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Contradicting results have been reported in the literature with respect to the performance of the numerical techniques employed for the study of supersonic turbulence. We aim at characterising the performance of different particle-based and grid-based techniques on the modelling of decaying supersonic turbulence. Four different grid codes (ENZO, FLASH, TVD, ZEUS) and three different SPH codes (GADGET, PHANTOM, VINE) are compared. We additionally analysed two calculations denoted as PHANTOM A and PHANTOM B using two different implementations of artificial viscosity. Our analysis indicates that grid codes tend to be less dissipative than SPH codes, though details of the techniques used can make large differences in both cases. For example, the Morris & Monaghan viscosity implementation for SPH results in less dissipation (PHANTOM B and VINE versus GADGET and PHANTOM A). For grid codes, using a smaller diffusion parameter leads to less dissipation, but results in a larger bottleneck effect (our ENZO versus FLASH runs). As a general result, we find that by using a similar number of resolution elements N for each spatial direction means that all codes (both grid-based and particle-based) show encouraging similarity of all statistical quantities for isotropic supersonic turbulence on spatial scales k

The formation of the first stars out of metal-free gas appears to result in stars at least an order of magnitude more massive than in the present-day case. We here consider what controls the transition from a primordial to a modern initial mass function. It has been proposed that this occurs when effective metal line cooling occurs at a metallicity threshold of Z/Z_sun > 10^{-3.5}. We study the influence of low levels of metal enrichment on the cooling and collapse of initially ionized gas in small protogalactic halos using three-dimensional, smoothed particle hydrodynamics simulations with particle splitting. Our initial conditions represent protogalaxies forming within a previously ionized H ii region that has not yet had time to cool and recombine. These differ considerably from those used in simulations predicting a metallicity threshold, where the gas was initially cold and only partially ionized. In the centrally condensed potential that we study here, a wide variety of initial conditions for the gas yield a monolithic central collapse. Our models show no fragmentation during collapse to number densities as high as 10^5 cm^{-3}, for metallicities reaching as high as 10^{-1} Z_sun in one rotating case, far above the threshold suggested by previous work. Rotation allows for the formation of gravitationally stable gas disks over large fractions of the local Hubble time. Turbulence slows the growth of the central density slightly, but both spherically symmetric and turbulent initial conditions collapse and form a single sink particle. We therefore argue that fragmentation at moderate density depends on the initial conditions for star formation more than on the metal abundances present., Comment: 29 pages, 8 figures, 3 tables, accepted for publication by ApJ

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 proceedings

We present a simplified chemical and thermal model designed to allow computationally efficient study of the thermal evolution of metal-poor gas within large numerical simulations. Our main simplification is the neglect of the molecular chemistry of the heavy elements. The only molecular chemistry retained within the model is the formation and destruction of molecular hydrogen. Despite this major simplification, the model allows for accurate treatment of the thermal evolution of the gas within a large volume of parameter space. It is valid for temperatures 50 < T < 10000 K and metallicities 0 < Z < 0.1 Z_solar. In gas with a metallicity Z = 0.1 Z_solar, and in the absence of an incident ultraviolet radiation field, it is valid for hydrogen number densities n_H < 500 / t_char cm^-3, where t_char is the size in Myr of the characteristic physical timescale of interest in the problem. If Z << 0.1 Z_solar, or if a strong ultraviolet radiation field is present, then the model remains accurate up to significantly higher densities. We also discuss some possible applications of this model., Comment: 55 pages, 1 figure. Accepted by ApJ. This revised version fixes a number of typographical errors

We study the formation of giant dense cloud complexes and of stars within them by means of SPH numerical simulations of the mildly supersonic collision of gas streams (``inflows'') in the warm neutral medium (WNM). The resulting compressions cause cooling and turbulence generation in the gas, forming a cloud that then becomes self-gravitating and undergoes global collapse. Simultaneously, the turbulent, nonlinear density fluctuations induce fast, local collapse events. The simulations show that: a) The clouds are not in a state of equilibrium. Instead, they undergo secular evolution. Initially, their mass and gravitational energy |Eg| increase steadily, while the turbulent energy Ek reaches a plateau. b) When |Eg| becomes comparable to Ek, global collapse begins, causing a simultaneous increase in both that maintains a near-equipartition condition |Eg| ~ 2 Ek. c) Longer inflow durations delay the onset of global and local collapse, by maintaining a higher turbulent velocity dispersion in the cloud over longer times. d) The star formation rate is large from the beginning, without any period of slow and accelerating star formation. e) The column densities of the local star-forming clumps are very similar to reported values of the column density required for molecule formation, suggesting that locally molecular gas and star formation occur nearly simultaneously. The MC formation mechanism discussed here naturally explains the apparent ``virialized'' state of MCs and the ubiquitous presence of HI halos around them. Within their assumptions, our simulations support the scenario of rapid star formation after MCs are formed, although long (>~ 15 Myr) accumulation periods do occur during which the clouds build up their gravitational energy, and which are expected to be spent in the atomic phase., Comment: Abstract matches version to be published. Corrected link to movies: http://www.astrosmo.unam.mx/~e.vazquez/turbulence/movies/VSetal06/VSetal06.html

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 simulations. Our initial conditions represent protogalaxies forming within a fossil HII region -- a previously ionized HII region which has not yet had time to cool and recombine. Prior to cosmological reionization, such regions should be relatively common, since the characteristic lifetimes of the likely ionizing sources are significantly shorter than a Hubble time. We show that in these regions, H_2 is the dominant and most effective coolant, and that it is the amount of H_2 formed that determines whether or not the gas can collapse and form stars. At the low metallicities (Z < 10^{-3} Z_sun) thought to be associated with the transition from population III to early population II star formation, metal line cooling has an almost negligible effect on the evolution of low density gas, altering 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. Although there is evidence that metal line cooling becomes more effective at higher density, we find no significant differences in behaviour from the metal-free case at any density below our sink particle creation threshold at n = 500 cm^{-3}. Increasing the metallicity also increases the importance of metal line cooling, but it does not significantly affect the dynamical evolution of the low density gas until Z = 0.1 Z_sun. This result holds regardless of whether or not an ultraviolet background is present., Comment: 38 pages, 8 figures, AASTex. Accepted by ApJ. Corrected typos and references

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"

(abridged version) 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). 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. We increase the polytropic exponent gamma from 0.7 to 1.1 at some chosen density n_c, which we vary from from 4.3x10^4 cm^-3 to 4.3x10^7 cm^-3. 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. We find a relation M_ch ~ n_c^-0.5, supporting the idea that the distribution of stellar masses largely depends on the thermodynamic state of the star-forming gas., Comment: 7 pages, including 2 figures: invited talk presented at the conference on "IMF@50: The Stellar Initial Mass Function Fifty Years Later" held at Abbazia di Spineto, Siena, Italy, May 2004; to be published by Kluwer Academic Publishers, edited by E. Corbelli, F. Palla, and H. Zinnecker

Using hydrodynamic simulations we investigate the rotational properties and angular momentum evolution of prestellar and protostellar cores formed from gravoturbulent fragmentation of interstellar gas clouds. We find the specific angular momentum j of prestellar cloud cores in our models to be on average comparable to the observed values. A fraction of prestellar cores is gravitationally unstable and goes into collapse to build up protostars and protostellar systems. Their specific angular momentum is one order of magnitude lower than their parental cores and in agreement with observations of main-sequence binaries. The ratio of rotational to gravitational energy of protostellar cores in the model turns out to be very similar to the observed values. We find, that it is roughly conserved during the main collapse phase. This leads to j proportional to M^{2/3}, where j is specific angular momentum and M core mass. Although the temporal evolution of the angular momentum of individual protostars or protostellar systems is complex and highly time variable, this correlation holds well in a statistical sense for a wide range of turbulent environmental parameters. In addition, high turbulent Mach numbers result in the formation of more numerous protostellar cores with, on average, lower mass. Therefore, models with larger Mach numbers result in cores with lower specific angular momentum. We find, however, no dependence on the spatial scale of the turbulence. Our models predict a close correlation between the angular momentum vectors of neighboring protostars during their main accretion phase. Possible observational signatures are aligned disks and parallel outflows. The latter are indeed observed in some low-mass isolated Bok globules., Comment: Accepted for publication in A&A, 11 pages with 8 figures

The complex impedance of a semiconductor superlattice biased into the regime of negative differential conductivity and driven by an additional GHz ac voltage is computed. From a simulation of the nonlinear spatio-temporal dynamics of traveling field domains we obtain strong variations of the amplitude and phase of the impedance with increasing driving frequency. These serve as fingerprints of the underlying quasiperiodic or frequency locking behavior. An anomalous phase shift appears as a result of phase synchronization of the traveling domains. If the imaginary part of the impedance is compensated by an external inductor, both the frequency and the intensity of the oscillations strongly increase., Comment: 3 pages, 5 figures

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.