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Register a new userThe mass function and dynamical mass of young star clusters: Why their initial crossing-time matters crucially
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Genevieve Parmentier
Publication date
2012
fields
Physics
and research's language is
English
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We highlight the impact of cluster-mass-dependent evolutionary rates upon the evolution of the cluster mass function during violent relaxation, that is, while clusters dynamically respond to the expulsion of their residual star-forming gas. Mass-dependent evolutionary rates arise when the mean volume density of cluster-forming regions is mass-dependent. In that case, even if the initial conditions are such that the cluster mass function at the end of violent relaxation has the same shape as the embedded-cluster mass function (i.e. infant weight-loss is mass-independent), the shape of the cluster mass function does change transiently {it during} violent relaxation. In contrast, for cluster-forming regions of constant mean volume density, the cluster mass function shape is preserved all through violent relaxation since all clusters then evolve at the same mass-independent rate. On the scale of individual clusters, we model the evolution of the ratio between the dynamical mass and luminous mass of a cluster after gas expulsion. Specifically, we map the radial dependence of the time-scale for a star cluster to return to equilibrium. We stress that fields-of-view a few pc in size only, typical of compact clusters with rapid evolutionary rates, are likely to reveal cluster regions which have returned to equilibrium even if the cluster experienced a major gas expulsion episode a few Myr earlier. We provide models with the aperture and time expressed in units of the initial half-mass radius and initial crossing-time, respectively, so that our results can be applied to clusters with initial densities, sizes, and apertures different from ours.
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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]
The initial mass function (IMF) is an essential tool with which to study star formation processes. We have initiated the photometric survey of young open clusters in the Galaxy, from which the stellar IMFs are obtained in a homogeneous way. A total of 16 famous young open clusters have preferentially been studied up to now. These clusters have a wide range of surface densities (log sigma = -1 to 3 [stars pc^2] for stars with mass larger than 5M_sun) and cluster masses (M_cl = 165 to 50,000M_sun), and also are distributed in five different spiral arms in the Galaxy. It is possible to test the dependence of star formation processes on the global properties of individual clusters or environmental conditions. We present a preliminary result on the variation of the IMF in this paper.
We present radiation-magneto-hydrodynamic simulations of star formation in self-gravitating, turbulent molecular clouds, modeling the formation of individual massive stars, including their UV radiation feedback. The set of simulations have cloud masses between $m_{rm gas}=10^3$~M$_odot$ to $3 times 10^5$~M$_odot$ and gas densities typical of clouds in the local universe ($overline n_{rm gas} sim 1.8times 10^2$~cm$^{-3}$) and 10$times$ and 100$times$ denser, expected to exist in high-redshift galaxies. The main results are: {it i}) The observed Salpeter power-law slope and normalisation of the stellar initial mass function at the high-mass end can be reproduced if we assume that each star-forming gas clump (sink particle) fragments into stars producing on average a maximum stellar mass about $40%$ of the mass of the sink particle, while the remaining $60%$ is distributed into smaller mass stars. Assuming that the sinks fragment according to a power-law mass function flatter than Salpeter, with log-slope $0.8$, satisfy this empirical prescription. {it ii}) The star formation law that best describes our set of simulation is $drho_*/dt propto rho_{gas}^{1.5}$ if $overline n_{gas}<n_{cri}approx 10^3$~cm$^{-3}$, and $drho_*/dt propto rho_{rm gas}^{2.5}$ otherwise. The duration of the star formation episode is roughly $6$ clouds sound crossing times (with $c_s=10$~km/s). {it iii}) The total star formation efficiency in the cloud is $f_*=2% (m_{rm gas}/10^4~M_odot)^{0.4}(1+overline n_{rm gas}/n_{rm cri})^{0.91}$, for gas at solar metallicity, while for metallicity $Z<0.1$~Z$_odot$, based on our limited sample, $f_*$ is reduced by a factor of $sim 5$. {it iv)} The most compact and massive clouds appear to form globular cluster progenitors, in the sense that star clusters remain gravitationally bound after the gas has been expelled.
We discuss the possibility that gravitational focusing, is responsible for the power-law mass function of star clusters $N(log M) propto M^{-1}$. This power law can be produced asymptotically when the mass accretion rate of an object depends upon the mass of the accreting body as $dot{M} propto M^2$. While Bondi-Hoyle-Littleton accretion formally produces this dependence on mass in a uniform medium, realistic environments are much more complicated. However, numerical simulations in SPH allowing for sink formation yield such an asymptotic power-law mass function. We perform pure N-body simulations to isolate the effects of gravity from those of gas physics and to show that clusters naturally result with the power-law mass distribution. We also consider the physical conditions necessary to produce clusters on appropriate timescales. Our results help support the idea that gravitationally-dominated accretion is the most likely mechanism for producing the cluster mass function.
The stellar initial mass function (IMF) is a fundamental property of star formation, offering key insight into the physics driving the process as well as informing our understanding of stellar populations, their by-products, and their impact on the surrounding medium. While the IMF appears to be fairly uniform in the Milky Way disk, it is not yet known how the IMF might behave across a wide range of environments, such as those with extreme gas temperatures and densities, high pressures, and low metallicities. We discuss new opportunities for measuring the IMF in such environments in the coming decade with JWST, WFIRST, and thirty-meter class telescopes. For the first time, we will be able to measure the high-mass slope and peak of the IMF via direct star counts for massive star clusters across the Milky Way and Local Group, providing stringent constraints for star formation theory and laying the groundwork for understanding distant and unresolved stellar systems.
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