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Cosmic ray feedback Diversity of cool cores AGN feedback: mechanical versus cosmic-ray heating Christoph Pfrommer in collaboration with Svenja Jacob Heidelberg Institute for Theoretical Studies, Germany June 16, 2015 / ICM physics and

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Cosmic ray feedback Diversity of cool cores

AGN feedback: mechanical versus cosmic-ray heating

Christoph Pfrommer

in collaboration with Svenja Jacob

Heidelberg Institute for Theoretical Studies, Germany

June 16, 2015 / ICM physics and modelling, MPA

Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores

Outline

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Cosmic ray feedback Observations of M87 Cosmic rays Heating

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Diversity of cool cores Cool core sample Bimodality Conclusions

Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Observations of M87 Cosmic rays Heating

Radio mode feedback by AGN: open questions

energy source: release of non-gravitational accretion energy of a black hole jet-ICM interaction and rising bubbles: 1.) magnetic draping → amplification 2.) CR confinement vs. release 3.) excitation of turbulence 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)

cosmic ray heating: 1.) are CRs efficiently mixed into the ICM? 2.) is the CR heating rate sufficient to balance cooling? 3.) how universal is this heating mechanism in cool cores?

Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Observations of M87 Cosmic rays Heating

Messier 87 at radio wavelengths

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

high-ν: freshly accelerated CR electrons low-ν: fossil CR electrons → time-integrated AGN feedback! LOFAR: halo confined to same region at all frequencies and no low-ν spectral steepening → puzzle of “missing fossil electrons”

Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Observations of M87 Cosmic rays 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 AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Observations of M87 Cosmic rays 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 AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Observations of M87 Cosmic rays Heating

Estimating the cosmic-ray pressure in M87

hypothesis: low state of γ-ray emission traces π0 decay in ICM: X-ray data → n and T profiles assume steady-state CR streaming: Pcr ∝ ργcr/2 ∝ Pth Fγ ∝

  • dV Pcrn enables to

estimate Xcr = Pcr/Pth = 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 AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Observations of M87 Cosmic rays Heating

Interactions of cosmic rays and magnetic fields

CRs scatter on magnetic fields → isotropization of CR momenta CR streaming instability: Kulsrud & Pearce 1969 if vcr > vA, CR current provides steady driving force, which amplifies an Alfvén wave field in resonance with the gyroradii of CRs scattering off of this wave field limits the (GeV) CRs’ bulk speed ∼ vA 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 of Alfvén waves

Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Observations of M87 Cosmic rays Heating

Cosmic-ray transport

total CR velocity vcr = v + vst + vdi (where v ≡ vgas) CRs are advected with the flux-frozen B field in the gas CRs stream adiabatically down their own pressure gradient relative to the gas: vst = −vA b b· ∇Pcr |b· ∇Pcr| with b = B |B| and vA =

  • B2

4πρ CRs diffuse in the wave frame due to pitch angle scattering by MHD waves: vdi = −κdi b b· ∇Pcr Pcr ,

Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Observations of M87 Cosmic rays Heating

Cosmic-ray heating vs. radiative cooling (1)

CR Alfvén-wave heating:

(Loewenstein, Zweibel, Begelman 1991, Guo & Oh 2008, Enßlin+ 2011)

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 inferred from 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 AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Observations of M87 Cosmic rays 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 AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Observations of M87 Cosmic rays Heating

Local stability analysis (1)

heating kT cooling

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

Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Observations of M87 Cosmic rays Heating

Local stability analysis (1)

heating kT unstable FP cooling

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

Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Observations of M87 Cosmic rays 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 AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Observations of M87 Cosmic rays 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 AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Observations of M87 Cosmic rays 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 AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Observations of M87 Cosmic rays Heating

Virgo cluster cooling flow: temperature profile

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

Matsushita+ (2002) Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Observations of M87 Cosmic rays Heating

Emerging picture of CR feedback by AGNs

(1) during buoyant rise of bubbles: CRs diffuse and stream outward → CR Alfvén-wave heating (2) if bubbles are disrupted, CRs are injected into the ICM and caught in a turbulent downdraft that is excited by the rising bubbles → CR advection with flux-frozen field → adiabatic CR compression and energizing: Pcr/Pcr,0 = δ4/3 ∼ 20 for compression factor δ = 10 (3) CR escape and outward stream- ing → CR Alfvén-wave heating

CR streaming and diffusion CR injection by bubble disruption and CR energization adiabatic compression turbulent advection: Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Observations of M87 Cosmic rays 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 AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Cool core sample Bimodality Conclusions

How universal is CR heating in cool core clusters?

no γ rays observed from other clusters → Pcr unconstrained strategy: construct sample of 24 cool cores (1) assume Hcr = Crad at r = rcool, 1 Gyr (2) assume steady-state CR streaming: Pcr ∝ ργcr/2 (3) adopt B model from Faraday rotation studies: B = 40 µG ×

  • n/0.1 cm−3αB where αB ∈ {2/3, 1}

(4) calculate hadronic radio and γ-ray emission and compare to observations consequences: ⇒ if Hcr = Crad ∀ r and hadr. emission below observational limits: successful CR heating model that is locally stabilized at ∼ 1 keV ⇒ otherwise CR heating ruled out as dominant heating source

Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Cool core sample Bimodality Conclusions

Cosmic-ray heating in cool core clusters (1)

10 100 r [kpc] 10−28 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} HydraA 10 100 r [kpc] 10−28 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} A383 10 100 r [kpc] 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} A2199 1 10 r [kpc] 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} Virgo 10 100 r [kpc] 10−29 10−28 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} A907 10 100 r [kpc] 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} 2A0335 10 100 r [kpc] 10−28 10−27 10−26 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} A133 10 100 r [kpc] 10−28 10−27 10−26 10−25 10−24 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} A1795 10 100 r [kpc] 10−29 10−28 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} A478 1 10 r [kpc] 10−28 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} A262 10 100 r [kpc] 10−28 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} A1991 10 100 r [kpc] 10−29 10−28 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} A1835

Jacob & C.P . (in prep.) Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Cool core sample Bimodality Conclusions

Cosmic-ray heating in cool core clusters (2)

1 10 100 r [kpc] 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} Perseus 10 100 r [kpc] 10−28 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} A2390 10 100 r [kpc] 10−29 10−28 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} RXJ1504 10 r [kpc] 10−27 10−26 10−25 10−24 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} Ophiuchus 10 100 r [kpc] 10−29 10−28 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} MS1455 100 r [kpc] 10−28 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} RXJ1532 10 100 r [kpc] 10−28 10−27 10−26 10−25 10−24 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} A2029 10 100 r [kpc] 10−29 10−28 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} RBS0797 10 100 r [kpc] 10−29 10−28 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} RXJ1720 10 100 1000 r [kpc] 10−29 10−28 10−27 10−26 10−25 10−24 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} A2204 100 r [kpc] 10−29 10−28 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} RXJ1347 100 r [kpc] 10−28 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} ZwCl3146

Jacob & C.P . (in prep.) Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Cool core sample Bimodality Conclusions

Cosmic-ray heating in Hydra A vs. Perseus

10 100 r [kpc] 10−28 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} HydraA 1 10 100 r [kpc] 10−27 10−26 10−25 Crad,Hcr [ergs−1 cm−3] Crad Hcr, no fluct. Hcr, B ∝ ραB,αB ∈ {2/3,1} Perseus

Jacob & C.P . (in prep.)

2 populations of cool cores emerging: pop 1 (Hydra A, Virgo, . . . ): Hcr = Crad → CR heated? pop 2 (Perseus, Ophiuchus, . . . ): Hcr = Crad: host radio-mini halos!

Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Cool core sample Bimodality Conclusions

Non-thermal pressure balance

0.00 0.05 0.10 0.15 0.20 0.25 0.30 Xcr 0.00 0.05 0.10 0.15 0.20 0.25 0.30 X Xcr,min Xcr,st Hydra A Xcr XB Xnt

Jacob & C.P . (in prep.)

define Xcr = Pcr/Pth and XB = PB/Pth CR heating rate: Hcr = −vA· ∇Pcr ∝ X 0.5

B Xcr

non-thermal pressure at fixed heating rate: Xnt ≡ (XB + Xcr)Hcr = AX −2

cr

+ Xcr → Xcr,min = (2A)1/3

Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Cool core sample Bimodality Conclusions

Hadronic emission: radio and γ rays

A 1 3 3 A 2 6 2 A 3 8 3 A 9 7 A 1 7 9 5 A 1 9 9 1 A 2 1 9 9 H y d r a A V i r g

  • 2

A 3 3 5 A 4 7 8 A 1 8 3 5 A 2 2 9 A 2 2 4 A 2 3 9 M S 1 4 5 5 O p h i u c h u s P e r s e u s R B S 7 9 7 R X J 1 3 4 7 R X J 1 5 4 R X J 1 5 3 2 R X J 1 7 2 Z w C l 3 1 4 6 10−5 10−4 10−3 10−2 10−1 100 101 102 103 Xcr Crad = Hcr Jacob & C.P . (in prep.) Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Cool core sample Bimodality Conclusions

Hadronic emission: radio and γ rays

A 1 3 3 A 2 6 2 A 3 8 3 A 9 7 A 1 7 9 5 A 1 9 9 1 A 2 1 9 9 H y d r a A V i r g

  • 2

A 3 3 5 A 4 7 8 A 1 8 3 5 A 2 2 9 A 2 2 4 A 2 3 9 M S 1 4 5 5 O p h i u c h u s P e r s e u s R B S 7 9 7 R X J 1 3 4 7 R X J 1 5 4 R X J 1 5 3 2 R X J 1 7 2 Z w C l 3 1 4 6 10−5 10−4 10−3 10−2 10−1 100 101 102 103 Xcr Crad = Hcr γ-ray obs., rmax = rcool,1Gyr Jacob & C.P . (in prep.) Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Cool core sample Bimodality Conclusions

Hadronic emission: radio and γ rays

A 1 3 3 A 2 6 2 A 3 8 3 A 9 7 A 1 7 9 5 A 1 9 9 1 A 2 1 9 9 H y d r a A V i r g

  • 2

A 3 3 5 A 4 7 8 A 1 8 3 5 A 2 2 9 A 2 2 4 A 2 3 9 M S 1 4 5 5 O p h i u c h u s P e r s e u s R B S 7 9 7 R X J 1 3 4 7 R X J 1 5 4 R X J 1 5 3 2 R X J 1 7 2 Z w C l 3 1 4 6 10−5 10−4 10−3 10−2 10−1 100 101 102 103 Xcr Crad = Hcr γ-ray obs., rmax = rcool,1Gyr NVSS data, rmax = rcool,1Gyr Jacob & C.P . (in prep.) Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Cool core sample Bimodality Conclusions

Hadronic emission: radio and γ rays

A 1 3 3 A 2 6 2 A 3 8 3 A 9 7 A 1 7 9 5 A 1 9 9 1 A 2 1 9 9 H y d r a A V i r g

  • 2

A 3 3 5 A 4 7 8 A 1 8 3 5 A 2 2 9 A 2 2 4 A 2 3 9 M S 1 4 5 5 O p h i u c h u s P e r s e u s R B S 7 9 7 R X J 1 3 4 7 R X J 1 5 4 R X J 1 5 3 2 R X J 1 7 2 Z w C l 3 1 4 6 10−5 10−4 10−3 10−2 10−1 100 101 102 103 Xcr Crad = Hcr γ-ray obs., rmax = rcool,1Gyr NVSS data, rmax = rcool,1Gyr Radiominihalo, rmax = rMH Jacob & C.P . (in prep.)

CR heating solution ruled out in radio mini-halos (Hcr = Crad)!

Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Cool core sample Bimodality Conclusions

Correlations in cool cores

101 102 rcool [kpc] 10−4 10−3 10−2 10−1 100 101 102 Fν,pred/Fν,obs 10−1 100 101 102 103 SFRIR [M⊙/yr] 10−4 10−3 10−2 10−1 100 101 102 Fν,pred/Fν,obs Jacob & C.P . (in prep.)

possibly cosmic ray-heated cool cores vs. radio mini halo clusters: Fν,obs > Fν,pred: strong radio source = abundant injection of CRs peaked CC profile (rcool 20 kpc) and simmering star formation: cosmic-ray(?) heating is effectively balancing cooling large star formation rates: heating out of balance

Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Cool core sample Bimodality Conclusions

Conclusions on AGN feedback by cosmic-ray heating

cosmic-ray heating in M87: LOFAR puzzle of “missing fossil electrons” in M87 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 central radio halo (r < 35 kpc) local thermal stability analysis predicts observed temperature floor at kT ≃ 1 keV diversity of cool cores: peaked cool cores: possibly stably heated by cosmic rays radio mini halo clusters: cosmic-ray heating ruled out systems are strongly cooling and form stars at large rates

Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Cool core sample Bimodality Conclusions

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. Jacob & Pfrommer, Diversity in cool core clusters: implications for cosmic-ray heating, in prep.

Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Cool core sample Bimodality Conclusions

Additional slides

Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Cool core sample Bimodality Conclusions

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 AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Cool core sample Bimodality Conclusions

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 AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Cool core sample Bimodality Conclusions

Critical length scale of the instability (∼ Fields length)

CR streaming transfers energy to a gas parcel with the rate Hcr = −vA· ∇Pcr ∼ fsvA|∇Pcr|,

where fs is the magnetic suppression factor

line and bremsstrahlung emission radiate energy with a rate Crad limiting size of unstable gas parcel since CR Alfvén-wave heating smoothes out temperature inhomogeneities on small scales: λcrit = fsvAPcr Crad however: unstable wavelength must be supported by the system → constraint on magnetic suppression factor fs

Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Cool core sample Bimodality Conclusions

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 AGN feedback: mechanical versus cosmic-ray heating

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Cosmic ray feedback Diversity of cool cores Cool core sample Bimodality Conclusions

Self-consistent CR pressure in steady state

CR streaming transfers energy per unit volume to the gas as ∆εth = −τAvA· ∇Pcr ≈ Pcr = XcrPth, where τA = δl/vA is the Alfvén crossing time and δl the CR pressure gradient length comparing the first and last term suggests that a constant CR-to-thermal pressure ratio Xcr is a necessary condition if CR streaming is the dominant heating process → thermal pressure profile adjusts to that of the streaming CRs!

Christoph Pfrommer AGN feedback: mechanical versus cosmic-ray heating