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Thus, cosmological hydrodynamic simulations must incorporate these dissipative effects to determine the formation sites and stellar masses of galaxies.
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Cooling is critically important in the conventional paradigm of galaxy formation, because it enables baryons to accumulate in the centres of haloes, where they act as a reservoir of cold, dense gas for forming stars. These numerical complications follow once radiative cooling of the gas is included. While cosmological SPH simulations have also provided a successful instrument for exploring galaxy formation, it has recently become clear that subtle numerical properties of existing algorithms severely influence characteristics of model galaxies, such as their luminosities and colours. Together with subsequent applications, these works demonstrated the reliability of the approach, and ultimately influenced our understanding of, e.g., quasar absorption-line systems, the intracluster medium, and galaxy interactions. The use of SPH to study the formation and evolution of galaxies was pioneered more than a decade ago by a number of researchers ( Evrard 1988, 1990 Hernquist 1989 Hernquist & Katz 1989 Barnes & Hernquist 1991 Hiotelis & Voglis 1991 Katz & Gunn 1991 Navarro & Benz 1991 Katz, Hernquist & Weinberg 1992 Thomas & Couchman 1992, among others). Steinmetz & Müller 1993), albeit at the expense of an artificial viscosity which broadens shocks over several smoothing lengths. It has been shown that SPH can produce accurate results in many situations (e.g. The Lagrangian nature of SPH enables it to adjust to the large dynamic range posed by problems such as the formation of galaxies and large-scale structure in a manner that is difficult to match with non-adaptive Eulerian methods.
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Smoothed particle hydrodynamics (SPH) was introduced by Gingold & Monaghan (1977) and Lucy (1977) as an alternative to grid-based fluid solvers, and has developed into a mature and popular simulation technique. Methods: numerical, galaxies: evolution, galaxies: starburst 1 Introduction We also demonstrate that the entropy method leads to a greatly reduced scatter in the density–temperature relation of the low-density Ly α forest relative to the thermal energy approach, in accord with theoretical expectations. In cosmological simulations of moderate size, we find that the fraction of baryons which cool and condense can be reduced by up to a factor ∼2 if the entropy equation is employed rather than the thermal energy equation, partly explaining discrepancies with semi-analytic treatments of galaxy formation. The cumulative effect of this overcooling can be significant. When the thermal energy equation is integrated and the resolution is low, the compressional heating of the gas in the inflow region is underestimated, violating entropy conservation and improperly accelerating cooling. We trace the origin of the differences to systematic resolution effects in the outer parts of cooling flows. For objects resolved with much larger particle numbers, the two approaches yield consistent results. When applied to these problems, the thermal energy version of SPH leads to substantial overcooling in haloes that are resolved with up to a few thousand particles, while the entropy formulation is biased only moderately low for these haloes under the same circumstances. We also examine the radiative cooling of gas spheres that collapse and virialize in isolation, and of haloes that form in cosmological simulations of structure formation. If the thermal energy is instead used as an independent variable, unphysical solutions can be obtained for this problem. To test various formulations of SPH, we consider point-like energy injection, as in certain models of supernova feedback, and find that powerful explosions are well represented by SPH even when the energy is deposited into a single particle, provided that the entropy equation is integrated. In this context, we derive a new version of SPH that, when appropriate, manifestly conserves both energy and entropy if smoothing lengths are allowed to adapt freely to the local mass resolution. We discuss differences in simulation results that arise between the use of either the thermal energy or the entropy as an independent variable in smoothed particle hydrodynamics (SPH).