Cosmic ray feedback in hydrodynamical simulations of galaxy and structure formation Canadian Institute for Theoretical Astrophysics, Toronto April, 13 26 / Workshop Dark halos, UBC Vancouver
Outline 1 Motivation Cosmic rays in galaxies Violent structure formation Gravitational heating by shocks 2 Cosmic rays in GADGET Mach number finder Cosmological simulations 3 Cluster radio halos CR pressure influences Sunyaev-Zel dovic effect
Cosmic rays in galaxies Violent structure formation Gravitational heating by shocks M51: cosmic ray electron population Fletcher, Beck, Berkhuijsen und Horellou, in prep.
Cosmic rays in galaxies Violent structure formation Gravitational heating by shocks Observations of cluster shock waves 1E 657-56 ( Bullet cluster ) (NASA/SAO/CXC/M.Markevitch et al.) Abell 3667 (Radio: Austr.TC Array. X-ray: ROSAT/PSPC.)
Gravitational heating by shocks Cosmic rays in galaxies Violent structure formation Gravitational heating by shocks The "cosmic web" today. Left: the projected gas density in a cosmological simulation. Right: gravitationally heated intracluster medium through cosmological shock waves.
Cosmic rays in GADGET Mach number finder Cosmological simulations Cosmic rays in GADGET collaboration The talk is based on the following papers: Detecting shock waves in cosmological smoothed particle hydrodynamics simulations, Pfrommer, Springel, Enßlin, & Jubelgas 26, MNRAS, 367, 113, astro-ph/63483 Cosmic ray physics in calculations of cosmological structure formation Enßlin, Pfrommer, Springel, & Jubelgas astro-ph/63484 of galaxy formation Jubelgas, Springel, Enßlin, & Pfrommer astro-ph/63485
Philosophy and description Cosmic rays in GADGET Mach number finder Cosmological simulations An accurate description of CRs should follow the evolution of the spectral energy distribution of CRs as a function of time and space, and keep track of their dynamical, non-linear coupling with the hydrodynamics. We seek a compromise between capturing as many physical properties as possible requiring as little computational resources as possible Assumptions: protons dominate the CR population a momentum power-law is a typical spectrum CR energy & particle number conservation
Philosophy and description Cosmic rays in GADGET Mach number finder Cosmological simulations An accurate description of CRs should follow the evolution of the spectral energy distribution of CRs as a function of time and space, and keep track of their dynamical, non-linear coupling with the hydrodynamics. We seek a compromise between capturing as many physical properties as possible requiring as little computational resources as possible Assumptions: protons dominate the CR population a momentum power-law is a typical spectrum CR energy & particle number conservation
Philosophy and description Cosmic rays in GADGET Mach number finder Cosmological simulations An accurate description of CRs should follow the evolution of the spectral energy distribution of CRs as a function of time and space, and keep track of their dynamical, non-linear coupling with the hydrodynamics. We seek a compromise between capturing as many physical properties as possible requiring as little computational resources as possible Assumptions: protons dominate the CR population a momentum power-law is a typical spectrum CR energy & particle number conservation
Philosophy and description Cosmic rays in GADGET Mach number finder Cosmological simulations CRs are coupled to the thermal gas by magnetic fields. We assume a single power-law CR spectrum: momentum cutoff q, normalization C, spectral index α (constant). determines CR energy density and pressure uniquely The CR spectrum can be expressed by three adiabatic invariants, which scale only with the gas density. Non-adiabatic processes are mapped into changes of the adiabatic constants using mass, energy and momentum conservation.
Cosmic rays in GADGET Mach number finder Cosmological simulations Cosmic rays in GADGET flowchart
Thermal & CR energy spectra Cosmic rays in GADGET Mach number finder Cosmological simulations Kinetic energy per logarithmic momentum interval: 1 ev 1 kev.1mev PSfrag replacements dtcr/d log p = p T p(p) f (p) in mp c 2 1..1 α = 2.25 α = 2.5 α = 2.75.1 MeV.1 1-4 1-3 1-2 1-1 1 1 1 1 2 1 3 p
Radiative cooling Cosmic rays in GADGET Mach number finder Cosmological simulations Cooling of primordial gas: Cooling of cosmic rays: 1 1. ρ = 2.386*1-25 g/cm 3 1-1 1. 1-2 τ cool [ Gyr ] 1-3 τ cool [ Gyr ].1 1-4.1 1-5 ρ = 2.386*1-25 g/cm 3 1 4 1 5 1 6 1 7 1 8 1 9 T [ K ].1.1.1 1. 1. 1. q
Cosmic rays in GADGET Mach number finder Cosmological simulations Cosmic rays in GADGET flowchart
Cosmic rays in GADGET Mach number finder Cosmological simulations Diffusive shock acceleration Fermi 1 mechanism Cosmic rays gain energy E/E υ 1 υ 2 through bouncing back and forth the shock front. Accounting for the loss probability υ 2 of particles leaving the shock downstream leads to power-law CR population. log f strong shock weak shock kev 1 GeV log p
Cosmic rays in GADGET Mach number finder Cosmological simulations Motivation for the Mach number finder cosmological shocks dissipate gravitational energy into thermal gas energy: where and when is the gas heated, and which shocks are mainly responsible for it? shock waves are tracers of the large scale structure and contain information about its dynamical history (warm-hot intergalactic medium) shocks accelerate cosmic rays through diffusive shock acceleration at structure formation shocks: what are the cosmological implications of such a CR component, and does this influence the cosmic thermal history? simulating realistic CR distributions within galaxy clusters provides detailed predictions for the expected radio synchrotron and γ-ray emission
Cosmic rays in GADGET Mach number finder Cosmological simulations Shock tube (CRs & gas, M = 1): thermodynamics Density 1.2 1..8.6.4.2. 1 2 3 4 5 Velocity 5 4 3 2 1 1 2 3 4 5 Pressure 2.5 1 5 2. 1 5 1.5 1 5 1. 1 5 5. 1 4 1 2 3 4 5 Mach number 1 1 1 2 3 4 5
Cosmic rays in GADGET Mach number finder Cosmological simulations Shock tube (CRs & gas): Mach number statistics duth dt d log M 7 1 8 6 1 8 5 1 8 4 1 8 3 1 8 2 1 8 1 1 8 1 1 1 log M replacements du th dt 1 1 9 8 1 8 6 1 8 4 1 8 2 1 8 1 1 1 log M
Cosmic rays in GADGET Mach number finder Cosmological simulations Shock tube (th. gas): Mach number statistics 1 1 8 8 1 7 duth dt d log M 6 1 7 4 1 7 2 1 7 1 1 1 log M 1.5 1 8 1. 1 8 replacements du th dt 5. 1 7 1 1 1 log M
1 8 6 4 2 2 4 6 8 1 Motivation Cosmic rays in GADGET Mach number finder Cosmological simulations Cosmological Mach numbers: weighted by ε diss 1 8 1 y [ h -1 Mpc ] 6 4 Mach number 2 2 4 6 8 1 x [ h -1 Mpc ] 1
1 8 6 4 2 2 4 6 8 1 Motivation Cosmic rays in GADGET Mach number finder Cosmological simulations Cosmological Mach numbers: weighted by ε CR 1 8 1 y [ h -1 Mpc ] 6 4 Mach number 2 2 4 6 8 1 x [ h -1 Mpc ] 1
Cosmic rays in GADGET Mach number finder Cosmological simulations Cosmological Mach number statistics more energy is dissipated in weak shocks internal to collapsed structures than in external strong shocks more energy is dissipated at later times mean Mach number decreases with time
Cosmic rays in GADGET Mach number finder Cosmological simulations Cosmological statistics: influence of reionization reionization epoch at z reion = 1 suppresses efficiently strong shocks at z < z reion due to jump in sound velocity cosmological constant causes structure formation to cease
Cluster radio halos CR pressure influences SZ effect Radio halos as window for non-equilibrium processes Exploring complementary methods for studying cluster formation Each frequency window is sensitive to different processes and cluster properties: optical: gravitational lensing of background galaxies, galaxy velocity dispersion measure gravitational mass X-ray: thermal plasma emission, F X n 2 th Tth thermal gas with abundances, cluster potential, substructure Sunyaev-Zel dovich effect: IC upscattering of CMB photons by thermal electrons, F SZ p th cluster velocity, turbulence, high-z clusters radio synchrotron halos: F sy ε B ε CRe magnetic fields, CR electrons, shock waves diffuse γ-ray emission: F γ n th n CRp CR protons
15 1 5-5 -1-15 -15-1 -5-5 55 1 15 Motivation Cluster radio halos CR pressure influences SZ effect Adiabatic cluster simulation: gas density 15 1 2 1 5 1 1 y [ h -1 Mpc ] -5 1 1 + δ gas -1 1-1 -15-15 -1-5 5 1 15 x [ h -1 Mpc ]
15 1 5-5 -1-15 -15-1 -5-5 55 1 15 Motivation Mass weighted temperature 15 Cluster radio halos CR pressure influences SZ effect 1 6 1 y [ h -1 Mpc ] 5-5 1 5 1 4 <( 1 + δ gas ) T > [ K ] -1 1 3-15 -15-1 -5 5 1 15 x [ h -1 Mpc ]
15 1 5-5 -1 Cluster radio halos CR pressure influences SZ effect -15-15 -1-5 5 1 15 Mach number distribution weighted by ε diss 15 1 1 5 y [ h -1 Mpc ] Mach number -5-1 -15-15 -1-5 5 1 15 x [ h -1 Mpc ] 1
2 1-1 Cluster radio halos CR pressure influences SZ effect -2-2 -1 1 2 Relative CR pressure P CR /P total 2 1 1 1-1 y [ h -1 Mpc ] P CR / ( P th + P CR ) 1-2 -1-2 -2-1 1 2 x [ h -1 Mpc ] 1-3
Cluster radio halos CR pressure influences SZ effect Radio halos as window for non-equilibrium processes Coma radio halo, ν = 1.4 GHz, largest emission diameter 3 Mpc Coma thermal X-ray emission, (2.7 2.5, credit: ROSAT/MPE/Snowden) (2.5 2., credit: Deiss/Effelsberg)
Cluster radio halos CR pressure influences SZ effect Models for radio synchrotron halos in clusters Halo characteristics: smooth unpolarized radio emission at scales of 3 Mpc. Different CR electron populations: Primary accelerated CR electrons: synchrotron/ic cooling times too short to account for extended diffuse emission Re-accelerated CR electrons through resonant interaction with turbulent Alfvén waves: possibly too inefficient, no first principle calculations (Jaffe 1977, Schlickeiser 1987, Brunetti 21) Hadronically produced CR electrons in inelastic collisions of CR protons with the ambient gas (Dennison 198, Vestrad 1982, Miniati 21, Pfrommer 24)
Cluster radio halos CR pressure influences SZ effect Hadronic cosmic ray proton interaction
Cluster radio halos CR pressure influences SZ effect Energetically preferred CR pressure profiles.1 Coma cluster: hadronic minimum energy condition X CRpmin X Bmin XBmin (r), X CRp min (r).1 PSfrag replacements.1 1 1 1 1 r [h 1 7 kpc] X CRp (r) = ε CRp ε th (r), X B (r) = ε B ε th (r) B Coma, min () = 2.4 +1.7 1. µg
1. 1..5.5.. -.5-1. -1. -.5..5 1. Motivation Cluster radio halos CR pressure influences SZ effect Compton y parameter in radiative cluster simulation 1..5 1-6 y [ h -1 Mpc ]. Compton y -.5 1-7 -1. -1. -.5..5 1. x [ h -1 Mpc ]
.5.5.. -.5 -.5..5 Cluster radio halos CR pressure influences SZ effect Compton y difference map: y CR y th 1-5 1-6 y [ h -1 Mpc ].5. -.5 1-7 1-8 -1-8 -1-7 Compton-y difference map: y CR - y th -1-6 -.5..5 x [ h -1 Mpc ] -1-5
Cluster radio halos CR pressure influences SZ effect Simulated CBI observation of y CR y th (with Sievers & Bond) 2 4 6 8 1 12 14 16 18 2 22 2 4 6 8 1 12 14 16 18 2 22
Cluster radio halos CR pressure influences SZ effect Pressure profiles with and without CRs 1. 1. P CR, P th [Code units] 1..1.1.1 1 1 1 R [ h -1 kpc ]
2 1-1 -2-3 -4-2 2 4 6 8 Motivation Cluster radio halos CR pressure influences SZ effect Phase-space diagram of radiative cluster simulation 2 1 4 1 1 3 log[ P CR / P th ] -1-2 1 2 1 1 probability density [arbitrary units] -3-4 -2 2 4 6 8 log[ 1 + δ gas ] 1
Preliminary emerging picture Cluster radio halos CR pressure influences SZ effect Importance of central CR pressure relative to the gas pressure seems to depend on subtle interplay of the following effects: Presence of well developed cool core region Violent merger history of the cluster resulting flat effective spectral index of CRs Cluster mass: ratio of CR-to-thermal cooling times changes with the cluster s virial temperature
Cluster radio halos CR pressure influences SZ effect Non-radiative simulation: entropy profile 1 1 non-radiative simulation 1 9 A th [Code units] 1 8 1 7 1 6 1 1 1 R [ h -1 kpc ]
Cluster radio halos CR pressure influences SZ effect Radiative simulation: entropy profile 1 1 radiative simulation 1 9 A th [Code units] 1 8 1 7 1 6 1 1 1 R [ h -1 kpc ]
Cluster radio halos CR pressure influences SZ effect Radiative simulation: Schwazschild criterion 2 15 Schwarzschild criterion 1 5-5 -1 1 1 1 R [ h -1 kpc ] Cluster profile instable with respect to convection effective mixing?
Cluster radio halos CR pressure influences SZ effect 1. radiative simulation 1. P CR, P th [Code units] 1..1.1.1 1 1 1 R [ h -1 kpc ]
Summary Motivation Cluster radio halos CR pressure influences SZ effect Understanding non-thermal processes is crucial for using clusters as cosmological probes (high-z scaling relations). Radio halos might be of hadronic origin as our simulations suggests tracer of structure formation Dynamical CR feedback influences Sunyaev-Zel dovic effect Outlook Galaxy evolution: CRs might influence energetic feedback, galactic winds, and disk galaxy formation Huge potential and predictive power of cosmological CR simulations/mach number finder provides detailed γ-ray/radio emission maps