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 M for an assumed cluster distance modulus of (m − M ) 0 = 6.30 mag (d ≈ 182 pc), within a radius of 3.5 • around the cluster centre. We derive a new cluster centre for Praesepe (α centre = 8 h 39 m 37 s , δ centre = 19 • 35 02 ). We also derive a total cluster mass of about 630 M 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 M . While more massive stars can be fit by a power-law ξ(m) ∼ m −α with slope α = 2.88 ± 0.22, stars less massive than m = 0.65 M are best fitted with α = 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 α = 2.32 ± 0.24 inside the half-mass radius to α = 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/M < 2.20 is required to explain the observed number of binaries in the colour-magnitude diagram (CMD).

Context. There are a number of methods that identify stellar sub-structure in star forming regions, but these do not quantify the degree of association of individual stars – something which is required if we are to better understand the mechanisms and physical processes that dictate structure. Aims. We 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). Methods. We employ a nearest neighbour approach to quantitatively compare the spatial distribution in the local neighbourhood of an object with that expected in an evenly spaced uniform (i.e. definitively non-clustered) field. Each object is assigned a clustering index (“I”) value, which is a quantitative measure of its clustering tendency. We have calibrated our tool against random distributions to aid interpretation and identification of significant I values. Results. Using INDICATE we successfully recover known stellar structure of the Carina Nebula, including the young Trumpler 14-16, Treasure Chest and Bochum 11 clusters. Four sub-clusters contain no, or very few, stars with a degree of association above random which suggests these sub-clusters 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 the NW and SE regions are also seen for OB stars and are even more pronounced; (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. In this paper we have discussed and demonstrated its application to trace morphological features of young massive clusters.

We have carried out a large grid of N -body simulations in order to investigate if massloss 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 ( 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.

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