Detecting shock waves in cosmological smoothed particle hydrodynamics simulations

By C. Pfrommer, Volker Springel, Torsten A. Ensslin, Martin Jubelgas Mpa, Cita. 2006

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We develop a formalism for the identification and accurate estimation of the strength of structure formation shocks during cosmological smoothed particle hydrodynamics simulations. Shocks play a decisive role not only for the thermalization of gas in virializing structures but also for the acceleration of relativistic cosmic rays (CRs) through diffusive shock acceleration. Our formalism is applicable both to ordinary non-relativistic thermal gas, and to plasmas composed of CRs and thermal gas. To this end, we derive an analytic solution to the one-dimensional Riemann shock tube problem for a composite plasma of CRs and thermal gas. We apply our methods to study the properties of structure formation shocks in high-resolution hydrodynamic simulations of the Lambda cold dark matter (� CDM) model. We find that most of the energy is dissipated in weak internal shocks with Mach numbers M ∼ 2 which are predominantly central flow shocks or merger shock waves traversing halo centres. Collapsed cosmological structures are surrounded by external shocks with much higher Mach numbers up to M ∼ 1000, but they play only a minor role in the energy balance of thermalization. This is because of the higher pre-shock gas densities within non-linear structures, and the significant increase of the mean shock speed as the characteristic halo mass grows with cosmic time. We show that after the epoch of cosmic reionization the Mach number distribution is significantly modified by an efficient suppression of strong external shock waves due to the associated increase of the sound speed of the diffuse gas. Invoking a model for CR acceleration in shock waves, we find that the average strength of shock waves responsible for CR energy injection is higher than that for shocks that dominate the thermalization of the gas. This implies that the dynamical importance of shock-injected CRs is comparatively large in the low-density, peripheral halo infalling regions, but is less important for the weaker flow shocks occurring in central highdensity regions of haloes. When combined with radiative dissipation and star formation, our formalism can also be used to study CR injection by supernova shocks, or to construct models for shock-induced star formation in the interstellar medium.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/84df5621b836c8520db98073be20c2531a330aae

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Citations in the corpus

Formation of Galaxy Clusters (2012, background): “…during cluster formation can be classified nto two broad categories: strong external shocks surrounding filaments and the virialized regions of DM halos and weaker internal shocks, located within the cluster virial radius (e.g., Pfrommer et al. 2006, Skillman et al. 2008, Vazza et al. 2009).”
Cosmic ray transport in galaxy clusters: implications for radio halos, gamma-ray signatures, and cool core heating (2010, background): “A good fraction, however, is directly dissipated in shock waves, mostly in the cluster center, however with the highest Mach number shock waves and therefore the most efficient CR acceleration sites appearing in the cluster outskirts (Miniati et al. 2000; Pfrommer et al. 2006, 2008).”
How do galaxies populate dark matter haloes (2009, background): “…of the dark matter component is combined with either a hydrodynamical (e.g. Cen & Ostriker 2000; Springel & Hernquist 2003; Kereš et al. 2005; Pfrommer et al. 2006; Sijacki et al. 2007) or a semi-analytic (e.g. Kauffmann et al. 1999; Springel et al. 2001; Hatton et al. 2003; Springel et al.…”
Acceleration of primary and secondary particles in galaxy clusters by compressible MHD turbulence: from radio haloes to gamma-rays (2010, background): “…are Galactic Winds and Starburst galaxies (e.g., Völk & Atoyan 1999) and shock waves (e.g., Ensslin et al 1998; Sarazin 1999; Ryu et al 2003; Pfrommer et al. 2006; Skillman et al 2008; Vazza et al 2009b), evidence for the latter process come from the observations of radio relics that…”
DIFFUSIVE SHOCK ACCELERATION SIMULATIONS OF RADIO RELICS (2012, background): “…in filaments and outside cluster virial radii, shocks produced by mergers and flow motions in hotter ICMs are relatively weak with Mach number M . a few (Ryu et al. 2003; Pfrommer et al. 2006; Kang et al. 2007; Skillman et al. 2008; Hoeft et al. 2008; Vazza et al. 2009; Brüggen et al. 2011).”
E pur si muove: Galilean-invariant cosmological hydrodynamical simulations on a moving mesh (2009, background): “…thermal energy per unit mass u1, the dissipative increase in thermal energy per unit time and unit shock surface area dF can be written as (see also Pfrommer et al., 2006) dEdiss dt dF = ρ1v1ρ γ−1 2 (A2 − A1)/(γ − 1), (53) where A1 and A2 are the pre- and postshock entropic functions, and ρ2 is…”
Radio signature of cosmological structure formation shocks (2006, background): “Numerical simulations indicate that those accretion (or ‘external’) shocks reach Mach numbers ≫ 10 (Miniati et al. 2000; Ryu et al. 2003; Pfrommer et al. 2006; Hoeft et al. 2006).”
Cosmic ray feedback in hydrodynamical simulations of galaxy formation (2006, methodology): “…that the strongest shocks occur at low to moderate overdensities in the accretion regions around halos and filaments (Kang et al., 1996; Quilis et al., 1998; Miniati, 2002; Ryu et al., 2003; Pfrommer et al., 2006), and also with the growing importance of cosmic ray loss processes at high densities.”
Smoothed Particle Hydrodynamics in Astrophysics (2010, methodology): “The latter also required the development of a technique to detect shock waves on the fly in SPH, and to measurtheir Mach number (Pfrommer et al., 2006).”
Cosmological Shocks in Adaptive Mesh Refinement Simulations and the Acceleration of Cosmic Rays (2008, methodology): “Attempts at tracing the cosmic ray pressure have been made by Pfrommer et al. (2006, 2007) using an SPH code, and we will be working towards the same goal in the near future within Enzo.”
Cosmological Parameters from Observations of Galaxy Clusters (2011, background): “The highest Mach numbers, of tens or more, should occur in the accretion shocks at the edges of clusters (e.g. Pfrommer et al. 2006).”
Simulating cosmic rays in clusters of galaxies – II. A unified scheme for radio haloes and relics with predictions of the γ-ray emission (2007, methodology): “Our simulations were carried out with an updated and extended version of the distributed-memory parallel TreeSPHcode GADGET-2 (Springel 2005; Springel et al. 2001) that includes s lfconsistent cosmic ray physics (Enßlin et al. 2007; Jubelgaset al. 2007; Pfrommer et al. 2006).”
SIMULATIONS OF DISK GALAXIES WITH COSMIC RAY DRIVEN GALACTIC WINDS (2013, methodology): “We have tested our CR implementation using a standard shock-tube test involving gas and CR fluids (Pfrommer et al. 2006) and found that results accurately match the analytic solution.”
SEARCH FOR COSMIC-RAY-INDUCED GAMMA-RAY EMISSION IN GALAXY CLUSTERS (2013, background): “The intracluster medium (ICM) consists of a hot (1-10 keV) plasma, which has primarily been heated through collisionless shocks that form as a result of the hierarchical build up of galaxy clusters (e.g., Ryu et al. 2003; Pfrommer et al. 2006; Skillman et al. 2008; Vazza et al. 2009).”
Science with the Murchison Widefield Array (2012, background): “When combined with seed magnetic fields, efficient cosmic ray acceleration is possible, resulting in steepspectrum synchrotron emission (Keshet et al. 2004; Pfrommer et al. 2006, 2008; Skillman et al. 2011; ArayaMelo et al. 2012).”
Galaxy growth in the concordance ΛCDM cosmology (2007, methodology): “The development path here has involved continual improvement of the simulation schemes to increase resolution and to treat the accessible physics more realistically (e.g. Cen & Ostriker 2000; Springel & Hernquist 2003; Pfrommer et al. 2006).”
ON THE CLUSTER PHYSICS OF SUNYAEV–ZEL'DOVICH AND X-RAY SURVEYS. I. THE INFLUENCE OF FEEDBACK, NON-THERMAL PRESSURE, AND CLUSTER SHAPES ON Y–M SCALING RELATIONS (2011, background): “…with star formation, supernova (SN) energy feedback and cosmic rays (CRs) from structure formation shocks (for more information on CRs, see Pfrommer et al. 2006a, 2007; Enßlin et al. 2007; Jubelgas et al. 2008); (3)AGN feedback in addition to radiative cooling, star formation, and SN…”