Cosmological smoothed particle hydrodynamics simulations: the entropy equation

By Volker Springel, Lars Hernquist Mpa, Harvard-CfA. 2001

794 citations recorded by the source corpus.

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). 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. 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. If the thermal energy is instead used as an independent variable, unphysical solutions can be obtained for this problem. 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. 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. For objects resolved with much larger particle numbers, the two approaches yield consistent results. We trace the origin of the differences to systematic resolution effects in the outer parts of cooling flows. 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. The cumulative effect of this overcooling can be significant. 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. We also demonstrate that the entropy method leads to a greatly reduced scatter in the density–temperature relation of the low-density Lyα forest relative to the thermal energy approach, in accord with theoretical expectations.

Subfields: Astronomy and Astrophysics, Computational Mechanics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/005c2bf53767eace48d2d8bc9579827ca6912e4c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Computational Mechanics

In Nuclear and High Energy Physics

Citations in the corpus

The meaning and consequences of star formation criteria in galaxy models with resolved stellar feedback (2013, background): “…Regardless of how mass turns into stars, a certain feedback strength, hence mass in young stars, is needed to inject enough momentum to offset 1 Smoothing lengths are set adaptively as in Springel & Hernquist (2002), with an approximately constant 64 neighbors enclosed within the smoothing kernel.”
Lyα COOLING EMISSION FROM GALAXY FORMATION (2010, methodology): “The gas dynamics is calculated using a smoothed particle hydrodynamics (SPH) algorithm (e.g., Lucy 1977; Gingold & Monaghan 1977) that conserves both energy and entropy (Springel & Hernquist 2002).”
Mass loss of galaxies due to an ultraviolet background (2008, methodology): “Hydrodynamics is treated with Smoothed Particle Hydrodynamics (SPH; Lucy 1977; Gingold & Monaghan 1977), employing a ‘conservative entropy’ formulation that manifestly conserves energy and entropy (Springel & Hernquist 2002).”
Constraints on the distribution and energetics of fast radio bursts using cosmological hydrodynamic simulations (2014, methodology): “Our simulations are based on the parallel cosmological TreePM-smoothed particle hydrodynamics (SPH) codePGADGET3 (Springel 2005).”
Determining the Properties and Evolution of Red Galaxies from the Quasar Luminosity Function (2005, background): “GADGET-2employs a fully conservative formulation (Springel & Hernquist 2002) of smoothed particle hydrodynamics (SPH), which maintains simultaneous energy and entropy conservation even when smoothing lengths evolve (see e.g., Hernquist 1993b, O’Shea et al. 2005).”
THE METALLICITY EVOLUTION OF INTERACTING GALAXIES (2011, methodology): “Gadget-2 is based on a formulation of SPH (Springel & Hernquist 2002) which conserves both energy and entropy simultaneously (when appropriate).”
Inferring the dark matter power spectrum from the Lyman α forest in high-resolution QSO absorption spectra (2004, methodology): “The simulations were performed with periodic boundary conditions with an equal number of dark matter and gas particles and used the c© 0000 RAS, MNRAS 000, 000–000 conservative ‘entropy-formulation’ of SPH proposed by Springel & Hernquist (2002).”