Context. The stellar dynamical evolution of massive star clusters formed during starburst periods leads to the segregation of greater than or similar to 10(4) M-circle dot stellar-mass black hole sub-clusters in their centres. In gas-rich environments, such as galactic central molecular zones, these black hole clusters are likely to accrete large amounts of the gas from their surroundings, which in turn affects their internal dynamics. Aims. In this Letter we estimated the corresponding accretion rate onto the black hole cluster and its radiative feedback. We assessed whether such an accretion flow can lead to the collapse of the black hole cluster into an intermediate-mass black hole. Methods. The estimates were obtained analytically, considering the astrophysical conditions and star formation history reported for the central molecular zone of our Galaxy. Results. We find that a stellar black hole cluster with mass greater than or similar to 10(4) M-circle dot located in the twisted ring of molecular clouds with radius approximate to 100 pc that is observed in the central molecular zone of our Galaxy can accrete about the same mass in gas on a timescale of a few million years. We suggest that this is sufficient for its subsequent collapse into an intermediate-mass black hole. Based on an estimate of the dynamical friction inspiral time, we further argue that the locations of the intermediate-mass black hole candidates recently observed in the central molecular zone are compatible with their formation therein during the last starburst period reported to have occurred approximate to 1 Gyr ago.

The relation between the maximum stellar mass in a very young cluster (m(max)) and the total stellar mass of the cluster (M-ecl), known as the m(max) - M-ecl relation, remains debated in the literature. To test the validity of this relation, we modelled young star clusters with masses between 10(2.5) and 10(5.0)M(circle dot) and ages of 1-4 Myr using the galIMF code, in which stellar masses are optimally sampled from a varying initial stellar mass function. We compared the results with literature observations of extragalactic young star clusters. We incorporated stellar evolution via PARSEC and COLIBRI tracks and computed H alpha luminosities using the P & eacute;gase code. To account for dynamical ejections, we stochastically removed stars based on their spectral type, following previous N-body simulations. Additional sources of scatter, including uncertainties in age determination and contamination by field stars, were considered. Our results indicate that, under the assumptions explored here, optimal sampling is consistent with the extragalactic star cluster observations considered, whereas purely random sampling produces distributions that are not in agreement. These findings support a highly self-regulated interpretation of cluster formation in which stellar masses align optimally with the initial mass function rather than being drawn independently at random.

Context. The dynamical evolution of binary populations in embedded star clusters shapes the statistical properties of binaries observed in the Galactic field. Accurately modelling this process requires resolving both the early cluster dynamics and binary interactions. Aims. We aim to characterize the early dynamical evolution of primordial binaries in embedded clusters and identify the key parameters that govern binary survival and disruption. Methods. We performed a set of direct N-body simulations starting from 100% primordial binaries in a time-varying gas potential of a gas-embedded cluster. To describe the evolution of binary orbital properties, we defined the empirical dynamical operators for the period, binding energy, and mass ratio. We then calibrated them across the simulated ensemble. Results. The binding energy and orbital period evolve in a consistent, sigmoidal fashion. Their dynamical operators reveal that hard binaries heat the cluster and suppress wide binary formation, while a small residual population of soft binaries survives. The evolution of the mass-ratio distribution is less directly linked to dynamical processing and more shaped by internal processes such as stellar physics process in the pre-main sequence phase. High-q systems tend to be enhanced, while low-q systems are prone to disruption. Conclusions. Binary evolution in clusters is primarily governed by binding energy and orbital period. Our model displays an improvement over previous parameterizations of the dynamical operator by allowing for the existence of wide binaries and incorporating the embedded cluster phase. For individual clusters, direct N-body modelling remains the only reliable approach. On Galactic scales, population synthesis methods based on the stellar dynamical operator approach developed in this work remain essential.

Context. The stellar dynamical evolution of massive star clusters formed during starburst periods leads to the segregation of ≳104 M⊙ stellar-mass black hole sub-clusters in their centres. In gas-rich environments, such as galactic central molecular zones, these black hole clusters are likely to accrete large amounts of the gas from their surroundings, which in turn affects their internal dynamics. Aims. In this Letter we estimated the corresponding accretion rate onto the black hole cluster and its radiative feedback. We assessed whether such an accretion flow can lead to the collapse of the black hole cluster into an intermediate-mass black hole. Methods. The estimates were obtained analytically, considering the astrophysical conditions and star formation history reported for the central molecular zone of our Galaxy. Results. We find that a stellar black hole cluster with mass ≳104 M⊙ located in the twisted ring of molecular clouds with radius ≈100 pc that is observed in the central molecular zone of our Galaxy can accrete about the same mass in gas on a timescale of a few million years. We suggest that this is sufficient for its subsequent collapse into an intermediate-mass black hole. Based on an estimate of the dynamical friction inspiral time, we further argue that the locations of the intermediate-mass black hole candidates recently observed in the central molecular zone are compatible with their formation therein during the last starburst period reported to have occurred ≈1 Gyr ago.

Strong lensing observations of the Bullet Cluster have traditionally been regarded as strong evidence for dark matter and a major challenge to Milgromian dynamics (MOND). The offset between the lensing mass and the X-ray gas centroids implies a substantial amount of unseen mass near the brightest cluster galaxies (BCGs). However, the high metallicities observed in both the intracluster gas and the massive early-type member galaxies suggest a past stellar population dominated by massive stars, whose evolved remnants contribute additional baryonic mass. This effect is naturally incorporated in the integrated galaxy-wide initial mass function (IGIMF) theory, which predicts substantially larger baryonic masses than a canonical IMF. In this work, we re-estimate the baryonic masses of the three BCG-centred core regions of the Bullet Cluster and compare them with MOND strong-lensing masses. We derive IGIMF masses using stellar population synthesis models with constant and (self-) enriched metallicities, representing lower and upper mass limits, respectively. We find that the MOND strong-lensing masses of all three cores lie within the range predicted by the IGIMF models. These results suggest that the baryonic mass budget inferred under the IGIMF framework is consistent with MOND requirements in the core regions of the Bullet Cluster. However, the physical viability of this scenario also depends on the spatial distribution and dynamical behavior of the remnant population, which remain to be established. More generally, regardless of the validity of MOND, the results imply that less dark matter may be required than previously inferred.

We construct a model by integrating observational constraints from the Milky Way and nearby galaxies to predict cloud-scale star formation rates (SFRs). In the model, we first estimate the initial total mass of clumps in a cloud based on the cloud mass, and then generate the initial clump population of the cloud using the initial clump mass function. Next, we model the star formation histories (SFHs) of the cloud to assign an age to each clump. We then sort out the intermediate-age clumps and calculate the total embedded cluster mass. Finally, we predict the SFR based on the duration of the embedded phase. The model-predicted SFR is broadly consistent with the observed SFR, supporting the plausibility of the model. The model primarily provides a theoretical framework that integrates a wide range of observational results, thereby clarifying the tasks for future observations.

Aims . Recent Gaia studies have identified numerous open clusters (OCs) and tidal tail catalogues, enabling systematic searches for white dwarfs (WDs) associated with clusters and their extended structures. We have compiled a literature-based sample of OC–WD pairs to validate WD membership in cluster cores and tidal tails, investigated the initial–final mass relation (IFMR), identified WDs formed through non-canonical evolution, and interpreted the observed WD populations using a grid of N -body simulations. Methods . We combined Gaia DR3 cluster and tidal tail catalogues with ultraviolet-to-infrared photometry to analyse the OC–WD pairs. The WD masses, cooling ages, radii, effective temperatures, and luminosities were estimated using colour–magnitude diagrams and spectral energy distributions. These observations were interpreted in the context of N -body simulations. Results . We identified 235 OC–WD pairs in 80 clusters, including 99 WDs in tidal tails. More than 28% of the pairs are likely spurious, with contamination substantially higher in the tails (>48%) than in the cluster cores (>13%), indicating significant field-star contamination in current Gaia -based catalogues. The Pleiades tidal tails also show severe contamination by old WDs. Simulations predict that the fraction of core WDs increases with cluster age, reaching ≳10%, whereas the observed fractions remain systematically lower, consistent with the WD deficit problem. Despite the high contamination rate, most tail WDs (≈83%) are consistent with having been born inside the tidal radius. We additionally identified 63 candidate binary-origin WDs and 47 new IFMR candidates. Conclusions . White dwarfs provide a powerful probe of contamination in cluster and tidal tail catalogues and place important constraints on cluster detection methods and N -body simulations. Resolving the WD deficit and improving membership validation will require improved observations, membership methods, WD physics, and spectroscopic follow-up to ultimately enable stronger constraints on dynamical cluster evolution and the WD IFMR.

Metals enhance the cooling efficiency of molecular clouds, promoting fragmentation. Consequently, increasing the metallicity may boost the formation of low-mass stars. Within the integrated galactic initial mass function (IGIMF) theory, this effect is empirically captured by a linear relation between the slope of the low-mass stellar IMF, α 1 , and the metal mass fraction, Z . This linear α 1 – Z relation has been calibrated up to ≈2 Z ⊙ , though higher metallicity environments are known to exist. We show that if the linear α 1 – Z relation extends to higher metallicities ([ Z ] ≳ 0.5), massive star formation is suppressed entirely. Alternatively, fragmentation efficiency may saturate beyond some metallicity threshold if gravitational collapse cascades rapidly enough. To model this behavior, we propose a logistic function describing the transition from metallicity-sensitive to metallicity-insensitive fragmentation regimes. We provide a user-friendly public code, pyIGIMF , which enables the instantaneous computation of the IGIMF theory with both linear and logistic α 1 – Z relations.

We examine the orbital evolution of a compact massive object orbiting a galaxy in both Newtonian and Modified Newtonian Dynamics (MOND) frameworks, considering two scenarios: one where the object starts inside the galaxy's baryonic matter distribution and another where it begins far outside the galaxy. Assuming the systems discussed here are in the MOND regime, in the first scenario, the dynamical friction (DF) time-scale is shorter in MOND than in Newtonian models because of stronger friction from enhanced gravitational effects of baryonic matter. We also find that increasing the galaxy's half-mass radius weakens DF in Newtonian models due to a lower dark-matter density at larger distances. In the second scenario, when the object starts far outside the galaxy, the lack of baryonic matter reduces DF in MOND. In contrast, dark matter in Newtonian models continues to have a significant effect. These results suggest that orbital decay during galaxy mergers may occur more slowly in MOND than in Lambda cold dark matter. We conclude that comparisons of DF in MOND and Newtonian models require caution, as DF is stronger in the Newtonian regime at large distances but more effective in MOND once the object reaches the baryonic matter distribution. The initial placement of a massive object within a galaxy affects the DF efficiency in MOND, with a stronger DF near the centre and a weaker DF at larger distances. We also identify a universal scaling relation for DF time-scales, which impacts galaxy mergers and the orbital behaviour of massive objects.

Recent Gaia studies have identified numerous open clusters (OCs) tidal tail catalogues, enabling systematic searches for white dwarfs (WDs) associated with clusters their extended structures. We compile a literature-based sample of OC-WD pairs to validate WD membership in cluster cores tails, investigate the initial-final mass relation (IFMR), identify WDs formed through non-canonical evolution, and interpret the observed WD populations using a grid of N-body simulations. We combine Gaia DR3 cluster tail catalogues with UV-IR photometry to analyse the OC-WD pairs. WD masses, cooling ages, radii, temperatures luminosities are estimated using colour-magnitude diagrams spectral energy distributions. These observations are interpreted in the context of N-body simulations. We identify 235 OC-WD pairs (99 in tails) in 80 clusters. More than 28

The relation between the maximum stellar mass in a very young cluster ( m max ) and the total stellar mass of the cluster ( M ecl ), known as the m max − M ecl relation, remains debated in the literature. To test the validity of this relation, we modelled young star clusters with masses between 10 2.5 and 10 5.0 M ⊙ and ages of 1–4 Myr using the galIMF code, in which stellar masses are optimally sampled from a varying initial stellar mass function. We compared the results with literature observations of extragalactic young star clusters. We incorporated stellar evolution via PARSEC and COLIBRI tracks and computed H α luminosities using the Pégase code. To account for dynamical ejections, we stochastically removed stars based on their spectral type, following previous N -body simulations. Additional sources of scatter, including uncertainties in age determination and contamination by field stars, were considered. Our results indicate that, under the assumptions explored here, optimal sampling is consistent with the extragalactic star cluster observations considered, whereas purely random sampling produces distributions that are not in agreement. These findings support a highly self-regulated interpretation of cluster formation in which stellar masses align optimally with the initial mass function rather than being drawn independently at random.

Within the Hot Big Bang picture, as usually interpreted in the standard LCDM framework and its hierarchical scenario for elliptical galaxy assembly, the cosmic microwave background (CMB) is associated with photon decoupling near z = 1100, and the Planck angular power spectra are taken to constrain primordial 10^-5-level fluctuations that seeded later structure formation. We show that, in addition to the LCDM model, two cosmological models based on Milgromian gravitation are also consistent with the Planck CMB power spectra, such that the spectra do not uniquely favor dark matter. We then argue that the published CMB spectra are not direct observables, but reconstructed quantities obtained after foreground subtraction and corrections for weak lensing, photon-electron scattering, and gravitational energy redshifts along the line of sight. Because these steps depend on the assumed growth history of structure, the resulting spectra depend on the cosmological model adopted in the data reduction. We also note that the reported correlation between the hemispherical CMB asymmetry and the excess on-sky distribution of elliptical galaxies may point to matter inhomogeneities spanning large portions of the observable universe. Motivated by observational tensions in the hierarchical assembly of elliptical galaxies, we review the consequences of elliptical-galaxy formation on a downsizing timescale, which implies a significant extragalactic foreground released at 15< z < 20. Under conservative assumptions, this foreground contributes at least 1.4 percent of the observed CMB energy density and has not been included in CMB analyses. It follows that the reported 10^-5-level fluctuations is introduced by overly aggressive foreground cleaning.

The stellar initial mass function (sIMF) is often treated as a stochastic probability distribution, yet such an interpretation implies Poisson noise that is inconsistent with growing observational evidence. In particular, the observed relation between the mass of the most massive star formed in an embedded cluster and the cluster's total stellar mass supports a deterministic sampling process, known as optimal sampling. However, the physical origin of optimal sampling has not been formally established in the literature. In this work, we show that the stellar mass distribution implied by optimal sampling emerges from applying the Maximum Entropy principle to the fragmentation of star-forming clumps, whose structure is set by density-dependent cooling in the optically thin regime. Here, the maximum entropy leads to unbiased distributions. By applying calculus of variations to minimize the entropy functional obtained assuming fragmentation, we recover the power-law form of the sIMF, and we show that any distribution deviating from the sIMF violates the Maximum Entropy principle. This work provides a first-principles foundation for the deterministic nature of star formation. Thus, the sIMF is the distribution resulting from a maximally unbiased system.

Context. Semi-analytical evolution models of galaxies are a useful and computationally inexpensive tool for a fast assessment of individual properties and their evolution. In this work, specifically the influence of a metallicity- and star-formation-rate- (SFR) dependent, galaxy-wide stellar initial mass function (IGIMF) on the self-regulation of star formation in a galaxy is of interest. Aims. We aim to investigate the impact of a variable IGIMF, and especially its influence on the equilibrium SFR of the system, its gas fraction, the metallicity evolution, and the gas depletion timescale, τgas, all in comparison with two non-varying galaxy-wide IMFs (gwIMFs). Methods. A two-phase two-component model with gas and stellar components was integrated using the Cash-Karp method with adaptive step size. For comparison, the calculations were carried out using non-varying gwIMFs and a variable IGIMF, implemented using the GalIMF code, which is based on the IGIMF theory. The input parameters were the effective radius, the final age, and the accretion rate of the galaxy. Our highly simplified model does not represent a full physical galactic network; however, it is suitable for the purpose of this study. Results. All models - both non-varying gwIMFs and the IGIMF - reproduce reasonable gas fractions, gas-depletion timescales, and the main sequence of star-forming galaxies. However, only the IGIMF model accurately predicts the mass-metallicity relation and provides a more comprehensive description of quenched elliptical galaxies. For massive ellipticals all models suggest the need for an additional gas-heating source to reach a quenched state. Using a different stellar yield table in the IGIMF model does not significantly affect the results. In all models, the galaxies evolve in a self-regulated way, which is determined by the accretion rate. The self-regulated constancy of the SFR reflects the constant SFRs of nearby star-forming galaxies. The specific gas-accretion rate of all galaxies appears to be comparable to the Hubble constant. The inclusion of outflows improves the results for the canonical gwIMF model, but not significantly, while for the IGIMF model it has no significant impact.

Most classical satellites of the Milky Way are known to display signs of tidal disturbance (e.g. tidal tails, substructures, and distorted shapes). This cannot be explained by the standard model of cosmology due to its prediction that the dark matter haloes of the classical satellites confer them with very strong self-gravity and make them resilient to the Milky Way's gravitational tides. In this work, we estimate the tidal susceptibility of the classical satellites by comparing their half-mass radius with their theoretical tidal radius at pericentre in both the standard model and in the Milgromian dynamics (MOND) model. With this approach, we demonstrate that most classical satellites are expected to be tidally perturbed in MOND, so their observed tidal features are generally in good agreement with MOND expectations. Since gravitational tides can also enhance the velocity dispersion of the satellites, we argue that MOND can plausibly explain the unusually high velocity dispersions reported for some of the classical satellites.

The stellar dynamical evolution of massive star clusters formed during starburst periods leads to the segregation of ≳10^4 M_⊙ stellar-mass black hole sub-clusters in their centres. In gas-rich environments, such as galactic central molecular zones, these black hole clusters are likely to accrete large amounts of the gas from their surroundings, which in turn affects their internal dynamics. In this Letter we estimated the corresponding accretion rate onto the black hole cluster and its radiative feedback. We assessed whether such an accretion flow can lead to the collapse of the black hole cluster into an intermediate-mass black hole. The estimates were obtained analytically, considering the astrophysical conditions and star formation history reported for the central molecular zone of our Galaxy. We find that a stellar black hole cluster with mass ≳10^4 M_⊙ located in the twisted ring of molecular clouds with radius ≈100 pc that is observed in the central molecular zone of our Galaxy can accrete about the same mass in gas on a timescale of a few million years. We suggest that this is sufficient for its subsequent collapse into an intermediate-mass black hole. Based on an estimate of the dynamical friction inspiral time, we further argue that the locations of the intermediate-mass black hole candidates recently observed in the central molecular zone are compatible with their formation therein during the last starburst period reported to have occurred ≈1 Gyr ago.

Using the Gaia DR3 open cluster catalog, we identified the most massive star in each observed cluster. Examining the m_max-M_cluster relations across different age ranges, we find that as clusters age, the relation gradually deviates from the initial m_max-M_ecl relation and eventually exhibits clear age stratification. We conducted N-body simulations for both individual cluster evolution and subcluster coalescence. Four gas expulsion modes were tested for individual clusters, and two scenarios were modeled for cluster coalescence. Under all four gas expulsion modes, the evolution of the m_max-M_cluster relation follows a similar trajectory, differing mainly in evolutionary speed. The coalescence simulations show comparable behavior but align better with the observations, as both exhibit systematically lower m_max-M_cluster relations than individual cluster simulations. This systematically lower observed m_max-M_cluster relation suggests slower cluster mass loss and smaller masses for the most massive stars-both conditions reproduced in the coalescence simulations. Observations also show that clusters older than 5 Myr have most massive stars significantly deviating from the initial m_max-M_ecl relation. From this perspective, the coalescence simulations also provide a better match to the observations. In conclusion, the evolution of the m_max-M_ecl relation supports subcluster coalescence as a dominant pathway for open cluster formation, consistent with our previous work.

Context. The mini-cavity is a low-density region observed in the complex of streams of ionized gas around the Galactic central supermassive black hole, Sgr A★, known as the mini-spiral. Its near-circular shape is suggestive of a formation due to the effect of stellar winds. No suitable stars are currently observed within the mini-cavity, however. Aims. In this study we assessed whether the mini-cavity could have been formed by the winds of the stars from the neighbouring IRS 13 cluster that were located at the position of the mini-cavity in the past but moved away from it later on owing to their orbital motions around Sgr A★. Furthermore, we estimated the rate of accretion of the then-abundant interstellar medium onto the putative intermediate-mass black hole that has been proposed to reside in the IRS 13 cluster and the corresponding X-ray luminosity of this black hole. Methods. The estimates were obtained analytically using the astrophysical properties reported for the involved objects and the environment. Resuts. Based on our results, we suggest that the mini-cavity was formed by the winds of the IRS 13 cluster member stars about 300 years ago, when this cluster went through the Bar region of the mini-spiral. The accompanying accretion of the interstellar medium onto the putative intermediate-mass black hole in this cluster may have produced multiple X-ray flares with luminosities of ≈1039 erg s−1. Such flares are compatible with the X-ray reflections currently observed on the molecular clouds in the complexes Sgr A, B, and C, including the necessary light-travel time delay.

Context. The mini-cavity is a low-density region observed in the complex of streams of ionized gas around the Galactic central supermassive black hole, Sgr A(star), known as the mini-spiral. Its near-circular shape is suggestive of a formation due to the effect of stellar winds. No suitable stars are currently observed within the mini-cavity, however. Aims. In this study we assessed whether the mini-cavity could have been formed by the winds of the stars from the neighbouring IRS 13 cluster that were located at the position of the mini-cavity in the past but moved away from it later on owing to their orbital motions around Sgr A(star). Furthermore, we estimated the rate of accretion of the then-abundant interstellar medium onto the putative intermediate-mass black hole that has been proposed to reside in the IRS 13 cluster and the corresponding X-ray luminosity of this black hole. Methods. The estimates were obtained analytically using the astrophysical properties reported for the involved objects and the environment. Resuts. Based on our results, we suggest that the mini-cavity was formed by the winds of the IRS 13 cluster member stars about 300 years ago, when this cluster went through the Bar region of the mini-spiral. The accompanying accretion of the interstellar medium onto the putative intermediate-mass black hole in this cluster may have produced multiple X-ray flares with luminosities of approximate to 10(39) erg s(-1). Such flares are compatible with the X-ray reflections currently observed on the molecular clouds in the complexes Sgr A, B, and C, including the necessary light-travel time delay.

In the framework of Milgromian dynamics (MOND), galaxy clusters have been thought to have about a factor of two less baryonic mass than gravitational mass. One hypothesized source of this missing mass is undetected baryons. Extensive observations and studies indicate that the baryon content of galaxy clusters is primarily composed of the intracluster medium (ICM). In this work we reevaluate the overall stellar mass in galaxy clusters taking into account recent work on the galaxy-wide stellar initial mass function of stars (gwIMF) needed to synthesise the metals observed in galaxies. Given their supersolar metallicities and short formation timescales, massive elliptical galaxies are inferred to have formed with highly top-heavy gwIMFs, which in turn leave behind a substantial mass in stellar remnants. The dependency of the gwIMF on the properties and evolution of a galaxy is well encapsulated by the integrated galaxy-wide initial mass function (IGIMF) theory, developed independently of MOND. We utilize observational data at redshifts z <0.1 from the Wide-field Nearby Galaxy-cluster Survey (WINGS) and the Two Micron All Sky Survey (2MASS). Masses of galaxies and intracluster light (ICL) are calculated for 46 galaxy clusters using the IGIMF theory. The resulting masses in stars and in remnants are combined with previously derived ICM masses to estimate the total baryonic masses of the clusters. These baryonic masses are then compared to the MOND dynamical masses of the clusters, which are derived from hydrostatic equilibrium of the ICM based on earlier studies. As a complement, we include a comparison with several weak/strong lensing masses in the MOND framework. Our results show that the stellar masses of galaxies and the ICL increase substantially when applying the galaxy-wide mass-to-light ratios derived from the IGIMF theory. This leads to a significant rise in the estimated baryonic masses of galaxy clusters. In the sample of 46 galaxy clusters, the baryonic component on average accounts for 52(-3)(+4)% of the MOND dynamical mass when considering only the ICM contribution. The baryonic mass in stars, remnants and the ICM accounts for at least 88(-4-1)(+5+2) % of the MOND dynamical mass. The contribution by stellar remnants that arises from nucleosynthesis constraints thus significantly alleviates the missing mass problem in MOND. Finally, we briefly discuss the compatibility of the IGIMF framework with the radial acceleration relation (RAR), and studies of MOND weak/strong lensing and related issues. A more comprehensive investigation will require future work that combines the IGIMF with self-consistent, spatially resolved formation, evolution, and resulting mass distribution models of galaxies.