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Radio mode theory Cosmic ray feedback Radio mode theory: mechanical versus cosmic-ray heating Christoph Pfrommer Heidelberg Institute for Theoretical Studies, Germany Jul 15, 2014 / Quenching and Quiescence, MPIA Christoph Pfrommer Radio mode theory

Radio mode theory Cosmic ray feedback Outline Radio mode theory 1 The big picture MHD interactions Open questions Cosmic ray feedback 2 Cosmic ray physics Observations of M87 Alfvén-wave heating Christoph Pfrommer Radio mode theory

The big picture Radio mode theory MHD interactions Cosmic ray feedback Open questions Radio mode feedback by AGN Paradigm: super-massive black holes with M ∼ ( 10 9 . . . 10 10 ) M ⊙ co-evolve with their hosting cD galaxies at the centers of galaxy clusters. They launch relativistic jets that blow bubbles, potentially providing energetic feedback to balance cooling. Key points: Perseus cluster (NRAO/VLA/G. Taylor) Christoph Pfrommer Radio mode theory

The big picture Radio mode theory MHD interactions Cosmic ray feedback Open questions Radio mode feedback by AGN Paradigm: super-massive black holes with M ∼ ( 10 9 . . . 10 10 ) M ⊙ co-evolve with their hosting cD galaxies at the centers of galaxy clusters. They launch relativistic jets that blow bubbles, potentially providing energetic feedback to balance cooling. Key points: energy source: release of non-gravitational energy due to accretion on a black hole and its spin jet-ICM interaction and rising of the bubbles: magnetic draping, cosmic ray confinement, entrainment of ICM plasma, duty cycle heating mechanism: 1.) self-regulated to avoid overcooling 2.) thermally stable to explain T floor 3.) low energy coupling efficiency Perseus cluster (NRAO/VLA/G. Taylor) Christoph Pfrommer Radio mode theory

The big picture Radio mode theory MHD interactions Cosmic ray feedback Open questions AGN feedback – energetics gravitational binding energy: E grav = M σ 2 , M − σ relation: M BH ∼ M / 500 available BH energy to be extracted is E ∼ 0 . 1 M BH c 2 Christoph Pfrommer Radio mode theory

The big picture Radio mode theory MHD interactions Cosmic ray feedback Open questions AGN feedback – energetics gravitational binding energy: E grav = M σ 2 , M − σ relation: M BH ∼ M / 500 available BH energy to be extracted is E ∼ 0 . 1 M BH c 2 it follows � 2 � 2 � 300 km/s E = 0 . 1 M BH � c ∼ 200 E grav M σ σ → there is more than enough energy available for AGN feedback! Christoph Pfrommer Radio mode theory

The big picture Radio mode theory MHD interactions Cosmic ray feedback Open questions AGN feedback – thermodynamics relativistic jets displace the ICM at the location of the cavities, i.e. they do pdV work against the ICM, as well as supply internal energy to the cavities total energy required to create the cavity equals its enthalpy γ b 1 H = U + PV = γ b − 1 PV + PV = γ b − 1 PV = 4 PV , with γ b = 4 / 3 Christoph Pfrommer Radio mode theory

The big picture Radio mode theory MHD interactions Cosmic ray feedback Open questions AGN feedback – thermodynamics relativistic jets displace the ICM at the location of the cavities, i.e. they do pdV work against the ICM, as well as supply internal energy to the cavities total energy required to create the cavity equals its enthalpy γ b 1 H = U + PV = γ b − 1 PV + PV = γ b − 1 PV = 4 PV , with γ b = 4 / 3 only 1 PV is directly available for mechanical work on the surroundings (3 PV is stored as internal energy); work done by 2 bubbles in one outburst W = PV = 2 4 b n ICM kT ∼ 10 59 erg 3 π r 3 with r b ∼ 20 kpc, n ICM ∼ 10 − 2 cm − 3 , kT ∼ 3 keV Christoph Pfrommer Radio mode theory

The big picture Radio mode theory MHD interactions Cosmic ray feedback Open questions AGN feedback – luminosity energy release time scale is of order the sound crossing time ∼ buoyant rise time ∼ refill time of displaced bubble volume ∼ 3 × 10 7 yr AGN heating rate ∼ 10 59 erg L AGN ∼ PV ∼ 10 44 erg ∼ L X 10 15 s t buoy s i.e. comparable to the X-ray luminosity → necessary condition for balancing X-ray cooling losses and increasing the core entropy K e = kT / n 2 / 3 of the ambient ICM! e Christoph Pfrommer Radio mode theory

The big picture Radio mode theory MHD interactions Cosmic ray feedback Open questions How efficient is heating by AGN feedback? E b, 2500 ( kT X = 5.9 keV) C.P., Chang, Broderick (2012) 10 4 E b, 2500 ( kT X = 3.5 keV) E b, 2500 ( kT X = 2.0 keV) E cav = 4 PV tot [10 58 erg] E b, 2500 ( kT X = 1.2 keV) 10 2 E b, 2500 ( kT X = 0.7 keV) 10 0 cool cores non-cool cores 10 -2 1 10 100 K e , 0 [keV cm 2 ] Christoph Pfrommer Radio mode theory

The big picture Radio mode theory MHD interactions Cosmic ray feedback Open questions How efficient is heating by AGN feedback? E b, 2500 ( kT X = 5.9 keV) C.P., Chang, Broderick (2012) 10 4 E b, 2500 ( kT X = 3.5 keV) E b, 2500 ( kT X = 2.0 keV) E cav = 4 PV tot [10 58 erg] E b, 2500 ( kT X = 1.2 keV) 10 2 E b, 2500 ( kT X = 0.7 keV) 10 0 cool cores non-cool cores 10 -2 1 10 100 K e , 0 [keV cm 2 ] Christoph Pfrommer Radio mode theory

The big picture Radio mode theory MHD interactions Cosmic ray feedback Open questions How efficient is heating by AGN feedback? E b, 2500 ( kT X = 5.9 keV) C.P., Chang, Broderick (2012) 10 4 E b, 2500 ( kT X = 3.5 keV) E b, 2500 ( kT X = 2.0 keV) E cav = 4 PV tot [10 58 erg] E b, 2500 ( kT X = 1.2 keV) 10 2 E b, 2500 ( kT X = 0.7 keV) 10 0 cool cores non-cool cores 10 -2 1 10 100 K e , 0 [keV cm 2 ] Christoph Pfrommer Radio mode theory

The big picture Radio mode theory MHD interactions Cosmic ray feedback Open questions How efficient is heating by AGN feedback? E b, 2500 ( kT X = 5.9 keV) C.P., Chang, Broderick (2012) 10 4 E b, 2500 ( kT X = 3.5 keV) E b, 2500 ( kT X = 2.0 keV) E cav = 4 PV tot [10 58 erg] E b, 2500 ( kT X = 1.2 keV) 10 2 E b, 2500 ( kT X = 0.7 keV) max K 0 10 0 cool cores non-cool cores 10 -2 1 10 100 K e , 0 [keV cm 2 ] AGNs cannot transform CC to NCC clusters (on a buoyancy timescale) Christoph Pfrommer Radio mode theory

The big picture Radio mode theory MHD interactions Cosmic ray feedback Open questions Magnetic draping around rising bubbles Christoph Pfrommer Radio mode theory

The big picture Radio mode theory MHD interactions Cosmic ray feedback Open questions What is magnetic draping? 10000.0 is magnetic draping (MD) similar to 1000.0 ram pressure compression? Density / ambient density 100.0 → no density enhancement for MD 10.0 analytical solution of MD for 1.0 incompressible flow 0.1 -8 -6 -4 -2 0 2 4 kpc from stagnation line ideal MHD simulations (right) Christoph Pfrommer Radio mode theory

The big picture Radio mode theory MHD interactions Cosmic ray feedback Open questions What is magnetic draping? 10000.0 is magnetic draping (MD) similar to 1000.0 ram pressure compression? Density / ambient density 100.0 → no density enhancement for MD 10.0 analytical solution of MD for 1.0 incompressible flow 0.1 -8 -6 -4 -2 0 2 4 kpc from stagnation line ideal MHD simulations (right) is magnetic flux still frozen into the plasma? yes, but plasma is pulled into the direction of the field lines while field lines get stuck at the obstacle Christoph Pfrommer Radio mode theory

The big picture Radio mode theory MHD interactions Cosmic ray feedback Open questions Magnetic draping at bubbles: density log ρ , non-draping versus draping case (Ruszkowski et al. 2007) Christoph Pfrommer Radio mode theory

The big picture Radio mode theory MHD interactions Cosmic ray feedback Open questions Magnetic draping at bubbles: magnetic pressure log B 2 , non-draping versus draping case (Ruszkowski et al. 2007) Christoph Pfrommer Radio mode theory

The big picture Radio mode theory MHD interactions Cosmic ray feedback Open questions Magnetic draping at bubbles: X-ray emission S X , non-draping versus draping case (Ruszkowski et al. 2007) Christoph Pfrommer Radio mode theory

The big picture Radio mode theory MHD interactions Cosmic ray feedback Open questions Conditions for magnetic draping ambient plasma sufficiently ionized such that flux freezing condition applies super-Alfvénic motion of a cloud through a weakly magnetized plasma: M 2 A = βγ M 2 / 2 > 1 magnetic coherence across the “cylinder of influence”: � β � − 1 / 2 λ B 1 > ∼ 0 . 1 × for sonic motions, ∼ R M A 100 R denotes the curvature radius of the working surface at the stagnation line C.P . & Dursi (2010), Dursi & C.P . (2008) Christoph Pfrommer Radio mode theory

The big picture Radio mode theory MHD interactions Cosmic ray feedback Open questions Open questions on radio mode AGN feedback how is accretion output thermalized? dissipation of waves, turbulence, releasing potential energy, thermal conduction, cosmic-ray heating is heating/cooling balance thermally stable? no: turbulence dissipation, conduction yes: cosmic-ray heating how is the accretion rate tuned? cooling radius (30 kpc) ∼ 10 8 Schwarzschild radius Schwarzschild radius r SMBH = 2 GM SMBH � M SMBH � ≃ 10 15 cm 5 × 10 9 M ⊙ c 2 Christoph Pfrommer Radio mode theory