Michael Marks

The stellar and sub-stellar IMF of simple and composite populations

The current knowledge on the stellar IMF is documented. It appears to become top-heavy when the star-formation rate density surpasses about 0.1Msun/(yr pc^3) on a pc scale and it may become increasingly bottom-heavy with increasing metallicity and in increasingly massive early-type galaxies. It declines quite steeply below about 0.07Msun with brown dwarfs (BDs) and very low mass stars having their own IMF. The most massive star of mass mmax formed in an embedded cluster with stellar mass Mecl correlates strongly with Mecl being a result of gravitation-driven but resource-limited growth and fragmentation induced starvation. There is no convincing evidence whatsoever that massive stars do form in isolation. Various methods of discretising a stellar population are introduced: optimal sampling leads to a mass distribution that perfectly represents the exact form of the desired IMF and the mmax-to-Mecl relation, while random sampling results in statistical variations of the shape of the IMF. The observed mmax-to-Mecl correlation and the small spread of IMF power-law indices together suggest that optimally sampling the IMF may be the more realistic description of star formation than random sampling from a universal IMF with a constant upper mass limit. Composite populations on galaxy scales, which are formed from many pc scale star formation events, need to be described by the integrated galactic IMF. This IGIMF varies systematically from top-light to top-heavy in dependence of galaxy type and star formation rate, with dramatic implications for theories of galaxy formation and evolution.

Inverse dynamical population synthesis - Constraining the initial conditions of young stellar clusters by studying their binary populations

Binary populations in young star clusters show multiplicit y fractions both lower and up to twice as high as those observed in the Galactic field. We follow the evolution of a population of bin ary stars in dense and loose star clusters starting with an in variant initial binary population and a formal multiplicity fracti on of unity, and demonstrate that these models can explain the observed binary properties in Taurus, ρ Ophiuchus, Chamaeleon, Orion, IC 348, Upper Scorpius A, Praesepe, and the Pleiades. The model needs to consider solely different birth densities for these regions. The evolved theore tical orbital-parameter distributions are highly probable parent distributions for the observed ones. We con strain the birth conditions (stellar mass, Mecl, and half-mass radius, rh) for the derived progenitors of the star clusters and the over all present-day binary fractions allowed by the present model. The results compare very well with properties of molecular cloud clumps on the verge of star formation. Combining these with previously and independently obtained constraints on the birth densities of globular clusters, we identify a weak stellar mass ‐ half- mass radius correlation for cluster-forming cloud clumps, rh/pc∝ (Mecl/M⊙) 0.13±0.04 . The ability of the model to reproduce the binary properties in all the investigated young objects, covering present-da y densities from 1− 10 stars pc −3 (Taurus) to 2× 10 4 stars pc −3 (Orion), suggests that environment-dependent dynamical evolution plays an important role in shaping the present-day properti es of binary populations in star clusters, and that the initial binary pr operties may not vary dramatically between different environments.

Evidence for top-heavy stellar initial mass functions with increasing density and decreasing metallicity

ABSTRACT Residual-gas expulsion after cluster formation has recently been shown to leave animprint in the low-mass present-day stellar mass function (PDMF) which allowedthe estimation of birth conditions of some Galactic globular clusters (GCs) such asmass, radius and star formation efficiency. We show that in order to explain theircharacteristics (masses, radii, metallicity, PDMF) their stellar initial mass function(IMF) must have been top-heavy. It is found that the IMF is required to becomemore top-heavy the lower the cluster metallicity and the larger the pre-GC cloud-core density are. The deduced trends are in qualitative agreement with theoreticalexpectation. The results are consistent with estimates of the shape of the high-massend of the IMF in the Arches cluster, Westerlund 1, R136 and NGC 3603, as wellas with the IMF independently constrained for ultra-compact dwarf galaxies (UCDs).The latter suggests that GCs and UCDs might have formed along the same channel orthat UCDs formed via mergers of GCs. A fundamental plane is found which describesthe variation of the IMF with density and metallicity of the pre-GC cloud-cores. Theimplications for the evolution of galaxies and chemical enrichment over cosmologicaltimes are expected to be major.Keywords: stars: formation – stars: mass-function – stars: early-type – stars: late-type – globular clusters: general

An analytical description of the evolution of binary orbital‐parameter distributions in N‐body computations of star clusters

A new method is presented to describe the evolution of the orbital-parameter distributions for an initially universal binary population in star clusters by means of the currently largest existing library of N-body models. It is demonstrated that a stellar-dynamical operator, M ecl,rh dyn (t), exists, which uniquely transforms an initial (t = 0) orbital parameter distribution function for binaries, Din, into a new distribution, D M ecl,rh (t), depending on the initial cluster mass, Mecl, and half-mass radius, rh, after some time t of dynamical evolution. For Din the distribution functions derived by Kroupa (1995a,b) are used, which are consistent with constraints for pre-main sequence and Class I binary populations. Binaries with a lower energy and a higher reduced-mass are dissolved preferentially. The -operator can be used to efficiently calculate and predict binary properties in clusters and whole galaxies without the need for further N-body computations. For the present set of N-body models it is found that the binary populations change their properties on a crossing time-scale such that M ecl,rh dyn (t) can be well parametrized as a function of the cluster density, ρecl. Furthermore it is shown that the binary-fraction in clusters with similar initial velocity dispersions follows the same evolutionary tracks as a function of the passed number of relaxation-times. Present-day observed binary populations in star clusters put constraints on their initial stellar densities, ρecl, which are found to be in the range 10 2 . ρecl(6 rh)/M⊙ pc −3 . 2 × 10 5 for open clusters and a few×10 3 . ρecl(6 rh)/M⊙ pc −3 . 10 8 for globular clusters, respectively.

The influence of gas expulsion and initial mass segregation on the stellar mass function of globular star clusters

Recently, De Marchi, Paresce & Pulone studied a sample of 20 globular clusters and found that all clusters with high concentrations have steep stellar mass functions while clusters with low concentration have comparatively shallow mass functions. No globular clusters were found with a flat mass function and high concentration. This seems curious since more concentrated star clusters are believed to be dynamically more evolved and should have lost more low-mass stars via evaporation, which would result in a shallower mass function in the low-mass part.

The state of globular clusters at birth II: primordial binaries

In this paper, we constrain the properties of primordial binary populations in Galactic globular clusters. Using the MOCCA Monte Carlo code for cluster evolution, our simulations cover three decades in present-day total cluster mass. Our results are compared to the observations of Milone et al. (2012) using the photometric binary populations as proxies for the true underlying distributions, in order to test the hypothesis that the data are consistent with an universal initial binary fraction near unity and the binary orbital parameter distributions of Kroupa (1995). With the exception of a few possible outliers, we find that the data are to first-order consistent with the universality hypothesis. Specifically, the present-day binary fractions inside the half-mass radius can be reproduced assuming either high initial binary fractions near unity with a dominant soft binary component as in the Kroupa distribution combined with high initial densities (10 4 -10 6 M⊙ pc −3 ), or low initial binary fractions (� 5-10%) with a dominant hard binary component combined with moderate initial densities near their present-day values (10 2 -10 3 M⊙ pc −3 ). This apparent degeneracy can potentially be broken using the binary fractions outside the half-mass radius only high initial binary fractions with a significant soft component combined with high initial densities can contribute to reproducing the observed anti-correlation between the binary fractions outside the half-mass radius and the total cluster mass. We further illustrate using the simulated present-day binary orbital parameter distributions and the technique first introduced in Leigh et al. (2012) that the relative fractions of hard and soft binaries can be used to further constrain both the initial cluster density and the initial mass-density relation. Our results favour an initial mass-density relation of

CHARACTERIZING THE BROWN DWARF FORMATION CHANNELS FROM THE INITIAL MASS FUNCTION AND BINARY-STAR DYNAMICS

The stellar initial mass function (IMF) is a key property of stellar populations. There is growing evidence that the classical star-formation mechanism by the direct cloud fragmentation process has difficulties reproducing the observed abundance and binary properties of brown dwarfs and very-low-mass stars. In particular, recent analytical derivations of the stellar IMF exhibit a deficit of brown dwarfs compared to observational data. Here we derive the residual mass function of brown dwarfs as an empirical measure of the brown dwarf deficiency in recent star-formation models with respect to observations and show that it is compatible with the substellar part of the Thies-Kroupa IMF and the mass function obtained by numerical simulations. We conclude that the existing models may be further improved by including a substellar correction term that accounts for additional formation channels like disk or filament fragmentation. The term peripheral fragmentation is introduced here for such additional formation channels. In addition, we present an updated analytical model of stellar and substellar binarity. The resulting binary fraction and the dynamically evolved companion mass-ratio distribution are in good agreement with observational data on stellar and very-low-mass binaries in the Galactic field, in clusters, and in dynamically unprocessed groups of stars if all stars form as binaries with stellar companions. Cautionary notes are given on the proper analysis of mass functions and the companion mass-ratio distribution and the interpretation of the results. The existence of accretion disks around young brown dwarfs does not imply that these form just like stars in direct fragmentation.

Revisiting the universality of (multiple) star formation in present-day star formation regions

Populations of multiple stars inside clustered regions are known to change through dynamical interactions. The efficiency of binary disruption is thought to be determined by stellar density. King and collaborators recently investigated the multiplicity properties in young star forming regions and in the Galactic field. They concluded that stellar density-dependent modification of a universal initial binary population (the standard or null hypothesis model) cannot explain the observations. We re-visit their results, analyzing the data within the framework of different model assumptions, namely non-universality without dynamical modification and universality with dynamics. We illustrate that the standard model does account for all known populations if regions were significantly denser in the past. Some of the effects of using present-day cluster properties as proxies for their past values are emphasized and that the degeneracy between age and density of a star forming region can not be omitted when interpreting multiplicity data. A new analysis of the Corona Australis region is performed within the standard model. It is found that this region is likely as unevolved as Taurus and an initial density of

M-dwarf binaries as tracers of star and brown dwarf formation

\approx190M_{\odot}\;pc^{-3}

Monte Carlo modeling of globular star clusters: many primordial binaries and IMBH formation

is required to produce the presently observed binary population, which is close to its present-day density.