Magneto-thermal condensation modes including the effects of charged dust particles

We study thermal instability in a magnetized and partially ionized plasma with charged dust particles. Our linear analysis shows that the growth rate of the unstable modes in the presence of dust particles strongly depends on the ratio of the cooling rate and the modified dust-cyclotron frequency. If the cooling rate is less than the modified dust-cyclotron frequency, then growth rate of the condensation modes does not modify due to the existence of the charged dust particles. But when the cooling rate is greater than (or comparable to) the modified dust-cyclotron frequency, the growth rate of unstable modes increases because of the dust particles. Also, wavenumber of the perturbations corresponding to the maximum growth rate shifts to the smaller values (larger wavelengths) as the cooling rate becomes larger than the modified dust-cyclotron frequency. We show that growth rate of the condensation modes increases with the electrical charge of the dust particles.Comment: accepted by MNRA

Massive stars reveal variations of the stellar initial mass function in the Milky Way stellar clusters

We investigate whether the stellar initial mass function (IMF) is universal, or whether it varies significantly among young stellar clusters in the Milky Way. We propose a method to uncover the range of variation of the parameters that describe the shape of the IMF for the population of young Galactic clusters. These parameters are the slopes in the low and high stellar mass regimes, $\gamma$ and $\Gamma$, respectively, and the characteristic mass, $M_{ch}$. The method relies exclusively on the high mass content of the clusters, but is able to yield information on the distributions of parameters that describe the IMF over the entire stellar mass range. This is achieved by comparing the fractions of single and lonely massive O stars in a recent catalog of the Milky Way clusters with a library of simulated clusters built with various distribution functions of the IMF parameters. The synthetic clusters are corrected for the effects of the binary population, stellar evolution, sample incompleteness, and ejected O stars. Our findings indicate that broad distributions of the IMF parameters are required in order to reproduce the fractions of single and lonely O stars in Galactic clusters. They also do not lend support to the existence of a cluster mass-maximum stellar mass relation. We propose a probabilistic formulation of the IMF whereby the parameters of the IMF are described by Gaussian distribution functions centered around $\gamma=0.91$, $\Gamma=1.37$, and $M_{ch}=0.41$ M$_{\odot}$, and with dispersions of $\sigma_{\gamma}=0.25$, $\sigma_{\Gamma}=0.60$, and $\sigma_{M_{ch}}=0.27$ M$_{\odot}$ around these values.Comment: Accepted to MNRAS, 17 pages, 13 figures. Larger observational sample. Conclusions strengthene

The galaxy-wide stellar initial mass function in the presence of cluster-to-cluster IMF variations

We calculate the integrated galactic initial stellar mass function (IGIMF) in the presence of IMF variations in clusters. IMF Variations for a population of clusters are taken into account in the form of Gaussian distributions of the IMF parameters. For the tapered power law function used here, these are the slopes at the high and low mass ends, $\Gamma$ and $\gamma$, and the characteristic mass $M_{ch}$. Variations are modeled by varying the width of the Gaussian distributions. The reference values are the standard deviations of the parameters observed for young clusters in the present-day Milky Way $\sigma_{\Gamma}=0.6$, $\sigma_{\gamma}=0.25$, and $\sigma_{M_{ch}}=0.27$ M$_{\odot}$. Increasing the dispersions of $\gamma$ and $\Gamma$ moderately flattens the IGIMF at the low and high mass ends. Increasing $\sigma_{M_{ch}}$ shifts the peak of the IGIMF to lower masses, rendering the IGIMF more bottom heavy. This can explain the bottom heavy stellar mass function of Early-type galaxies as they are the result of the merger of disk galaxies where the physical conditions of the star forming gas vary significantly both in time and space. The effect of IMF variations is compared to that due to other effects such as variations in the shape of the initial cluster mass function, metallicity, and galactic SFR. We find that the effect of IMF variations is a dominant factor that always affects the characteristic mass of the IGIMF. We compare our results to a sample of ultra-faint dwarf satellite galaxies (UFDs). Their present-day stellar mass function is an analog to their IGIMF at the time their stellar populations have formed. We show that the slope of the IGIMF of the UFDs can only be reproduced when IMF variations of the same order as those measured in the present-day Milky Way are included. (Abridged)Comment: Submitte

Feedback Regulated Star Formation: From Star Clusters to Galaxies

This paper summarises results from semi-analytical modelling of star formation in protocluster clumps of different metallicities. In this model, gravitationally bound cores form uniformly in the clump following a prescribed core formation efficiency per unit time. After a contraction timescale which is equal to a few times their free-fall times, the cores collapse into stars and populate the IMF. Feedback from the newly formed OB stars is taken into account in the form of stellar winds. When the ratio of the effective wind energy of the winds to the gravitational energy of the system reaches unity, gas is removed from the clump and core and star formation are quenched. The power of the radiation driven winds has a strong dependence on metallicity and increases with increasing metallicity. Thus, winds from stars in the high metallicity models lead to a rapid evacuation of the gas from the protocluster clump and to a reduced star formation efficiency, SFE_{exp}, as compared to their low metallicity counterparts. By combining SFE_{exp} with the timescales on which gas expulsion occurs, we derive the metallicity dependent star formation rate per unit time in this model as a function of the gas surface density Sigma_{g}. This is combined with the molecular gas fraction in order to derive the dependence of the surface density of star formation Sigma_{SFR} on Sigma_{g}. This feedback regulated model of star formation reproduces very well the observed star formation laws extending from low gas surface densities up to the starburst regime. Furthermore, the results show a dependence of Sigma_{SFR} on metallicity over the entire range of gas surface densities, and can also explain part of the scatter in the observations.Comment: 21 pages, 13 figures, proceedings of "Stellar Clusters and Associations- A RIA workshop on GAIA", 23-27 May 2011, Granada, Spai

Variation of the high-mass slope of the stellar initial mass function: Theory meets observations

We present observational evidence of the correlation between the high-mass slope of the stellar initial mass function (IMF) in young star clusters and their stellar surface density, $\sigma_{*}$. When the high-mass end of the IMF is described by a power law of the form $dN/d{\rm log}{M_{*}}\propto M_{*}^{-\Gamma}$, the value of $\Gamma$ is seen to weakly decrease with increasing $\sigma_{*}$, following a $\Gamma=1.31~\sigma_{*}^{-0.095}$ relation. We also present a model that can explain these observations. The model is based on the idea that the coalescence of protostellar cores in a protocluster forming clump is more efficient in high density environments where cores are more closely packed. The efficiency of the coalescence process is calculated as a function of the parental clump properties and in particular the relation between its mass and radius as well as its core formation efficiency. The main result of this model is that the increased efficiency of the coalescence process leads to shallower slopes of the IMF in agreement with the observations of young clusters, and the observations are best reproduced with compact protocluster forming clumps. These results have significant implications for the shape of the IMF in different Galactic and extragalactic environments and have very important consequences for galactic evolution.Comment: Submitted. Feedback is welcom

Feedback regulated star formation: II. dual constraints on the SFE and the age spread of stars in massive clusters

We show that the termination of the star formation process by winds from massive stars in protocluster forming clumps imposes dual constraints on the star formation efficiencies (SFEs) and stellar age spreads ($\Delta \tau_{*}$) in stellar clusters. We have considered two main classes of clump models. One class of models in one in which the core formation efficiency (CFE) per unit time and as a consequence the star formation rate (SFR) is constant in time and another class of models in which the CFE per unit time, and as a consequence the SFR, increases with time. Models with an increasing mode of star formation yield shorter age spreads (a few 0.1 Myrs) and typically higher SFEs than models in which star formation is uniform in time. We find that the former models reproduce remarkably well the SFE$-\Delta \tau_{*}$ values of starburst clusters such as NGC 3603 YC and Westerlund 1, while the latter describe better the star formation process in lower density environments such as in the Orion Nebula Cluster. We also show that the SFE and $\Delta \tau_{*}$ of massive clusters are expected to be higher in low metallicity environments. This could be tested with future large extragalactic surveys of stellar clusters. We advocate that placing a stellar cluster on the SFE-$\Delta \tau_{*}$ diagram is a powerful method to distinguish between different stellar clusters formation scenarios such as between generic gravitational instability of a gas cloud/clump or as the result of cloud-cloud collisions. It is also a very useful tool for testing star formation theories and numerical models versus the observations.Comment: Accepted to MNRA

Properties of an accretion disc with a power-law stress-pressure relationship

Recent numerical simulations of magnetized accretion discs show that the radial-azimuthal component of the stress tensor due to the magnetorotational instability (MRI) is well represented by a power-law function of the gas pressure rather than a linear relation which has been used in most of the accretion disc studies. The exponent of this power-law function which depends on the net flux of the imposed magnetic field is reported in the range between zero and unity. However, the physical consequences of this power-law stress-pressure relation within the framework of the standard disc model have not been explored so far. In this study, the structure of an accretion disc with a power-law stress-pressure relation is studied using analytical solutions in the steady-state and time-dependent cases. The derived solutions are applicable to different accreting systems, and as an illustrative example, we explore structure of protoplanetary discs using these solutions. We show that the slopes of the radial surface density and temperature distributions become steeper with decreasing the stress exponent. However, if the disc opacity is dominated by icy grains and value of the stress exponent is less than about $0.5$, the surface density and temperature profiles become so steep that make them unreliable. We also obtain analytical solutions for the protoplanetary discs which are irradiated by the host star. Using these solutions, we find that the effect of the irradiation becomes more significant with decreasing the stress exponent.Comment: Accepted for publication in MNRA