A Possible Solution for the M/L−[Fe/H]M/L-\mathrm{[Fe/H]} Relation of Globular Clusters in M31. II. the Age-Metallicity Relation

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 Ap

Evolution of star clusters on eccentric orbits: semi-analytical approach

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 MNRA

Identifying the possible ex-situ origin of the globular clusters of the Milky Way: A kinematic study

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 MNRA