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.     

Captured older stars as the reason for apparently prolonged star formation in young star clusters

The existence of older stars within a young star cluster can be interpreted to imply that star formation occurs on time-scales longer than a free-fall time of a pre-cluster cloud core. Here, the idea is explored that these older stars are not related to the star formation process forming the young star cluster but rather that the orbits of older field stars are focused by the collapsing pre-cluster cloud core. Two effects appear: the focusing of stellar orbits leads to an enhancement of the density of field stars in the vicinity of the centre of the young star cluster; and due to the time-dependent potential of the forming cluster some of these stars can get bound gravitationally to the cluster. These stars exhibit similar kinematical properties to the newly formed stars and cannot be distinguished from them on the basis of radial velocity or proper motion surveys. Such contaminations may lead to a wrong apparent star formation history of a young cluster. In the case of the ONC, the theoretical number of gravitationally bound older low-mass field stars agrees with the number of observed older low-mass stars.     

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.     

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.     

Stellar tidal disruption by a massive binary black hole

The effects of formation of a binary black hole in a dense star cluster are found to have significant effects on the dynamics of the cluster. Tidal destruction of stars captured into bound orbits during the formation of the black hole binary provide a sizeable source of very high temperature thermal radiation as well as a source of radially outward moving clouds of gas. The efficiency of subsequently accreted matter onto the binary components as an energy source is investigated and suggestive evolutionary models of the dynamics of the binary system are presented. Lifetimes of the system are shown to be compatible with contemporary estimates. It is suggested that the high-density cluster core provides a suitable environment for the operation of a number of models for the core of active galactic nuclei.     

Photoionizing feedback in star cluster formation

We present the first ever hydrodynamic calculations of star cluster formation that incorporate the effect of feedback from ionizing radiation. In our simulations, the ionizing source forms in the cluster core at the intersection of several dense filaments of inflowing gas. We show that these filaments collimate ionized outflows and suggest such an environmental origin for at least some observed outflows in regions of massive star formation. Our simulations show both positive feedback (i.e. promotion of star formation in neutral gas compressed by expanding H  ii regions) and negative feedback (i.e. suppression of the accretion flow in to the central regions). We show that the volume filling factor of ionized gas is very different in our simulations from the result from the case where the central source interacted with an azimuthally smoothed gas density distribution. As expected, gas density is the key parameter in determining whether or not clusters are unbound by photoionizing radiation. Nevertheless, we find – on account of the acceleration of a small fraction of the gas to high velocities in the outflows – that the deposition in the gas of an energy that exceeds the binding energy of the cluster is not a sufficient criterion for unbinding the bulk of the cluster mass.     

球状星团的金属丰度特征与其恒星形成史

本文根据球状星团所特有的金属丰度特征,利用星族综合方法,探讨了球状星团诸恒星的形成史。研究表明,这些恒星不可能通过恒星形成率和初始质量函数均不随时间变化的单一恒星形成模式产生。原初云通过恒星演化而得到金属丰度污染的过程和多数恒星的形成过程必须分为两个不同的阶段。 球状星团得到金属丰度污染的过程中,若恒星形成具有通常的初始质量函数,则其恒星形成率必须较低,且初始质量函数不能太陡,从而使污染过程中只形成数量较少的低质量恒星,以保证单个球状星团内金属丰度的均匀性。另一种可能性是污染阶段有非常特殊的初始质量函数,只形成大质量的恒星,从而除提供适量污染外不留下任何痕迹。 多数恒星应是在原初云不同部位得到适当污染后通过局域的短暂的爆发性恒星形成(星暴过程)产生。本文进一步探讨了在Fan和Rees球状星团形成模型的框架下,两相介质中温云块相互碰撞造成星暴过程的可能性。     

On the infant weight loss of low- to intermediate-mass star clusters

Star clusters are born in a highly compact configuration, typically with radii of less than about 1 pc roughly independently of mass. Since the star formation efficiency is less than 50 per cent by observation and because the residual gas is removed from the embedded cluster, the cluster must expand. In the process of doing so it only retains a fraction f _st of its stars. To date there are no observational constraints for f _st, although N -body calculations by Kroupa, Aarseth & Hurley suggest it to be about 20–30 per cent for Orion-type clusters. Here we use the data compiled by Testi et al., Testi, Palla & Natta and Testi, Palla & Natta for clusters around young Ae/Be stars and by de Wit et al. and de Wit et al. around young O stars and the study of de Zeeuw et al. of OB associations and combine these measurements with the expected number of stars in clusters with primary Ae/Be and O stars, respectively, using the empirical correlation between maximal stellar mass and star cluster mass of Weidner & Kroupa. We find that   f _st < 50  per cent with a decrease to higher cluster masses/more massive primaries. The interpretation would be that cluster formation is very disruptive. It appears that clusters with a birth stellar mass in the range  10–10³ M_⊙  keep at most 50 per cent of their stars.     

Correlations, spectra, and instability of phase-space density fluctuations in open-cluster models

The dynamical evolution of six open star cluster models is analyzed using the correlation and spectral analysis of phase-space density fluctuations. The two-time and mutual correlation functions are computed for the fluctuations of the phase-space density of cluster models. The data for two-time and two-particle correlations are used to determine the correlation time for phase-space density fluctuations ((0.1–1) τ _v.r., where τ _v.r. is the violent relaxation time of the model) and the average phase velocities of the propagation of such fluctuations in cluster models. These velocities are 2–20 times smaller than the root mean square velocities of the stars in the cluster core. The power spectra and dispersion curves of phase-space density fluctuations are computed using the Fourier transform of mutual correlation functions. The results confirm the presence of known unstable phase-space density fluctuations due to homologous fluctuations of the cluster cores. The models are found to exhibit a number of new unstable phase-space density fluctuations (up to 32–41 pairs of fluctuations with different complex conjugate frequencies in each model; the e-folding time of the amplitude growth of such fluctuations is (0.4–10) τ _v.r. and their phases are distributed rather uniformly). Astrophysical applications of the obtained results (irregular structure of open star clusters, formation and decay of quasi-stationary states in such clusters) are discussed.     

Hierarchical star formation from the time–space distribution of star clusters in the Large Magellanic Cloud

The average age difference between pairs of star clusters in the Large Magellanic Cloud (LMC) increases with their separation as the ∼ 0.35 power. This suggests that star formation is hierarchical in space and in time. Small regions form stars quickly and large regions, which often contain the small regions, form stars over a longer period. A similar result found previously for Cepheid variables is statistically less certain than the cluster result.     

The UV-optical colours of brightest cluster galaxies in optically and X-ray selected clusters

Many brightest cluster galaxies (BCGs) at the centres of X-ray selected clusters exhibit clear evidence for recent star formation. However, studies of BCGs in optically selected clusters show that star formation is not enhanced when compared to control samples of non-BCGs of similar stellar mass. Here, we analyse a sample of 113 BCGs in low-redshift  ( z < 0.1)  , optically selected clusters, a matched control sample of non-BCGs, and a smaller sample of BCGs in X-ray selected clusters. We convolve the Sloan Digital Sky Survey images of the BCGs to match the resolution of the Galaxy Evolution Explorer ( GALEX ) data and we measure UV-optical colours in their inner and outer regions. We find that optically selected BCGs exhibit smaller scatter in optical colours and redder inner  NUV − r   colours than the control galaxies, indicating that they are a homogenous population with very little ongoing star formation. The BCGs in the X-ray selected cluster sample span a similar range in optical colours, but have bluer  NUV − r   colours. Among X-ray selected BCGs, those located in clusters with central cooling times of less than 1 Gyr are significantly bluer than those located in clusters where the central gas cooling times are long. Our main conclusion is that the location of a galaxy at the centre of its halo is not sufficient to determine whether or not it is currently forming stars. One must also have information about the thermodynamic state of the gas in the core of the halo.     

Open star clusters in the spiral arms of our Galaxy

We consider the age distributions of open star clusters attributed to three segments of Galactic spiral arms. The smoothed distributions of clusters on the age-Galactocentric angle plane show a great nonuniformity. The time dependence of the formation rate of Galactic disk clusters recovered by taking into account selection effects and dynamical evolution of clusters shows that, on average, the formation rate of open star clusters decreases with time. This is in agreement with the increase in star formation rate into the past, as follows from the study of this process by the method of stellar population synthesis. The present time is the epoch of a current maximum of the cluster formation rate. In addition to the current maximum, there have been at least three more maxima with a period of 300–400 Myr and a duration of no more than 300 Myr. The age distributions are consistent with the pattern of star formation governed by the successive passages of density waves through each examined volume of the Galactic disk. The spiral structure becomes more complex when passing from the inner regions of the Galaxy to its outer regions.     

疏散星团的质量分层

对疏散星团质量分层的有关问题做了简要的评述,包括空间质量分层和速度质量分层的表现形式和探测途径,质量分层形成机制的研究现状.最后概要介绍了2MASS测光资料对探讨疏散星团质量分层效应的作用.     

On the onset of runaway stellar collisions in dense star clusters – I. Dynamics of the first collision

We study the circumstances under which first collisions occur in young and dense star clusters. The initial conditions for our direct N -body simulations are chosen such that the clusters experience core collapse within a few million years, before the most massive stars have left the main sequence. It turns out that the first collision is typically driven by the most massive stars in the cluster. Upon arrival in the cluster core, by dynamical friction, massive stars tend to form binaries. The enhanced cross-section of the binary compared to a single star causes other stars to engage the binary. A collision between one of the binary components and the incoming third star is then mediated by the encounters between the binary and other cluster members. Due to the geometry of the binary–single star engagement the relative velocity at the moment of impact is substantially different than in a two-body encounter. This may have profound consequences for the further evolution of the collision product.     

Hydrodynamical Simulations of Galaxy Clusters

In my contribution I discuss the relevance that hydrodynamical simulation of clusters can play to understand the ICM physics and to calibrate mass estimates from X-ray observable quantities. Using hydrodynamical simulations, which cover quite a large dynamical range and include a fairly advanced treatment of the gas physics (cooling, star formation and SN feedback), I show that scaling relations among X-ray observable quantities can be reproduced quite well. At the sametime, these simulations fail at accounting for several observational quantities, which are related to the cooling structure of the ICM: the fraction of stars, the temperature profiles and the gas entropy in central cluster regions. This calls for the need of introducing in simulations suitable physical mechanisms which should regulate the cooling structure of the ICM.     

Stellar contents of two young open clusters: NGC 663 and 654

UBVRI CCD photometry in a wide field around two young open clusters, NGC 663 and 654, has been carried out. Hα and polarimetric observations for the cluster NGC 654 have also been obtained. We use the photometric data to construct colour–colour and colour–magnitude diagrams, from which we can investigate the reddening, age, mass and evolutionary states of the stellar contents of the these clusters. The reddening across the cluster regions is found to be variable. There is evidence for anomalous reddening law in both clusters; however, more infrared and polarimetric data are needed to conclude about the reddening law. Both clusters are situated at about a distance of 2.4 kpc. Star formation in both clusters is found to be a continuous process. In the case of NGC 663, star formation seems to have taken place sequentially, in the sense that formation of low-mass stars precedes the formation of most massive stars. Whereas, in the case of NGC 654, formation of low-mass stars did not cease after the formation of most massive stars in the cluster.     

Analysis of the structure and dynamics of the stellar tails of open star clusters

We have analyzed the formation, structure, and dynamical evolution of the population of stars that escaped from open clusters by numerical simulations using S. Aarseth’s modified NBODY6 code. In the Galactic tidal field, the population of stars that escaped from a cluster is shown to be elongated along the orbit of the cluster symmetrically about its core in the form of stellar tails of increasing sizes. We analyze the parameters of stellar tails as a function of such initial simulation conditions as the number of stars, the cluster density, the eccentricity of the Galactic cluster orbit in the plane of the Galactic disk, and the z velocity component. As a result, we constructed a grid of model stellar tails of open clusters. The grid includes such time-dependent parameters of the stellar tails as the length, the cross section, the number of stars, the velocity distribution, etc. Our simulations allow us to clarify the origin of moving clusters and stellar streams and to assess the role of star clusters in forming the stellar velocity field in the solar neighborhood.     

Hierarchical star formation: stars and stellar clusters in the Gould Belt

We perform a study of the spatial and kinematical distribution of young open clusters in the solar neighbourhood, discerning between bound clusters and transient stellar condensations within our sample. Then, we discriminate between Gould Belt (GB) and local Galactic disc (LGD) members, using our previous estimate of the structural parameters of both systems obtained from a sample of O-B6 Hipparcos stars. Single membership probabilities of the clusters are also calculated in the separation process. Using this classified sample, we analyse the spatial structure and the kinematic behaviour of the cluster system in the GB. The two star formation regions that dominate and give the GB its characteristic-inclined shape show a striking difference in their content of star clusters: while Ori OB1 is richly populated by open clusters, not a single one can be found within the boundaries of Sco OB2. This is mirrored in the velocity space, translating again into an abundance of clusters in the region of the kinematic space populated by the members of Ori OB1, and a marginal number of them associated with Sco OB2. We interpret all these differences by characterizing the Orion region as a cluster complex typically surrounded by a stellar halo, and the Sco-Cen region as an OB association in the outskirts of the complex. In the light of these results, we study the nature of the GB with respect to the optical segment of the Orion Arm, and we propose that the different content of star clusters, the different heights over the Galactic plane and the different residual velocities of Ori OB1 and Sco OB2 can be explained in terms of their relative position to the density maximum of the Local Arm in the solar neighbourhood. Although morphologically intriguing, the GB appears to be the result of our local and biased view of a larger star cluster complex in the Local Arm, that could be explained by the internal dynamics of the Galactic disc.     

恒星形成过程中的天体物理现象

恒星形成于分子云环境中。近30多年的观测研究使得天文学家对小质量恒星的形成有了相对明确的认识：小质量恒星通过坍缩、吸积和外向流的路标而形成。至于大质量恒星，其形成过程还存在着许多不确定因素，现有的观测证据表明：大质量恒星也可能通过坍缩、吸积和外向流的路标来形成，但也不排除在星团中通过中小质量恒星聚合而成的因素。大质量恒星形成与致密电离氢区(UCHII)成协较好，而与大质量恒星形成区成协的分子云环境中，既有大质量恒星也有小质量恒星形成。综述了恒星形成各个阶段的观测结果和研究现状以及成协的天体物理环境情况。未来的观测和研究重点在于，大质量恒星形成以及星团环境中的恒星形成。     

High-mass star forming regions: An ALMA view

The advent of ALMA is bound to improve our knowledge of OB star formation dramatically. Here, we present an overview of this topic outlining how high angular resolution and sensitivity may contribute to shed light on the structure of high-mass star forming regions and hence on the process itself of massive star formation. The impact of this new generation instrument will range from establishing the mass function of pre-stellar cores inside IR-dark clouds, to investigating the kinematics of the gas from which OB stars are built up, to assessing or ruling out the existence of circumstellar accretion disks in these objects.