Competitive accretion in embedded stellar clusters

We investigate the physics of gas accretion in young stellar clusters. Accretion in clusters is a dynamic phenomenon as both the stars and the gas respond to the same gravitational potential. Accretion rates are highly non-uniform with stars nearer the centre of the cluster, where gas densities are higher, accreting more than others. This competitive accretion naturally results in both initial mass segregation and a spectrum of stellar masses. Accretion in gas-dominated clusters is well modelled using a tidal-lobe radius instead of the commonly used Bondi–Hoyle accretion radius. This works as both the stellar and gas velocities are under the influence of the same gravitational potential and are thus comparable. The low relative velocity which results means that R _tidal< R _BH in these systems. In contrast, when the stars dominate the potential and are virialized, R _BH< R _tidal and Bondi–Hoyle accretion is a better fit to the accretion rates.     

On the formation of massive stars

We present a model for the formation of massive ( M ≳10 M⊙) stars through accretion-induced collisions in the cores of embedded dense stellar clusters. This model circumvents the problem of accreting on to a star whose luminosity is sufficient to reverse the infall of gas. Instead, the central core of the cluster accretes from the surrounding gas, thereby decreasing its radius until collisions between individual components become sufficient. These components are, in general, intermediate-mass stars that have formed through accretion on to low-mass protostars. Once a sufficiently massive star has formed to expel the remaining gas, the cluster expands in accordance with this loss of mass, halting further collisions. This process implies a critical stellar density for the formation of massive stars, and a high rate of binaries formed by tidal capture.     

Star formation in unbound giant molecular clouds: the origin of OB associations?

We investigate the formation of star clusters in an unbound giant molecular cloud, where the supporting kinetic energy is twice as large as the cloud's self-gravity. This cloud manages to form a series of star clusters and disperse, all within roughly two crossing times (10 Myr), supporting recent claims that star formation is a rapid process. Simple assumptions about the nature of the star formation occurring in the clusters allows us to place an estimate for the star formation efficiency at about 5–10 per cent, consistent with observations. We also propose that unbound clouds can act as a mechanism for forming OB associations. The clusters that form in the cloud behave as OB subgroups. These clusters are naturally expanding from one another due to the unbound nature of the flows that create them. The properties of the cloud we present here are consistent with those of classic OB associations.     

Evolution of multimass globular clusters in the Galactic tidal field with the effects of velocity anisotropy

We study the evolution of globular clusters with mass spectra under the influence of the steady Galactic tidal field, including the effects of velocity anisotropy. Similarly to single-mass models, velocity anisotropy develops as the cluster evolves, but the degree of anisotropy is much smaller than in isolated clusters. Except for very early epochs of the cluster evolution, the velocity distributions of nearly all mass components become tangentially anisotropic at the outer parts. We examine how the mass function (MF) changes in time. Specifically, we find that the power-law index of the MF decreases monotonically with the total mass of the cluster, in agreement with previous findings based on isotropic models or N -body studies. This is also consistent with the behaviour of the observed slopes of MFs for a limited number of clusters. We attempt to compare our results with multimass King models, although it is almost impossible to fit the entire density profiles for all mass components. When the MF is fixed, the central densities of individual components show significant differences between Fokker–Planck and King models. We obtain 'best-fitting' multimass King models, for which the central density of individual components as well as the total density distribution agrees with the Fokker–Planck models by adjusting the MF. The MFs obtained in this way closely resemble the MF within the half-mass radius of the Fokker–Planck result. Also, we find that the local MFs predicted by Fokker–Planck calculations vary more rapidly with radius than best-fitting multimass King models. The projected velocity profiles for anisotropic models show significant flattening toward the tidal radius compared with the isotropic model. This is caused by the fact that the tangential velocity dispersion becomes dominant at the outer parts. Such a behaviour of velocity profile appears to be consistent with the observed profiles of the collapsed cluster M15.     

The Jeans mass and the origin of the knee in the IMF

We use numerical simulations of the fragmentation of a  1000 M_⊙  molecular cloud and the formation of a stellar cluster to study how the initial conditions for star formation affect the resulting initial mass function (IMF). In particular, we are interested in the relation between the thermal Jeans mass in a cloud and the knee of the IMF, i.e. the mass separating the region with a flat IMF slope from that typified by a steeper, Salpeter-like, slope. In three isothermal simulations with   M _Jeans= 1, 2  and  5 M_⊙  , the number of stars formed, at comparable dynamical times, scales roughly with the number of initial Jeans masses in the cloud. The mean stellar mass also increases (though less than linearly) with the initial Jeans mass in the cloud. It is found that the IMF in each case displays a prominent knee, located roughly at the mass scale of the initial Jeans mass. Thus clouds with higher initial Jeans masses produce IMFs which are shallow to higher masses. This implies that a universal IMF requires a physical mechanism that sets the Jeans mass to be near  1 M_⊙  . Simulations including a barotropic equation of state as suggested by Larson, with cooling at low densities followed by gentle heating at higher densities, are able to produce realistic IMFs with the knee located at  ≈1 M_⊙  , even with an initial   M _Jeans= 5 M_⊙  . We therefore suggest that the observed universality of the IMF in the local Universe does not require any fine tuning of the initial conditions in star forming clouds but is instead imprinted by details of the cooling physics of the collapsing gas.     

Magnetospheric accretion and pre-main-sequence stellar masses

We present a method of determining lower limits on the masses of pre-main-sequence (PMS) stars and so constraining the PMS evolutionary tracks. This method uses the redshifted absorption feature observed in some emission-line profiles of T Tauri stars, indicative of infall. The maximum velocity of the accreting material measures the potential energy at the stellar surface, which, combined with an observational determination of the stellar radius, yields the stellar mass. This estimate is a lower limit owing to uncertainties in the geometry and projection effects. Using available data, we show that the computed lower limits can be larger than the masses derived from PMS evolutionary tracks for M   0.5 M. Our analysis also supports the notion that accretion streams do not impact near the stellar poles but probably hit the stellar surface at moderate latitudes.     

The effect of gas loss on the formation of bound stellar clusters

The effect of gas ejection on the structure and binding energy of newly formed stellar clusters is investigated. The star formation efficiency (SFE), necessary for forming a gravitationally bound stellar cluster, is determined.
Two sets of numerical N -body simulations are presented. As a first simplified approach we treat the residual gas as an external potential. The gas expulsion is approximated by reducing the gas mass to zero on a given time-scale, which is treated as a free parameter. In a second set of simulations we use smoothed particle hydrodynamics (SPH) to follow the dynamics of the outflowing residual gas self-consistently. We investigate cases where gas outflow is induced by an outwards propagating shock front and where the whole gas cloud is heated homogeneously, leading to ejection.
If the stars are in virial equilibrium with the gaseous environment initially, bound clusters only form in regions where the local SFE is larger than 50 per cent or where the gas expulsion time-scale is long compared with the dynamical time-scale. A small initial velocity dispersion of the stars leads to a compaction of the cluster during the expulsion phase and reduces the SFE needed to form bound clusters to less than 10 per cent.     

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.