We discuss the cosmological simulation code GADGET-2, a new massively parallel TreeSPH code, capable of following a collisionless fluid with the N-body method, and an ideal gas by means of smoothed particle hydrodynamics (SPH). Our implementation of SPH manifestly conserves energy and entropy in regions free of dissipation, while allowing for fully adaptive smoothing lengths. Gravitational forces are computed with a hierarchical multipole expansion, which can optionally be applied in the form of a TreePM algorithm, where only short-range forces are computed with the ‘tree’ method while long-range forces are determined with Fourier techniques. Time integration is based on a quasi-symplectic scheme where long-range and short-range forces can be integrated with different time-steps. Individual and adaptive short-range time-steps may also be employed. The domain decomposition used in the parallelization algorithm is based on a space-filling curve, resulting in high flexibility and tree force errors that do not depend on the way the domains are cut. The code is efficient in terms of memory consumption and required communication bandwidth. It has been used to compute the first cosmological N-body simulation with more than 10 10 dark matter particles, reaching a homogeneous spatial dynamic range of 10 5 per dimension in a three-dimensional box. It has also been used to carry out very large cosmological SPH simulations that account for radiative cooling and star formation, reaching total particle numbers of more than 250 million. We present the algorithms used by the code and discuss their accuracy and performance using a number of test problems. GADGET-2 is publicly released to the research community. Ke yw ords: methods: numerical ‐ galaxies: interactions ‐ dark matter.

/pdf/the-cosmological-simulation-code-gadget-2-48ba4eyb8k.pdf

The Cosmological simulation code GADGET-2

Understanding the formation of stars in galaxies is central to much of modern astrophysics. However, a quantitative prediction of the star formation rate and the initial distribution of stellar masses remains elusive. For several decades it has been thought that the star formation process is primarily controlled by the interplay between gravity and magnetostatic support, modulated by neutral-ion drift (known as ambipolar diffusion in astrophysics). Recently, however, both observational and numerical work has begun to suggest that supersonic turbulent flows rather than static magnetic fields control star formation. To some extent, this represents a return to ideas popular before the importance of magnetic fields to the interstellar gas was fully appreciated. This review gives a historical overview of the successes and problems of both the classical dynamical theory and the standard theory of magnetostatic support, from both observational and theoretical perspectives. The outline of a new theory relying on control by driven supersonic turbulence is then presented. Numerical models demonstrate that, although supersonic turbulence can provide global support, it nevertheless produces density enhancements that allow local collapse. Inefficient, isolated star formation is a hallmark of turbulent support, while efficient, clustered star formation occurs in its absence. The consequences of this theory are then explored for both local star formation and galactic-scale star formation. It suggests that individual star-forming cores are likely not quasistatic objects, but dynamically collapsing. Accretion onto these objects varies depending on the properties of the surrounding turbulent flow; numerical models agree with observations showing decreasing rates. The initial mass distribution of stars may also be determined by the turbulent flow. Molecular clouds appear to be transient objects forming and dissolving in the larger-scale turbulent flow, or else quickly collapsing into regions of violent star formation. Global star formation in galaxies appears to be controlled by the same balance between gravity and turbulence as small-scale star formation, although modulated by cooling and differential rotation. The dominant driving mechanism in star-forming regions of galaxies appears to be supernovae, while elsewhere coupling of rotation to the gas through magnetic fields or gravity may be important.

Control of star formation by supersonic turbulence

Although fundamental for astrophysics, the processes that produce massive stars are not well understood. Large distances, high extinction, and short timescales of critical evolutionary phases make observations of these processes challenging. Lacking good observational guidance, theoretical models have remained controversial. This review offers a basic description of the collapse of a massive molecular core and a critical discussion of the three competing concepts of massive star formation: ▪  monolithic collapse in isolated cores ▪  competitive accretion in a protocluster environment ▪  stellar collisions and mergers in very dense systems We also review the observed outflows, multiplicity, and clustering properties of massive stars, the upper initial mass function and the upper mass limit. We conclude that high-mass star formation is not merely a scaled-up version of low-mass star formation with higher accretion rates, but partly a mechanism of its own, primarily owing to the role of stellar mass ...

Toward Understanding Massive Star Formation

Although fundamental for astrophysics, the processes that produce massive stars are not well understood. Large distances, high extinction, and short timescales of critical evolutionary phases make observations of these processes challenging. Lacking good observational guidance, theoretical models have remained controversial. This review offers a basic description of the collapse of a massive molecular core and a critical discussion of the three competing concepts of massive star formation: 
- monolithic collapse in isolated cores 
- competitive accretion in a protocluster environment 
- stellar collisions and mergers in very dense systems 
We also review the observed outflows, multiplicity, and clustering properties of massive stars, the upper initial mass function and the upper mass limit. We conclude that high-mass star formation is not merely a scaled-up version of low-mass star formation with higher accretion rates, but partly a mechanism of its own, primarily owing to the role of stellar mass and radiation pressure in controlling the dynamics.

/pdf/control-of-star-formation-by-supersonic-turbulence-7wf7lt35b2.pdf

Control of Star Formation by Supersonic Turbulence

A method is described for the numerical calculation of the hydrodynamic evolution of a self-gravitating configuration in two space dimensions with assumed axial symmetry. The calculation is formulated in cylindrical coordinates with respect to a moving Eulerian grid and is solved using explicit hydrodynamics combined with implicit radiative transfer. The physics included is appropriate for calculation of the collapse of a rotating protostellar cloud. The gravitational field is obtained by means of an alternating-direction iterative technique. Numerical tests to demonstrate the correctness of the method are presented for special cases.

Evolution of rotating interstellar clouds. I - Numerical techniques

Evolutionary calculations continuing until well past turnoff are presented for models of low-mass Population II stars which take into account the effects of the diffusion of helium relative to hydrogen. Evolutionary tracks, cluster isochrones and hydrogen distributions were obtained for stellar masses in the range 0.75 to 1.01 solar masses, both in the presence and absence of diffusion. It is found that for a star of a given mass, diffusion speeds up the evolutionary process on the main sequence, although after turnoff evolution is slowed with respect to the case without diffusion. As the stars ascend the red giant branch, their outer regions are remixed so that evidence of helium diffusion is erased, and the evolutionary tracks of the models with and without diffusion converge. Thus, if the age of a globular cluster is determined from the absolute magnitude at turnoff or from fitting isochrones, diffusion results in a 25% reduction in the derived age at a turnoff magnitude of 4.23, and a 14% reduction at a turnoff magnitude of 3.45.

Evolutionary effects of helium diffusion in population II stars

The collapse of an isothermal protostellar cloud with pressure, gravity, and rotation included is followed with two independent computer codes. For the initial condition, a nonaxisymmetric perturbation of mode m = 2 and 50% amplitude is introduced into a cloud of 1 solar mass with a mean density of 1.44 x 10 to the -17g/cu cm and a uniform angular velocity of 1.6 x 10 to the -12 rad/sec. The collapse is followed through an increase in density of over four orders of magnitude to the point where a binary protostar forms. The agreement between the results of the two calculations is good.

Fragmentation in a rotating protostar - A comparison of two three-dimensional computer codes

Numerical calculations have been made for the early stages of collapse of axisymmetric rotating protostars of 1, 2, and 5 solar masses. The calculations employ a range of values of total angular momentum, as well as two types of initial density distribution. The effects of boundary conditions are tested by using constant volume and constant surface pressure with identical initial conditions. The principal result of the calculations is that, in all cases tried, the collapse leads to the formation of a ring structure in the interior of the cloud, with a local density minimum at the center of the cloud. The rings approach equilibrium with a structure consistent with that of previous analytic determinations, after which they undergo further gravitational collapse. The collapse of a two-solar-mass cloud, similar to that assumed by Cameron and Pine (1973), does not appear to lead to the equilibrium nebula these authors construct.

Evolution of rotating interstellar clouds. II - The collapse of protostars of 1, 2, and 5 solar masses

The isothermal collapse of a rotating protostar with pressure and self-gravity is calculated by a hydrodynamic computer code that treats three space dimensions. A number of initial conditions are tested to determine the conditions under which a cloud is unstable to fragmentation. It is shown that fragmentation does not proceed to a significant extent during the first free-fall time, but that in most cases fragmentation has occurred by 1.5 to 2 times the initial free-fall time. The extent to which the density in the fragments is enhanced over that in their surroundings on this time scale depends on the initial ratio of thermal to gravitational energy, but is only weakly dependent on the type and amplitude of the perturbation and on the initial rotational energy.

Criteria for fragmentation in a collapsing rotating cloud

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