On the mass function of stars growing in a flocculent medium

Stars form in regions of very inhomogeneous densities and may have chaotic orbital motions. This leads to a time variation of the accretion rate, which will spread the masses over some mass range. We investigate the mass distribution functions that arise from fluctuating accretion rates in non-linear accretion, $\dot{m} \propto m^{\alpha}$. The distribution functions evolve in time and develop a power law tail attached to a lognormal body, like in numerical simulations of star formation. Small fluctuations may be modelled by a Gaussian and develop a power-law tail $\propto m^{-\alpha}$ at the high-mass side for $\alpha > 1$ and at the low-mass side for $\alpha < 1$. Large fluctuations require that their distribution is strictly positive, for example, lognormal. For positive fluctuations the mass distribution function develops the power-law tail always at the high-mass hand side, independent of $\alpha$ larger or smaller than unity. Furthermore, we discuss Bondi-Hoyle accretion in a supersonically turbulent medium, the range of parameters for which non-linear stochastic growth could shape the stellar initial mass function, as well as the effects of a distribution of initial masses and growth times.Comment: 9 pages, 7 figures, MNRAS in pres

A new method to derive star formation histories of galaxies from their star cluster distributions

Star formation happens in a clustered way which is why the star cluster population of a particular galaxy is closely related to the star formation history of this galaxy. From the probabilistic nature of a mass function follows that the mass of the most-massive cluster of a complete population, M_max, has a distribution with the total mass of the population as a parameter. The total mass of the population is connected to the star formation rate (SFR) by the length of a formation epoch. Since due to evolutionary effects only massive star clusters are observable up to high ages it is convenient to use this M_max(SFR) relation for the reconstruction of a star formation history. The age-distribution of the most-massive clusters can therefore be used to constrain the star formation history of a galaxy. The method, including an assessment of the inherent uncertainties, is introduced with this contribution, while following papers will apply this method to a number of galaxies.Comment: MNRAS: in press, 10 pages, 9 figure

Star formation in galaxies and star clusters

This thesis is devoted to star formation from galaxy-scales (approx. 10 000 pc) to sub-star cluster-scales (approx. 0.1 pc). I develop and test a new method to derive star formation histories of Galaxies from their star cluster content, in particular the most massive star clusters. This is followed by an application of this method to the Large Magellanic Cloud, where the results of this new method are confirmed with results obtained from counting individual stars. Stars form in a grouped way, in the basic unit of a star cluster, so that both the mass function of stars formed within a star cluster and the mass function of star clusters in a galaxy need to be known for a quantitative description of galaxy-wide star formation. These mass functions have a power-law functional form, for which I develop statistical tools to estimate the parameters and to perform goodness-of-fit tests, with a particular emphasis on the upper mass end. The statistical methods are applied to the star clusters in M51 to investigate the shape of the initial star cluster mass function and the early evolution of it. I also investigate the upper mass end of the stellar initial mass function, both in observations and theory. The analysis of a numerical simulation of star cluster formation (time-evolution of substructure, mass segregation, stellar mass function) concludes this thesis.Diese Dissertation widmet sich der Entstehung von Sternen, von galaxienweiten Skalen (ca. 10 000 pc) bis zu Sub-Sternhaufen Skalen (ca. 0.1 pc). Ich entwickle und teste ein Verfahren zur Bestimmung der Sternentstehungsgeschichten von Galaxien aus deren Sternhaufenpopulation, insbesondere deren schwerste Sternhaufen. Es folgt die Anwendung dieser Methode auf die Große Magellansche Wolke, wo die Ergebnisse der neuen Methode bestätigt werden durch die Ergebnisse die man erhält vom Zählen einzelner Sterne. Sterne entstehen in Gruppen, in der Basisieinheit eines Sternhaufens, so daß sowohl die Massenfunktion von Sternen, die sich in einem Sternhaufen gebildet haben, als auch die Massenfunktion von Sternhaufen in einer Galaxie bestimmt werden müssen um galaxien-weite Sternentstehung quantitativ zu Beschreiben. Diese Massenfunktion folgen Potenzgesetzen, für welche ich statistische Methoden zur Parameterschätzung und Hypothesentests entwickle unter besonderer Berücksichtigung des oberen Massenbereichs. Die statistischen Methoden werden angewandt auf die Sternhaufen der Galaxie M51 um die Form der anfäglichen Haufenmassenfunktion und deren frühe Entwicklung zu untersuchen. Ich untersuche ebenfalls den oberen Massenbereich der stellaren Anfangsmassenfunktion, sowohl in Beobachtungen und in Theorie. Die Analyse einer numerischen Simulation der Entstehung eines Sternhaufens (Zeitentwicklung von Substruktur, Massensegregation und stellare Massenfunktion) beschließt diese Dissertation

Hubble-Lema\^itre fragmentation and the path to equilibrium of merger-driven cluster formation

This paper discusses a new method to generate self-coherent initial conditions for young substructured stellar cluster. The expansion of a uniform system allows stellar sub-structures (clumps) to grow from fragmentation modes by adiabatic cooling. We treat the system mass elements as stars, chosen according to a Salpeter mass function, and the time-evolution is performed with a collisional N-body integrator. This procedure allows to create a fully-coherent relation between the clumps' spatial distribution and the underlying velocity field. The cooling is driven by the gravitational field, as in a cosmological Hubble-Lema\^itre flow. The fragmented configuration has a `fractal'-like geometry but with a self-grown velocity field and mass profile. We compare the characteristics of the stellar population in clumps with that obtained from hydrodynamical simulations and find a remarkable correspondence between the two in terms of the stellar content and the degree of spatial mass-segregation. In the fragmented configuration, the IMF power index is ~0.3 lower in clumps in comparison to the field stellar population, in agreement with observations in the Milky Way. We follow in time the dynamical evolution of fully fragmented and sub-virial configurations, and find a soft collapse, leading rapidly to equilibrium (timescale of 1 Myr for a ~ 10^4 Msun system). The low-concentration equilibrium implies that the dynamical evolution including massive stars is less likely to induce direct collisions and the formation of exotic objects. Low-mass stars already ejected from merging clumps are depleted in the end-result stellar clusters, which harbour a top-heavy stellar mass function.Comment: 22 pages, accepted for publication in MNRA

The star formation history of the Large Magellanic Cloud as seen by star clusters and stars

The aim of this work is to test to what extent the star cluster population of a galaxy can be utilised to constrain or estimate the star formation history, with the Large Magellanic Cloud as our testbed. We follow two methods to extract information about the star formation rate from star clusters, either using only the most massive clusters (Maschberger & Kroupa 2007) or using the whole cluster population, albeit this is only possible for a shorter age span. We compare these results with the star formation history derived from colour-magnitude diagrams and find good overall agreement for the most recent approximately 1 Gyr. For later ages, and especially during the "cluster age gap", there is a deficiency of star clusters in relation to the star formation rate derived from the colour-magnitude diagram. The star formation rates following from the whole cluster population lie a factor of approximately 10 lower than the star formation rates deduced from the most massive clusters or from the colour-magnitude diagram, suggesting that only approximately 10 per cent of all stars form in long-lived bound star clusters.Comment: MNRAS, in press, 9 pages, 8 figure

A search for mass segregation of stars and brown dwarfs in \rho\ Ophiuchi

We apply two different algorithms to search for mass segregation to a recent observational census of the rho Ophiuchi star forming region. Firstly, we apply the Lambda_MSR method, which compares the minimum spanning tree (MST) of a chosen subset of stars to MSTs of random subsets of stars in the cluster, and determine the mass segregation ratio, Lambda_MSR. Secondly, we apply the m-Sigma method, which calculates the local stellar surface density around each star and determines the statistical significance of the average surface density for a chosen mass bin, compared to the average surface density in the whole cluster. Using both methods, we find no indication of mass segregation (normal or inverse) in the spatial distribution of stars and brown dwarfs in rho Ophiuchi. Although rho Ophiuchi suffers from high visual extinction, we show that a significant mass segregation signature would be detectable, albeit slightly diluted, despite dust obscuration of centrally located massive stars.Comment: 8 pages, 5 figures, accepted for publication in MNRA

The dynamical state of stellar structure in star-forming regions

The fraction of star formation that results in bound star clusters is influenced by the density spectrum in which stars are formed and by the response of the stellar structure to gas expulsion. We analyse hydrodynamical simulations of turbulent fragmentation in star-forming regions to assess the dynamical properties of the resulting population of stars and (sub)clusters. Stellar subclusters are identified using a minimum spanning tree algorithm. When considering only the gravitational potential of the stars and ignoring the gas, we find that the identified subclusters are close to virial equilibrium (the typical virial ratio Q_vir~0.59, where virial equilibrium would be Q_vir~0.5). This virial state is a consequence of the low gas fractions within the subclusters, caused by the accretion of gas onto the stars and the accretion-induced shrinkage of the subclusters. Because the subclusters are gas-poor, up to a length scale of 0.1-0.2 pc at the end of the simulation, they are only weakly affected by gas expulsion. The fraction of subclusters that reaches the high density required to evolve to a gas-poor state increases with the density of the star-forming region. We extend this argument to star cluster scales, and suggest that the absence of gas indicates that the early disruption of star clusters due to gas expulsion (infant mortality) plays a smaller role than anticipated, and is potentially restricted to star-forming regions with low ambient gas densities. We propose that in dense star-forming regions, the tidal shocking of young star clusters by the surrounding gas clouds could be responsible for the early disruption. This `cruel cradle effect' would work in addition to disruption by gas expulsion. We suggest possible methods to quantify the relative contributions of both mechanisms.Comment: 13 pages, 10 figures; Accepted for publication in MNRA

New insights into the star formation histories of candidate intermediate-age early-type galaxies from K'-band imaging of globular clusters

We investigate age and metallicity distributions of bright globular clusters (GCs) in the candidate intermediate-age early-type galaxies NGC 3610, NGC 584 and NGC 3377 using a combination of new Gemini/NIRI K'-band imaging and existing optical V,I photometry from HST data. The V-I vs I-K' colour-colour diagram is found to break the age-metallicity degeneracy present in optical colours, as I-K' primarily measures a populations' metallicity and is relatively insensitive, unlike optical spectroscopy, to the effect of hot horizontal branch (HB) stars, known to be present in massive old GCs. We derive GCs' photometric age, Z and masses. In general, metal-poor ([Z/H]<-0.7dex) GCs are older than more metal-rich GCs. For the most massive GCs (M>6x10^5 M_sol) in NGC 3610 with available spectroscopic data, photometric ages are older by ~2 Gyr, and this difference is more pronounced for the metal-poor GCs. However, photometric and spectroscopic metallicities are in good agreement. We suggest that this indicates the presence of a hot HB in these massive clusters, which renders spectroscopic ages from Balmer line strengths to be underestimated. To support this suggestion we show that all Galactic GCs with M>6x10^5 M_sol feature hot HBs, except 47 Tuc. Using the relation between the most massive GC mass and the galaxy's SFR, we find that the galaxies' peak SFR was attained at the epoch of the formation of the oldest (metal-poor) GCs. Age and [Z/H] distributions of the metal-rich GCs are broad, indicating prolonged galaxy star formation histories. The peak value of the age and [Z/H] distributions of the GCs correlates with host galaxy integrated age and [Z/H], showing that GCs can indeed be used as relevant proxies of the star formation histories of galaxies.(Abridged)Comment: Accepted by MNRAS; 18 pages, 12 figures, 6 tables (v2 added references