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Register a new userThe evolution of the global stellar mass function of star clusters: an analytic description
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The evolution of the global stellar mass function (MF) of star clusters is studied based on a large set of N-body simulations of clusters with a range of initial masses, initial concentrations, in circular or elliptical orbits in different tidal environments. Models with and without initial mass segregation are included. The depletion of low mass stars in initially Roche-volume (tidal) filling clusters starts typically on a time scale of the order of the core collapse time. In clusters that are initially underfilling their Roche-volume it takes longer because the clusters have to expand to their tidal radii before dynamical mass loss becomes important. We introduce the concept of the differential mass function (DMF), which describes the changes with respect to the initial mass function (IMF). We show that the evolution of the DMF can be described by a set of very simple analytic expressions that are valid for a wide range of initial cluster parameters and for different IMFs. The agreement between this description and the models is very good, except for initially Roche-volume underfilling clusters that are severely mass segregated.
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We show that a model consisting of individual, log-normal star formation histories for a volume-limited sample of $zapprox0$ galaxies reproduces the evolution of the total and quiescent stellar mass functions at $zlesssim2.5$ and stellar masses $M_*geq10^{10},{rm M_odot}$. This model has previously been shown to reproduce the star formation rate/stellar mass relation (${rm SFR}$--$M_*$) over the same interval, is fully consistent with the observed evolution of the cosmic ${rm SFR}$ density at $zleq8$, and entails no explicit quenching prescription. We interpret these results/features in the context of other models demonstrating a similar ability to reproduce the evolution of (1) the cosmic ${rm SFR}$ density, (2) the total/quiescent stellar mass functions, and (3) the ${rm SFR}$--$M_*$ relation, proposing that the key difference between modeling approaches is the extent to which they stress/address diversity in the (starforming) galaxy population. Finally, we suggest that observations revealing the timescale associated with dispersion in ${rm SFR}(M_*)$ will help establish which models are the most relevant to galaxy evolution.
We describe the interplay between stellar evolution and dynamical mass loss of evolving star clusters, based on the principles of stellar evolution and cluster dynamics and on a grid of N-body simulations of cluster models. The cluster models have different initial masses, different orbits, including elliptical ones, and different initial density profiles. We use two sets of cluster models: initially Roche-lobe filling and Roche-lobe underfilling. We identify four distinct mass loss effects: (1) mass loss by stellar evolution, (2) loss of stars induced by stellar evolution and (3) relaxation-driven mass loss before and (4) after core collapse. Both the evolution-induced loss of stars and the relaxation-driven mass loss need time to build up. This is described by a delay-function of a few crossing times for Roche-lobe filling clusters and a few half mass relaxation times for Roche-lobe underfilling clusters. The relaxation-driven mass loss can be described by a simple power law dependence of the mass dM/dt =-M^{1-gamma}/t0, (with M in Msun) where t0 depends on the orbit and environment of the cluster. Gamma is 0.65 for clusters with a King-parameter W0=5 and 0.80 for more concentrated clusters with W0=7. For initially Roche-lobe underfilling clusters the dissolution is described by the same gamma=0.80. The values of the constant t0 are described by simple formulae that depend on the orbit of the cluster. The mass loss rate increases by about a factor two at core collapse and the mass dependence of the relaxation-driven mass loss changes to gamma=0.70 after core collapse. We also present a simple recipe for predicting the mass evolution of individual star clusters with various metallicities and in different environments, with an accuracy of a few percent in most cases. This can be used to predict the mass evolution of cluster systems.
We have undertaken the largest systematic study of the high-mass stellar initial mass function (IMF) to date using the optical color-magnitude diagrams (CMDs) of 85 resolved, young (4 Myr < t < 25 Myr), intermediate mass star clusters (10^3-10^4 Msun), observed as part of the Panchromatic Hubble Andromeda Treasury (PHAT) program. We fit each clusters CMD to measure its mass function (MF) slope for stars >2 Msun. For the ensemble of clusters, the distribution of stellar MF slopes is best described by $Gamma=+1.45^{+0.03}_{-0.06}$ with a very small intrinsic scatter. The data also imply no significant dependencies of the MF slope on cluster age, mass, and size, providing direct observational evidence that the measured MF represents the IMF. This analysis implies that the high-mass IMF slope in M31 clusters is universal with a slope ($Gamma=+1.45^{+0.03}_{-0.06}$) that is steeper than the canonical Kroupa (+1.30) and Salpeter (+1.35) values. Using our inference model on select Milky Way (MW) and LMC high-mass IMF studies from the literature, we find $Gamma_{rm MW} sim+1.15pm0.1$ and $Gamma_{rm LMC} sim+1.3pm0.1$, both with intrinsic scatter of ~0.3-0.4 dex. Thus, while the high-mass IMF in the Local Group may be universal, systematics in literature IMF studies preclude any definitive conclusions; homogenous investigations of the high-mass IMF in the local universe are needed to overcome this limitation. Consequently, the present study represents the most robust measurement of the high-mass IMF slope to date. We have grafted the M31 high-mass IMF slope onto widely used sub-solar mass Kroupa and Chabrier IMFs and show that commonly used UV- and Halpha-based star formation rates should be increased by a factor of ~1.3-1.5 and the number of stars with masses >8 Msun are ~25% fewer than expected for a Salpeter/Kroupa IMF. [abridged]
We present a new technique to quantify cluster-to-cluster variations in the observed present-day stellar mass functions of a large sample of star clusters. Our method quantifies these differences as a function of both the stellar mass and the total cluster mass, and offers the advantage that it is insensitive to the precise functional form of the mass function. We applied our technique to data taken from the ACS Survey for Globular Clusters, from which we obtained completeness-corrected stellar mass functions in the mass range 0.25-0.75 M$_{odot}$ for a sample of 27 clusters. The results of our observational analysis were then compared to Monte Carlo simulations for globular cluster evolution spanning a range of initial mass functions, total numbers of stars, concentrations, and virial radii. We show that the present-day mass functions of the clusters in our sample can be reproduced by assuming an universal initial mass function for all clusters, and that the cluster-to-cluster differences are consistent with what is expected from two-body relaxation. A more complete exploration of the initial cluster conditions will be needed in future studies to better constrain the precise functional form of the initial mass function. This study is a first step toward using our technique to constrain the dynamical histories of a large sample of old Galactic star clusters and, by extension, star formation in the early Universe.
We study the effects of galaxy environment on the evolution of the stellar-mass function (SMF) over 0.2 < z < 2.0 using the FourStar Galaxy Evolution (ZFOURGE) survey and NEWFIRM Medium-Band Survey (NMBS) down to the stellar-mass completeness limit, log M / Msun > 9.0 (9.5) at z = 1.0 (2.0). We compare the SMFs for quiescent and star-forming galaxies in the highest and lowest environments using a density estimator based on the distance to the galaxies third-nearest neighbors. For star-forming galaxies, at all redshifts there are only minor differences with environment in the shape of the SMF. For quiescent galaxies, the SMF in the lowest densities shows no evolution with redshift, other than an overall increase in number density (phi*) with time. This suggests that the stellar-mass dependence of quenching in relatively isolated galaxies is both universal and does not evolve strongly. While at z >~ 1.5 the SMF of quiescent galaxies is indistinguishable in the highest and lowest densities, at lower redshifts it shows a rapidly increasing number density of lower-mass galaxies, log M / Msun ~= 9-10. We argue this evolution can account for all the redshift evolution in the shape of the total quiescent-galaxy SMF. This evolution in the quiescent-galaxy SMF at higher redshift (z > 1) requires an environmental-quenching efficiency that decreases with decreasing stellar mass at 0.5 < z < 1.5 or it would overproduce the number of lower-mass quiescent galaxies in denser environments. This requires a dominant environment process such as starvation combined with rapid gas depletion and ejection at z > 0.5 - 1.0 for galaxies in our mass range. The efficiency of this process decreases with redshift allowing other processes (such as galaxy interactions and ram-pressure stripping) to become more important at later times, z < 0.5.
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