Gravoturbulent Star Formation: Effects of the Equation of State on Stellar Masses

Stars form by gravoturbulent fragmentation of interstellar gas clouds. The supersonic turbulence ubiquitously observed in Galactic molecular gas generates strong density fluctuations with gravity taking over in the densest and most massive regions. Collapse sets in to build up stars and star clusters. Turbulence plays a dual role. On global scales it provides support, while at the same time it can promote local collapse. Stellar birth is thus intimately linked to the dynamic behavior of parental gas clouds, which governs when and where protostellar cores form, and how they contract and grow in mass via accretion from the surrounding cloud material to build up stars. The equation of state plays a pivotal role in the fragmentation process. Under typical cloud conditions, massive stars form as part of dense clusters following the "normal" mass function observed, e.g. in the solar neighborhood. However, for gas with an effective polytropic index greater than unity star formation becomes biased towards isolated massive stars. This is relevant for understanding the properties of zero-metallicity stars (Population III) or stars that form under extreme environmental conditions like in the Galactic center or in luminous starbursts.Comment: 9 pages, 4 figure, to be published in the Proceedings of the IAU Colloquium No. 227, 2005, "Massive Star Birth: A Crossroads of Astrophysics

The Influence of Metallicity on Star Formation in Protogalaxies

In cold dark matter cosmological models, the first stars to form are believed to do so within small protogalaxies. We wish to understand how the evolution of these early protogalaxies changes once the gas forming them has been enriched with small quantities of heavy elements, which are produced and dispersed into the intergalactic medium by the first supernovae. Our initial conditions represent protogalaxies forming within a fossil H II region, a previously ionized region that has not yet had time to cool and recombine. We study the influence of low levels of metal enrichment on the cooling and collapse of ionized gas in small protogalactic halos using three-dimensional, smoothed particle hydrodynamics (SPH) simulations that incorporate the effects of the appropriate chemical and thermal processes. Our previous simulations demonstrated that for metallicities Z < 0.001 Z_sun, metal line cooling alters the density and temperature evolution of the gas by less than 1% compared to the metal-free case at densities below 1 cm-3) and temperatures above 2000 K. Here, we present the results of high-resolution simulations using particle splitting to improve resolution in regions of interest. These simulations allow us to address the question of whether there is a critical metallicity above which fine structure cooling from metals allows efficient fragmentation to occur, producing an initial mass function (IMF) resembling the local Salpeter IMF, rather than only high-mass stars.Comment: 3 pages, 2 figures, First Stars III conference proceeding

The formation of the first galaxies and the transition to low-mass star formation

The formation of the first galaxies at redshifts z ~ 10-15 signaled the transition from the simple initial state of the universe to one of ever increasing complexity. We here review recent progress in understanding their assembly process with numerical simulations, starting with cosmological initial conditions and modelling the detailed physics of star formation. In this context we emphasize the importance and influence of selecting appropriate initial conditions for the star formation process. We revisit the notion of a critical metallicity resulting in the transition from primordial to present-day initial mass functions and highlight its dependence on additional cooling mechanisms and the exact initial conditions. We also review recent work on the ability of dust cooling to provide the transition to present-day low-mass star formation. In particular, we highlight the extreme conditions under which this transition mechanism occurs, with violent fragmentation in dense gas resulting in tightly packed clusters.Comment: 16 pages, 7 figures, appeared in the conference proceedings for IAU Symposium 255: Low-Metallicity Star Formation: From the First Stars to Dwarf Galaxies, a high resolution version (highly recommended) can be found at http://www.ita.uni-heidelberg.de/~tgreif/files/greif08.pd

Cosmological Implications of the Uncertainty in H– Destruction Rate Coefficients

In primordial gas, molecular hydrogen forms primarily through associative detachment of H- and H, thereby destroying the H-. The H- anion can also be destroyed by a number of other reactions, most notably by mutual neutralization with protons. However, neither the associative detachment nor the mutual neutralization rate coefficients are well determined: both may be uncertain by as much as an order of magnitude. This introduces a corresponding uncertainty into the H2 formation rate, which may have cosmological implications. Here we examine the effect that these uncertainties have on the formation of H2 and the cooling of protogalactic gas in a variety of situations. We show that the effect is particularly large for protogalaxies forming in previously ionized regions, affecting our predictions of whether or not a given protogalaxy can cool and condense within a Hubble time, and altering the strength of the ultraviolet background that is required to prevent collapse

Cosmological Implications of the Uncertainty in Astrochemical Rate Coefficients

The cooling of neutral gas of primordial composition, or with very low levels of metal enrichment, depends crucially on the formation of molecular coolants, such as H2 and HD within the gas. Although the chemical reactions involved in the formation and destruction of these molecules are well known, the same cannot be said for the rate coefficients of these reactions, some of which are uncertain by an order of magnitude. Here we discuss two reactions for which large uncertainties exist the formation of H2 by associative detachment of H- with H and the destruction of H- by mutual neutralization with protons. We show that these uncertainties can have a dramatic impact on the effectiveness of cooling during protogalactic collapse

The dependence of the IMF on the density-temperature relation of pre-stellar gas

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)

The stellar mass spectrum from non-isothermal gravoturbulent fragmentation

Identifying the processes that determine the initial mass function of stars (IMF) is a fundamental problem in star formation theory. One of the major uncertainties is the exact chemical state of the star forming gas and its influence on the dynamical evolution. Most simulations of star forming clusters use an isothermal equation of state (EOS). However, theoretical predictions and observations suggest that the effective polytropic exponent gamma in the EOS varies with density. We address these issues and study the effect of a piecewise polytropic EOS on the formation of stellar clusters in turbulent, self-gravitating molecular clouds using three-dimensional, smoothed particle hydrodynamics simulations. To approximate the results of published predictions of the thermal behavior of collapsing clouds, we increase the polytropic exponent gamma from 0.7 to 1.1 at some chosen density n_c, which we vary. The change of thermodynamic state at n_c selects a characteristic mass scale for fragmentation M_ch, which we relate to the peak of the observed IMF. Our investigation generally supports the idea that the distribution of stellar masses depends mainly on the thermodynamic state of the star-forming gas. The thermodynamic state of interstellar gas is a result of the balance between heating and cooling processes, which in turn are determined by fundamental atomic and molecular physics and by chemical abundances. Given the abundances, the derivation of a characteristic stellar mass can thus be based on universal quantities and constants.Comment: 13 pages, 7 figures, accepted by A&

The effect of the dynamical state of clusters on gas expulsion and infant mortality

The star formation efficiency (SFE) of a star cluster is thought to be the critical factor in determining if the cluster can survive for a significant (>50 Myr) time. There is an often quoted critical SFE of ~30 per cent for a cluster to survive gas expulsion. I reiterate that the SFE is not the critical factor, rather it is the dynamical state of the stars (as measured by their virial ratio) immediately before gas expulsion that is the critical factor. If the stars in a star cluster are born in an even slightly cold dynamical state then the survivability of a cluster can be greatly increased.Comment: 6 pages, 2 figures. Review talk given at the meeting on "Young massive star clusters - Initial conditions and environments", E. Perez, R. de Grijs, R. M. Gonzalez Delgado, eds., Granada (Spain), September 2007, Springer: Dordrecht. Replacement to correct mistake in a referenc