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The road to star formation Thus far we have studied the places where stars form – molecular clouds. We have discussed the ways in which molecular clouds can be observed. We have explored the various constituents of molecular clouds – gas, dust, magnetic fields, cosmic rays and electromagnetic radiation. We have, so to speak, assembled the ingredients. In this chapter we discuss how these ingredients might come together to begin to form a star. In the first half of the chapter we discuss theoretical considerations. We consider the collapse of an isothermal sphere of gas, ignoring the effects of rotation and magnetic fields, and we examine qualitatively what happens. We describe the method of solving the problem using similarity solutions. We go on to discuss hierarchical fragmentation, as a means of breaking a large molecular cloud into an ensemble of stars. We also discuss the thermodynamics of protostellar gas, and explain how the minimum mass for star formation might be determined by the protostellar gas becoming optically thick to its own cooling radiation. We discuss the manner of the collapse to form a star and the possible effects of a magnetic field on this process. In the second half of the chapter we examine some of the observational evidence. At the end we consider the initial mass function for stars. Note that in this chapter we concentrate mainly on relatively low-mass stars, i.e. stars of less than a few times the mass of the Sun. In Chapter 6 we continue to discuss relatively low-mass star formation.

The feedback form pre-main sequence and young stars influences their vicinity. The stars are formed in clusters, which implies that the winds of individual stars collide with each other. Inside of a star cluster, winds thermalize a fraction of their kinetic energy, forming a very hot medium able to escape from the cluster in the form of a large-scale wind. Outside of the cluster, the cluster wind forms a shock front as it interacts with the ambient medium which is accreted onto the expanding shell. A variety of instabilities may develop in such shells, and in some cases they fragment, triggering second generation of star formation. However, if the cluster surpasses a certain mass (depending on the radius and other parameters) the hot medium starts to be thermally unstable even inside of the cluster, forming dense warm clumps. The formation of next generations of stars may start if the clumps are big enough to self-shield against stellar radiation creating cold dense cores.

We study the fragmentation of expanding shells in the context of the linear thin-shell analysis. We simulate shell fragmentation using the flash AMR code and a variant of the Benz SPH code.

We present results of hydrodynamic simulations of star formation triggered by cloud-cloud collisions. During the early stages of star formation, low-mass objects form by gravitational instabilities in protostellar discs. A number of these low-mass objects are in the sub-stellar mass range, including a few objects of planetary mass. The disc instabilities that lead to the formation of low-mass objects in our simulations are the product of disc-disc interactions and/or interactions between the discs and their surrounding gas., 8 pages, 7 figures; accepted for publication in the proceedings of IAU Symposium 249: Exoplanets: Detection, Formation and Dynamics, Y.-S. Sun, S. Ferraz-Mello & J.-L. Zhou (eds.), Cambridge University Press

It has been recently shown by several authors that fragmentation of pre-stellar gas (i.e. at densities from 104 to 1010 particles cm−3 and temperatures of order 10-30 K) depends on the gas thermodynamics much more than it was anticipated in earlier studies, in which only an isothermal behaviour has been assumed for the gas. Here we review the results of a number of numerical hydrodynamic simulations (e.g. Li et al. 2003, Jappsen et al. 2005, Bonnell et al. 2006) in which departure from isothermality has been attempted by employing a polytropic equation of state (eos) with exponent different from unity. In particular, in these studies it has been shown that the dominant fragmentation scale of pre-stellar gas, and hence the peak of the initial mass function (IMF), depends on a polytropic exponent that changes value, from below to above unity, at a critical density (Larson 2005). Furthermore, this piecewise polytropic eos depends on the gas metallicity and fundamental constants. Therefore, the peak of the IMF depends, in turn, also on the gas metallicity and fundamental constants rather than on initial conditions, as it has been previously suggested (e.g. Larson 1995). Hence, we are for the first time in a position to infer theoretically the notion of a universal IMF (at least for its low-mass end).We also present two test cases in which a non-isothermal eos has been used in the context of smoothed particle hydrodynamic (SPH) numerical simulations. In the first case star formation is triggered by means of low-mass clump collisions. These calculations have shown that clump collisions can be a relatively efficient mechanism for the formation of solar-mass protostars and their lower-mass companions (efficiency greater or of order 20-25%; Kitsionas & Whitworth 2006). We have also found that in such collisions protostars form mainly by fragmentation of dense filaments along which it is likely that pairs of protostars capture each other in close binaries surrounded by circumbinary discs. In the second case, the use of a polytropic eos with a varying exponent appropriate for the metallicity of starburst regions (Spaans & Silk 2000, 2005) is shown to be sufficient to obtain a top heavy IMF similar to that observed e.g. in the Galactic centre (Klessen, Spaans & Jappsen 2006). These are preliminary results in the direction of revisiting earlier isothermal calculations that were resolving all densities up to the opacity limit for fragmentation (e.g. Bate et al. 2002ab, 2003), this time also taking into account the thermal properties of the gas in the density range between 104 and 1010 particles cm−3. The next step would be to include self-consistent radiation transport in the calculations, the first attempts for which are already in the making (e.g. Whitehouse & Bate 2004).