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Register a new userStellar collisions in flattened and rotating Pop. III star clusters
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Added by
Marcelo Alberto Cort\\'es Vergara
Publication date
2021
fields
Physics
and research's language is
English
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Fragmentation often occurs in disk-like structures, both in the early Universe and in the context of present-day star formation. Supermassive black holes (SMBHs) are astrophysical objects whose origin is not well understood; they weigh millions of solar masses and reside in the centers of galaxies. An important formation scenario for SMBHs is based on collisions and mergers of stars in a massive cluster, in which the most massive star moves to the center of the cluster due to dynamical friction. This increases the rate of collisions and mergers since massive stars have larger collisional cross sections. This can lead to runaway growth of a very massive star which may collapse to become an intermediate-mass black hole. Here we investigate the dynamical evolution of Miyamoto-Nagai models that allow us to describe dense stellar clusters, including flattening and different degrees of rotation. We find that the collisions in these clusters depend mostly on the number of stars and the initial stellar radii for a given radial size of the cluster. By comparison, rotation seems to affect the collision rate by at most $20%$. For flatness, we compared spherical models with systems that have a scale height of about $10%$ of their radial extent, in this case finding a change in the collision rate of less than $25%$. Overall, we conclude that the parameters only have a minor effect on the number of collisions. Our results also suggest that rotation helps to retain more stars in the system, reducing the number of escapers by a factor of $2-3$ depending on the model and the specific realization. After two million years, a typical lifetime of a very massive star, we find that about $630$ collisions occur in typical models with $N=10^4$, $R=100$ $rm~R_odot$ and a half-mass radius of $0.1$ $rm~pc$, leading to a mass of about $6.3times10^3$ $rm~M_odot$ for the most massive object.
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We present preliminary results of an incoming theoretical work concerning the integrated properties of the Population III clusters of stars. On the basis of synthetic Color-Magnitude Diagrams, we provide a grid of optical and near-IR colors of Simple Stellar Populations with very low metallicity (Z=10$^{-10}$ and Z=10$^{-6}$) and age which spans from 10 Myr to 15 Gyr. A comparison with higher metallicities up to 0.006 is also shown, disclosing sizable differences in the CMD morphology, integrated colors and Spectral Energy Distribution (SED).
We investigated stellar winds from zero/low-metallicity low-mass stars by magnetohydrodynamical simulations for stellar winds driven by Alfven waves from stars with mass $M_{star}=(0.6-0.8)M_{odot}$ and metallicity $Z=(0-1)Z_{odot}$, where $M_{odot}$ and $Z_{odot}$ are the solar mass and metallicity, respectively. Alfvenic waves, which are excited by the surface convection, travel upward from the photosphere and heat up the corona by their dissipation. For lower $Z$, denser gas can be heated up to the coronal temperature because of the inefficient radiation cooling. The coronal density of Pop.II/III stars with $Zle 0.01Z_{odot}$ is 1-2 orders of magnitude larger than that of the solar-metallicity star with the same mass, and as a result, the mass loss rate, $dot{M}$, is $(4.5-20)$ times larger. This indicates that metal accretion on low-mass Pop.III stars is negligible. The soft X-ray flux of the Pop.II/III stars is also expected to be $approx (1-30)$ times larger than that of the solar-metallicity counterpart owing to the larger coronal density, even though the radiation cooling efficiency is smaller. A larger fraction of the input Alfvenic wave energy is transmitted to the corona in low $Z$ stars because they avoid severe reflection owing to the smaller density difference between the photosphere and the corona. Therefore, a larger fraction is converted to the thermal energy of the corona and the kinetic energy of the stellar wind. From this energetics argument, we finally derived a scaling of $dot{M}$ as $dot{M}propto L R_{star}^{11/9}M_{star}^{-10/9}T_{rm eff}^{11/2}left[max (Z/Z_{odot},0.01)right]^{-1/5}$, where $L$, $R_{star}$, and $T_{rm eff}$ are stellar luminosity, radius, and effective temperature, respectively.
In this paper, I review to what extent we can understand the photometric properties of star clusters, and of low-mass, unresolved galaxies, in terms of population synthesis models designed to describe `simple stellar populations (SSPs), i.e., groups of stars born at the same time, in the same volume of space, and from a gas cloud of homogeneous chemical composition. The photometric properties predicted by these models do not readily match the observations of most star clusters, unless we properly take into account the expected variation in the number of stars occupying sparsely populated evolutionary stages, due to stochastic fluctuations in the stellar initial mass function. In this case, population synthesis models reproduce remarkably well the full ranges of observed integrated colours and absolute magnitudes of star clusters of various ages and metallicities. The disagreement between the model predictions and observations of cluster colours and magnitudes may indicate problems with or deficiencies in the modelling, and dioes not necessarily tell us that star clusters do not behave like SSPs. Matching the photometric properties of star clusters using SSP models is a necessary (but not sufficient) condition for clusters to be considered simple stellar populations. Composite models, characterized by complex star-formation histories, also match the observed cluster colours.
Stellar encounters potentially affect the evolution of the protoplanetary discs in the Orion Nebula Cluster (ONC). However, the role of encounters in other cluster environments is less known. We investigate the effect of the encounter-induced disc-mass loss in different cluster environments. Starting from an ONC-like cluster we vary the cluster size and density to determine the correlation of collision time scale and disc-mass loss. We use the NBODY6++ code to model the dynamics of these clusters and analyze the effect of star-disc encounters. We find that the disc-mass loss depends strongly on the cluster density but remains rather unaffected by the size of the stellar population. The essential outcome of the simulations are: i) Even in clusters four times sparser than the ONC the effect of encounters is still apparent. ii) The density of the ONC itself marks a threshold: in less dense and less massive clusters it is the massive stars that dominate the encounter-induced disc-mass loss whereas in denser and more massive clusters the low-mass stars play the major role for the disc mass removal. It seems that in the central regions of young dense star clusters -- the common sites of star formation -- stellar encounters do affect the evolution of the protoplanetary discs. With higher cluster density low-mass stars become more heavily involved in this process. This finding allows for the extrapolation towards extreme stellar systems: in case of the Arches cluster one would expect stellar encounters to destroy the discs of most of the low- and high-mass stars in several hundred thousand years, whereas intermediate mass stars are able to retain to some extant their discs even under these harsh environmental conditions.
Collisions were suggested to potentially play a role in the formation of massive stars in present day clusters, and have likely been relevant during the formation of massive stars and intermediate mass black holes within the first star clusters. In the early Universe, the first stellar clusters were particularly dense, as fragmentation typically only occurred at densities above $10^9$cm$^{-3}$, and the radii of the protostars were enhanced due to the larger accretion rates, suggesting a potentially more relevant role of stellar collisions. We present here a detailed parameter study to assess how the number of collisions as well as the mass growth of the most massive object depends on the properties of the cluster, and we characterize the time evolution with three effective parameters, the time when most collisions occur, the duration of the collisions period, as well as the normalization required to obtain the total number of collisions. We apply our results to typical Population III (Pop.III) clusters of about $1000$M$_odot$, finding that a moderate enhancement of the mass of the most massive star by a factor of a few can be expected. For more massive Pop.III clusters as expected in the first atomic cooling halos, we expect a more significant enhancement by a factor of $15-32$. We therefore conclude that collisions in massive Pop.III clusters were likely relevant to form the first intermediate mass black holes.
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