COCOA Code for Creating Mock Observations of Star Cluster Models

We introduce and present results from the COCOA (Cluster simulatiOn Comparison with ObservAtions) code that has been developed to create idealized mock photometric observations using results from numerical simulations of star cluster evolution. COCOA is able to present the output of realistic numerical simulations of star clusters carried out using Monte Carlo or \textit{N}-body codes in a way that is useful for direct comparison with photometric observations. In this paper, we describe the COCOA code and demonstrate its different applications by utilizing globular cluster (GC) models simulated with the MOCCA (MOnte Carlo Cluster simulAtor) code. COCOA is used to synthetically observe these different GC models with optical telescopes, perform PSF photometry and subsequently produce observed colour magnitude diagrams. We also use COCOA to compare the results from synthetic observations of a cluster model that has the same age and metallicity as the Galactic GC NGC 2808 with observations of the same cluster carried out with a 2.2 meter optical telescope. We find that COCOA can effectively simulate realistic observations and recover photometric data. COCOA has numerous scientific applications that maybe be helpful for both theoreticians and observers that work on star clusters. Plans for further improving and developing the code are also discussed in this paper.Comment: 18 pages, 12 figures, accepted for publication in MNRAS. Revised manuscript has a new title, better quality figures and many other improvements. COCOA can be downloaded from: https://github.com/abs2k12/COCOA (comments are welcome

The Horizontal Branch in the UV Colour Magnitude Diagrams. II. The case of M3, M13 and M79

We present a detailed comparison between far-UV/optical colour Magnitude Diagrams obtained with high-resolution Hubble Space Telescope data and suitable theoretical models for three Galactic Globular Clusters: M3, M13 and M79. These systems represents a classical example of clusters in the intermediate metallicity regime that, even sharing similar metal content and age, show remarkably different Horizontal Branch morphologies. As a consequence, the observed differences in the colour distributions of Horizontal Branch stars cannot be interpreted in terms of either first (metallicity) or a second parameter such as age. We investigate here the possible role of variations of initial Helium abundance (Y). Thanks to the use of a proper setup of far-UV filters, we are able to put strong constraints on the maximum Y (Y_{max}) values compatible with the data. We find differences Delta Y_{max} ~ 0.02-0.04 between the clusters with M13 showing the largest value (Y_{max} ~ 0.30) and M3 the smallest (Y_{max} ~ 0.27). In general we observe that these values are correlated with the colour extensions of their Horizontal Branches and with the range of the observed Na-O anti-correlations.Comment: Accepted for publication by MNRAS. 15 pages, 15 figures, 1 tabl

Spatial mixing of binary stars in multiple-population globular clusters

We present the results of a study aimed at investigating the effects of dynamical evolution on the spatial distribution and mixing of primordial binary stars in multiple-population globular clusters. Multiple stellar population formation models predict that second-generation (SG) stars form segregated in the inner regions of a more extended first-generation (FG) cluster. Our study, based on the results of a survey of N-body simulations, shows that the spatial mixing process for binary stars is more complex than that of single stars since additional processes such as binary ionization, recoil and ejection following binary-single and binary-binary interactions play a key role in determining the spatial distribution of the population of surviving binaries. The efficiency and relative importance of these additional effects depends on the binary binding energy and determines the timescale of the spatial mixing of FG and SG binaries. Our simulations illustrate the role of ionization, recoil and ejection combined with the effects of mass segregation driven by two-body relaxation and show that the complex interplay of all these processes results in a significant extension of the time needed for the complete spatial mixing of FG and SG binaries compared to that of single stars. Clusters in which FG and SG single stars have already reached complete spatial mixing might be characterized by a significant radial gradient in the ratio of the FG-to-SG binary fraction. The implications of the delayed mixing of FG and SG binaries for the differences between the kinematics of the two populations are discussed.Comment: 8 pages, 7 figures, 1 table; accepted for publication in MNRA

The dynamical state of the globular clusters Rup 106 and IC 4499

The dynamical evolution of globular clusters is theoretically described by a series of well known events typical of N-body systems. Still, the identification of observational signatures able to empirically describe the stage of dynamical evolution of a stellar system of the density typical of a globular cluster, represents a challenge. In this paper we study the dynamical age of the globular clusters Rup 106 and IC 4499. To this aim, we study the radial distribution of the Blue Straggler Stars via the A+ parameter and of the slope of the Main Sequence Mass Function. Both tracers show that Rup 106 and IC 4499 are dynamically young clusters where dynamical friction has just started to segregate massive stars towards the clusters' centre. In fact, we observe that the Blue Straggler stars are more centrally concentrated in both clusters than the reference population. On the same line, we find that in both cases the slope of the mass function significantly decreases as a function of the cluster-centric distances. This result provides additional support for the use of the the radial distribution of the blue stragglers as a powerful observationally convenient indicator of the cluster dynamical age.Comment: Accepted for publication on A&

Deep multi-telescope photometry of NGC 5466. II. The radial behaviour of the mass function slope

We use a combination of data acquired with the Advanced Camera for Survey (ACS) on board the Hubble Space Telescope and the Large Binocular Camera (LBC-blue) mounted on the Large Binocular Telescope, to sample the main sequence stars of the globular cluster NGC~5466 in the mass range $0.3<M/M_\odot<0.8$. We derive the cluster's Luminosity Function in several radial regions, from the center of the cluster out to the tidal radius. After corrections for incompleteness and field-contamination, this has been compared to theoretical Luminosity Functions, obtained by multiplying a simple power law Mass Function in the form dN/dm$\propto m^{\alpha}$ by the derivative of the mass-luminosity relationship of the best-fit isochrone. We find that $\alpha$ varies from -0.6 in the core region to -1.9 in the outer region. This fact allows us to observationally prove that the stars in NGC 5466 have experienced the effects of mass segregation. We compare the radial variation of $\alpha$ from the center out to 5 core radii (r$_c$) in NGC 5466 and the globular cluster M10, finding that the gradient of $\alpha$ in the first 5r$_c$ is more than a factor of 2 shallower in NGC 5466 than in M10, in line with the differences in the clusters' relaxation timescales. NGC 5466 is dynamically younger than M10, with two-body relaxation processes only recently starting to shape the distribution of main sequence stars. This result fully agrees with the conclusion obtained in our previous works on the radial distribution of Blue Straggler Stars, further confirming that this can be used as an efficient clock to measure the dynamical age of stellar systems.Comment: Accepted for publications on Ap

Modelling the Observed Stellar Mass Function and its Radial Variation in Galactic Globular Clusters

We measure how the slope $\alpha$ of the stellar mass function (MF) changes as a function of clustercentric distance $r$ in five Galactic globular clusters and compare $\alpha(r)$ to predictions from direct $N$-body star cluster simulations. Theoretical studies predict that $\alpha(r)$ (which traces the degree of mass segregation in a cluster) should steepen with time as a cluster undergoes two-body relaxation and that the amount by which the global MF can evolve from its initial state due to stellar escape is directly linked to $\alpha(r)$. We find that the amount of mass segregation in M10, NGC 6218, and NGC 6981 is consistent with their dynamical ages, but only the global MF of M10 is consistent with its degree of mass segregation as well. NGC 5466 and NGC 6101 on the other hand appear to be less segregated than their dynamical ages would indicate. Furthermore, despite the fact that the escape rate of stars in non-segregated clusters is independent of stellar mass, both NGC 5466 and NGC 6101 have near-flat MFs. We discuss various mechanisms which could produce non-segregated clusters with near-flat MFs, including higher mass-loss rates and black hole retention, but argue that for some clusters (NGC 5466 and NGC 6101) explaining the present-day properties might require either a non-universal IMF or a much more complex dynamical history.Comment: 12 pages, 9 figures, Accepted for publication in MNRA