Early star formation and the evolution of the stellar initial mass function in galaxies

It has frequently been suggested in the literature that the stellar IMF in galaxies was top-heavy at early times. This would be plausible physically if the IMF depended on a mass-scale such as the Jeans mass that was higher at earlier times because of the generally higher temperatures that were present then. In this paper it is suggested, on the basis of current evidence and theory, that the IMF has a universal Salpeter-like form at the upper end, but flattens below a characteristic stellar mass that may vary with time. Much of the evidence that has been attributed to a top-heavy early IMF, including the ubiquitous G-dwarf problem, the high abundance of heavy elements in clusters of galaxies, and the high rate of formation of massive stars in high-redshift galaxies, can be accounted for with such an IMF if the characteristic stellar mass was several times higher during the early stages of galaxy evolution. However, significant variations in the mass-to-light ratios of galaxies and large amounts of dark matter in stellar remnants are not as easily explained in this way, because they require more extreme and less plausible assumptions about the form and variability of the IMF. Metal-free 'population III' stars are predicted to have an IMF that consists exclusively of massive stars, and they could help to account for some of the evidence that has been attributed to a top-heavy early IMF, as well as contributing importantly to the energetics and chemical enrichment of the early Universe.     

Gas removal and the initial mass function of star clusters

We explore how the expulsion of gas from star-forming cores due to supernova explosions affects the shape of the initial cluster mass function, that is, the mass function of star clusters when cluster infant weight-loss triggered by gas expulsion is over. We demonstrate that if the radii of cluster-forming gas ‘cores’ are roughly constant over the core mass range, as supported by observations, then more massive cores undergo slower gas expulsion. Therefore, for a given star-formation efficiency, more massive cores retain a larger fraction of stars after gas expulsion. The initial cluster mass function may thus substantially differ from the core mass function, with the final shape depending on the star-formation efficiency. A mass-independent star-formation efficiency of about 20% turns a power-law core mass function into a bell-shaped initial cluster mass function, while mass-independent efficiencies of order 40% preserve the shape of the core mass function.     

On the universality of initial mass function of open star clusters

Die photometrische Untersuchung einer Reihe offener Sternhaufen mit einem Alter von weniger als 10⁹ Jahren bestätigt die Hypothese über die Einheitlichkeit der Nullalter-Leuchtkraftfunktion von offenen Sternhaufen.     

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.
We show that this effect can be explained by residual-gas expulsion from initially mass segregated star clusters, and is enhanced further through unresolved binaries. If gas expulsion is the correct mechanism to produce the observed trend in the   c –α  -plane, then observation of these parameters would allow to constrain cluster starting conditions such as star formation efficiency and the time-scale of gas expulsion.     

The early evolution of the star cluster mass function

Several recent studies have shown that the star cluster initial mass function (CIMF) can be well approximated by a power law, with indications for a steepening or truncation at high masses. This contribution considers the evolution of such a mass function due to cluster disruption, with emphasis on the part of the mass function that is observable in the first ∼1 Gyr. A Schechter type function is used for the CIMF, with a power-law index of −2 at low masses and an exponential truncation at M _*. Cluster disruption due to the tidal field of the host galaxy and encounters with giant molecular clouds flattens the low-mass end of the mass function, but there is always a part of the 'evolved Schechter function' that can be approximated by a power law with index −2. The mass range for which this holds depends on age, τ, and shifts to higher masses roughly as  τ^0.6  . Mean cluster masses derived from luminosity-limited samples increase with age very similarly due to the evolutionary fading of clusters. Empirical mass functions are, therefore, approximately power laws with index −2, or slightly steeper, at all ages. The results are illustrated by an application to the star cluster population of the interacting galaxy M51, which can be well described by a model with   M _*= (1.9 ± 0.5) × 10⁵ M_⊙  and a short (mass-dependent) disruption time destroying M _* clusters in roughly a Gyr.     

The influence of multiple stars on the high-mass stellar initial mass function and age dating of young massive star clusters

The study of young stellar populations has revealed that most stars are in binary or higher order multiple systems. In this study, the influence on the stellar initial mass function (IMF) of large quantities of unresolved multiple massive stars is investigated by taking into account the stellar evolution and photometrically determined system masses. The models, where initial masses are derived from the luminosity and colour of unresolved multiple systems, show that even under extreme circumstances (100 per cent binaries or higher order multiples), the difference between the power-law index of the mass function (MF) of all stars and the observed MF is small (≲0.1). Thus, if the observed IMF has the Salpeter index  α= 2.35  , then the true stellar IMF has an index not flatter than  α= 2.25  . Additionally, unresolved multiple systems may hide between 15 and 60 per cent of the underlying true mass of a star cluster. While already a known result, it is important to point out that the presence of a large number of unresolved binaries amongst pre-main-sequence stars induces a significant spread in the measured ages of these stars even if there is none. Also, lower mass stars in a single-age binary-rich cluster appear older than the massive stars by about 0.6 Myr.     

The dependence of star formation on initial conditions and molecular cloud structure

We investigate the dependence of stellar properties on the initial kinematic structure of the gas in star-forming molecular clouds. We compare the results from two large-scale hydrodynamical simulations of star cluster formation that resolve the fragmentation process down to the opacity limit, the first of which was reported by Bate, Bonnell & Bromm. The initial conditions of the two calculations are identical, but in the new simulation the power spectrum of the velocity field imposed on the cloud initially and allowed to decay is biased in favour of large-scale motions. Whereas the calculation of Bate et al. began with a power spectrum   P ( k ) ∝ k ⁻⁴  to match the Larson scaling relations for the turbulent motions observed in molecular clouds, the new calculation begins with a power spectrum   P ( k ) ∝ k ⁻⁶  .
Despite this change to the initial motions in the cloud and the resulting density structure of the molecular cloud, the stellar properties resulting from the two calculations are indistinguishable. This demonstrates that the results of such hydrodynamical calculations of star cluster formation are relatively insensitive to the initial conditions. It is also consistent with the fact that the statistical properties of stars and brown dwarfs (e.g. the stellar initial mass function) are observed to be relatively invariant within our Galaxy and do not appear to depend on environment.     

The mass to light ratio and the initial mass function in galactic discs

A low mass-to-light ratio for the baryonic component of spiral galaxies is advocated by a number of dynamical studies and by cosmological simulations of galaxy formation. We discuss the possibility of obtaining low mass-to-light ratios for the stellar component in discs, by changing the Initial Mass Function and the Star Formation History. This revised version was published online in August 2006 with corrections to the Cover Date.     

Differential efficiency of massive star formation in NGC 628

The efficiency ratio of massive star formation in the arms of the spiral NGC 628 to that in the interarm region has been determined from the sizes and positions of itsHii regions following the method described in Cepa and Beckman (1989a, b). The variation of this relative star formation efficiency with radius shows a very similar behaviour for each of the three arms of this galaxy with a minimum at 100 arc sec from the centre, which can be identified with the corotation radius distances at which the arms show bifurcations or sudden changes in their pitch angles. This result, together with the higher star formation efficiency in the arms than that in the interarm zones, is evidence supporting the hypothesis that the spiral arms of NGC 628 are driven by a density wave which triggers the star formation according to the spiral density wave theory.     

Binary stars and the fundamental initial mass function

We have carried out Monte Carlo simulations in which we generate a random pairing of objects drawn from a pre-assumed single-star power-law initial mass function (IMF), which we call the fundamental IMF. We show how the mass functions of primary stars and secondary stars and the mass function of the total mass of systems (if we could resolve them) differ from the underlying fundamental IMF for different slopes of this IMF. We also compare our results with the observed IMF, the binary frequency and the binary mass-ratio distributions for field stars and conclude that the fundamental IMF of subsolar mass stars could be steeper than is currently believed. In other words, the low-mass turn-over of the observed ('apparent') IMF could be spurious, if the main-sequence binary fraction of field stars is close to 100 per cent (perhaps owing to invisible companions).