Semi-analytical homologous solutions of the gravo-magnetic contraction

We propose an extension of the semi-analytical solutions derived by Lin et al. (1965) describing the two-dimensional homologous collapse of a self-gravitating rotating cloud having uniform density and spheroidal shape, which includes magnetic field (with important restrictions) and thermal pressure. The evolution of the cloud is reduced to three time dependent ordinary equations allowing to conduct a quick and preliminary investigation of the cloud dynamics during the precollapse phase, for a wide range of parameters. We apply our model to the collapse of a rotating and magnetized oblate and prolate isothermal core. Hydrodynamical numerical simulations are performed and comparison with the semi-analytical solutions is discussed. Under the assumption that all cores are similar, an apparent cloud axis ratio distribution is calculated from the sequence of successive evolutionary states for each of a large set of initial conditions. The comparison with the observational distribution of the starless dense cores belonging to the catalog of Jijina et al. (1999) shows a good agreement for the rotating and initially prolate cores (aspect ratio $\simeq 0.5$) permeated by an helical magnetic field ($\simeq 17-20 \mu$G for a density of $\simeq 10^4$ cm$^{-3}$).Comment: accepted for publication in A&

Theory of Feedback in Clusters and Molecular Cloud Turbulence

I review recent numerical and analytical work on the feedback from both low- and high-mass cluster stars into their gasoeus environment. The main conclusions are that i) outflow driving appears capable of maintaing the turbulence in parsec-sized clumps and retarding their collapse from the free-fall rate, although there exist regions within molecular clouds, and even some examples of whole clouds, which are not actively forming stars, yet are just as turbulent, so that a more universal turbulence-driving mechanism is needed; ii) outflow-driven turbulence exhibits specific spectral features that can be tested observationally; iii) feedback plays an important role in reducing the star formation rate; iv) nevertheless, numerical simulations suggest that feedback cannot completely prevent a net contracting motion of clouds and clumps. Therefore, an appealing source for driving the turbulence everywhere in GMCs is the accretion from the environment, at all scales. In this case, feedback's most important role may be to prevent a fraction of the gas nearest to newly formed stars from actually reaching them, thus reducing the star formation efficiency.Comment: 8 pages, no figures. Invited review for IAU symposium 270 'Computational star formation', Ed., J. Alves, B. Elmegreen, J. Girart, V. Trimbl

On the origin of non self-gravitating filaments in the ISM

{Filaments are ubiquitous in the interstellar medium as recently emphasized by Herschel, yet their physical origin remains elusive} {It is therefore important to understand the physics of molecular clouds to investigate how filaments form and what is the role played by various processes such as turbulence and magnetic field.} {We use ideal MHD simulations to study the formation of clumps in various conditions including different magnetization and Mach numbers as well as two completely different setup. We then perform several analysis to compute the shape of the clumps and their link to velocities and forces using various approaches.} {We find that on average, clumps in MHD simulations are more filamentary that clumps in hydrodynamical simulations. Detailed analyses reveal that the filaments are in general preferentially aligned with the strain which means that these structures simply result from the strech induced by turbulence. Moreover filaments tend to be confined by the Lorentz force which therefore lead them to survive longer in magnetized flows. We show that they have in all simulations a typical thickness equal to a few grid cells suggesting that they are primarily associated to the energy dissipation within the flow. We estimate the order of magnitude of the dissipation length associated to the ion-neutral friction and conclude that in well UV shielded regions it is of the order of 0.1 pc and therefore could possibly set the typical size of non self-gravitating filaments.} {Filaments are ubiquitous because they are the results of the very generic turbulent strain and because magnetic field help to keep them coherent. We suggest that energy dissipation is playing a determinant role in their formation.}Comment: 18 pages, to be published in A&

Theories of the initial mass function

We review the various theories which have been proposed along the years to explain the origin of the stellar initial mass function. We pay particular attention to four models, namely the competitive accretion and the theories based respectively on stopped accretion, MHD shocks and turbulent dispersion. In each case, we derive the main assumptions and calculations that support each theory and stress their respective successes and failures or difficulties.Comment: Invited review for IAU symposium 270 'Computational star formation', Ed., J. Alves, B. Elmegreen, J. Girart, V. Trimbl

Analytical star formation rate from gravoturbulent fragmentation

We present an analytical determination of the star formation rate (SFR) in molecular clouds, based on a time-dependent extension of our analytical theory of the stellar initial mass function (IMF). The theory yields SFR's in good agreement with observations, suggesting that turbulence {\it is} the dominant, initial process responsible for star formation. In contrast to previous SFR theories, the present one does not invoke an ad-hoc density threshold for star formation; instead, the SFR {\it continuously} increases with gas density, naturally yielding two different characteristic regimes, thus two different slopes in the SFR vs gas density relationship, in agreement with observational determinations. Besides the complete SFR derivation, we also provide a simplified expression, which reproduces reasonably well the complete calculations and can easily be used for quick determinations of SFR's in cloud environments. A key property at the heart of both our complete and simplified theory is that the SFR involves a {\it density-dependent dynamical time}, characteristic of each collapsing (prestellar) overdense region in the cloud, instead of one single mean or critical freefall timescale. Unfortunately, the SFR also depends on some ill determined parameters, such as the core-to-star mass conversion efficiency and the crossing timescale. Although we provide estimates for these parameters, their uncertainty hampers a precise quantitative determination of the SFR, within less than a factor of a few.Comment: accepted for publication in ApJ

Analytical theory for the initial mass function: III time dependence and star formation rate

The present paper extends our previous theory of the stellar initial mass function (IMF) by including the time-dependence, and by including the impact of magnetic field. The predicted mass spectra are similar to the time independent ones with slightly shallower slopes at large masses and peak locations shifted toward smaller masses by a factor of a few. Assuming that star-forming clumps follow Larson type relations, we obtain core mass functions in good agreement with the observationally derived IMF, in particular when taking into account the thermodynamics of the gas. The time-dependent theory directly yields an analytical expression for the star formation rate (SFR) at cloud scales. The SFR values agree well with the observational determinations of various Galactic molecular clouds. Furthermore, we show that the SFR does not simply depend linearly on density, as sometimes claimed in the literature, but depends also strongly on the clump mass/size, which yields the observed scatter. We stress, however, that {\it any} SFR theory depends, explicitly or implicitly, on very uncertain assumptions like clump boundaries or the mass of the most massive stars that can form in a given clump, making the final determinations uncertain by a factor of a few. Finally, we derive a fully time-dependent model for the IMF by considering a clump, or a distribution of clumps accreting at a constant rate and thus whose physical properties evolve with time. In spite of its simplicity, this model reproduces reasonably well various features observed in numerical simulations of converging flows. Based on this general theory, we present a paradigm for star formation and the IMF.Comment: accepted for publication in Ap

Star formation: statistical measure of the correlation between the prestellar core mass function and the stellar initial mass function

We present a simple statistical analysis of recent numerical simulations exploring the correlation between the core mass function obtained from the fragmentation of a molecular cloud and the stellar mass function which forms from these collapsing cores. Our analysis shows that the distributions of bound cores and sink particles obtained in the simulations are consistent with the sinks being formed predominantly from their parent core mass reservoir, with a statistical dispersion of the order of one third of the core mass. Such a characteristic dispersion suggests that the stellar initial mass function is relatively tightly correlated to the parent core mass function, leading to two similar distributions, as observed. This in turn argues in favor of the IMF being essentially determined at the early stages of core formation and being only weakly affected by the various environmental factors beyond the initial core mass reservoir, at least in the mass range explored in the present study. Accordingly, the final IMF of a star forming region should be determined reasonably accurately, statistically speaking, from the initial core mass function, provided some uniform efficiency factor. The calculations also show that these statistical fluctuations, due e.g. to variations among the core properties, broaden the low-mass tail of the IMF compared with the parent CMF, providing an explanation for the fact that this latter appears to underestimate the number of "pre brown dwarf" cores compared with the observationally-derived brown dwarf IMF.Comment: To appear in ApJ Letter

Simulations of magnetized multiphase galactic disk regulated by supernovae explosions

What exactly controls star formation in the Galaxy remains controversial. In particular, the role of feedback and magnetic field are still partially understood. We investigate the role played by supernovae feedback and magnetic field onto the star formation and the structure of the Galactic disk. We perform numerical simulations of the turbulent, magnetized, self-gravitating, multi-phase, supernovae regulated ISM within a 1 kpc stratified box. We implemented various schemes for the supernovae. This goes from a random distribution at a fixed rate to distributions for which the supernovae are spatially and temporally correlated to the formation of stars. To study the influence of magnetic field on star formation, we perform both hydrodynamical and magneto-hydrodynamical simulations. We find that supernovae feedback has a drastic influence on the galactic evolution. The supernovae distribution is playing a very significant role. When the supernovae are not correlated with star formation events, they do not modify significantly the very high star formation rate obtained without feedback. When the supernovae follow the accretion, the star formation rate can be reduced by a factor up to 30. Magnetic field is also playing a significant role. It reduces the star formation rate by a factor up to 2-3 and reduces the number of collapse sites by a factor of about 2. The exact correlation between the supernovae and the dense gas appears to have significant consequences on the galactic disk evolution and the star formation. This implies that small scale studies are necessary to understand and quantify the feedback efficiency. Magnetic field does influence the star formation at galactic scales by reducing the star formation rate and the number of star formation sites.Comment: to be published in A&

Turbulent molecular clouds

Stars form within molecular clouds but our understanding of this fundamental process remains hampered by the complexity of the physics that drives their evolution. We review our observational and theoretical knowledge of molecular clouds trying to confront the two approaches wherever possible. After a broad presentation of the cold interstellar medium and molecular clouds, we emphasize the dynamical processes with special focus to turbulence and its impact on cloud evolution. We then review our knowledge of the velocity, density and magnetic fields. We end by openings towards new chemistry models and the links between molecular cloud structure and star--formation rates.Comment: To be published in AARv, 58 pages, 13 figures (higher resolution figures will be available on line