1. Sami Dib NBI, STARPLAN Unveiling the diversity of the MW stellar clusters + Sacha Hony (ITA/Heidelberg) Stefan Schmeja (ARI/ Heidelberg) Dimitrios Gouliermis (ITA/Heidelberg) Åke Nordlund (NBI, STARPLAN)

2. The multi- exponent power law: Kroupa 2002 The lognormal distribution+power law: Chabrier 2003, 2005 The TPL IMF: de Marchi & Parecse 2002; Parravano et al. 2010 The Galactic field IMF Maschberger (2013): L 3 function (low mass + high mass power laws) Basu et al. (2015): MLP (modified lognormal+ power law)

3. Luhman & Rieke 1999; Luhman 2000, ++ rho-Ophiucus Taurus The IMF of young clusters

4. comparing the slope at the intermediate-to-high mass end Massey et al. 1995a,b Massey 2003 The IMF of Open Stellar Clusters Sharma et al. 2008

5. Figer 1999; Stolte et al. 2005, Kim et al. 2006 Espinoza et al. 2010, Habibi et al. 2014 The IMF of Starburst clusters: Arches, NGC 3603: shallower than Salpeter Stolte et al. 2006

6. Characterizing The IMF of stellar clusters with Bayesian statistics Avoids:  The effects of the bin size  Making subjective choices about break points Allows for:  Including the effects of individual uncertainties on masses  Effects of completness  Use of prior information

7. Test on synthetic data Likelihood: TPL Flat prior functions on the parameters (in linear space) MCMC

8. Application to young clusters: TPL Likelihood Dib 2014

9. Application to young Galactic Stellar Clusters Case of “Chabrier”-like likelihood function Dib 2014 No overlap in the parameters at the 1σ confidence limit

10. Effect of completeness & mass uncertainties: ONC Dib 2014

11. The statistics of massive stars in young clusters The MWSC (Kharchenko et al. 2012,13, Schmeja et al. 2014, Schmeja, Dib et al. 2015) Based on 2MASS + PPXML data; 3145 clusters within < 2 kpc; complete to ~ 1.8 kpc from the Sun Extract statictics from the MWSC catalogue that can be contrasted with large sample of synthetic clusters  extract order zero statistics i.e, scalars  order 1: distributions of specific quantities  Order 2: relations between 2 quantities

12. Some statistics (among others)  The fraction of “lonely” O stars of masses and no massive B stars (between 10 and 15 Msol)

13. Construct a statistical sample of clusters Model chart Define how much mass is present in clusters that contains stars with M > M O,lim Define cluster mass function (slope, mininum & maximum cluster Masses) And distribute over this distribution For each cluster of mass  Define the distributions of the IMF parameters From which they are draw for each cluster. Sample the masses of stars: i.e., the IMF with the chosen set of parameter for each cluster  assign an age to each cluster For each O system of mass in each cluster:  Define a binarity probability  For binary system, define a mass ratio  Correct for stellar evolution Correct for CLMF completeness Measure the fractions & other statistics

14. Sampling the IMF parameters Which distributions of the IMF parameters allow us to match the statistics from the MWSC ?

15. How does the sample look like ? ICLMF, CLMF, CLMF-lonOSystem IMFs

16. Comparing the statistical sample to the MWSC Sampling the IMF parameters no M max -M cl relation. IMF sampled between 0.02 and 150 Msol Reproducing the observations is only compatible with the IMF parameters having

17. Dependence onthe sampling parameters Effect of the CLMF exponent. Best match for Effect of the choice of M cl,min Best match for M cl,min =50 Msol

18. with a M *,max -M cl relation (Weidner& Kroupa 2013)

19. Summary (1)The IMF of Galactic clusters is not universal !..given the data (2) Better not describe the IMF by a set of 3 (or more) parameters, but by distribution functions of the parameters that may vary from galaxy to galaxy (3) The cluster mass function has a slope of -2 (4) Minimum mass cutoff of ~50 M sol in young cluster masses required (or a turnover) (5) M max -M cl relation incompatible with the matching of statisticals models and the MWSC data ------------------------- Implications/suggestions: In local simulations: aim should be to recover distributions of IMF parameters rather than single values In global simulations: implement distributions of the IMF rather than single values

20. Variations of CMF and IMF Effect of accretion on cores

21. Dib et al. 2010 Data points: Orion A+B cloud Johnstone & Bally 2006

22. Dib et al. 2010 In low-mass clusters: no tail at high stellar masses

23. Application to the Orion Cloud and the ONC Dib et al. (2010)

24. Dib et al. 2010 Variations with the cores properties: making a Taurus cluster Effect of varying the lifetimes of the cores+stopping effect of feedback

25.  =0.4  =1.8 Slope= -3/(4-  )-1=-2.33 calculate instanteneous cross section of collision between contracting objects of Masses M i and M j and integrate over the mass spectrum. Initial conditions from turbulent fragmentation (Padoan & Nordlund 2002) Variation of the IMF Effects of core coalescence Dib et al. 2007

26. Core coalescence: application to Starburst Clusters Dib et al. 2007 time