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

Galactic winds driven by cosmic-ray streaming

Galactic winds are observed in many spiral galaxies with sizes from dwarfs up to the Milky Way, and they sometimes carry a mass in excess of that of newly formed stars by up to a factor of ten. Multiple driving processes of such winds have been proposed, including thermal pressure due to supernova-heating, UV radiation pressure on dust grains, or cosmic ray (CR) pressure. We here study wind formation due to CR physics using a numerical model that accounts for CR acceleration by supernovae, CR thermalization, and advective CR transport. In addition, we introduce a novel implementation of CR streaming relative to the rest frame of the gas. We find that CR streaming drives powerful and sustained winds in galaxies with virial masses M_200 < 10^{11} Msun. In dwarf galaxies (M_200 ~ 10^9 Msun) the winds reach a mass loading factor of ~5, expel ~60 per cent of the initial baryonic mass contained inside the halo's virial radius and suppress the star formation rate by a factor of ~5. In dwarfs, the winds are spherically symmetric while in larger galaxies the outflows transition to bi-conical morphologies that are aligned with the disc's angular momentum axis. We show that damping of Alfven waves excited by streaming CRs provides a means of heating the outflows to temperatures that scale with the square of the escape speed. In larger haloes (M_200 > 10^{11} Msun), CR streaming is able to drive fountain flows that excite turbulence. For halo masses M_200 > 10^{10} Msun, we predict an observable level of H-alpha and X-ray emission from the heated halo gas. We conclude that CR-driven winds should be crucial in suppressing and regulating the first epoch of galaxy formation, expelling a large fraction of baryons, and - by extension - aid in shaping the faint end of the galaxy luminosity function. They should then also be responsible for much of the metal enrichment of the intergalactic medium.Comment: 25 pages, 14 figures, accepted by MNRA

Cosmic ray driven outflows from high redshift galaxies

We study winds in high redshift galaxies driven by a relativistic cosmic ray (proton) component in addition to the hot thermal gas component. Cosmic rays (CRs) are likely to be efficiently generated in supernova shocks inside galaxies. We obtain solutions of such CR driven free winds in a gravitational potential of the NFW form, relevant to galaxies. Cosmic rays naturally provide the extra energy and/or momentum input to the system, needed for a transonic wind solution in a gas with adiabatic index $\gamma=5/3$. We show that CRs can effectively drive winds even when the thermal energy of the gas is lost due to radiative cooling. These wind solutions predict an asymptotic wind speed closely related to the circular velocity of the galaxy. Furthermore, the mass outflow rate per unit star formation rate (eta_w) is predicted to be ~ 0.2-0.5 for massive galaxies, with masses $M \sim 10^{11}-10^{12} M_\odot$. We show eta_w to be inversely proportional to the square of the circular velocity. Magnetic fields at the $\mu$G levels are also required in these galaxies to have a significant mass loss. A large eta_w for small mass galaxies implies that CR driven outflows could provide a strong negative feedback to the star formation in dwarf galaxies. Further, our results will also have important implications to the metal enrichment of the IGM. These conclusions are applicable to the class of free wind models where the source region is confined to be within the sonic point.Comment: Now accepted for publication in MNRAS, Change in the "Discussion and conclusions" sectio

Satellite galaxies in hydrodynamical simulations of Milky Way sized galaxies

Collisionless simulations of the CDM cosmology predict a plethora of dark matter substructures in the halos of Milky Way sized galaxies, yet the number of known luminous satellites galaxies is very much smaller, a discrepancy that has become known as the `missing satellite problem'. The most massive substructures have been shown to be plausibly the hosts of the brightest satellites, but it remains unclear which processes prevent star formation in the many other, purely dark substructures. We use high-resolution hydrodynamic simulations of the formation of Milky Way sized galaxies in order to test how well such self-consistent models of structure formation match the observed properties of the Galaxy's satellite population. For the first time, we include in such calculations feedback from cosmic rays injected into the star forming gas by supernovae as well as the energy input from supermassive black holes growing at the Milky Way's centre and its progenitor systems. We find that non-thermal particle populations quite strongly suppress the star formation efficiency of the smallest galaxies. In fact, our cosmic ray model is able to reproduce the observed faint-end of the satellite luminosity function, while models that include only the effects of cosmic reionization, or galactic winds, do significantly worse. Our simulated satellite population approximately matches available kinematic data on the satellites and their observed spatial distribution. We conclude that a proper resolution of the missing satellite problem likely requires the inclusion of non-standard physics for regulating star formation in the smallest halos, and that cosmic reionization alone may not be sufficient.Comment: 20 pages, 17 figure

Thermal conduction in cosmological SPH simulations

Thermal conduction in the intracluster medium has been proposed as a possible heating mechanism for offsetting central cooling losses in rich clusters of galaxies. In this study, we introduce a new formalism to model conduction in a diffuse ionised plasma using smoothed particle hydrodynamics (SPH), and we implement it in the parallel TreePM/SPH-code GADGET-2. We consider only isotropic conduction and assume that magnetic suppression can be described in terms of an effective conductivity, taken as a fixed fraction of the temperature-dependent Spitzer rate. We also account for saturation effects in low-density gas. Our formulation manifestly conserves thermal energy even for individual and adaptive timesteps, and is stable in the presence of small-scale temperature noise. This allows us to evolve the thermal diffusion equation with an explicit time integration scheme along with the ordinary hydrodynamics. We use a series of simple test problems to demonstrate the robustness and accuracy of our method. We then apply our code to spherically symmetric realizations of clusters, constructed under the assumptions of hydrostatic equilibrium and a local balance between conduction and radiative cooling. While we confirm that conduction can efficiently suppress cooling flows for an extended period of time in these isolated systems, we do not find a similarly strong effect in a first set of clusters formed in self-consistent cosmological simulations. However, their temperature profiles are significantly altered by conduction, as is the X-ray luminosity.Comment: 14 pages, 7 figures, accepted by MNRAS, high resolution version available at http://www.mpa-garching.mpg.de/~jubelgas/conduction.pdf. Fixed typos in eq. 20,22,2