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Register a new userDynamical equivalence, the origin of the Galactic field stellar and binary population, and the initial radius--mass relation of embedded clusters
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In order to allow a better understanding of the origin of Galactic field populations, dynamical equivalence of stellar-dynamical systems has been postulated by Kroupa and Belloni et al. to allow mapping of solutions of the initial conditions of embedded clusters such that they yield, after a period of dynamical processing, the Galactic field population. Dynamically equivalent systems are defined to initially and finally have the same distribution functions of periods, mass ratios and eccentricities of binary stars. Here we search for dynamically equivalent clusters using the {sc mocca} code. The simulations confirm that dynamically equivalent solutions indeed exist. The result is that the solution space is next to identical to the radius--mass relation of Marks & Kroupa, $left( r_h/{rm pc} right)= 0.1^{+0.07}_{-0.04}, left( M_{rm ecl}/{rm M}_odot right)^{0.13pm0.04}$. This relation is in good agreement with the observed density of molecular cloud clumps. According to the solutions, the time-scale to reach dynamical equivalence is about 0.5~Myr which is, interestingly, consistent with the lifetime of ultra-compact HII regions and the time-scale needed for gas expulsion to be active in observed very young clusters as based on their dynamical modelling.
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Young stellar clusters across nearly five orders of magnitude in mass appear to follow a power-law mass-radius relationship (MRR), $R_{star} propto M_{star}^{alpha}$, with $alpha approx 0.2 - 0.33$. We develop a simple analytic model for the cluster mass-radius relation. We consider a galaxy disc in hydrostatic equilibrium, which hosts a population of molecular clouds that fragment into clumps undergoing cluster formation and feedback-driven expansion. The model predicts a mass-radius relation of $R_{star} propto M_{star}^{1/2}$ and a dependence on the kpc-scale gas surface density $R_{star} propto Sigma_{rm g}^{-1/2}$, which results from the formation of more compact clouds (and cluster-forming clumps within) at higher gas surface densities. This environmental dependence implies that the high-pressure environments in which the most massive clusters can form also induce the formation of clusters with the smallest radii, thereby shallowing the observed MRR at high-masses towards the observed $R_{star} propto M_{star}^{1/3}$. At low cluster masses, relaxation-driven expansion induces a similar shallowing of the MRR. We combine our predicted MRR with a simple population synthesis model and apply it to a variety of star-forming environments, finding good agreement. Our model predicts that the high-pressure formation environments of globular clusters at high redshift naturally led to the formation of clusters that are considerably more compact than those in the local Universe, thereby increasing their resilience to tidal shock-driven disruption and contributing to their survival until the present day.
The stellar initial mass function (IMF) plays a crucial role in determining the number of surviving stars in galaxies, the chemical composition of the interstellar medium, and the distribution of light in galaxies. A key unsolved question is whether the IMF is universal in time and space. Here we use state-of-the-art results of stellar evolution to show that the IMF of our Galaxy made a transition from an IMF dominated by massive stars to the present-day IMF at an early phase of the Galaxy formation. Updated results from stellar evolution in a wide range of metallicities have been implemented in a binary population synthesis code, and compared with the observations of carbon-enhanced metal-poor (CEMP) stars in our Galaxy. We find that applying the present-day IMF to Galactic halo stars causes serious contradictions with four observable quantities connected with the evolution of AGB stars. Furthermore, a comparison between our calculations and the observations of CEMP stars may help us to constrain the transition metallicity for the IMF which we tentatively set at [Fe/H] = -2. A novelty of the current study is the inclusion of mass loss suppression in intermediate-mass AGB stars at low-metallicity. This significantly reduces the overproduction of nitrogen-enhanced stars that was a major problem in using the high-mass star dominated IMF in previous studies. Our results also demonstrate that the use of the present day IMF for all time in chemical evolution models results in the overproduction of Type I.5 supernovae. More data on stellar abundances will help to understand how the IMF has changed and what caused such a transition.
Most globular clusters have half-mass radii of a few pc with no apparent correlation with their masses. This is different from elliptical galaxies, for which the Faber-Jackson relation suggests a strong positive correlation between mass and radius. Objects that are somewhat in between globular clusters and low-mass galaxies, such as ultra-compact dwarf galaxies, have a mass-radius relation consistent with the extension of the relation for bright ellipticals. Here we show that at an age of 10 Gyr a break in the mass-radius relation at ~10^6 Msun is established because objects below this mass, i.e. globular clusters, have undergone expansion driven by stellar evolution and hard binaries. From numerical simulations we find that the combined energy production of these two effects in the core comes into balance with the flux of energy that is conducted across the half-mass radius by relaxation. An important property of this `balanced evolution is that the cluster half-mass radius is independent of its initial value and is a function of the number of bound stars and the age only. It is therefore not possible to infer the initial mass-radius relation of globular clusters and we can only conclude that the present day properties are consistent with the hypothesis that all hot stellar systems formed with the same mass-radius relation and that globular clusters have moved away from this relation because of a Hubble time of stellar and dynamical evolution.
Observations and semianalytical galaxy formation and evolution models (SAMs) have suggested the existence of a stellar mass-stellar metallicity relation (MZR), which is shown to be universal for different types of galaxies over a large range of stellar masses ($M_*sim 10^3$-$10^{11}M_odot$) and dark matter (DM) halo masses ($M_{rm halo}sim 10^9$-$10^{15}h^{-1}M_odot$). In this work, we construct a chemical evolution model to investigate the origin of the MZR, including both the effects of gas inflows and outflows in galaxies. We solve the MZR from the chemical evolution model, by assuming that the cold gas mass ($M_{rm cold}$) and the stellar feedback efficiency ($beta$) follow some power-law scaling relationships with $M_*$ during the growth of a galaxy, i.e., $M_{rm cold}propto M_*^{alpha_{rm gs}}$ and $betapropto M_*^{alpha_{beta{rm s}}}$. We use the SAM to obtain these power-law scaling relations, which appear to be roughly universal over a large range of stellar masses for both satellites and central galaxies within a large range of halo masses. The range of the MZRs produced by our models is in a narrow space, which provides support to the universality of the MZRs. The formation of the MZR is a result caused jointly by that the cold gas fraction decreases with increasing $M_*$ and by that the stellar feedback efficiency decreases with increasing $M_*$ in the galaxy growth, and the exponent in the MZR is around $-alpha_{beta{rm s}}$ or $1-alpha_{rm gs}$. The MZR represents an average evolutional track for the stellar metallicity of a galaxy. The comparison of our model with some previous models for the origin of MZRs is also discussed.
Early-type galaxies obey a narrow relation traced by their stellar content between the mass and size (Mass- Radius relation). The wealth of recently acquired observational data essentially confirms the classical relations found by Burstein, Bender, Faber, and Nolthenius, i.e. log(R_1/2) propto log(Ms)simeq 0.54 for high mass galaxies and log(R_1/2) propto log(Ms) simeq 0.3 for dwarf systems (shallower slope), where R_1/2 and Ms are the half-light radius and total mass in stars, respectively. Why do galaxies follow these characteristic trends? What can they tell us about the process of galaxy formation? We investigate the mechanisms which concur to shape the Mass-Radius relation, in order to cast light on the physical origin of its slope, its tightness, and its zero point. We perform a theoretical analysis, and couple it with the results of numerical hydrodynamical (NB-TSPH) simulations of galaxy formation, and with a simulation of the Mass-Radius plane itself. We propose a novel interpretation of the Mass-Radius relation, which we claim to be the result of two complementary mechanisms: on one hand, the result of local physical processes, which fixes the ratio between masses and radii of individual objects; on the other hand, the action of cosmological global, statistical principles, which shape the distribution of objects in the plane. We reproduce the Mass-Radius relation with a simple numerical technique based on this view.
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