient apparent overconcentration of 1P RGB stars, in agreement with earlier MOCCA predictions.

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arXiv2026

Distance Estimation and Sky Localization of Eccentric Double White Dwarf Binaries from Gravitational Wave Observations inside Globular Clusters

The cosmic distance scale is built on multiple different techniques for estimating distances in space that are often connected and dependent on multiple measurements and assumptions. Double white dwarf binaries (DWDs) are common objects and are expected to produce gravitational wave (GW) signals that can be observed with space-based detectors such as LISA. By analyzing these signals we should be able to estimate the distance and sky location of the source. Previous studies have done this for circular binaries which, while they are abundant, have, in general, weaker signals than eccentric binaries and it is not possible to differentiate whether a circular binary is in the field or in a dense environment such as a globular cluster (GC). In this paper we used eccentric binaries from MOCCA GC simulations, simulated the GW signal from each binary at locations related to GCs in the Milky Way and estimated the precision on the distance and the sky location of the source. We find that distances can be estimated with higher precision than current day methods even with low eccentricity binaries and higher eccentricity further increases this precision. Although the probability of finding a tight and eccentric DWD is far lower than a circular one, we can expect to find at least a few in the dense environments of the Milky Way, such as GCs. These estimations would be independent measurements with high precision to objects inside dense environments, such as GCs inside the Milky Way and the Magellanic Clouds.

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arXiv2026

Exploring the dynamical evolution of binary stars in multiple-population globular clusters

The presence of multiple stellar populations in globular clusters leads to a complex dynamical environment that significantly influences the evolution of binary stars, which in turn impacts the evolution of the cluster itself. For this study, we used a series of Monte Carlo simulations run with the MOCCA code to investigate the long-term dynamical evolution of binary stars in globular clusters hosting two distinct stellar populations. We explored how global binary properties such as incidence, fraction, and spatial distribution evolve over time due to the unique dynamical environment associated with each population. Our results show how binaries in the more centrally concentrated second population (P2) experience increased rates of hardening and disruption relative to the first population (P1), leading to distinct radial profiles in binary incidence and fraction. We also demonstrate the difference in spatial mixing timescales for binaries compared to single stars, where binary stars in each population retain some memory of their initial configurations even after complete single star mixing. Additionally, we investigated the formation and evolution of mixed binaries (binaries composed of a P1 component and a P2 component), which form primarily within the core through dynamical interactions. Finally, we studied main sequence--white dwarf binaries and find that they represent a larger fraction of binaries in P1 compared to P2. The results of this paper highlight the interplay between cluster dynamics and the evolution of binary stars and how binaries can act as tracers of the cluster's initial conditions and dynamical evolution.

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arXiv2025

Efficient black hole seed formation in low metallicity and dense stellar clusters with implications for JWST sources

Recent observations with the James Webb Space Telescope (JWST) reveal young massive clusters (YMCs) as key building blocks of early galaxies. They are not only important constituents of galaxies, but also potential birthplaces of very massive stars (VMSs) and black hole (BH) seeds. We explore stellar dynamics in extremely dense clusters with initial half-mass densities of $\rho_h \gtrsim 10^8M_\odot{\rm pc}^{-3}$ at very low metallicity, comparable to some of the densest clusters seen by JWST. Using direct N-body and Monte Carlo simulations with stellar evolution, we show that VMS formation through collisions is unavoidable, with final masses reaching $5\times10^3$ to $4\times10^4M_\odot$. These results support the existence of a critical mass scale above which collisions become highly efficient, enabling the formation of VMSs and intermediate-mass BHs (IMBHs). Our models, using nbody6++gpu and MOCCA with updated SSE/BSE routines, show that dense clusters rapidly form VMSs via stellar bombardment. The VMSs then collapse into BH seeds of a few $10^3$ to $10^4M_\odot$ in less than 4 Myr. We identify a critical mass-density threshold beyond which clusters undergo runaway collisions that yield massive BH seeds. For typical YMCs detected by JWST, efficiencies up to 10% are expected, implying BH masses up to $10^5M_\odot$ if formed via collisions. We predict a scaling relation for BH mass, $\log(M_{\rm BH}/M_\odot)=-0.76+0.76\log(M/M_\odot)$. Frequent VMS formation may also explain the high nitrogen abundance observed in galaxies at high redshift.

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arXiv2025

Multiple stellar populations in MOCCA globular cluster models: Transient spatial over-concentration of pristine red giant stars driven by strong dynamical encounters

Recent findings show that, in some Milky Way globular clusters (GCs), pristine red giant branch (RGB) stars are more centrally concentrated than enriched RGB stars. This contradicts most multiple-population formation scenarios, which predict that the enriched population 2p should initially be more concentrated than the pristine population 1P. We analyze a MOCCA GC model that exhibits a higher spatial concentration of 1P RGB stars than 2P RGB stars at 13 Gyr. The MOCCA models assume the asymptotic giant branch (AGB) pollution scenario, where 2P stars are initially more concentrated than 1P stars. Our results indicate that the observed spatial distributions of multiple populations, and possibly their kinematics, are significantly shaped by dynamical interactions. These interactions preferentially eject 2P RGB progenitors from the central regions, leading to a transient over-concentration of 1P RGB stars at late times. This effect is particularly relevant for GCs with present-day of a few $10^5 M_{\odot}$, which have retained only about 10 - 20 percent of their initial mass. Such clusters may appear dynamically young due to heating from a black hole subsystem, even if they have undergone significant mass loss and dynamical evolution. Additionally, the relatively small number of RGB stars in these clusters suggests that interpreting the spatial distributions of multiple populations solely from RGB stars may lead to biased conclusions about the overall distribution of 2P and 1P. The apparent over-concentration of the 1P relative to the 2P is likely a transient effect driven by the preferential removal of 2P RGB progenitors via strong dynamical encounters. MOCCA models of multiple stellar populations based on the AGB scenario may explain anomalous features observed in some Galactic GCs, such as NGC 3201 and NGC 6101.

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arXiv2024

Energy equipartition in multiple-population globular clusters

We present the results of Monte Carlo simulations aimed at exploring the evolution towards energy equipartition of first- (1G) and second-generation (2G) stars in multiple-population globular clusters and how this evolution is affected by the initial differences between the spatial distributions of the two populations. Our results show that these initial differences have fundamental implications for the evolution towards energy equipartition of the two populations. We find that 2G stars, which are assumed to be initially more centrally concentrated than 1G stars, are generally characterized by a more rapid evolution towards energy equipartition. The evolution towards energy equipartition depends on the velocity dispersion component and is more rapid for the tangential velocity dispersion. The extent of the present-day differences between the degree of energy equipartition of 2G and 1G stars depends on the cluster's dynamical age and may be more significant in the tangential velocity dispersion and at intermediate distances from the cluster's center around the half-mass radius.

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arXiv2022

MOCCA-Survey Database: Extra Galactic Globular Clusters. III. The population of black holes in Milky Way and Andromeda-like galaxies

In this work, we investigate the black hole (BH) population of globular clusters (GCs) in Milky Way- (MW) and Andromeda- (M31) like galaxies. We combine the population synthesis code MASinGa and the MOCCA-Survey Database I to infer the properties of GCs harbouring a BH subsystem (BHS), an IMBH, or neither of those. We find that the typical number of GCs with a BHS, an IMBH, or none become comparable in the galactic outskirts, whilst the inner galactic regions are dominated by GCs without a significant dark component. Our models suggest that GCs harbouring a BHS are slightly heavier and with larger half-mass radii compared to the overall population. We retrieve the properties of binary BHs (BBHs) that have either merged in the last 3 Gyr or survived in their parent cluster until present-day. We find that around 80\% of the merging BBHs form due to dynamical interactions while the remaining originate from evolution of primordial binaries. We infer a merger rate for BBHs in the local Universe of $1.0-23\,\,\rm{yr^{-1}\,Gpc^{-3}}$, depending on the adopted assumptions. We find around 100-240 BBHs survive until present-day and are mostly concentrated in the inner few kpc of the galaxy. We estimate also the number of BHs transported into the galactic nucleus by infalling star clusters, finding around 1,000-3,000 BHs and 100-200 BBHs are transported over a time span of 12 Gyr. This enables us to constrains the total amount of BHs and BBHs binaries lurking in nuclear star cluster, i.e. $N_{BHs}=(1.4-2.2)\times10^4$ and $N_{BBHs}=700-1,100$.

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arXiv2022

MOCCA-Survey Database: Extra Galactic Globular Clusters. II. Milky Way and Andromeda

A comprehensive study of the co-evolution of globular cluster systems (GCS) in galaxies requires the ability to model both the large scale dynamics (0.01 - 10 kpc) regulating their orbital evolution, and the small scale dynamics (sub-pc - AU) regulating the internal dynamics of each globular cluster (GC). In this work we present a novel method that combine semi-analytic models of GCS with fully self-consistent Monte Carlo models to simultaneously evolve large GCSs. We use the population synthesis code MASinGa and the MOCCA-Survey Database I to create synthetic GC populations aimed at representing the observed features of GCs in the Milky Way (MW) and Andromeda (M31). Our procedure enables us to recover the spatial and mass distribution of GCs in such galaxies, and to constrain the amount of mass that GCs left either in the halo as dispersed debris, or in the galactic centre, where they can contribute to the formation of a nuclear star cluster (NSC) and can bring stellar and possibly intermediate mass black holes there. The final masses reported by our simulations are of a few order of magnitudes smaller than the observed values. These differences show that mass build-up of a NSC and central BHs in galaxies like MW and M31 cannot be solely explained by the infalling GC scenario. This build-up is likely to depend on the interplay between interactions and mergers of infalling GCs and gas. The latter can contribute to both in-situ star formation in the NSC and growth of the central BH.

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arXiv2021

Preparing the next gravitational million-body simulations: Evolution of single and binary stars in Nbody6++GPU, MOCCA and McLuster

We present the implementation of updated stellar evolution recipes in the codes \texttt{Nbody6++GPU, MOCCA} and \texttt{McLuster}. We test them through numerical simulations of star clusters containing $1.1\times 10^5$ stars (with $2.0\times 10^4$ in primordial hard binaries) performing high-resolution direct $N$-body (\texttt{Nbody6++GPU}) and Monte-Carlo (\texttt{MOCCA}) simulations to an age of 10~Gyr. We compare models implementing either delayed or core-collapse supernovae mechanisms, a different mass ratio distribution for binaries, and white dwarf natal kicks enabled/disabled. Compared to \texttt{Nbody6++GPU}, the \texttt{MOCCA} models appear to be denser, with a larger scatter in the remnant masses, and a lower binary fraction on average. The \texttt{MOCCA} models produce more black holes (BHs) and helium white dwarfs (WDs), whilst \texttt{Nbody6++GPU} models are characterised by a much larger amount of WD-WD binaries. The remnant kick velocity and escape speed distributions are similar for the BHs and neutron stars (NSs), and some NSs formed via electron-capture supernovae, accretion-induced collapse or merger-induced collapse escape the cluster in all simulations. The escape speed distributions for the WDs, on the other hand, are very dissimilar. We categorise the stellar evolution recipes available in \texttt{Nbody6++GPU}, \texttt{MOCCA} and \texttt{Mcluster} into four levels: the one implemented in previous \texttt{Nbody6++GPU} and \texttt{MOCCA} versions (\texttt{level A}), state-of-the-art prescriptions (\texttt{level B}), some in a testing phase (\texttt{level C}), and those that will be added in future versions of our codes.

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arXiv2020

The evolutionary roads leading to low effective spins, high black hole masses, and O1/O2 rates of LIGO/Virgo binary black holes

All ten LIGO/Virgo binary black hole (BH-BH) coalescences reported from the O1/O2 runs have near zero effective spins. There are only three potential explanations of this fact. If the BH spin magnitudes are large then (i) either both BH spin vectors must be nearly in the orbital plane or (ii) the spin angular momenta of the BHs must be oppositely directed and similar in magnitude. Or, (iii) the BH spin magnitudes are small. We test the third hypothesis within the framework of the classical isolated binary evolution scenario of the BH-BH merger formation. We test three models of angular momentum transport in massive stars: a mildly efficient transport by meridional currents (as employed in the Geneva code), an efficient transport by the Tayler-Spruit magnetic dynamo (as implemented in the MESA code), and a very-efficient transport (as proposed by Fuller et al.) to calculate natal BH spins. We allow for binary evolution to increase the BH spins through accretion and account for the potential spin-up of stars through tidal interactions. Additionally, we update the calculations of the stellar-origin BH masses, include revisions to the history of star formation and to the chemical evolution across cosmic time. We find that we can match simultaneously the observed BH-BH merger rate density, BH masses, and effective spins. Models with efficient angular momentum transport are favored. The updated stellar-mass weighted gas-phase metallicity evolution now used in our models appears to be a key in better reproducing the LIGO/Virgo merger rate estimate. Mass losses during the pair-instability pulsation supernova phase are likely overestimated if the merger GW170729 hosts a BH more massive than 50 Msun. We also estimate rate of BH-NS mergers from recent LIGO/Virgo observations. Our updated models of BH-BH, BH-NS and NS-NS mergers are now publicly available at www.syntheticuniverse.org.

astro-ph.HE↗

arXiv2018

MOCCA-SURVEY Database I: Assessing GW kick retention fractions for BH-BH mergers in globular clusters

Anisotropy of gravitational wave (GW) emission results in a net momentum gained by the black hole (BH) merger product, leading to a recoil velocity up to $\sim10^3\text{ km s}^{-1}$, which may kick it out of a globular cluster (GC). We estimate GW kick retention fractions of merger products assuming different models for BH spin magnitude and orientation (MS0 - random, MS1 - spin as a function of mass and metalicity, MS2 - constant value of $0.5$). We check how they depend on BH-BH merger time and properties of the cluster. We analyze the implications of GW kick retention fractions on intermediate massive BH (IMBH) formation by repeated mergers in a GC. We also calculate final spin of the merger product, and investigate how it correlates with effective spin of the binary. We used data from MOCCA (MOnte Carlo Cluster simulAtor) GC simulations to get a realistic sample of BH-BH mergers, assigned each BH spin value according to a studied model, and calculated recoil velocity and final spin based on most recent theoretical formulas. We discovered that for physically motivated models, GW kick retention fractions are about $30\%$ and display small dependence on assumptions about spin, but are much more prone to cluster properties. In particular, we discovered a strong dependence of GW kick retention fractions on cluster density. We also show that GW kick retention fractions are high in final life stages of the cluster, but low at the beginning. Finally, we derive formulas connecting final spin with effective spin for primordial binaries, and with maximal effective spin for dynamical binaries.

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arXiv2018

The origin of the first neutron star -- neutron star merger

The first neutron star-neutron star (NS-NS) merger was discovered on August 17, 2017 through gravitational waves (GW170817) and followed with electromagnetic observations. This merger was detected in an old elliptical galaxy with no recent star formation. We perform a suite of numerical calculations to understand the formation mechanism of this merger. We probe three leading formation mechanisms of double compact objects: classical isolated binary star evolution, dynamical evolution in globular clusters and nuclear cluster formation to test whether they are likely to produce NS-NS mergers in old host galaxies. Our simulations with optimistic assumptions show current NS-NS merger rates at the level of 10^-2 yr^-1 from binary stars, 5 x 10^-5 yr^-1 from globular clusters and 10^-5 yr^-1 from nuclear clusters for all local elliptical galaxies (within 100 Mpc^3). These models are thus in tension with the detection of GW170817 with an observed rate 1.5 yr^-1 (per 100 Mpc^3; LIGO/Virgo estimate). Our results imply that either (i) the detection of GW170817 by LIGO/Virgo at their current sensitivity in an elliptical galaxy is a statistical coincidence; or that (ii) physics in at least one of our three models is incomplete in the context of the evolution of stars that can form NS-NS mergers; or that (iii) another very efficient (unknown) formation channel with a long delay time between star formation and merger is at play.

astro-ph.HE↗

arXiv2016

MOCCA Code for Star Cluster Simulations - IV. A new Scenario for Intermediate Mass Black Hole Formation in Globular Clusters

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 later or earlier in the cluster evolution and require smaller or extremely large central densities, respectively. In our simulations, the formation of intermediate mass black holes is highly stochastic. In general, higher formation probabilities follow from larger cluster concentrations (i.e. central densities). We further discuss possible observational signatures of the presence of intermediate mass black holes in globular clusters that follow from our simulations. These include the spatial and kinematic structure of the host cluster, possible radio, X-ray and gravitational wave emissions due to dynamical collisions or mass-transfer and the creation of hypervelocity main sequence escapers during strong dynamical interactions between binaries and an intermediate mass black hole. All simulations discussed in this paper were performed with the MOCCA Monte Carlo code. MOCCA accurately follows most of the important physical processes that occur during the dynamical evolution of star clusters but, as with other dynamical codes, it approximates the dissipative processes connected with stellar collisions and binary mergers.

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