Cosmological shock waves Cosmic rays in galaxy clusters Summary Cosmological shock waves in SPH simulations Exploring cosmic ray feedback Christoph Pfrommer Canadian Institute for Theoretical Astrophysics, Toronto Mar. 20 2006 / "Contents and Structures of the Universe", Rencontres de Moriond C. Pfrommer Cosmological shock waves in SPH simulations
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Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Cosmological shock waves in SPH simulationsExploring cosmic ray feedback
Christoph Pfrommer
Canadian Institute for Theoretical Astrophysics, Toronto
Mar. 20 2006 / "Contents and Structures of the Universe",Rencontres de Moriond
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Outline
1 Cosmological shock wavesCosmic rays in GADGET
Mach number finderCosmological and cluster simulations
2 Cosmic rays in galaxy clustersCluster radio halosEnergetically preferred CR pressure profilesCR pressure influences Sunyaev-Zel’dovic effect
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finderCosmological and cluster simulations
Cosmic rays in GADGET(Pfrommer, Springel, Enßlin, Jubelgas, 2006, MNRAS)
The "cosmic web" today. Left: the projected gas density in a cosmological simulation.
Right: gravitationally heated intracluster medium through cosmological shock waves.
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finderCosmological and cluster simulations
Cosmic rays in GADGET– flowchart
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finderCosmological and cluster simulations
Diffusive shock acceleration – Fermi 1 mechanism
Cosmic rays gain energy ∆E/E ∝ υ1 − υ2 through bouncing back and forth
the shock front. Accounting for the loss probability ∝ υ2 of particles leaving
the shock downstream leads to power-law CR population.
log p
strong shock
10 GeV
weak shock
keV
log f
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finderCosmological and cluster simulations
Observations of cluster shock waves
1E 0657-56 (“Bullet cluster”)(NASA/SAO/CXC/M.Markevitch et al.)
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finderCosmological and cluster simulations
Motivation for the Mach number finder
cosmological shocks dissipate gravitational energy intothermal 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 andcontain information about its dynamical history (warm-hotintergalactic medium)
shocks accelerate cosmic rays through diffusive shockacceleration at structure formation shocks: what are thecosmological implications of such a CR component, anddoes this influence the cosmic thermal history?
simulating realistic CR distributions within galaxy clustersprovides detailed predictions for the expected radiosynchrotron and γ-ray emission
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finderCosmological and cluster simulations
Shock tube (CRs & gas,M = 10): thermodynamics
0 100 200 300 400 5000.0
0.2
0.4
0.6
0.8
1.0
1.2D
ensi
ty
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 Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finderCosmological and cluster 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
dtd
logM
⟩
⟨
duth
dt
⟩
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finderCosmological and cluster simulations
Shock tube (th. gas): 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
dtd
logM
⟩
⟨
duth
dt
⟩
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finderCosmological and cluster 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
100
y [ h
-1 M
pc ]
0 20 40 60 80 1000
20
40
60
80
100
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finderCosmological and cluster 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
100
y [ h
-1 M
pc ]
0 20 40 60 80 1000
20
40
60
80
100
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finderCosmological and cluster simulations
Cosmological Mach number statistics
more energy is dissipated in weak shocks internal to collapsedstructures than in external strong shocks
more energy is dissipated at later times
mean Mach number decreases with time
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finderCosmological and cluster simulations
Cosmological statistics: influence of reionization
reionization epoch at zreion = 10 suppresses efficiently strongshocks at z < zreion due to jump in sound velocity
cosmological constant causes structure formation to cease
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finderCosmological and cluster 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
15
y [ h
-1 M
pc ]
-15 -10 -5 0 5 10 15-15
-10
-5
0
5
10
15
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finderCosmological and cluster 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
15
y [ h
-1 M
pc ]
-15 -10 -5 0 5 10 15-15
-10
-5
0
5
10
15
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finderCosmological and cluster 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
15
y [ h
-1 M
pc ]
-15 -10 -5 0 5 10 15-15
-10
-5
0
5
10
15
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finderCosmological and cluster simulations
Relative CR pressure PCR/Ptotal
10-3
10-2
10-1
100
PC
R /
( 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
2
y [ h
-1 M
pc ]
-2 -1 0 1 2-2
-1
0
1
2
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
OutlookGalaxy evolution: influence on energetic feedback, starformation, and galactic windsHuge potential and predictive power of cosmological CRsimulations/Mach number finder→ provides detailedγ-ray/radio emission maps
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Cosmological statistics: resolution studyDifferential distributions: 2× 2563 versus 2× 1283
more energy is dissipated at later times
mean Mach number decreases with time
differential Mach number distributions are converged for z < 3
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Cosmological statistics: resolution study
in higher resolution simulations structure forms earlier
more energy is dissipated in shocks internal to collapsedstructures than in external shocks of pristine gas
integrated Mach number distribution converged
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Idea of the Mach number finder in SPH
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 Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Minimum energy criterion (MEC): the idea
What is the energetically least expensive distribution ofnon-thermal energy density εNT given the observedsynchrotron emissivity?εNT = εB + εCRp + εCRe
→ minimum energy criterion: ∂εNT∂εB
∣∣∣jν
!= 0
ε ε
ε
minBB
NT defining tolerancelevels: deviationfrom minimum byone e-fold
C. Pfrommer Cosmological shock waves in SPH simulations
Cosmological shock wavesCosmic rays in galaxy clusters
Summary
Philosophy and description
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 uniquely
The CR spectrum can be expressed by three adiabatic invariants, which scale
only with the gas density. Non-adiabatic processes are mapped into changes
of the adiabatic constants using mass, energy and momentum conservation.
C. Pfrommer Cosmological shock waves in SPH simulations