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After their birth a significant fraction of all stars pass through the tidal threshold (prah) of their cluster of origin into the classical tidal tails. The asymmetry between the number of stars in the leading and trailing tails tests gravitational theory. All five open clusters with tail data (Hyades, Praesepe, Coma Berenices, COIN-Gaia 13, NGC 752) have visibly more stars within dcl = 50 pc of their centre in their leading than their trailing tail. Using the Jerabkova-compact-convergent-point (CCP) method, the extended tails have been mapped out for four nearby 600-2000 Myr old open clusters to dcl>50 pc. These are on near-circular Galactocentric orbits, a formula for estimating the orbital eccentricity of an open cluster being derived. Applying the Phantom of Ramses code to this problem, in Newtonian gravitation the tails are near-symmetrical. In Milgromian dynamics (MOND) the asymmetry reaches the observed values for 50 < dcl/pc < 200, being maximal near peri-galacticon, and can slightly invert near apo-galacticon, and the Küpper epicyclic overdensities are asymmetrically spaced. Clusters on circular orbits develop orbital eccentricity due to the asymmetrical spill-out, therewith spinning up opposite to their orbital angular momentum. This positive dynamical feedback suggests Milgromian open clusters to demise rapidly as their orbital eccentricity keeps increasing. Future work is necessary to better delineate the tidal tails around open clusters of different ages and to develop a Milgromian direct n-body code., 28 pages, 19 figures, MNRAS, published

The James Webb Space Telescope (JWST) discovered several luminous high-redshift galaxy candidates with stellar masses of $M_{*} \gtrsim 10^{9} \, \rm{M_{\odot}}$ at photometric redshifts $z_{\mathrm{phot}} \gtrsim 10$ which allows to constrain galaxy and structure formation models. For example, Adams et al. identified the candidate ID 1514 with $\log_{10}(M_{*}/M_{\odot}) = {9.8}_{-0.2}^{+0.2}$ located at $z_{\mathrm{phot}} = 9.85_{-0.12}^{+0.18}$ and Naidu et al. found even more distant candidates labeled as GL-z11 and GL-z13 with $\log_{10}(M_{*}/M_{\odot}) = 9.4_{-0.3}^{+0.3}$ at $z_{\mathrm{phot}}=10.9_{-0.4}^{+0.5}$ and $\log_{10}(M_{*}/M_{\odot}) = 9.0_{-0.4}^{+0.3}$ at $z_{\mathrm{phot}} = 13.1_{-0.7}^{+0.8}$, respectively. Assessing the computations of the IllustrisTNG (TNG50-1 and TNG100-1) and EAGLE projects, we investigate if the stellar mass buildup as predicted by the $\Lambda$CDM paradigm is consistent with these observations assuming that the early JWST calibration is correct and that the candidates are indeed located at $z \gtrsim 10$. Galaxies formed in the $\Lambda$CDM paradigm are by more than an order of magnitude less massive in stars than the observed galaxy candidates implying that the stellar mass buildup is more efficient in the early Universe than predicted by the $\Lambda$CDM models. This in turn would suggest that structure formation is more enhanced at $z \gtrsim 10$ than predicted by the $\Lambda$CDM framework. We show that different star formation histories could reduce the stellar masses of the galaxy candidates alleviating the tension. Finally, we calculate the galaxy-wide initial mass function (gwIMF) of the galaxy candidates assuming the integrated galaxy IMF theory. The gwIMF becomes top-heavy for metal-poor starforming galaxies decreasing therewith the stellar masses compared to an invariant canonical IMF., Comment: Accepted for publication in ApJL, 10 pages, 4 figures, 1 tables

Some ultra-compact dwarf galaxies (UCDs) have elevated observed dynamical V-band mass-to-light ($M/L_{\rm V}$) ratios with respect to what is expected from their stellar populations assuming a canonical initial mass function (IMF). Observations have also revealed the presence of a compact dark object in the centers of several UCDs, having a mass of a few to 15\% of the present-day stellar mass of the UCD. This central mass concentration has typically been interpreted as a super-massive black hole, but can in principle also be a sub-cluster of stellar remnants. We explore the following two formation scenarios of UCDs, i) monolithic collapse and ii) mergers of star clusters in cluster complexes as are observed in massively star-bursting regions. We explore the physical properties of the UCDs at different evolutionary stages assuming different initial stellar masses of the UCDs and the IMF being either universal or changing systematically with metallicity and density according to the Integrated Galactic IMF (IGIMF) theory. While the observed elevated $M/L_{\rm V}$ ratios of the UCDs cannot be reproduced if the IMF is invariant and universal, the empirically derived IMF which varies systematically with density and metallicity shows agreement with the observations. Incorporating the UCD-mass-dependent retention fraction of dark remnants improves this agreement. In addition we apply the results of N-body simulations to young UCDs and show that the same initial conditions describing the observed $M/L_{\rm V}$ ratios reproduce the observed relation between the half-mass radii and the present-day masses of the UCDs. The findings thus suggest that the majority of UCDs that have elevated $M/L_{\rm V}$ ratios could have formed monolithically with significant remnant-mass components that are centrally concentrated, while those with small $M/L_V$ values may be merged star-cluster complexes., Accepted for publication in MNRAS. 16 pages, 11 figures, 1 table

Using numerical simulations, we have studied the escape of globular clusters (GCs) from the satellite dwarf spheroidal galaxies (dSphs) of the Milky Way (MW). We start by following the orbits of a large sample of GCs around dSphs in the presence of the MW potential field. We then obtain the fraction of GCs leaving their host dSphs within a Hubble Time. We model dSphs by a Hernquist density profile with masses between $10^7\,\mathrm{M}_{\odot}$ and $7\times 10^9\,\mathrm{M}_{\odot}$. All dSphs lie on the Galactic disc plane, but they have different orbital eccentricities and apogalactic distances. We compute the escape fraction of GCs from 13 of the most massive dSphs of the MW, using their realistic orbits around the MW (as determined by Gaia). The escape fraction of GCs from 13 dSphs is in the range $12\%$ to $93\%$. The average escape time of GCs from these dSphs was less than 8 $\,\mathrm{Gyrs}$, indicating that the escape process of GCs from dSphs was over. We then adopt a set of observationally-constrained density profiles for specific case of the Fornax dSph. According to our results, the escape fraction of GCs shows a negative correlation with both the mass and the apogalactic distance of the dSphs, as well as a positive correlation with the orbital eccentricity of dSphs. In particular, we find that the escape fraction of GCs from the Fornax dSph is between $13\%$ and $38\%$. Finally, we observe that when GCs leave their host dSphs, their final orbit around the MW does not differ much from their host dSphs., 16 pages, 7 figures (including 1 in the appendix), 6 tables (including 2 in the appendix). Accepted for publication in MNRAS

Globular clusters display an anticorrelation between the fraction of the first generation of stars ($N({\rm G1})/N({\rm tot})$) and the slope of the present-day mass function of the clusters ($\alpha_{pd}$), which is particularly significant for massive clusters. In the framework of the binary-mediated collision scenario for the formation of the second-generation stars in globular clusters, we test the effect of a varying stellar initial mass function (IMF) of the G1 stars on the $(N({\rm G1})/N({\rm tot}))-\alpha_{pd}$ anticorrelation. We use a simple collision model that has only two input parameters, the shape of the IMF of G1 stars and the fraction of G1 stars that coalesce to form second-generation stars. We show that a variable efficiency of the collision process is necessary in order to explain the $(N({\rm G1})/N({\rm tot}))-\alpha_{pd}$ anticorrelation; however, the scatter in the anticorrelation can only be explained by variations in the IMF, and in particular by variations in the slope in the mass interval $\approx$ (0.1-0.5) M$_{\odot}$. Our results indicate that in order to explain the scatter in the $(N({\rm G1})/N({\rm tot}))-\alpha_{pd}$ relation, it is necessary to invoke variations in the slope in this mass range between $\approx -0.9$ and $\approx -1.9$. Interpreted in terms of a Kroupa-like broken power law, this translates into variations in the mean mass of between $\approx 0.2$ and $0.55$ M$_{\odot}$. This level of variation is consistent with what is observed for young stellar clusters in the Milky Way and may reflect variations in the physical conditions of the globular cluster progenitor clouds at the time the G1 population formed or may indicate the occurrence of collisions between protostellar embryos before stars settle on the main sequence., Comment: Accepted to A&A. Matches the published version. Typo for the sign of alpha1 and alpha2 corrected in Figures 1-4

The Kennicutt-Schmidt law is an empirical relation between the star formation rate surface density ($\Sigma_{SFR}$) and the gas surface density ($\Sigma_{gas}$) in disc galaxies. The relation has a power-law form $\Sigma_{SFR} \propto \Sigma_{gas}^n$. Assuming that star formation results from gravitational collapse of the interstellar medium, $\Sigma_{SFR}$ can be determined by dividing $\Sigma_{gas}$ by the local free-fall time $t_{ff}$. The formulation of $t_{ff}$ yields the relation between $\Sigma_{SFR}$ and $\Sigma_{gas}$, assuming that a constant fraction ($\varepsilon_{SFE}$) of gas is converted into stars every $t_{ff}$. This is done here for the first time using Milgromian dynamics (MOND). Using linear stability analysis of a uniformly rotating thin disc, it is possible to determine the size of a collapsing perturbation within it. This lets us evaluate the sizes and masses of clouds (and their $t_{ff}$) as a function of $\Sigma_{gas}$ and the rotation curve. We analytically derive the relation $\Sigma_{SFR} \propto \Sigma_{gas}^{n}$ both in Newtonian and Milgromian dynamics, finding that $n=1.4$. The difference between the two cases is a change only to the constant pre-factor, resulting in increased $\Sigma_{SFR}$ of up to 25\% using MOND in the central regions of dwarf galaxies. Due to the enhanced role of disk self-gravity, star formation extends out to larger galactocentric radii than in Newtonian gravity, with the clouds being larger. In MOND, a nearly exact representation of the present-day main sequence of galaxies is obtained if $\epsilon_{SFE} = \text{constant} \approx 1.1\%$. We also show that empirically found correction terms to the Kennicutt-Schmidt law are included in the here presented relations. Furthermore, we determine that if star formation is possible, then the temperature only affects $\Sigma_{SFR}$ by at most a factor of $\sqrt{2}$., Comment: Accepted for publication in MNRAS. 12 pages, 10 figures

Several observational and theoretical studies suggest that the initial mass function (IMF) slope for massive stars in globular clusters (GCs) depends on the initial cloud density and metallicity, such that the IMF becomes increasingly top-heavy with decreasing metallicity and increasing the gas density of the forming object. Using N-body simulations of GCs starting with a top-heavy IMF and undergo early gas expulsion within a Milky Way-like potential, we show how such a cluster would evolve. By varying the degree of top-heaviness, we calculate the dissolution time and the minimum cluster mass needed for the cluster to survive after 12 Gyr of evolution., Comment: 4 pages, 2 figures, Accepted for publication in Proceedings of the International Astronomical Union

The surface brightness fluctuation (SBF) technique is one of the distance measurement methods that has been applied on the low surface brightness galaxy NGC 1052-DF2 yielding a distance of about 20 Mpc implying it to be a dark matter deficient galaxy. We assume the number of giant stars above a given luminosity threshold to represent the SBF magnitude. The SBF magnitude depends on the distance, but this is degenerate with the star formation history (SFH). Using a stellar population synthesis model we calculate the number of giant stars for stellar populations with different galaxy-wide stellar initial mass functions (gwIMFs), ages, metallicities and SFHs. If the gwIMF is the invariant canonical IMF, the 1$\sigma$ (3$\sigma$) uncertainty in colour allows a distance as low as 12 Mpc (8 Mpc). If instead the true underlying gwIMF is the integrated galaxy-wide IMF (IGIMF) then overestimating distances for low-mass galaxies would be a natural result, allowing NGC 1052-DF2 to have a distance of 11 Mpc within the 1$\sigma$ colour uncertainty. Finally, we show that our main conclusion on the existence of a bias in the SBF distance estimation is not much affected by changing the luminosity lower limit for counting giant stars., Comment: Accepted for publication in MNRAS. 9 pages, 7 figures, updated according to the received comments

Several observational and theoretical indications suggest that the initial mass function (IMF) becomes increasingly top-heavy (i.e., overabundant in high-mass stars with mass $m > 1M_{\odot}$) with decreasing metallicity and increasing gas density of the forming object. This affects the evolution of globular clusters (GCs) owing to the different mass-loss rates and the number of black holes formed. Previous numerical modeling of GCs usually assumed an invariant canonical IMF. Using the state-of-the-art $NBODY6$ code, we perform a comprehensive series of direct $N$-body simulations to study the evolution of star clusters, starting with a top-heavy IMF and undergoing early gas expulsion. Utilizing the embedded cluster mass-radius relation of Marks & Kroupa (2012) for initializing the models, and by varying the degree of top-heaviness, we calculate the minimum cluster mass needed for the cluster to survive longer than 12 Gyr. We document how the evolution of different characteristics of star clusters such as the total mass, the final size, the density, the mass-to-light ratio, the population of stellar remnants, and the survival of GCs is influenced by the degree of top-heaviness. We find that the lifetimes of clusters with different IMFs moving on the same orbit are proportional to the relaxation time to a power of $x$ that is in the range of 0.8 to 1. The observed correlation between concentration and the mass function slope in Galactic GCs can be accounted for excellently in models starting with a top-heavy IMF and undergoing an early phase of rapid gas expulsion., 21 pages, 18 figures, 4 tables. Accepted for publication in ApJ

Mass models of a sample of 171 low- and high-surface brightness galaxies are presented in the context of the cold dark matter (CDM) theory using the NFW dark matter halo density distribution to extract a new concentration-viral mass relation ($c-M_{vir}$). The rotation curves (RCs) are calculated from the total baryonic matter based on the 3.6 $\mu m $-band surface photometry, the observed distribution of neutral hydrogen, and the dark halo, in which the three adjustable parameters are the stellar mass-to-light ratio, halo concentration and virial mass. Although accounting for a NFW dark halo profile can explain rotation curve observations, the implied $c-M_{vir}$ relation from RC analysis strongly disagrees with that resulting from different cosmological simulations. Also, the $M/L-$color correlation of the studied galaxies is inconsistent with that expected from stellar population synthesis models with different stellar initial mass functions. Moreover, we show that the best-fitting stellar $M/L-$ ratios of 51 galaxies (30\% of our sample) have unphysically negative values in the framework of the $\Lambda $CDM theory. This can be interpreted as a serious crisis for this theory. This suggests either that the commonly used NFW halo profile, which is a natural result of $\Lambda $CDM cosmological structure formation, is not an appropriate profile for the dark halos of galaxies, or, new dark matter physics or alternative gravity models are needed to explain the rotational velocities of disk galaxies., Comment: 15 pages, 5 figures, 2 tables. Accepted for publication in MNRAS

Recent observations of rotationally supported galaxies show a tight correlation between the observed radial acceleration at every radius and the Newtonian acceleration generated by the baryonic mass distribution, the so-called radial acceleration relation (RAR). The rotation curves (RCs) of the SPARC sample of disk galaxies with different morphologies, masses, sizes and gas fractions are investigated in the context of modified Newtonian dynamics (MOND). We include the effect of cold dark baryons by scaling the measured mass in the atomic form by a factor of $c$ in the mass budget of galaxies. In addition to the standard interpolating function, we also fit the RCs and the RAR with the empirical RAR-inspired interpolating function. Slightly better fits for about $47\%$ of galaxies in our sample are achieved in the presence of dark baryons ($c>1$) with the mean value of $c = 2.4\pm 1.3$. Although the MOND fits are not significantly improved by including dark baryons, it results in a decrease in the characteristic acceleration $g_���$ by $40\%$. We find no correlation between the MOND critical acceleration $a_0$ and the central surface brightness of the stellar disk, $��_{3.6}$. This supports $a_0$ being a universal constant for all galaxies., Published in the Monthly Notices of the Royal Astronomical Society; 19 pages, 9 figures, 1 table

The ultra-diffuse dwarf galaxy NGC 1052-DF2 (DF2) has ten (eleven) measured globular clusters (GCs) with a line-of-sight velocity dispersion of $\sigma=7.8^{+5.2}_{-2.2}\,$km/s ($\sigma=10.6^{+3.9}_{-2.3}\,$km/s). Our conventional statistical analysis of the original ten GCs gives $\sigma=8.0^{+4.3}_{-3.0}\,$km/s. The overall distribution of velocities agrees well with a Gaussian of this width. Due to the non-linear Poisson equation in MOND, a dwarf galaxy has weaker self-gravity when in close proximity to a massive host. This external field effect is investigated using a new analytic formulation and fully self-consistent live $N$-body models in MOND. Our formulation agrees well with that of Famaey and McGaugh (2012). These new simulations confirm our analytic results and suggest that DF2 may be in a deep-freeze state unique to MOND. The correctly calculated MOND velocity dispersion agrees with our inferred dispersion and that of van Dokkum et al. (2018b) if DF2 is within 150 kpc of NGC 1052 and both are 20 Mpc away. The GCs of DF2 are however significantly brighter and larger than normal GCs, a problem which disappears if DF2 is significantly closer to us. A distance of 10-13 Mpc makes DF2 a normal dwarf galaxy even more consistent with MOND and the 13 Mpc distance reported by Trujillo et. al. (2019). We discuss the similar dwarf DF4, finding good agreement with MOND. We also discuss possible massive galaxies near DF2 and DF4 along with their distances and peculiar velocities, noting that NGC 1052 may lie at a distance near 10 Mpc., Comment: 14 pages, 9 figures, 2 Tables, accepted for publication in MNRAS

We study the dynamical evolution of star clusters on eccentric orbits using a semi-analytical approach. In particular we adapt and extend the equations of EMACSS code, introduced by Gieles et al. (2014), to work with eccentric orbits. We follow the evolution of star clusters in terms of mass, half-mass radius, core radius, Jacobi radius and the total energy over their dissolution time. Moreover, we compare the results of our semi-analytical models against $N$-body computations of clusters with various initial half-mass radius, number of stars and orbital eccentricity to cover both tidally filling and under-filling systems. The evolution profiles of clusters obtained by our semi-analytical approach closely follow those of $N$-body simulations in different evolutionary phases of star clusters, from pre-collapse to post-collapse. Given that the average runtime of our semi-analytical models is significantly less than that of $N$-body models, our approach makes it feasible to study the evolution of large samples of globular clusters on eccentric orbits., Comment: 11 pages, 4 figures, 1 table. Accepted for publication in MNRAS

Unlike Newtonian dynamics which is linear and obeys the strong equivalence principle, in any nonlinear gravitation such as Milgromian dynamics (MOND), the strong version of the equivalence principle is violated and the gravitational dynamics of a system is influenced by the external gravitational field in which it is embedded. This so called External Field Effect (EFE) is one of the important implications of MOND and provides a special context to test Milgromian dynamics. Here, we study the rotation curves (RCs) of 18 spiral galaxies and find that their shapes constrain the EFE. We show that the EFE can successfully remedy the overestimation of rotation velocities in 80\% of the sample galaxies in Milgromian dynamics fits by decreasing the velocity in the outer part of the RCs. We compare the implied external field with the gravitational field for non-negligible nearby sources of each individual galaxy and find that in many cases it is compatible with the EFE within the uncertainties. We therefore argue that in the framework of Milgromian dynamics, one can constrain the gravitational field induced from the environment of galaxies using their RCs. We finally show that taking into account the EFE yields more realistic values for the stellar mass-to-light ratio in terms of stellar population synthesis than the ones implied without the EFE., 18 pages, Accepted for publication in MNRAS

The observed present-day stellar mass function (PDMF) of the solar neighborhood is a mixture of stellar populations born in star-forming events that occurred over the life-time of the thin disk of the Galaxy. Assuming stars form in embedded clusters which have stellar initial mass functions (IMFs) which depend on the metallicity and density of the star-forming gas clumps, the integrated galaxy-wide IMF (IGIMF) can be calculated. The shape of the IGIMF thus depends on the SFR and metallicity. Here, the shape of the PDMF for stars more massive than $1\,M_\odot$ in combination with the mass density in low-mass stars is used to constrain the current star-formation rate (SFR), the star formation history (SFH) and the current stellar plus remnant mass ($M_*$) in the Galactic thin disk. This yields the current SFR, $\dot{M}_*= 4.1^{+3.1}_{-2.8}~M_\odot$yr$^{-1}$, a declining SFH and $M_*=2.1^{+3.0}_{-1.5}\times 10^{11}M_\odot$, respectively, with a V-band stellar mass-to-light ratio of $M_*/L_V=2.79^{+0.48}_{-0.38}$.These values are consistent with independent measurements. We also quantify the surface density of black holes and neutron stars in the Galactic thin disk. The invariant canonical IMF can reproduce the PDMF of the Galaxy as well as the IGIMF, but in the universal IMF framework it is not possible to constrain any of the above Galactic properties. Assuming the IGMF theory is the correct framework and in combination with the vertical velocity dispersion data of stars, it follows that the Milky Way would have appeared as a chain galaxy at high redshift., 12 pages, 9 figures, Accepted for publication in MNRAS

A great challenge in present-day physics is to understand whether the observed internal dynamics of galaxies is due to dark matter matter or due to a modification of the law of gravity. Recently, van Dokkum et al. reported that the ultra-diffuse dwarf galaxy NGC1052-DF2 lacks dark matter, and they claimed that this would -- paradoxically -- be problematic for modified gravity theories like Milgromian dynamics (MOND). However, NGC1052-DF2 is not isolated, so that a valid prediction of its internal dynamics in MOND cannot be made without properly accounting for the external gravitational fields from neighbouring galaxies. Including this external field effect following Haghi et al. shows that NGC1052-DF2 is consistent with MOND., 15 pages, including supplementary information (the external field formulae), published by Nature: https://rdcu.be/6uZn

In order to understand the orbital history of Galactic halo objects, such as globular clusters, authors usually assume a static potential for our Galaxy with parameters that appear at the present-day. According to the standard paradigm of galaxy formation, galaxies grow through a continuous accretion of fresh gas and a hierarchical merging with smaller galaxies from high redshift to the present day. This implies that the mass and size of disc, bulge, and halo change with time. We investigate the effect of assuming a live Galactic potential on the orbital history of halo objects and its consequences on their internal evolution. We numerically integrate backwards the equations of motion of different test objects located in different Galactocentric distances in both static and time-dependent Galactic potentials in order to see if it is possible to discriminate between them. We show that in a live potential, the birth of the objects, 13 Gyr ago, would have occurred at significantly larger Galactocentric distances, compared to the objects orbiting in a static potential. Based on the direct N-body calculations of star clusters carried out with collisional N-body code, NBODY6, we also discuss the consequences of the time-dependence of a Galactic potential on the early- and long-term evolution of star clusters in a simple way, by comparing the evolution of two star clusters embedded in galactic models, which represent the galaxy at present and 12 Gyr ago, respectively. We show that assuming a static potential over a Hubble time for our Galaxy as it is often done, leads to an enhancement of mass-loss, an overestimation of the dissolution rates of globular clusters, an underestimation of the final size of star clusters, and a shallower stellar mass function., Comment: 12 pages, 11 figures, 4 tables, accepted for publication in MNRAS

This is the second of a series of papers in which we present a new solution to reconcile the prediction of single stellar population (SSP) models with the observed stellar mass-to-light ($M/L$) ratios of globular clusters (GCs) in M31 and its trend with respect to $\mathrm{[Fe/H]}$. In the present work our focus is on the empirical relation between age and metallicity for GCs and its effect on the $M/L$ ratio. Assuming that there is an anti-correlation between the age of M31 GCs and their metallicity, we evolve dynamical SSP models of GCs to establish a relation between the $M/L$ ratio (in the $V$ and $K$ band) and metallicity. We then demonstrate that the established $M/L-\mathrm{[Fe/H]}$ relation is in perfect agreement with that of M31 GCs. In our models we consider both the canonical initial mass function (IMF) and the top-heavy IMF depending on cluster birth density and metallicity as derived independently from Galactic GCs and ultra-compact dwarf galaxies by Marks et al. Our results signify that the combination of the density- and metallicity-dependent top-heavy IMF, the anti-correlation between age and metallicity, stellar evolution and standard dynamical evolution yields the best possible agreement with the observed trend of $M/L-\mathrm{[Fe/H]}$ for M31 GCs., 8 pages, 4 figures, 1 table. Accepted for publication in ApJ

We use direct $N$-body calculations to investigate the impact of primordial mass segregation on the size scale and mass-loss rate of star clusters in a galactic tidal field. We run a set of simulations of clusters with varying degrees of primordial mass segregation at various galactocentric radii and show that, in primordially segregated clusters, the early, impulsive mass-loss from stellar evolution of the most massive stars in the innermost regions of the cluster leads to a stronger expansion than for initially non-segregated clusters. Therefore, models in stronger tidal fields dissolve faster due to an enhanced flux of stars over the tidal boundary. Throughout their lifetimes, the segregated clusters are more extended by a factor of about 2, suggesting that (at least) some of the very extended globular clusters in the outer halo of the Milky Way may have been born with primordial mass segregation. We finally derive a relation between star-cluster dissolution time, $T_{diss}$, and galactocentric radius, $R_G$, and show how it depends on the degree of primordial mass segregation., 12 pages, 8 figures, accepted for publication in MNRAS

We use direct $N$-body calculations to study the evolution of the unusually extended outer halo globular cluster Palomar 4 (Pal~4) over its entire lifetime in order to reproduce its observed mass, half-light radius, velocity dispersion and mass function slope at different radii. We find that models evolving on circular orbits, and starting from a non-mass segregated, canonical initial mass function (IMF) can reproduce neither Pal 4's overall mass function slope nor the observed amount of mass segregation. Including either primordial mass segregation or initially flattened IMFs does not reproduce the observed amount of mass segregation and mass function flattening simultaneously. Unresolved binaries cannot reconcile this discrepancy either. We find that only models with both a flattened IMF and primordial segregation are able to fit the observations. The initial (i.e. after gas expulsion) mass and half-mass radius of Pal~4 in this case are about 57000 M${\odot}$ and 10 pc, respectively. This configuration is more extended than most globular clusters we observe, showing that the conditions under which Pal~4 formed must have been significantly different from that of the majority of globular clusters. We discuss possible scenarios for such an unusual configuration of Pal~4 in its early years., 14 pages, 12 figures, 1 table

A central problem of contemporary physics is whether the law of gravity is non-Newtonian on galaxy scales. Rodrigues et al. argue that Milgromian gravitation, which solves the flat rotation curve problem without the need for dark matter particles, is ruled out at > 10{\sigma} significance. To a large extent, this conclusion relies on galaxies with very uncertain distances and/or nearly edge-on orientations, where dust obscuration often becomes significant. Applying appropriate quality cuts to the data leaves only a handful of outliers to the predictions of Milgromian gravitation according to the analysis of Rodrigues et al., but even these outliers can be explained with Milgromian gravitation., Comment: Author version, published in Nature Astronomy on 13.Nov.2018 (free version: https://rdcu.be/bbuvP) as a Correspondence to the article by Rodrigues et al. http://adsabs.harvard.edu/abs/2018NatAs...2..668R; see also McGaugh et al. for a parallel Correspondence (https://www.nature.com/articles/s41550-018-0615-9); for a reply by Rodrigues et al. see https://www.nature.com/articles/s41550-018-0614-x

The observed line-of-sight velocity dispersion $\sigma_{los}$ of the ultra diffuse galaxy Dragonfly 44 (DF44) requires a Newtonian dynamical mass-to-light ratio of $M_{dyn}/L_I=26^{+7}_{-6}$ Solar units. This is well outside the acceptable limits of our stellar population synthesis (SPS) models, which we construct using the integrated galactic initial mass function (IGIMF) theory. Assuming DF44 is in isolation and using Jeans analysis, we calculate $\sigma_{los}$ profiles of DF44 in Milgromian dynamics (MOND) and modified gravity (MOG) theories without invoking dark matter. Comparing with the observed kinematics, the best-fitting MOND model has $M_{dyn}/L_I = 3.6_{-1.2}^{+1.6}$ and a constant orbital anisotropy of $\beta=-0.5_{-1.6}^{+0.4}$. In MOG, we first fix its two theoretical parameters $\alpha$ and $\mu$ based on previous fits to the observed rotation curve data of The HI Nearby Galaxy Survey (THINGS). The DF44 $\sigma_{los}$ profile is best fit with $M_{dyn}/L_I=7.4_{-1.4}^{+1.5}$, larger than plausible SPS values. MOG produces a $\sigma_{los}$ profile for DF44 with acceptable $M_{dyn}/L_I$ and isotropic orbits if $\alpha$ and $\mu$ are allowed to vary. MOND with the canonical $a_0$ can explain DF44 at the $2.40 \sigma$ confidence level (1.66\%) if considering both its observed kinematics and typical star formation histories in an IGIMF context. However, MOG is ruled out at $5.49 \sigma$ ($P$-value of $4.07 \times 10^{-8}$) if its free parameters are fixed at the highest values consistent with THINGS data., Comment: 10 pages, 3 figures, accepted for publication in The Astrophysical Journal Letters

We have obtained membership probabilities of stars within a field of radius $\sim3^\circ$ around the centre of the open cluster Alpha Persei using proper motions and photometry from the PPMXL and WISE catalogues. We have identified 810 possible stellar members of Alpha Persei. We derived the global and radial present-day mass function (MF) of the cluster and found that they are well matched by two-stage power-law relations with different slopes at different radii. The global MF of Alpha Persei shows a turnover at $m=0.62\,\mathrm{M}_{\odot}$ with low and high-mass slopes of $\alpha_\mathrm{low}=0.50\pm0.09$ ($0.1, Comment: 10 pages, 8 figures, 5 tables. Accepted for publication in MNRAS

The observed mass-to-light ($M/L$) ratios of a large sample of GCs in M31 show an inverse trend with metallicity compared to what is expected from Simple Stellar Population (SSP) models with an invariant canonical stellar IMF, in the sense that the observed $M/L$ ratios decrease with increasing metallicity. We show that incorporating the effect of dynamical evolution the SSP models with a canonical IMF can not explain the decreasing $M/L$ ratios with increasing metallicity for the M31 GCs. The recently derived top-heavy IMF as a function of metallicity and embedded cluster density is proposed to explain the lower than expected $M/L$ ratios of metal-rich GCs. We find that the SSP models with a top-heavy IMF, retaining a metallicity- and cluster mass- dependent fraction of the remnants within the clusters, and taking standard dynamical evolution into account can successfully explain the observed $M/L-[Fe/H]$ relation of M31 GCs. Thus we propose that the kinematical data of GCs can be used to constrain the top-heaviness of the IMF in GCs., Comment: Accepted for publication in ApJ, 8 pages, 7 figures

We present the first ever direct N-body computations of an old Milky Way globular cluster over its entire lifetime on a star-by-star basis. Using recent GPU hardware at Bonn University, we have performed a comprehensive set of N-body calculations to model the distant outer halo globular cluster Palomar 14 (Pal 14). Pal 14 is unusual in that its mean density is about 10 times smaller than that in the solar neighbourhood. Its large radius as well as its low-mass make it possible to simulate Pal 14 on a star-by-star basis. By varying the initial conditions, we aim at finding an initial N-body model which reproduces the observational data best in terms of its basic parameters, i.e. half-light radius, mass and velocity dispersion. We furthermore focus on reproducing the stellar mass function slope of Pal 14 which was found to be significantly shallower than in most globular clusters. While some of our models can reproduce Pal 14’s basic parameters reasonably well, we find that dynamical mass segregation alone cannot explain the mass function slope of Pal 14 when starting from the canonical Kroupa initial mass function (IMF). In order to seek an explanation for this discrepancy, we compute additional initial models with varying degrees of primordial mass segregation as well as with a flattened IMF. The necessary degree of primordial mass segregation turns out to be very high, though, such that we prefer the latter hypothesis which we discuss in detail. This modelling has shown that the initial conditions of Pal 14 after gas expulsion must have been a half-mass radius of about 20 pc, a mass of about 50 000 M⊙, and possibly some mass segregation or an already established non-canonical IMF depleted in low-mass stars. Such conditions might be obtained by a violent early gas-expulsion phase from an embedded cluster born with mass segregation. Only at large Galactocentric radii are clusters likely to survive as bound entities the destructive gas-expulsion process we seem to have uncovered for Pal 14. In addition, we compute a model with a 5 per cent primordial binary fraction to test if such a population has an effect on the cluster’s evolution. We see no significant effect, though, and moreover find that the binary fraction of Pal 14 stays almost the same and gives the final fraction over its entire lifetime due to the cluster’s extremely low density. Low-density, halo globular clusters might therefore be good targets to test primordial binary fractions of globular clusters. © 2010 The Authors Monthly Notices of the Royal Astronomical Society © 2010 RAS

We present $N$-body simulations of globular clusters, exploring the effect of different galactic potentials on cluster sizes, $r_h$. For various galactocentric distances, $R_G$, we assess how cluster sizes change when we vary the virial mass and concentration of the host galaxy's dark-matter halo. We show that sizes of GCs are determined by the local galactic mass density rather than the virial mass of the host galaxy. We find that clusters evolving in the inner haloes of less concentrated galaxies are significantly more extended than those evolving in more concentrated ones, while the sizes of those orbiting in the outer halo are almost independent of concentration. Adding a baryonic component to our galaxy models does not change these results much, since its effect is only significant in the very inner halo. Our simulations suggest that there is a relation between $r_h$ and $R_G$, which systematically depends on the physical parameters of the halo. Hence, observing such relations in individual galaxies can put a new observational constraint on dark-matter halo characteristics. However, by varying the halo mass in a wide range of $10^{9}\leq M_{vir}/\msun \leq10^{13}$, we find that the $r_h-R_G$ relationship will be nearly independent of halo mass, if one assumes $M_{vir}$ and $c_{vir}$ as two correlated parameters, as is suggested by cosmological simulations., 15 pages, 10 figures, 4 tables, Accepted for publication in ApJ

We perform a series of direct $N$-body calculations to investigate the effect of residual gas expulsion from the gas-embedded progenitors of present-day globular clusters (GCs) on the stellar mass function (MF). Our models start either tidally filling or underfilling, and either with or without primordial mass segregation. We cover 100 Myr of the evolution of modeled clusters and show that the expulsion of residual gas from initially mass-segregated clusters leads to a significantly shallower slope of the stellar MF in the low- ($m\leq 0.50 M_\odot$) and intermediate-mass ($\simeq 0.50-0.85 M_\odot$) regime. Therefore, the imprint of residual gas expulsion and primordial mass segregation might be visible in the present-day MF. We find that the strength of the external tidal field, as an essential parameter, influences the degree of flattening, such that a primordially mass-segregated tidally-filling cluster with $r_h/r_t\geq 0.1$ shows a strongly depleted MF in the intermediate stellar mass range. Therefore, the shape of the present-day stellar MF in this mass range probes the birth place of clusters in the Galactic environment. We furthermore find that this flattening agrees with the observed correlation between the concentration of a cluster and its MF slope, as found by de Marchi et al.. We show that if the expansion through the residual gas expulsion in primordial mass segregated clusters is the reason for this correlation then GCs most probably formed in strongly fluctuating local tidal fields in the early proto-Milky Way potential, supporting the recent conclusion by Marks \& Kroupa., 16 pages, 12 figures, 1 tables, accepted for publication in MNRAS

Palomar 4 (Pal 4) is a low-density globular cluster (GC) with a current mass ≈30 000 M⊙ in the outer halo of the Milky Way with a two-body relaxation time of the order of a Hubble time. Yet, it is strongly mass segregated and contains a stellar mass function depleted of low-mass stars. Pal 4 was either born this way or it is a result of extraordinary dynamical evolution. Since two-body relaxation cannot explain these signatures alone, enhanced mass-loss through tidal shocking may have had a strong influence on Pal 4. Here, we compute a grid of direct N-body simulations to model Pal 4 on various eccentric orbits within the Milky Way potential to find likely initial conditions that reproduce its observed mass, half-light radius, stellar slope of the mass function and line-of-sight velocity dispersion. We find that Pal 4 is most likely orbiting on an eccentric orbit with an eccentricity of e ≈ 0.9 and pericentric distance of R ≈ 5 kpc. In this scenario, the required 3D half-mass radius at birth is similar to the average sizes of typical GCs (R ≈ 4-5 pc), while its birth mass is about M ≈ 10 M⊙. We also find a high degree of primordial mass segregation among the cluster stars, which seems to be necessary in every scenario we considered. Thus, using the tidal effect to constrain the perigalactic distance of the orbit of Pal 4, we predict that the proper motion of Pal 4 should be in the range −0.52 ≤ μ ≤ −0.38 mas yr and −0.30 ≤ μαcos ≤ − 0.15 mas yr

Outer-halo globular clusters show large half-light radii and flat stellar mass functions, depleted in low-mass stars. Using N-body simulations of globular clusters on eccentric orbits within a Milky Way-like potential, we show how a cluster's half-mass radius and its mass function develop over time. The slope of the central mass function flattens proportionally to the amount of mass a cluster has lost, and the half-mass radius grows to a size proportional to the average strength of the tidal field. The main driver of these processes is mass segregation of dark remnants. We conclude that the extended, depleted clusters observed in the Milky Way must have had small half-mass radii in the past, and that they expanded due to the weak tidal field they spend most of their lifetime in. Moreover, their mass functions must have been steeper in the past but flattened significantly as a cause of mass segregation and tidal mass loss., Comment: 2 pages, proceedings of IAU Symposium 316 Formation, Evolution, and Survival of Massive Star Clusters

We model the dynamics of Magellanic Stream with the ram-pressure scenario in the logarithmic and power-law galactic halo models and construct numerically the past orbital history of Magellanic clouds and Magellanic Stream. The parameters of models include the asymptotic rotation velocity of spiral arms, halo flattening, core radius and rising or falling parameter of rotation curve. We obtain the best fit parameters of galactic models through the maximum likelihood analysis, comparing the high resolution radial velocity data of HI in Magellanic Stream with that of theoretical models. The initial condition of the Magellanic Clouds is taken from the six different values reported in the literature. We find that oblate and nearly spherical shape halos provide a better fit to the observation than the prolate halos. This conclusion is almost independent of choosing the initial conditions and is valid for both logarithmic and power-law models., 17 pages, 6 figures, accepted in New Astronomy