Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
Cosmic rays in galaxy clusters andcosmological shock waves
Going beyond gas physics
Christoph Pfrommer
Canadian Institute for Theoretical Astrophysics, Toronto
Mar. 13 2006 / Colloquium UBC, Vancouver
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
Outline
1 Non-equilibrium processes in clustersIntroductionCluster radio halosMinimum energy condition
2 Cosmic rays in GADGET
Importance of cosmic ray feedbackPhilosophy and description
3 Cosmological shock wavesObservations of cluster shocksMach number finderCosmological simulationsCluster simulations
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
Outline
1 Non-equilibrium processes in clustersIntroductionCluster radio halosMinimum energy condition
2 Cosmic rays in GADGET
Importance of cosmic ray feedbackPhilosophy and description
3 Cosmological shock wavesObservations of cluster shocksMach number finderCosmological simulationsCluster simulations
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
Outline
1 Non-equilibrium processes in clustersIntroductionCluster radio halosMinimum energy condition
2 Cosmic rays in GADGET
Importance of cosmic ray feedbackPhilosophy and description
3 Cosmological shock wavesObservations of cluster shocksMach number finderCosmological simulationsCluster simulations
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
IntroductionCluster radio halosMinimum energy condition
Galaxy clusters
Galaxy clusters are dynamically evolving dark matter potential wells:
protons and electronsshock waves inject CR
CRe: ~ 10 GeV
gas: ~ 3 keVB: ~ 3 muG
synchrotron emission
Energy
diffuse radio (GHz)
Space
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
IntroductionCluster radio halosMinimum energy condition
Radio halos as window for non-equilibrium processesExploring complementary methods for studying cluster formation
Each frequency window is sensitive to different processes andcluster properties:
optical: gravitational lensing of background galaxies, galaxy velocitydispersion measure gravitational mass
X-ray: thermal plasma emission, FX ∝ n2th√
Tth → thermal gas withabundances, cluster potential, substructure
Sunyaev-Zel’dovich effect: IC upscattering of CMB photons by thermalelectrons, FSZ ∝ pth → cluster velocity, turbulence, high-z clusters
radio synchrotron halos: Fsy ∝ εBεCRe → magnetic fields, CR electrons,shock waves
diffuse γ-ray emission: Fγ ∝ nthnCRp → CR protons
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
IntroductionCluster radio halosMinimum energy condition
Radio halos as window for non-equilibrium processesExploring complementary methods for studying cluster formation
Each frequency window is sensitive to different processes andcluster properties:
optical: gravitational lensing of background galaxies, galaxy velocitydispersion measure gravitational mass
X-ray: thermal plasma emission, FX ∝ n2th√
Tth → thermal gas withabundances, cluster potential, substructure
Sunyaev-Zel’dovich effect: IC upscattering of CMB photons by thermalelectrons, FSZ ∝ pth → cluster velocity, turbulence, high-z clusters
radio synchrotron halos: Fsy ∝ εBεCRe → magnetic fields, CR electrons,shock waves
diffuse γ-ray emission: Fγ ∝ nthnCRp → CR protons
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
IntroductionCluster radio halosMinimum energy condition
Radio halos as window for non-equilibrium processesExploring complementary methods for studying cluster formation
Each frequency window is sensitive to different processes andcluster properties:
optical: gravitational lensing of background galaxies, galaxy velocitydispersion measure gravitational mass
X-ray: thermal plasma emission, FX ∝ n2th√
Tth → thermal gas withabundances, cluster potential, substructure
Sunyaev-Zel’dovich effect: IC upscattering of CMB photons by thermalelectrons, FSZ ∝ pth → cluster velocity, turbulence, high-z clusters
radio synchrotron halos: Fsy ∝ εBεCRe → magnetic fields, CR electrons,shock waves
diffuse γ-ray emission: Fγ ∝ nthnCRp → CR protons
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
IntroductionCluster radio halosMinimum energy condition
Radio halos as window for non-equilibrium processesExploring complementary methods for studying cluster formation
Each frequency window is sensitive to different processes andcluster properties:
optical: gravitational lensing of background galaxies, galaxy velocitydispersion measure gravitational mass
X-ray: thermal plasma emission, FX ∝ n2th√
Tth → thermal gas withabundances, cluster potential, substructure
Sunyaev-Zel’dovich effect: IC upscattering of CMB photons by thermalelectrons, FSZ ∝ pth → cluster velocity, turbulence, high-z clusters
radio synchrotron halos: Fsy ∝ εBεCRe → magnetic fields, CR electrons,shock waves
diffuse γ-ray emission: Fγ ∝ nthnCRp → CR protons
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
IntroductionCluster radio halosMinimum energy condition
Coma cluster: optical emission
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
IntroductionCluster radio halosMinimum energy condition
Coma cluster: infra-red emission
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
IntroductionCluster radio halosMinimum energy condition
Coma cluster: X-ray emission
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
IntroductionCluster radio halosMinimum energy condition
Coma cluster: radio synchrotron emission
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
IntroductionCluster radio halosMinimum energy condition
Models for radio synchrotron halos in clusters
Halo characteristics: smooth unpolarized radio emission atscales of 3 Mpc.Different CR electron populations:
Primary accelerated CR electrons: synchrotron/IC coolingtimes too short to account for extended diffuse emissionRe-accelerated CR electrons through resonant interactionwith turbulent Alfvén waves: possibly too inefficient, no firstprinciple calculations (Jaffe 1977, Schlickeiser 1987, Brunetti 2001)
Hadronically produced CR electrons in inelastic collisionsof CR protons with the ambient gas (Dennison 1980, Vestrad1982, Miniati 2001, Pfrommer 2004)
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
IntroductionCluster radio halosMinimum energy condition
Hadronic cosmic ray proton interaction
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
IntroductionCluster radio halosMinimum energy condition
Cosmic rays in clusters of galaxiesWhat do we know about CRs?
predictions for the CR pressurespan between 10% and 50% of thecluster’s pressure budgetescape of cosmic ray protons onlypossible for energiesECRp > 2× 1016 eVenergy losses (for particles withE ∼ 10 GeV):CRe: synchrotron, inverseCompton: τ ∼ 108 yrCRp: inelastic collisions, Coulomblosses: τ ∼ 1010 yr ∼ Hubble time
Coma cluster: radio halo,
ν = 1.4 GHz, 2.5◦ × 2.0◦
(Credit: Deiss/Effelsberg)
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
IntroductionCluster radio halosMinimum energy condition
Cooling core clusters are efficient CRp detectors
Credit: NASA/IoA/A.Fabian et al.
Credit: ROSAT/PSPC
Chandra observation:central region of Perseus
ROSAT observation:Perseus galaxy cluster
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
IntroductionCluster radio halosMinimum energy condition
Cooling core cluster model of CRp detection
Chandra observation:central region of Perseus
Perseus galaxy cluster CRp CRp th= Xε ε
CRp
γ
π0
γp
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
IntroductionCluster radio halosMinimum energy condition
Gamma-ray flux of the Perseus galaxy clusterIC emission of secondary CRes (B = 0), π0-decay induced γ-ray emission:
0.001 0.010 0.100 1.000 10.000 100.00010-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
PSfrag replacements
Eγ [GeV]
dFγ/d
E γ[X
EGRE
TCR
pγ
cm−
2s−
1G
eV−
1 ] αp = 2.1αp = 2.3αp = 2.5αp = 2.7
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
IntroductionCluster radio halosMinimum energy condition
Upper limits on XCRp using EGRET limits
0.01 0.10 1.00 10.00
A85
Perseus
A2199
Centaurus
Ophiuchus
Triagulum Australis
Virgo
Coma
A2256
A2319
A35710
PSfrag replacements
XCRp = εCRp/εth
αp = 2.1αp = 2.3αp = 2.7αp = 2.3, radio
B = 10 µG
B = 1 µG
Cool core cluster:
Non-cool core cluster:
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
IntroductionCluster radio halosMinimum energy condition
Radio halos: Coma and Perseus
Coma radio halo, ν = 1.4 GHz,
largest emission diameter ∼ 3 Mpc
(Credit: Deiss/Effelsberg)
Perseus mini-halo, ν = 1.4 GHz,
largest emission size ∼ 0.5 Mpc
(Credit: Pedlar/VLA)
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
IntroductionCluster radio halosMinimum energy condition
Minimum energy criterion (MEC): the idea
εNT = εB + εCRp + εCRe
→ minimum energy criterion: ∂εNT∂εB
∣∣∣jν
!= 0
classical MEC: εCRp = kpεCRe
hadronic MEC: εCRp ∝ (εB + εCMB) ε−(αν+1)/2B
ε ε
ε
minB B
NT defining tolerancelevels: deviationfrom minimum byone e-fold
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
IntroductionCluster radio halosMinimum energy condition
Classical minimum energy criterion
XCRp(r) =εCRpεth
(r), XB(r) = εBεth
(r)
10 100 1000
0.0001
0.0010
0.0100
PSfrag replacements
r [h−170 kpc]
X Bm
in(r
),X C
Rem
in(r
)
XCRemin
XBmin
Coma cluster: classical minimum energy criterion
BComa(0) = 1.1+0.7−0.4µG
1 10 1000.0001
0.0010
0.0100
PSfrag replacements
r [h−170 kpc]
X Bm
in(r
),X C
Rem
in(r
)
XCRemin
XBmin
Perseus cluster: classical minimum energy criterion
BPerseus(0) = 7.2+4.5−2.8µG
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
IntroductionCluster radio halosMinimum energy condition
Hadronic minimum energy criterion
XCRp(r) =εCRpεth
(r), XB(r) = εBεth
(r)
1 10 100 1000
0.001
0.010
0.100
PSfrag replacements
r [h−170 kpc]
X Bm
in(r
),X C
Rpm
in(r
)
XCRpmin
XBmin
Coma cluster: hadronic minimum energy condition
BComa(0) = 2.4+1.7−1.0µG
1 10 100
0.001
0.010
0.100
PSfrag replacements
r [h−170 kpc]
X Bm
in(r
),X C
Rpm
in(r
)
XCRpmin
XBmin
Perseus cluster: hadronic minimum energy condition
BPerseus(0) = 8.8+13.8−5.4 µG
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
Cosmic ray feedbackPhilosophy and description
Cosmic rays in GADGET(Enßlin, Jubelgas, Pfrommer, Springel)
A galactic outflow seen at high redshift. Left: the projected gas density around some of
the first star forming galaxies. Right: generated bubbles of hot gas, as seen in the
temperature map (Springel & Hernquist 2002).
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
Cosmic ray feedbackPhilosophy and description
Potential effects of cosmic ray feedbackMostly speculations so far
Feedback on galactic scales:Regulation of star formation efficiency due to extra CRpressure.Driving Galactic outflows due to buoyant rise of CRs in starforming regions.radiative cooling losses of galaxies altered by different CRcooling times→ gas flow in halos might be affected.
Feedback on larger scales:Changing the total baryonic fraction that ends up incollapsed structures due to effects of different CR coolingtimes and equation of state.CRs might change the absorption properties at highredshift.
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
Cosmic ray feedbackPhilosophy and description
Potential effects of cosmic ray feedbackMostly speculations so far
Feedback on galactic scales:Regulation of star formation efficiency due to extra CRpressure.Driving Galactic outflows due to buoyant rise of CRs in starforming regions.radiative cooling losses of galaxies altered by different CRcooling times→ gas flow in halos might be affected.
Feedback on larger scales:Changing the total baryonic fraction that ends up incollapsed structures due to effects of different CR coolingtimes and equation of state.CRs might change the absorption properties at highredshift.
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
Cosmic ray feedbackPhilosophy and description
Philosophy and descriptionOur model describes the CR physics by three adiabatic invariants
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
In adiabatic processes, q and C scale only with the density. Non-adiabaticprocesses are mapped into changes of the adiabatic constants q0 and C0.
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
Cosmic ray feedbackPhilosophy and description
Cosmic rays in GADGET– flowchart
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
ObservationsMach number finderCosmological simulationsCluster simulations
Diffusive shock acceleration – Fermi 1 mechanism
Cosmic rays gain energy ∆E/E ∝ υ1 − υ2 through bouncing back and forththe shock front. Accounting for the loss probability ∝ υ2 of particles leavingthe shock downstream leads to power-law CR population.
log p
strong shock
10 GeV
weak shock
keV
log f
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
ObservationsMach number finderCosmological simulationsCluster simulations
Observations of cluster shock waves
1E 0657-56 (“Bullet cluster”)(NASA/SAO/CXC/M.Markevitch et al.)
Abell 3667(Radio: Austr.TC Array. X-ray: ROSAT/PSPC.)
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
ObservationsMach number finderCosmological simulationsCluster simulations
Applications for a shock finder in SPH simulations
cosmological shocks dissipate gravitational energy intothermal gas energyshock waves are tracers of the large scale structure andcontain information about its dynamical history (warm-hotintergalactic medium)shocks accelerate energetic particles (cosmic rays)through diffusive shock acceleration at structure formationshockscosmic ray injection by supernova remnants (whencombined with radiative dissipation and star formation)shock-induced star formation in the interstellar medium
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
ObservationsMach number finderCosmological simulationsCluster simulations
Idea of the Mach number finder
SPH shock is broadened to a scale of the order of thesmoothing length h, i.e. fhh, and fh ∼ 2approximate instantaneous particle velocity by pre-shockvelocity (denoted by υ1 =M1c1)
Using the entropy conserving formalism of Springel &Hernquist 2002 (A(s) = Pρ−γ is the entropic function):
A2
A1=
A1 + dA1
A1= 1 +
fhhM1c1A1
dA1
dt=
P2
P1
(ρ1
ρ2
)γ
ρ2
ρ1=
(γ + 1)M21
(γ − 1)M21 + 2
P2
P1=
2γM21 − (γ − 1)
γ + 1
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
ObservationsMach number finderCosmological simulationsCluster simulations
Complications of the numerical implementation
Broad Mach number distributions f (M) = duthdt d logM
because particle quantities within the (broadened) shockfront do not correspond to those of the pre-shock regime.Solution: introduce decay time ∆tdec = fhh/(M1c),meanwhile the Mach number is set to the maximum (onlyallowing for its rise in the presence of multiple shocks).Weak shocks imply large values of ∆tdec:Solution: ∆tdec = min[fhh/(M1c),∆tmax]
Strong shocks withM > 5 are slightly underestimatedbecause there is no universal shock length.Solution: recalibrate strong shocks!
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
ObservationsMach number finderCosmological simulationsCluster simulations
Shock tube (M = 10): thermodynamics
0 100 200 300 400 5000.00.2
0.4
0.6
0.8
1.01.2
Den
sity
0 100 200 300 400 5000
100
200
300
Vel
ocity
0 100 200 300 400 5000
2•104
4•104
6•104
8•104
Pres
sure
0 100 200 300 400 5001
10
Mac
h nu
mbe
r
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
ObservationsMach number finderCosmological simulationsCluster simulations
Shock tube: Mach number statistics
1 10 1000
2•107
4•107
6•107
8•107
1•108
1 10 1000
5.0•107
1.0•108
1.5•108
PSfrag replacements
logM
logM
⟨
duth
dtdl
ogM
⟩
⟨
duth dt⟩
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
ObservationsMach number finderCosmological simulationsCluster simulations
Shock tube (CRs & gas,M = 10): thermodynamics
0 100 200 300 400 5000.00.2
0.4
0.6
0.8
1.01.2
Den
sity
0 100 200 300 400 5000
100
200
300
400
500
Vel
ocity
0 100 200 300 400 5000
5.0•104
1.0•105
1.5•105
2.0•105
2.5•105
Pres
sure
0 100 200 300 400 5001
10
Mac
h nu
mbe
r
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
ObservationsMach number finderCosmological simulationsCluster simulations
Shock tube (CRs & gas): Mach number statistics
1 10 1000
1•108
2•108
3•108
4•108
5•108
6•108
7•108
1 10 1000
2•108
4•108
6•108
8•108
1•109
PSfrag replacements
logM
logM
⟨
duth
dtdl
ogM
⟩
⟨
duth dt⟩
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
ObservationsMach number finderCosmological simulationsCluster simulations
Cosmological Mach numbers: weighted by εdiss
1
10
Mac
h nu
mbe
r
0 20 40 60 80 1000
20
40
60
80
100
0 20 40 60 80 100x [ h-1 Mpc ]
0
20
40
60
80
100y
[ h-1
Mpc
]
0 20 40 60 80 1000
20
40
60
80
100
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
ObservationsMach number finderCosmological simulationsCluster simulations
Cosmological Mach numbers: weighted by εCR
1
10
Mac
h nu
mbe
r
0 20 40 60 80 1000
20
40
60
80
100
0 20 40 60 80 100x [ h-1 Mpc ]
0
20
40
60
80
100y
[ h-1
Mpc
]
0 20 40 60 80 1000
20
40
60
80
100
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
ObservationsMach number finderCosmological simulationsCluster simulations
Cosmological statistics: resolution study
1 10 100 1000 10000103
104
105
106
107
108 z = 9.2z = 8.1z = 7.2z = 6.1z = 5.1z = 4.1z = 3.1z = 2.0z = 1.0z = 0.5z = 0.0
1 10 100 1000 10000103
104
105
106
107
108 z = 9.2z = 8.1z = 7.2z = 6.1z = 5.1z = 4.1z = 3.1z = 2.0z = 1.0z = 0.5z = 0.0
1 10 100 1000 10000103
104
105
106
107
108
10 110-7
10-6
10-5
10-4
10-3
10-2
10-1
100
with reionization:
without reionization:
PSfrag replacements
Mach numberM
Mach numberMMach numberM
d2 εdi
ss(a,M
)dl
oga
dlogM
[
1050
ergs
(h−
1M
pc)−
3]
d2 εdi
ss(a,M
)dl
oga
dlogM
[
1050
ergs
(h−
1M
pc)−
3]dε
diss
(M)
dlogM
[
1050
ergs
(h−
1M
pc)−
3]
〈(1+δ)k
T〉V
[keV
]2 × 643
2 × 1283
2 × 1283
2 × 1283
2 × 2563
2 × 2563
2 × 2563
z + 1
all shocksinternal shocksexternal shocks
with reionization:without reionization:
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
ObservationsMach number finderCosmological simulationsCluster simulations
Cosmological statistics: influence of reionization
1 10 100 1000 10000103
104
105
106
107
108 z = 9.2z = 8.1z = 7.2z = 6.1z = 5.1z = 4.1z = 3.1z = 2.0z = 1.0z = 0.5z = 0.0
1 10 100 1000 10000103
104
105
106
107
108 z = 9.2z = 8.1z = 7.2z = 6.1z = 5.1z = 4.1z = 3.1z = 2.0z = 1.0z = 0.5z = 0.0
1 10 100 1000 10000103
104
105
106
107
108
0.1 1.0103
104
105
106
107
108
PSfrag replacements
Mach numberM
Mach numberMMach numberM
d2 εdi
ss(a,M
)dl
oga
dlogM
[
1050
ergs
(h−
1M
pc)−
3]
d2 εdi
ss(a,M
)dl
oga
dlogM
[
1050
ergs
(h−
1M
pc)−
3]dε
diss,C
R(M
)dl
ogM
[
1050
ergs
(h−
1M
pc)−
3]
dεdi
ss(a
)dl
oga[
1050
ergs
(h−
1M
pc)−
3]
Scale factor a
dεdiss(M)/(d logM) :
dεCR(M)/(d logM) :
with reionization
with reionization
with reionization
without reionization
without reionization
all shocksinternal shocksexternal shocks
εth(>M)[
1050ergs (h−1 Mpc)−3]
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
ObservationsMach number finderCosmological simulationsCluster simulations
Adiabatic cluster simulation: gas density
10-1
100
101
102
1 +
δ gas
-15 -10 -5 0 5 10 15-15
-10
-5
0
5
10
15
-15 -10 -5 0 5 10 15x [ h-1 Mpc ]
-15
-10
-5
0
5
10
15y
[ h-1
Mpc
]
-15 -10 -5 0 5 10 15-15
-10
-5
0
5
10
15
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
ObservationsMach number finderCosmological simulationsCluster simulations
Mass weighted temperature
103
104
105
106
<( 1
+ δ
gas )
T >
[ K ]
-15 -10 -5 0 5 10 15-15
-10
-5
0
5
10
15
-15 -10 -5 0 5 10 15x [ h-1 Mpc ]
-15
-10
-5
0
5
10
15y
[ h-1
Mpc
]
-15 -10 -5 0 5 10 15-15
-10
-5
0
5
10
15
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
ObservationsMach number finderCosmological simulationsCluster simulations
Mach number distribution weighted by εdiss
1
10
Mac
h nu
mbe
r
-15 -10 -5 0 5 10 15-15
-10
-5
0
5
10
15
-15 -10 -5 0 5 10 15x [ h-1 Mpc ]
-15
-10
-5
0
5
10
15y
[ h-1
Mpc
]
-15 -10 -5 0 5 10 15-15
-10
-5
0
5
10
15
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
ObservationsMach number finderCosmological simulationsCluster simulations
Relative CR pressure PCR/Ptotal
10-3
10-2
10-1
100
P CR /
( Pth
+ P
CR )
-2 -1 0 1 2-2
-1
0
1
2
-2 -1 0 1 2x [ h-1 Mpc ]
-2
-1
0
1
2y
[ h-1
Mpc
]
-2 -1 0 1 2-2
-1
0
1
2
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
ObservationsMach number finderCosmological simulationsCluster simulations
Equation of state for CRs
100
101
102
103
104
prob
abilit
y de
nsity
[arb
itrar
y un
its]
-2 0 2 4 6 8-4
-3
-2
-1
0
1
2
-2 0 2 4 6 8log[ 1 + δgas]
-4
-3
-2
-1
0
1
2lo
g[ P
CR /
P th ]
-2 0 2 4 6 8-4
-3
-2
-1
0
1
2
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
Summary
Understanding non-thermal processes is crucial for usingclusters as cosmological probes (high-z scaling relations).Radio halos might be of hadronic origin as our simulationssuggests.Huge potential and predictive power of cosmological CRsimulations/Mach number finder→ provides detailedγ-ray/radio emission maps
OutlookGalaxy evolution: influence on energetic feedback, starformation, and galactic windsExploring the CR influence on the absorption properties athigh redshift.
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
Summary
Understanding non-thermal processes is crucial for usingclusters as cosmological probes (high-z scaling relations).Radio halos might be of hadronic origin as our simulationssuggests.Huge potential and predictive power of cosmological CRsimulations/Mach number finder→ provides detailedγ-ray/radio emission maps
OutlookGalaxy evolution: influence on energetic feedback, starformation, and galactic windsExploring the CR influence on the absorption properties athigh redshift.
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
Summary
Understanding non-thermal processes is crucial for usingclusters as cosmological probes (high-z scaling relations).Radio halos might be of hadronic origin as our simulationssuggests.Huge potential and predictive power of cosmological CRsimulations/Mach number finder→ provides detailedγ-ray/radio emission maps
OutlookGalaxy evolution: influence on energetic feedback, starformation, and galactic windsExploring the CR influence on the absorption properties athigh redshift.
C. Pfrommer Cosmic rays and cosmological shock waves
Cluster non-equilibrium processesCosmic rays in GADGET
Cosmological shock wavesSummary
Summary
Understanding non-thermal processes is crucial for usingclusters as cosmological probes (high-z scaling relations).Radio halos might be of hadronic origin as our simulationssuggests.Huge potential and predictive power of cosmological CRsimulations/Mach number finder→ provides detailedγ-ray/radio emission maps
OutlookGalaxy evolution: influence on energetic feedback, starformation, and galactic windsExploring the CR influence on the absorption properties athigh redshift.
C. Pfrommer Cosmic rays and cosmological shock waves