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We investigate the impact of primordial mass segregation on the formation and evolution of dark star clusters (DSCs). Considering a wide range of initial conditions, we conducted $N$-body simulations of globular clusters (GCs) around the Milky Way. In particular, we assume a canonical IMF for all GCs without natal kicks for supernovae remnants, namely neutron stars or black holes. Our results demonstrate that clusters with larger degrees of primordial mass segregation reach their DSC phase earlier and spend a larger fraction of their dissolution time in such a phase, compared to clusters without mass segregation. In primordially segregated clusters, the maximum Galactocentric distance that the clusters can have to enter the DSC phase is almost twice that of the clusters without primordial mass segregation. Primordially segregated clusters evolve with a higher number of stellar mass black holes, accelerating energy creation in their central regions and consequently increasing evaporation rates and cluster sizes during dark phases. The simulations reveal that aggregating heavy components at the centre doubles the time spent in the dark phase. Additionally, the study identifies potential links between simulated dark clusters and initial conditions of Milky Way globular clusters, suggesting some may transition to dark phases before dissolution. Higher primordial mass segregation coefficients amplify the average binary black hole formation rate by 2.5 times, raising higher expectations for gravitational wave emissions., Comment: 10 pages, 7 Figures, 1 Table, Accepted for publication in MNRAS

This is the second paper in a series, which studies the likelihood that some globular clusters (GCs) of the Milky Way (MW) could have originated from a dwarf satellite galaxy (DSG). Using a large suite of three-body simulations we determine the present-day orbital properties of 154 GCs that could have escaped from 41 MW DSGs over the past $8\,\mathrm{Gyrs}$. For the MW we considered two sets of static and dynamic models which account for the sustained growth of the MW since its birth. We focus on the Magellanic Clouds and Sagittarius. We compare the apogalactic distance, eccentricity, and orbital inclination of the MW GCs with those of runaway GCs from DSGs, to constrain their possible ex-situ origin. We observe a positive correlation between a DSG mass and the dispersion of its runaway GCs in the orbital parameter space of ($R_\mathrm{ap}$, $e$). We provide tables of the identified MW GCs and their likely associated progenitors. In total, we find 29 (19%) MW GCs which could be kinematically associated with MW DSGs. We report, for the first time, 6 and 10 new associations with the Large Magellanic Cloud and the Sagittarius, respectively. For the Sagittarius we predict a concentration of runaway GCs at large apogalactic distances of $R_\mathrm{ap}\approx275-375\,\mathrm{kpc}$, $e\approx0.8$, and a relative inclination of $\Delta\theta\approx20^{\circ}$. So far, there has not been any observed GCs with such orbital elements. Complemented with photometric and spectroscopic observations, and cosmological simulations, the findings from the present study could conclusively settle the debate over the in-situ vs. ex-situ origin of the MW GCs., Comment: 20 pages, 16 figures, 5 tables, references amended. Accepted for publication in MNRAS

Using 3D radiation-hydrodynamical simulations, we study the effects of ionising radiation on the formation of second-generation (SG) stars in Globular Clusters (GCs) with multiple stellar populations. In particular, we focus on massive ($10^7 \mathrm{M}_{\odot}$) and young (40-Myr old) GCs. We consider stellar winds from asymptotic giant branch (AGB) stars, ram pressure, gas accretion onto the cluster, and photoionisation feedback of binary stars. We find that the stellar luminosity is strong enough to warm and ionise the intracluster medium, but it does not lead to a significant gas expulsion. The cluster can thus retain the ejecta of AGB stars and the accreted pristine gas. In addition, efficient cooling occurs in the central region of the cluster within $50 \mathrm{Myr}$ from the formation of first generation stars, leading to the formation of SG stars. Our results indicate that the inclusion of photoionisation does not suppress SG formation, but rather delays it by about $\sim10 \mathrm{Myr}$. The time delay depends on the density of the pristine gas, so that a denser medium exhibits a shorter delay in star formation. Moreover, photoionisation leads to a modest decrease in the total SG mass, compared to a model without it., Comment: 13 pages, 8 figures, 2 table. Accepted for publication in MNRAS

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., Comment: 16 pages, 7 figures (including 1 in the appendix), 6 tables (including 2 in the appendix). 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

We introduce our new code MYOSOTIS (Make Your Own Synthetic ObservaTIonS) which is designed to produce synthetic observations from simulated clusters. The code can synthesise observations from both ground- and spaced-based observatories, for a range of different filters, observational conditions and angular/spectral resolution. In this paper, we highlight some of the features of MYOSOTIS, creating synthetic observations from young massive star clusters. Our model clusters are simulated using nbody6 code and have different total masses, half-mass radii, and binary fractions. The synthetic observations are made at the age of 2 Myr with Solar metallicity and under different extinction conditions. For each cluster, we create synthetic images of the Hubble Space Telescope (HST) in the visible (WFPC2/F555W) as well as Very Large Telescopes (VLT) in the nearIR (SPHERE/IRDIS/Ks). We show how MYOSOTIS can be used to look at mass function (MF) determinations. For this aim we re-estimate stellar masses using a photometric analysis on the synthetic images. The synthetic MF slopes are compared to their actual values. Our photometric analysis demonstrate that depending on the adopted filter, extinction, angular resolution and pixel sampling of the instruments, the power-law index of the underlying MFs can be shallower than the observed ones by at least 0.25 dex which is in agreement with the observed discrepancies reported in the literature, specially for young star clusters., Comment: 11 pages, 9 figures, Accepted to be published in MNRAS

Aims. To present the new novel statistical clustering tool 'INDICATE' which assesses and quantifies the degree of spatial clustering of each object in a dataset, discuss its applications as a tracer of morphological stellar features in star forming regions, and to look for these features in the Carina Nebula (NGC 3372). Results. We successfully recover known stellar structure of the Carina Nebula, including the 5 young star clusters in this region. Four sub-clusters contain no, or very few, stars with a degree of association above random which suggests they may be fluctuations in the field rather than real clusters. In addition we find: (1) Stars in the NW and SE regions have significantly different clustering tendencies, which is reflective of differences in the apparent star formation activity in these regions. Further study is required to ascertain the physical origin of the difference; (2) The different clustering properties between these two regions are even more pronounced for OB stars; (3) There are no signatures of classical mass segregation present in the SE region - massive stars here are not spatially concentrated together above random; (4) Stellar concentrations are more frequent around massive stars than typical for the general population, particularly in the Tr14 cluster; (5) There is a relation between the concentration of OB stars and the concentration of (lower mass) stars around OB stars in the centrally concentrated Tr14 and Tr15, but no such relation exists in Tr16. We conclude this is due to the highly sub-structured nature of Tr16. Conclusions. INDICATE is a powerful new tool employing a novel approach to quantify the clustering tendencies of individual objects in a dataset within a user-defined parameter space. As such it can be used in a wide array of data analysis applications., Comment: Accepted for publication in A&A; 15 pages, 10 figures, 3 appendices

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., Comment: 8 pages, 4 figures, 1 table. Accepted for publication in ApJ

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

Many of the scenarios proposed to explain the origin of chemically peculiar stars in globular clusters (GCs) require significant mass-loss ($\ge95\%$) to explain the observed fraction of such stars. In the GCs of the Fornax dwarf galaxy significant mass-loss could be a problem. Larsen et al. (2012) showed that there is a large ratio of GCs to metal-poor field stars in Fornax and about $20-25\%$ of all the stars with ${\rm [Fe/H]}<-2$ belong to the four metal-poor GCs. This imposes an upper limit of $\sim80\%$ mass-loss that could have happened in Fornax GCs. In this paper, we propose a solution to this problem by suggesting that stars can leave the Fornax galaxy. We use a series of $N$-body simulations, to determine the limit of mass-loss from Fornax as a function of the initial orbital radii of GCs and the speed with which stars leave Fornax GCs. We consider a set of cored and cuspy density profiles for Fornax. Our results show that with a cuspy model for Fornax, the fraction of stars which leave the galaxy, can be as high as $\sim90\%$, when the initial orbital radii of GCs are $R=2-3\,\rm{kpc}$ and the initial speed of stars is $v>20\,\rm{km\,s^{-1}}$. We show that such large velocities can be achieved by gas expulsion induced mass-loss but not stellar evolution induced mass-loss. Our results imply that one cannot interpret the metallicity distribution of Fornax field stars as evidence against significant mass-loss in Fornax GCs, if mass-loss is due to gas expulsion., Comment: 9 pages, 7 figures, 1 table, typos corrected. Accepted for publication in MNRAS

We have carried out a large grid of N-body simulations in order to investigate if mass-loss as a result of primordial gas expulsion can be responsible for the large fraction of second generation stars in globular clusters (GCs) with multiple stellar populations (MSPs). Our clusters start with two stellar populations in which $10\%$ of all stars are second generation stars. We simulate clusters with different initial masses, different ratios of the half-mass radius of first to second generation stars, different primordial gas fractions and Galactic tidal fields with varying strength. We then let our clusters undergo primordial gas-loss and obtain their final properties such as mass, half-mass radius and the fraction of second generation stars. Using our N-body grid we then perform a Monte Carlo analysis to constrain the initial masses, radii and required gas expulsion time-scales of GCs with MSPs. Our results can explain the present-day properties of GCs only if (1) a substantial amount of gas was present in the clusters after the formation of second generation stars and (2) gas expulsion time-scales were extremely short ($\lesssim 10^5$ yr). Such short gas expulsion time-scales are in agreement with recent predictions that dark remnants have ejected the primordial gas from globular clusters, and pose a potential problem for the AGB scenario. In addition, our results predict a strong anti-correlation between the number ratio of second-generation stars in GCs and the present-day mass of GCs. So far, the observational data show only a significantly weaker anti-correlation, if any at all., Comment: 14 pages, 6 figures, 3 tables, typos corrected. Accepted for publication in MNRAS

We have determined possible cluster members of the nearby open cluster Praesepe (M44) based on J and K photometry and proper motions from the PPMXL catalogue and z photometry from the Sloan Digital Sky Survey (SDSS). In total we identified 893 possible cluster members down to a magnitude of J = 15.5 mag, corresponding to a mass of about 0.15 Msun for an assumed cluster distance modulus of (m-M)_0 = 6.30 mag (d ~ 182 pc), within a radius of 3.5{\deg} around the cluster centre. We derive a new cluster centre for Praesepe ({\alpha}_centre = 8h 39m 37s, {\delta}_centre = 19{\deg} 35' 02"). We also derive a total cluster mass of about 630 Msun and a 2D half-number and half-mass radius of 4.25 pc and 3.90 pc respectively. The global mass function (MF) of the cluster members shows evidence for a turnover around m = 0.65 Msun. While more massive stars can be fit by a power-law {\xi}(m) ~ m^(-{\alpha}) with slope {\alpha} = 2.88 +/- 0.22, stars less massive than m = 0.65 Msun are best fitted with {\alpha} = 0.85 +/- 0.10. In agreement with its large dynamical age, we find that Praesepe is strongly mass segregated and that the mass function slope for high mass stars steepens from a value of {\alpha} = 2.32 +/- 0.24 inside the half-mass radius to {\alpha} = 4.90 +/- 0.51 outside the half-mass radius. We finally identify a significant population of binaries and triples in the colour-magnitude diagram of Praesepe. Assuming non-random pairing of the binary components, a binary fraction of about 35% for primaries in the mass range 0.6 < m/Msun < 2.20 is required to explain the observed number of binaries in the colour-magnitude diagram (CMD)., Comment: 11 pages, 10 figures. Accepted for publication in MNRAS