Cosmological Hydrodynamics: Thermal Conduction and Cosmic Rays

Hydrodynamische Simulationen haben sich in den letzten Jahren zu einem wichtigen Werkzeug in der Kosmologie entwickelt. Es ist Ziel dieser Arbeit, einen bestehenden Simulationscode durch weitere physikalische Effekte zu erweitern, um deren Auswirkungen in selbstkonsistenter Art und Weise untersuchen zu können. Es wird ein Formalismus vorgestellt, der die Wärmeleitung in einem heißen, diffusen Plasma nachgebildet. Ferner präsentiere ich eine neuartige Methode, kosmische Teilchenstrahlung durch ein als einfach parametrisiert angenommenes Impulssprektrum der Strahlungsteilchen in hydrodynamischen Simulationen mitsamt ihren dynamischen Effekten zu berücksichtigen und untersuchen. Es zeigt sich in durchgeführten Simulationen, daß die Wärmeleitung, obwohl sie unter bestimmten Umständen die Kühleffekte ausgleichen kann, in den durchgeführten kosmologischen Simulationen nicht zu einer Reduzierung der Akkretionsrate in Galaxienhaufen führte. Es zeigen sich dennoch in Temperatur- und Strahlungsprofilen der simulierten Objekte starke Auswirkungen der Wärmeleitung. Die kosmische Teilchenstrahlung zeigt in weiteren Simulationen deutliche Auswirkungen auf die Evolution von Strukturen, insbesondere bei der Regulierung von Sternentstehung in kleinen Galaxien (solchen mit Virialgeschwindigkeiten von unter ∼ 80km/s). Hier führt sie zu einer staken Unterdrückung der Sternenbildung, in zunehmendem Maße für kleinere Galaxien mit einer geringeren Gesamtmasse. Durch diese Unterdrückung wird bei statistischer Betrachtung auch die Steigung der Leuchtkrafts-Verteilungfunktion von Galaxien an ihrem leuchtschwachen Ende stark beeinflußt; letztere wird deutlich flacher und bringt Simulationsergebnisse somit merklich näher an beobachtete Werte

Detecting shock waves in cosmological smoothed particle hydrodynamics simulations

We develop a formalism for the identification and accurate estimation of the strength of structure formation shocks during cosmological smoothed particle hydrodynamics simulations. Shocks not only play a decisive role for the thermalization of gas in virialising 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 analytical 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 LCDM 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. We show that after the epoch of cosmic reionisation 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. 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. (abridged)Comment: 20 pages, 7 figures, just appeared in MNRAS, full resolution version available at http://www.cita.utoronto.ca/~pfrommer/Publications/MNRAS.367.113.pd

Cosmic ray feedback in hydrodynamical simulations of galaxy and galaxy cluster formation

It is well known that cosmic rays (CRs) contribute significantly to the pressure of the interstellar medium in our own Galaxy, suggesting that they may play an important role in regulating star formation during the formation and evolution of galaxies. We will present a novel numerical treatment of the physics of CRs and its implementation in the parallel smoothed particle hydrodynamics (SPH) code GADGET-2. In our methodology, the non-thermal CR population is treated self-consistently in order to assess its dynamical impact on the thermal gas as well as other implications on cosmological observables. In simulations of galaxy formation, we find that CRs can significantly reduce the star formation efficiencies of small galaxies. This effect becomes progressively stronger towards low mass scales. In cosmological simulations of the formation of dwarf galaxies at high redshift, we find that the total mass-to-light ratio of small halos and the faint-end of the luminosity function are affected. In high resolution simulations of galaxy clusters, we find lower contributions of CR pressure, due to the smaller CR injection efficiencies at low Mach number flow shocks inside halos, and the softer adiabatic index of CRs, which disfavours them when a composite of thermal gas and CRs is adiabatically compressed. Within cool core regions, the CR pressure reaches equipartition with the thermal pressure leading to an enhanced compressibility of the central intra-cluster medium, an effect that increases the central density and pressure of the gas. While the X-ray luminosity in low mass cool core clusters is boosted, the integrated Sunyaev-Zel'dovich effect is only slightly changed. The resolved Sunyaev-Zel'dovich maps, however, show a larger variation with an increased central flux decrement.Comment: 4 pages, 2 figures, to appear in the Proceedings of "Cosmic Frontiers", August 2006, Durham (UK), full resolution version available at http://www.cita.utoronto.ca/~pfrommer/Proceedings/Durham.pd

Cosmological structure formation shocks and cosmic rays in hydrodynamical simulations

Cosmological shock waves during structure formation not only play a decisive role for the thermalization of gas in virializing structures but also for the acceleration of relativistic cosmic rays (CRs) through diffusive shock acceleration. We discuss a novel numerical treatment of the physics of cosmic rays in combination with a formalism for identifying and measuring the shock strength on-the-fly during a smoothed particle hydrodynamics simulation. In our methodology, the non-thermal CR population is treated self-consistently in order to assess its dynamical impact on the thermal gas as well as other implications on cosmological observables. Using this formalism, we study the history of the thermalization process in high-resolution hydrodynamic simulations of the Lambda cold dark matter model. Collapsed cosmological structures are surrounded by shocks with high Mach numbers up to 1000, but they play only a minor role in the energy balance of thermalization. However, this finding has important consequences for our understanding of the spatial distribution of CRs in the large-scale structure. In high resolution simulations of galaxy clusters, we find a low contribution of the averaged CR pressure, due to the small acceleration efficiency of lower Mach numbers of flow shocks inside halos and the softer adiabatic index of CRs. However, within cool core regions, the CR pressure reaches equipartition with the thermal pressure leading there to a lower effective adiabatic index and thus to an enhanced compressibility of the central intracluster medium. This effect increases the central density and pressure of the cluster and thus the resulting X-ray emission and the central Sunyaev-Zel'dovich flux decrement. The integrated Sunyaev-Zel'dovich effect, however, is only slightly changed.Comment: 6 pages, 3 figures, to appear in the Proceedings of "Heating vs. Cooling in Galaxies and Clusters of Galaxies", August 2006, Garching (Germany), full resolution version available at http://www.cita.utoronto.ca/~pfrommer/Proceedings/Garching.pd

Simulating cosmic rays in clusters of galaxies - I. Effects on the Sunyaev-Zel'dovich effect and the X-ray emission

We performed high-resolution simulations of a sample of 14 galaxy clusters that span a mass range from 5 x 10^13 M_solar/h to 2 x 10^15 M_solar/h to study the effects of cosmic rays (CRs) on thermal cluster observables such as X-ray emission and the Sunyaev-Zel'dovich effect. We analyse the CR effects on the intra-cluster medium while simultaneously taking into account the cluster's dynamical state as well as the mass of the cluster. The modelling of the cosmic ray physics includes adiabatic CR transport processes, injection by supernovae and cosmological structure formation shocks, as well as CR thermalization by Coulomb interaction and catastrophic losses by hadronic interactions. While the relative pressure contained in CRs within the virial radius is of the order of 2 per cent in our non-radiative simulations, their contribution rises to 32 per cent in our simulations with dissipative gas physics including radiative cooling, star formation, and supernova feedback. Interestingly, in the radiative simulations the relative CR pressure reaches high values of the order of equipartition with the thermal gas in each cluster galaxy due to the fast thermal cooling of gas which diminishes the thermal pressure support relative to that in CRs. This also leads to a lower effective adiabatic index of the composite gas that increases the compressibility of the intra-cluster medium. This effect slightly increases the central density, thermal pressure and the gas fraction. While the X-ray luminosity in low mass cool core clusters is boosted by up to 40 per cent, the integrated Sunyaev-Zel'dovich effect appears to be remarkably robust and the total flux decrement only slightly reduced by typically 2 per cent. The resolved Sunyaev-Zel'dovich maps, however, show a larger variation with an increased central flux decrement. [abridged]Comment: 25 pages, 15 figures, accepted by MNRAS, full resolution version available at http://www.cita.utoronto.ca/~pfrommer/Publications/CRs_clusters.pd

Cosmic ray feedback in hydrodynamical simulations of galaxy formation

It is well known that cosmic rays (CRs) contribute significantly to the pressure of the interstellar medium in our own Galaxy, suggesting that they may play an important role in regulating star formation during the formation and evolution of galaxies. We here discuss a novel numerical treatment of the physics of CRs and its implementation in the parallel smoothed particle hydrodynamics code GADGET-2. In our methodology, the non-thermal CR population of each gaseous fluid element is approximated by a simple power law spectrum in particle momentum, characterized by an amplitude, a cut-off, and a fixed slope. Adiabatic compression, and a number of physical source and sink terms are modelled which modify the CR pressure of each particle. The most important sources considered are injection by supernovae and diffusive shock acceleration, while the primary sinks are thermalization by Coulomb interactions, and catastrophic losses by hadronic interactions. We also include diffusion of CRs. Our scheme allows us to carry out the first cosmological structure formation simulations that self-consistently account for CR physics. In simulations of isolated galaxies, we find that CRs can significantly reduce the star formation efficiencies of small galaxies, with virial velocities below \~80 km/s, an effect that becomes progressively stronger towards low mass scales. In cosmological simulations at high redshift, the total mass-to-light ratio of small halos and the faint-end of the luminosity function are strongly affected. When CR acceleration in shocks is followed as well, up to ~40% of the energy dissipated at structure formation shocks can appear as CR pressure at z~3-6, but this fraction drops to ~10% at low redshifts when the shock distribution becomes increasingly dominated by lower Mach numbers. (abridged)Comment: submitted to A&A, 36 pages, 27 figures (partially in reduced resolution

Thermal Conduction in Simulated Galaxy Clusters

We study the formation of clusters of galaxies using high-resolution hydrodynamic cosmological simulations that include the effect of thermal conduction with an effective isotropic conductivity of 1/3 the classical Spitzer value. We find that, both for a hot ($T_{\rm ew}\simeq 12$ keV) and several cold ($T_{\rm ew}\simeq 2$ keV) galaxy clusters, the baryonic fraction converted into stars does not change significantly when thermal conduction is included. However, the temperature profiles are modified, particularly in our simulated hot system, where an extended isothermal core is readily formed. As a consequence of heat flowing from the inner regions of the cluster both to its outer parts and into its innermost resolved regions, the entropy profile is altered as well. This effect is almost negligible for the cold cluster, as expected based on the strong temperature dependence of the conductivity. Our results demonstrate that while thermal conduction can have a significant influence on the properties of the intra--cluster medium of rich galaxy clusters, it appears unlikely to provide by itself a solution for the overcooling problem in clusters, or to explain the current discrepancies between the observed and simulated properties of the intra--cluster medium.Comment: 4 Pages, 3 Figures, Submitted to ApJ-Letter

The importance of the merging activity for the kinetic polarization of the Sunyaev-Zel'dovich signal from galaxy clusters

The polarization sensitivity of the upcoming millimetric observatories will open new possibilities for studying the properties of galaxy clusters and for using them as powerful cosmological probes. For this reason it is necessary to investigate in detail the characteristics of the polarization signals produced by their highly ionized intra-cluster medium (ICM). This work is focussed on the polarization effect induced by the ICM bulk motions, the so-called kpSZ signal, which has an amplitude proportional to the optical depth and to the square of the tangential velocity. In particular we study how this polarization signal is affected by the internal dynamics of galaxy clusters and what is its dependence on the physical modelling adopted to describe the baryonic component. This is done by producing realistic kpSZ maps starting from the outputs of two different sets of high-resolution hydrodynamical N-body simulations. The first set (17 objects) follows only non-radiative hydrodynamics, while for each of 9 objects of the second set we implement four different kinds of physical processes. Our results shows that the kpSZ signal turns out to be a very sensitive probe of the dynamical status of galaxy clusters. We find that major merger events can amplify the signal up to one order of magnitude with respect to relaxed clusters, reaching amplitude up to about 100 nuK. This result implies that the internal ICM dynamics must be taken into account when evaluating this signal because simplicistic models, based on spherical rigid bodies, may provide wrong estimates. Finally we find that the dependence on the physical modelling of the baryonic component is relevant only in the very inner regions of clusters.Comment: 13 pages, 7 figures, submitted to A&

An implementation of radiative transfer in the cosmological simulation code GADGET

We present a novel numerical implementation of radiative transfer in the cosmological smoothed particle hydrodynamics (SPH) simulation code {\small GADGET}. It is based on a fast, robust and photon-conserving integration scheme where the radiation transport problem is approximated in terms of moments of the transfer equation and by using a variable Eddington tensor as a closure relation, following the `OTVET'-suggestion of Gnedin & Abel. We derive a suitable anisotropic diffusion operator for use in the SPH discretization of the local photon transport, and we combine this with an implicit solver that guarantees robustness and photon conservation. This entails a matrix inversion problem of a huge, sparsely populated matrix that is distributed in memory in our parallel code. We solve this task iteratively with a conjugate gradient scheme. Finally, to model photon sink processes we consider ionisation and recombination processes of hydrogen, which is represented with a chemical network that is evolved with an implicit time integration scheme. We present several tests of our implementation, including single and multiple sources in static uniform density fields with and without temperature evolution, shadowing by a dense clump, and multiple sources in a static cosmological density field. All tests agree quite well with analytical computations or with predictions from other radiative transfer codes, except for shadowing. However, unlike most other radiative transfer codes presently in use for studying reionisation, our new method can be used on-the-fly during dynamical cosmological simulation, allowing simultaneous treatments of galaxy formation and the reionisation process of the Universe.Comment: 21 pages, 17 figures, published in MNRA

Particle hydrodynamics with tessellation techniques

Lagrangian smoothed particle hydrodynamics (SPH) is a well-established approach to model fluids in astrophysical problems, thanks to its geometric flexibility and ability to automatically adjust the spatial resolution to the clumping of matter. However, a number of recent studies have emphasized inaccuracies of SPH in the treatment of fluid instabilities. The origin of these numerical problems can be traced back to spurious surface effects across contact discontinuities, and to SPH's inherent prevention of mixing at the particle level. We here investigate a new fluid particle model where the density estimate is carried out with the help of an auxiliary mesh constructed as the Voronoi tessellation of the simulation particles instead of an adaptive smoothing kernel. This Voronoi-based approach improves the ability of the scheme to represent sharp contact discontinuities. We show that this eliminates spurious surface tension effects present in SPH and that play a role in suppressing certain fluid instabilities. We find that the new `Voronoi Particle Hydrodynamics' described here produces comparable results than SPH in shocks, and better ones in turbulent regimes of pure hydrodynamical simulations. We also discuss formulations of the artificial viscosity needed in this scheme and how judiciously chosen correction forces can be derived in order to maintain a high degree of particle order and hence a regular Voronoi mesh. This is especially helpful in simulating self-gravitating fluids with existing gravity solvers used for N-body simulations.Comment: 26 pages, 24 figures, currentversion is accepted by MNRA