Cosmic ray feedback in hydrodynamical simulations. simulations of galaxy and structure formation
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1 Cosmic ray feedback in hydrodynamical simulations of galaxy and structure formation Canadian Institute for Theoretical Astrophysics, Toronto April, / Colloquium University of Victoria
2 Outline 1 Cosmic rays in galaxies Violent structure formation Gravitational heating by shocks 2 Cosmic rays in GADGET Cosmic rays in isolated galaxies Dwarf galaxy formation 3
3 Cosmic rays in galaxies Violent structure formation Gravitational heating by shocks M51: cosmic ray electron population Fletcher, Beck, Berkhuijsen und Horellou, in prep.
4 Cosmic rays in galaxies Violent structure formation Gravitational heating by shocks M82: optical disk, H-α wind, & CR electron halo Thierbach, Wielebinski, Neininger (24, unpublished)
5 Cosmic rays in galaxies Violent structure formation Gravitational heating by shocks Observations of cluster shock waves 1E ( Bullet cluster ) (NASA/SAO/CXC/M.Markevitch et al.) Abell 3667 (Radio: Austr.TC Array. X-ray: ROSAT/PSPC.)
6 Cosmic rays in galaxies Violent structure formation Gravitational heating by shocks Abell 2256: giant radio relic & small halo X-ray (red) & radio (blue, contours) fractional polarisation in color Clarke & Enßlin (26)
7 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.
8 Cosmic rays in GADGET Cosmic rays in isolated galaxies Dwarf galaxy formation 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
9 Philosophy and description Cosmic rays in GADGET Cosmic rays in isolated galaxies Dwarf galaxy formation 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
10 Philosophy and description Cosmic rays in GADGET Cosmic rays in isolated galaxies Dwarf galaxy formation 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
11 Philosophy and description Cosmic rays in GADGET Cosmic rays in isolated galaxies Dwarf galaxy formation 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
12 CR spectral description Cosmic rays in GADGET Cosmic rays in isolated galaxies Dwarf galaxy formation f (p) = q(ρ) = C(ρ) = dn dp dv = C p α θ(p q) ( ρ ρ ) 1 3 q ( ρ ρ ) α+2 3 C p = P p /m p c n CR = C q1 α α 1 P CR = C ( mpc2 6 B α q 2 2, 3 α ) 2
13 Thermal & CR energy spectra Cosmic rays in GADGET Cosmic rays in isolated galaxies Dwarf galaxy formation 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 α = 2.25 α = 2.5 α = MeV p
14 Radiative cooling Cosmic rays in GADGET Cosmic rays in isolated galaxies Dwarf galaxy formation Cooling of primordial gas: Cooling of cosmic rays: 1 1. ρ = 2.386*1-25 g/cm τ cool [ Gyr ] 1-3 τ cool [ Gyr ] ρ = 2.386*1-25 g/cm T [ K ] q
15 Cosmic rays in GADGET Cosmic rays in isolated galaxies Dwarf galaxy formation Cosmic rays in GADGET flowchart
16 Isolated galaxies projections Cosmic rays in GADGET Cosmic rays in isolated galaxies Dwarf galaxy formation 1 1 M 1 11 M 1 12 M z [ h -1 kpc ] x [ h -1 kpc ] z [ h -1 kpc ] x [ h -1 kpc ] z [ h -1 kpc ] x [ h -1 kpc ] z [ h -1 kpc ] z [ h -1 kpc ] z [ h -1 kpc ] x [ h -1 kpc ] x [ h -1 kpc ] -1 1 x [ h -1 kpc ]
17 ] ] ] Isolated galaxies stellar profiles Cosmic rays in GADGET Cosmic rays in isolated galaxies Dwarf galaxy formation 1 1 M 1 11 M 1 12 M z [ h -1 kpc ] x [ h -1 kpc ] z [ h -1 kpc ] x [ h -1 kpc ] z [ h -1 kpc ] x [ h -1 kpc ] Σ(R) [ h M O kpc -12 Σ(R) [ h M O kpc Σ(R) [ h M O kpc R [ h -1 kpc ] R [ h -1 kpc ] R [ h -1 kpc ]
18 Cosmic rays in GADGET Cosmic rays in isolated galaxies Dwarf galaxy formation Isolated galaxies star formation history 1 1 M 1 11 M 1 12 M z [ h -1 kpc ] x [ h -1 kpc ] z [ h -1 kpc ] x [ h -1 kpc ] z [ h -1 kpc ] x [ h -1 kpc ] 6.5 M halo = 1 1 M O M halo = 1 11 M O M halo = 1 12 M O SFR [ M O / yr ].3 SFR [ M O / yr ] 4 SFR [ M O / yr ] T [ Gyr ] T [ Gyr ] T [ Gyr ]
19 Effective equation of state Cosmic rays in GADGET Cosmic rays in isolated galaxies Dwarf galaxy formation Supernova heating balances cooling P [ dyn ] ζ SN =.3 ζ SN = ρ / ρ
20 Cosmic rays in GADGET Cosmic rays in isolated galaxies Dwarf galaxy formation Effective equation of state & phase space distribution Supernova heating balances cooling M galaxy M halo = 1 12 M O P [ dyn ] ζ SN =.3 ζ SN =.1 T eff [ K ] ρ / ρ ρ / ρ
21 Cosmic rays in GADGET Cosmic rays in isolated galaxies Dwarf galaxy formation Effective equation of state & phase space distribution 1 9 M galaxy 1 12 M galaxy M halo = 1 9 M O M halo = 1 12 M O T eff [ K ] T eff [ K ] ρ / ρ ρ / ρ
22 Quenching of dwarf galaxies Cosmic rays in GADGET Cosmic rays in isolated galaxies Dwarf galaxy formation Star formation efficiency suppressed in small halos: 1. no CR M * / Mbaryons.1 z SN =.1 z SN = M halo [ h -1 M O ]
23 Quenching of dwarf galaxies Cosmic rays in GADGET Cosmic rays in isolated galaxies Dwarf galaxy formation Star formation efficiency suppressed in small halos: Averaged mass-to-light ratio: 1 with CR feedback without CR feedback 1. M * / Mbaryons.1 no CR z SN =.1 M halo / M star 1 z SN =.3 1 z = M halo [ h -1 M O ] M halo [ h -1 M O ]
24 Quenching of small galaxies Cosmic rays in GADGET Cosmic rays in isolated galaxies Dwarf galaxy formation Luminosity function (z=3): Averaged mass-to-light ratio: 1 z = 3 1 with CR feedback without CR feedback number of galaxies 1 M halo / M star z = Μ K M halo [ h -1 M O ]
25 Cosmic rays in GADGET flowchart
26 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
27 for the 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
28 Idea of the in SPH SPH shock is broadened to a scale of the order of the smoothing length h, i.e. f h h, and f h 2 approximate instantaneous particle velocity by pre-shock velocity (denoted by υ 1 = M 1 c 1 ) Using the entropy conserving formalism of Springel & Hernquist 22 (A(s) = Pρ γ is the entropic function): A 2 = A 1 + da 1 = 1 + f hh da 1 A 1 A 1 M 1 c 1 A 1 dt ρ 2 ρ 1 = (γ + 1)M 2 1 (γ 1)M P 2 = 2γM2 1 (γ 1) P 1 γ + 1 = P 2 P 1 ( ) γ ρ1 ρ 2
29 Shock tube (CRs & gas, M = 1): thermodynamics Density Velocity Pressure Mach number
30 Shock tube (CRs & gas): Mach number statistics duth dt d log M log M replacements du th dt log M
31 Shock tube (th. gas): Mach number statistics duth dt d log M log M replacements du th dt log M
32 Cosmological Mach numbers: weighted by ε diss y [ h -1 Mpc ] 6 4 Mach number x [ h -1 Mpc ] 1
33 Cosmological Mach numbers: weighted by ε CR y [ h -1 Mpc ] 6 4 Mach number x [ h -1 Mpc ] 1
34 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
35 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
36 Cosmological statistics: resolution study Differential distributions: versus differential Mach number distributions are converged for z < 3 at earlier epochs, weak internal shocks are missing in low resolution simulations
37 Cosmological statistics: resolution study in higher resolution simulations structure forms earlier integrated Mach number distribution converged
38 Adiabatic cluster simulation: gas density y [ h -1 Mpc ] δ gas x [ h -1 Mpc ]
39 Mass weighted temperature y [ h -1 Mpc ] <( 1 + δ gas ) T > [ K ] x [ h -1 Mpc ]
40 Mach number distribution weighted by ε diss y [ h -1 Mpc ] Mach number x [ h -1 Mpc ] 1
41 Relative CR pressure P CR /P total y [ h -1 Mpc ] P CR / ( P th + P CR ) x [ h -1 Mpc ] 1-3
42 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, ( , credit: ROSAT/MPE/Snowden) (2.5 2., credit: Deiss/Effelsberg)
43 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)
44 Hadronic cosmic ray proton interaction
45 Minimum energy criterion (MEC): the idea ε NT What is the energetically least expensive distribution of non-thermal energy density ε NT given the observed synchrotron emissivity? ε NT = ε B + ε CRp + ε CRe minimum energy criterion: ε NT jν! = ε B defining tolerance levels: deviation from minimum by one e-fold ε B min ε B
46 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 r [h 1 7 kpc] X CRp (r) = ε CRp ε th (r), X B (r) = ε B ε th (r) B Coma, min () = µg
47 Compton y parameter in radiative cluster simulation y [ h -1 Mpc ]. Compton y x [ h -1 Mpc ]
48 Compton y difference map: y CR y th y [ h -1 Mpc ] Compton-y difference map: y CR - y th x [ h -1 Mpc ] -1-5
49 Simulated CBI observation of y CR y th (with Sievers & Bond)
50 Pressure profiles with and without CRs P CR, P th [Code units] R [ h -1 kpc ]
51 Phase-space diagram of radiative cluster simulation log[ P CR / P th ] probability density [arbitrary units] log[ 1 + δ gas ] 1
52 Summary Galaxy evolution: CRs significantly reduce the star formation efficiency in small galaxies 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 Outlook Galaxy evolution: CRs might influence energetic feedback, galactic winds, and disk galaxy formation Huge potential and predictive power of cosmological CR simulations/ provides detailed γ-ray/radio emission maps
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