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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

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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

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Radio mode theory Cosmic ray feedback

Outline

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Radio mode theory The big picture MHD interactions Open questions

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Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback The big picture MHD interactions Open questions

Radio mode feedback by AGN

Paradigm: super-massive black holes with M ∼ (109 . . . 1010)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

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Radio mode theory Cosmic ray feedback The big picture MHD interactions Open questions

Radio mode feedback by AGN

Paradigm: super-massive black holes with M ∼ (109 . . . 1010)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

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Radio mode theory Cosmic ray feedback The big picture MHD interactions Open questions

AGN feedback – energetics

gravitational binding energy: Egrav = Mσ2, M − σ relation: MBH ∼ M/500 available BH energy to be extracted is E ∼ 0.1MBHc2

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback The big picture MHD interactions Open questions

AGN feedback – energetics

gravitational binding energy: Egrav = Mσ2, M − σ relation: MBH ∼ M/500 available BH energy to be extracted is E ∼ 0.1MBHc2 it follows E Egrav = 0.1 MBH M c σ 2 ∼ 200 300 km/s σ 2 → there is more than enough energy available for AGN feedback!

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback The big picture MHD interactions 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 H = U+PV = 1 γb − 1 PV+PV = γb γb − 1 PV = 4PV, with γb = 4/3

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback The big picture MHD interactions 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 H = U+PV = 1 γb − 1 PV+PV = γb γb − 1 PV = 4PV, with γb = 4/3

  • nly 1PV is directly available for mechanical work on the

surroundings (3PV is stored as internal energy); work done by 2 bubbles in one outburst W = PV = 2 4 3πr 3

b nICMkT ∼ 1059 erg

with rb ∼ 20 kpc, nICM ∼ 10−2 cm−3, kT ∼ 3 keV

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback The big picture MHD interactions 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 × 107 yr AGN heating rate LAGN ∼ PV tbuoy ∼ 1059 erg 1015 s ∼ 1044 erg s ∼ LX i.e. comparable to the X-ray luminosity → necessary condition for balancing X-ray cooling losses and increasing the core entropy Ke = kT/n2/3

e

  • f the ambient ICM!

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback The big picture MHD interactions Open questions

How efficient is heating by AGN feedback?

1 10 100 10-2 100 102 104

Eb, 2500(kTX = 0.7 keV) Eb, 2500(kTX = 1.2 keV) Eb, 2500(kTX = 2.0 keV) Eb, 2500(kTX = 3.5 keV) Eb, 2500(kTX = 5.9 keV)

cool cores non-cool cores

Ecav = 4PVtot [1058 erg] Ke,0 [keV cm2] C.P., Chang, Broderick (2012) Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback The big picture MHD interactions Open questions

How efficient is heating by AGN feedback?

1 10 100 10-2 100 102 104

Eb, 2500(kTX = 0.7 keV) Eb, 2500(kTX = 1.2 keV) Eb, 2500(kTX = 2.0 keV) Eb, 2500(kTX = 3.5 keV) Eb, 2500(kTX = 5.9 keV)

cool cores non-cool cores

Ecav = 4PVtot [1058 erg] Ke,0 [keV cm2] C.P., Chang, Broderick (2012) Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback The big picture MHD interactions Open questions

How efficient is heating by AGN feedback?

1 10 100 10-2 100 102 104

Eb, 2500(kTX = 0.7 keV) Eb, 2500(kTX = 1.2 keV) Eb, 2500(kTX = 2.0 keV) Eb, 2500(kTX = 3.5 keV) Eb, 2500(kTX = 5.9 keV)

cool cores non-cool cores

Ecav = 4PVtot [1058 erg] Ke,0 [keV cm2] C.P., Chang, Broderick (2012) Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback The big picture MHD interactions Open questions

How efficient is heating by AGN feedback?

1 10 100 10-2 100 102 104

Eb, 2500(kTX = 0.7 keV) Eb, 2500(kTX = 1.2 keV) Eb, 2500(kTX = 2.0 keV) Eb, 2500(kTX = 3.5 keV) Eb, 2500(kTX = 5.9 keV)

cool cores non-cool cores

Ecav = 4PVtot [1058 erg] Ke,0 [keV cm2]

max K0

C.P., Chang, Broderick (2012)

AGNs cannot transform CC to NCC clusters (on a buoyancy timescale)

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback The big picture MHD interactions Open questions

Magnetic draping around rising bubbles

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback The big picture MHD interactions Open questions

What is magnetic draping?

is magnetic draping (MD) similar to ram pressure compression? → no density enhancement for MD analytical solution of MD for incompressible flow ideal MHD simulations (right)

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2 4 kpc from stagnation line 0.1 1.0 10.0 100.0 1000.0 10000.0 Density / ambient density

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback The big picture MHD interactions Open questions

What is magnetic draping?

is magnetic draping (MD) similar to ram pressure compression? → no density enhancement for MD analytical solution of MD for incompressible flow 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

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  • 4
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2 4 kpc from stagnation line 0.1 1.0 10.0 100.0 1000.0 10000.0 Density / ambient density

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback The big picture MHD interactions Open questions

Magnetic draping at bubbles: density

log ρ, non-draping versus draping case (Ruszkowski et al. 2007)

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback The big picture MHD interactions Open questions

Magnetic draping at bubbles: magnetic pressure

log B2, non-draping versus draping case (Ruszkowski et al. 2007)

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback The big picture MHD interactions Open questions

Magnetic draping at bubbles: X-ray emission

SX, non-draping versus draping case (Ruszkowski et al. 2007)

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback The big picture MHD interactions 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: M2

A = βγM2/2 > 1

magnetic coherence across the “cylinder of influence”: λB R

>

∼ 1 MA ∼ 0.1 × β 100 −1/2 for sonic motions, 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

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Radio mode theory Cosmic ray feedback The big picture MHD interactions 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) ∼ 108 Schwarzschild radius Schwarzschild radius rSMBH = 2GMSMBH c2 ≃ 1015

  • MSMBH

5 × 109 M⊙

  • cm

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Galactic cosmic ray spectrum

data compiled by Swordy

power-law momentum spectrum with 33 decades in flux and 12 decades in energy likely origin: diffusive shock acceleration at supernova remnants (E 1017 eV)

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Galactic cosmic ray spectrum

data compiled by Swordy

power-law momentum spectrum with 33 decades in flux and 12 decades in energy likely origin: diffusive shock acceleration at supernova remnants (E 1017 eV) pressure of cosmic rays, magnetic fields, and turbulence in the interstellar gas all similar: → CR pressure in cluster cores? → impact of CRs on cooling gas and star formation in ellipticals?

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Interactions of CRs and magnetic fields

CRs scatter on magnetic fields → isotropization of CR momenta CR streaming instability: Kulsrud & Pearce 1969 if vcr > vwaves with respect to the gas, CR excite Alfvén waves scattering off this wave field limits the CRs’ bulk speed ≪ c wave damping: transfer of CR energy and momentum to the thermal gas

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Interactions of CRs and magnetic fields

CRs scatter on magnetic fields → isotropization of CR momenta CR streaming instability: Kulsrud & Pearce 1969 if vcr > vwaves with respect to the gas, CR excite Alfvén waves scattering off this wave field limits the CRs’ bulk speed ≪ c wave damping: transfer of CR energy and momentum to the thermal gas

→ CRs exert a pressure on the thermal gas by means of scattering off Alfvén waves and heat the surrounding gas

cool-core heating: Loewenstein+ 1991, Guo & Oh 2008, C.P . 2013

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

CR transport

total CR velocity vcr = v + vst + vdi (where v ≡ vgas) CRs stream down their own pressure gradient relative to the gas, CRs diffuse in the wave frame due to pitch angle scattering by MHD waves (both transports are along the local direction of B): vst = −vA ∇Pcr |∇Pcr| with vA =

  • B2

4πρ, vdi = −κdi ∇Pcr Pcr ,

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

CR transport

total CR velocity vcr = v + vst + vdi (where v ≡ vgas) CRs stream down their own pressure gradient relative to the gas, CRs diffuse in the wave frame due to pitch angle scattering by MHD waves (both transports are along the local direction of B): vst = −vA ∇Pcr |∇Pcr| with vA =

  • B2

4πρ, vdi = −κdi ∇Pcr Pcr , energy equations with ε = εth + ρv2/2: ∂ε ∂t + ∇· [(ε + Pth + Pcr)v] = Pcr∇· v + |vst· ∇Pcr| ∂εcr ∂t + ∇· (εcrv) + ∇· [(εcr + Pcr)vst] = −Pcr∇· v − |vst· ∇Pcr|

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Messier 87 at radio wavelengths

ν = 1.4 GHz (Owen+ 2000)

expectation: low frequencies sensitive to fossil electrons (E ∼ 100 MeV) → time-integrated activity of AGN feedback!

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Messier 87 at radio wavelengths

ν = 1.4 GHz (Owen+ 2000) ν = 140 MHz (LOFAR/de Gasperin+ 2012)

expectation: low frequencies sensitive to fossil electrons (E ∼ 100 MeV) → time-integrated activity of AGN feedback! LOFAR: halo confined to same region at all frequencies and no low-ν spectral steepening → puzzle of “missing fossil electrons”

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Solutions to the “missing fossil electrons” problem

solutions: special time: M87 turned on ∼ 40 Myr ago after long silence ⇔ conflicts order unity duty cycle inferred from stat. AGN feedback studies (Birzan+ 2012)

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Solutions to the “missing fossil electrons” problem

solutions: special time: M87 turned on ∼ 40 Myr ago after long silence ⇔ conflicts order unity duty cycle inferred from stat. AGN feedback studies (Birzan+ 2012) Coulomb cooling removes fossil electrons → efficient mixing of CR electrons and protons with dense cluster gas → predicts γ rays from CRp-p interactions: p + p → π0 + . . . → 2γ + . . .

100 101 102 103 104 100 101 102 103 104 105 p = ˜ p/mec electron loss timescales, τ = E/ ˙ E [Myr]

  • synch. + IC

Coulomb: 10−1 total loss B = 10µG B = 20µG Coulomb ne [cm−3] = 10−2

C.P . (2013) Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

The gamma-ray picture of M87

high state is time variable → jet emission low state: (1) steady flux (2) γ-ray spectral index (2.2) = CRp index = CRe injection index as probed by LOFAR (3) spatial extension is under investigation (?)

Rieger & Aharonian (2012)

→ confirming this triad would be smoking gun for first γ-ray signal from a galaxy cluster!

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Estimating the CR pressure in M87

X-ray data → n and T profiles assume Xcr = Pcr/Pth = const. (self-consistency requirement) Fγ ∝

  • dV Pcrn enables to

estimate Xcr = 0.31 (allowing for Coulomb cooling with τCoul = 40 Myr)

Rieger & Aharonian (2012)

→ in agreement with non-thermal pressure constraints from dynamical potential estimates (Churazov+ 2010)

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Cosmic-ray heating vs. radiative cooling (1)

CR Alfvén-wave heating: Hcr = −vA· ∇Pcr = −vA

  • Xcr∇rPthΩ + δPcr

δl

  • Alfvén velocity vA = B/√4πρ with

B ∼ Beq from LOFAR and ρ from X-ray data Xcr calibrated to γ rays Pth from X-ray data pressure fluctuations δPcr/δl (e.g., due to weak shocks of M ≃ 1.1)

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Cosmic-ray heating vs. radiative cooling (1)

CR Alfvén-wave heating: Hcr = −vA· ∇Pcr = −vA

  • Xcr∇rPthΩ + δPcr

δl

  • Alfvén velocity vA = B/√4πρ with

B ∼ Beq from LOFAR and ρ from X-ray data Xcr calibrated to γ rays Pth from X-ray data pressure fluctuations δPcr/δl (e.g., due to weak shocks of M ≃ 1.1) radiative cooling: Crad = neniΛcool(T, Z) cooling function Λcool with Z ≃ Z⊙, all quantities determined from X-ray data

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Cosmic-ray heating vs. radiative cooling (2)

Global thermal equilibrium on all scales in M87

1 10 100 10-28 10-27 10-26 10-25 10-24

radius [kpc] Crad, HCR [ergs cm−3 s−1] HCR, Psmooth + δP HCR, Psmooth Crad(0.7 Z⊙ Z 1.3 Z⊙) radial extent of radio halo:

C.P . (2013) Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Local stability analysis (1)

heating kT cooling

isobaric perturbations to global thermal equilibrium CRs are adiabatically trapped by perturbations

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Local stability analysis (1)

heating kT unstable FP cooling

isobaric perturbations to global thermal equilibrium CRs are adiabatically trapped by perturbations

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Local stability analysis (1)

cooling kT unstable FP heating stable FP

isobaric perturbations to global thermal equilibrium CRs are adiabatically trapped by perturbations

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Local stability analysis (1)

cooling unstable FP region of stability region of instability separatrix heating stable FP kT

isobaric perturbations to global thermal equilibrium CRs are adiabatically trapped by perturbations

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Local stability analysis (2)

Theory predicts observed temperature floor at kT ≃ 1 keV

105 106 107 108

  • 5

5 temperature T [K] instability criterion, arsinh(D) “islands of stability” “ocean of instability” XCR = 0.31 XCR = 0.031

C.P . (2013) Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Virgo cluster cooling flow: temperature profile

X-ray observations confirm temperature floor at kT ≃ 1 keV

(Matsushita+ 2002) Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Impact of varying Alfvén speed on CR heating

global thermal equilibrium:

1 10 100 10-28 10-27 10-26 10-25 10-24 radius [kpc] Crad, HCR [erg cm−3 s−1] HCR,⊥, υA ∝ ρ1/2 HCR,, υA ∝ ρ−1/2 HCR, υA = const. Crad(0.7 Z⊙ Z 1.3 Z⊙) radial extent of radio halo:

local stability criterion:

105 106 107 108

  • 5

5 temperature T [K] instability criterion, arsinh(D) “islands of stability” “ocean of instability” HCR,⊥, υA ∝ ρ1/2 HCR,, υA ∝ ρ−1/2 HCR, υA = const.

parametrize B ∝ ραB, which implies vA = B/√4πρ ∝ ραB−1/2: αB = 0.5 is the geometric mean, implying vA = const. αB = 0 for collapse along B, implying vA, ∝ ρ−1/2 αB = 1 for collapse perpendicular to B, implying vA,⊥ ∝ ρ1/2

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Critical length scale of the instability (∼ Fields length)

1 10 100 1 10 100

radius [kpc] critical instability length λcrit [kpc] fsup = 1.0, Z = 0.7 Z⊙ fsup = 1.0, Z = 1.3 Z⊙ fsup = 0.3, Z = 0.7 Z⊙ fsup = 0.3, Z = 1.3 Z⊙ λcrit = r stabilized by CR streaming thermally unstable unstable wavelength larger than system

C.P . (2013) Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

CR heating dominates over thermal conduction

1 10 100 0.1 1.0 10.0 radius [kpc] HCR/Hcond HCR, Psmooth + δP HCR, Psmooth

C.P . (2013) Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Prediction: flattening of high-ν radio spectrum

101 102 103 104 105 1 10 100 1000 10000 frequency ν [MHz] flux density [Jy] radio data continuous inj. continuous inj., switch off hadronically induced emission

C.P . (2013) Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Conclusions on AGN feedback by cosmic-ray heating

LOFAR puzzle of “missing fossil electrons” solved by mixing with dense cluster gas and Coulomb cooling predicted γ rays identified with low state of M87 → estimate CR-to-thermal pressure of Xcr = 0.31 CR Alfvén wave heating balances radiative cooling on all scales within the radio halo (r < 35 kpc) local thermal stability analysis predicts observed temperature floor at kT ≃ 1 keV

  • utlook: simulate steaming CRs coupled to MHD, cosmological

cluster simulations, improve γ-ray and radio observations . . .

  • cf. Loewenstein et al. (1991), Guo & Oh (2008), Enßlin et al. (2011)

Christoph Pfrommer Radio mode theory

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Radio mode theory Cosmic ray feedback Cosmic ray physics Observations of M87 Alfvén-wave heating

Literature for the talk

AGN feedback by cosmic rays:

Pfrommer, Toward a comprehensive model for feedback by active galactic nuclei: new insights from M87 observations by LOFAR, Fermi and H.E.S.S., 2013, ApJ, 779, 10.

Christoph Pfrommer Radio mode theory