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Register a new userAges, Distances, and the Initial Mass Functions of Stellar Clusters
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J. R. Stauffer
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We provide a review of the current status of several topics on the ages, distances, and mass functions of open clusters, with a particular emphasis on illuminating the areas of uncertainty. Hipparcos has obtained parallaxes for nearby open clusters that have expected accuracies much better than has been previously achievable. By using the lithium depletion boundary method and isochrone fitting based on much improved new theoretical evolutionary models for low mass stars, it is arguable that we will soon have have much better age scales for clusters and star-forming regions. With improved optical and near-IR cameras, we are just now beginning to extend the mass function of open clusters like the Pleiades into the regime below the hydrogen burning mass limit. Meanwhile, observations in star-forming regions are in principle capable of identifying objects down to of order 10 Jupiter masses.
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(... abridged) The observed luminosity function can be constructed in a range of absolute integrated magnitudes $I_{M_V}= [-10, -0.5]$ mag, i.e. about 5 magnitudes deeper than in the most nearby galaxies. It increases linearly from the brightest limit to a turnover at about $I_{M_V}approx-2.5$. The slope of this linear portion is $a=0.41pm0.01$, which agrees perfectly with the slope deduced for star cluster observations in nearby galaxies. (...) We find that the initial mass function of open clusters (CIMF) has a two-segment structure with the slopes $alpha=1.66pm0.14$ in the range $log M_c/M_odot=3.37...4.93$ and $alpha=0.82pm0.14$ in the range $log M_c/M_odot=1.7...3.37$. The average mass of open clusters at birth is $4.5cdot 10^3 M_odot$, which should be compared to the average observed mass of about $700 M_odot$. The average cluster formation rate derived from the comparison of initial and observed mass functions is $bar{upsilon}=0.4 mathrm{kpc}^{-2}mathrm{Myr}^{-1}$. Multiplying by the age of the Galactic disc (T = 13 Gyr) the predicted surface density of Galactic disc field stars originating from dissolved open clusters amounts to $22 M_odot mathrm{pc}^{-2}$ which is about 40% of the total surface density of the Galactic disc in the solar neighbourhood. Thus, we conclude that almost half of all field stars were born in open clusters, a much higher fraction than previously thought.
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.
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]
Using the Oxford Short Wavelength Integral Field specTrograph (SWIFT), we investigate radial variations of several initial mass function (IMF) dependent absorption features in M31 and M32. We obtain high signal-to-noise spectra at six pointings along the major axis of M31 out to ~ 700 (2.7 kpc) and a single pointing of the central 10 pc for M32. In M31 the sodium NaI {lambda}8190 index shows a flat equivalent width profile at ~ 0.4 {AA} through the majority of the bulge, with a strong gradient up to 0.8 {AA} in the central 10 (38 pc); the Wing-Ford FeH {lambda}9916 index is measured to be constant at 0.4 {AA} for all radii; and calcium triplet CaT {lambda}8498, 8542, 8662 shows a gradual increase through the bulge towards the centre. M32 displays flat profiles for all three indices, with FeH at ~ 0.5 {AA}, very high CaT at ~ 0.8 {AA} and low NaI at ~ 0.1 {AA}. We analyse these data using stellar population models. We find that M31 is well described on all scales by a Chabrier IMF, with a gradient in sodium enhancement of [Na/Fe] ~ +0.3 dex in the outer bulge, rising within the central 10 to perhaps [Na/Fe] ~ +1.0 dex in the nuclear region. We find M32 is described by a Chabrier IMF and young stellar age in line with other studies. Models show that CaT is much more sensitive to metallicity and [{alpha}/Fe] than to IMF. We note that the centres of M31 and M32 have very high stellar densities and yet we measure Chabrier IMFs in these regions.
I review progress towards understanding the time-scales of star and cluster formation and of the absolute ages of young stars. I focus in particular on the areas in which Francesco Palla made highly significant contributions - interpretation of the Hertzsprung-Russell diagrams of young clusters and the role of photospheric lithium as an age diagnostic.
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