Cosmological shock waves in SPH simulations

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Cosmological shock waves in SPH simulations
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
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Outline
1
Cosmological shock waves
Cosmic rays in GADGET
Mach number finder
Cosmological and cluster simulations
2
Cosmic rays in galaxy clusters
Cluster radio halos
Energetically preferred CR pressure profiles
CR pressure influences Sunyaev-Zel’dovic effect
C. Pfrommer
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finder
Cosmological 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 waves
Cosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finder
Cosmological and cluster simulations
Cosmic rays in GADGET– flowchart
C. Pfrommer
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finder
Cosmological 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 f
strong shock
weak shock
keV
10 GeV
C. Pfrommer
log p
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finder
Cosmological and cluster 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
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finder
Cosmological and cluster simulations
Motivation for the Mach number finder
cosmological shocks dissipate gravitational energy into
thermal 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 and
contain information about its dynamical history (warm-hot
intergalactic medium)
shocks accelerate cosmic rays through diffusive shock
acceleration at structure formation shocks: what are the
cosmological implications of such a CR component, and
does this influence the cosmic thermal history?
simulating realistic CR distributions within galaxy clusters
provides detailed predictions for the expected radio
synchrotron and γ-ray emission
C. Pfrommer
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finder
Cosmological and cluster simulations
1.2
500
1.0
400
0.8
Velocity
Density
Shock tube (CRs & gas, M = 10): thermodynamics
0.6
0.4
300
200
100
0.2
0.0
0
0
100
200
300
400
500
0
100
200
300
400
500
0
100
200
300
400
500
2.5•105
10
Mach number
Pressure
2.0•105
1.5•105
1.0•105
5.0•104
0
1
0
100
200
300
400
500
C. Pfrommer
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finder
Cosmological and cluster simulations
Shock tube (CRs & gas): Mach number statistics
7•108
5•108
duth
dt d log M
6•108
3•108
2•108
1•108
0
1
10
100
10
100
log M
1•109
8•108
duth
dt
6•108
4•108
g replacements
4•108
2•108
0
1
log M
C. Pfrommer
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finder
Cosmological and cluster simulations
Shock tube (th. gas): Mach number statistics
8•107
duth
dt d log M
1•108
6•107
4•107
2•107
0
1
10
100
10
100
log M
1.5•108
duth
dt
1.0•108
g replacements
5.0•107
0
1
log M
C. Pfrommer
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finder
Cosmological and cluster simulations
Cosmological Mach numbers: weighted by εdiss
100
100
10
60
40
20
80
60
Mach number
y [ h-1 Mpc ]
80
40
20
0
0
0
0
20
40
20
40
-1
x [ h Mpc ]
C. Pfrommer
60
80
100
60
80
100
1
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finder
Cosmological and cluster simulations
Cosmological Mach numbers: weighted by εCR
100
100
10
60
40
20
80
60
Mach number
y [ h-1 Mpc ]
80
40
20
0
0
0
0
20
40
20
40
-1
x [ h Mpc ]
C. Pfrommer
60
80
100
60
80
100
1
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finder
Cosmological and cluster simulations
Cosmological Mach number statistics
more energy is dissipated in weak shocks internal to collapsed
structures 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 waves
Cosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finder
Cosmological and cluster simulations
Cosmological statistics: influence of reionization
reionization epoch at zreion = 10 suppresses efficiently strong
shocks 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 waves
Cosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finder
Cosmological and cluster simulations
Adiabatic cluster simulation: gas density
10
y [ h-1 Mpc ]
5
0
102
15
15
10
10
101
5
1 + δgas
15
0
100
-5
-10
-5
-10
-10
10-1
-15
-15
-15
-15
-15
-10
-5
0
5
10
10
15
15
-10
-5
0
x [ h-1 Mpc ]
5
10
15
C. Pfrommer
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finder
Cosmological and cluster simulations
Mass weighted temperature
15
15
15
106
y [ h-1 Mpc ]
5
0
10
10
105
5
<( 1 + δgas ) T > [ K ]
10
0
104
-5
-10
-5
103
-10
-10
-15
-15
-15
-15
-15
-10
-5
0
5
10
10
15
15
-10
-5
0
x [ h-1 Mpc ]
5
10
15
C. Pfrommer
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finder
Cosmological and cluster simulations
Mach number distribution weighted by εdiss
10
y [ h-1 Mpc ]
5
0
-5
-10
15
10
10
5
Mach number
15
0
-5
-10
-15
-15
-15
-15
-10
-5
0
5
10
15
-10
-5
0
x [ h-1 Mpc ]
5
10
15
C. Pfrommer
1
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Cosmic rays in GADGET
Mach number finder
Cosmological and cluster simulations
Relative CR pressure PCR /Ptotal
2
1
100
2
1
0
PCR / ( Pth + PCR )
y [ h-1 Mpc ]
10-1
0
10-2
-1
-1
-2
-2
-2
-2
-1
0
1
2
-1
0
x [ h-1 Mpc ]
1
2
C. Pfrommer
10-3
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Cluster radio halos
Energetically preferred CR pressure profiles
CR pressure influences SZ effect
Radio halos as window for non-equilibrium processes
Coma radio halo, ν = 1.4 GHz,
Coma thermal X-ray emission,
largest emission diameter ∼ 3 Mpc
(2.7◦ × 2.5◦ , credit: ROSAT/MPE/Snowden)
(2.5◦ × 2.0◦ , credit: Deiss/Effelsberg)
C. Pfrommer
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Cluster radio halos
Energetically preferred CR pressure profiles
CR pressure influences SZ effect
Models for radio synchrotron halos in clusters
Halo characteristics: smooth unpolarized radio emission at
scales of 3 Mpc.
Different CR electron populations:
Primary accelerated CR electrons: synchrotron/IC cooling
times too short to account for extended diffuse emission
Re-accelerated CR electrons through resonant interaction
with turbulent Alfvén waves: possibly too inefficient, no first
principle calculations (Jaffe 1977, Schlickeiser 1987, Brunetti 2001)
Hadronically produced CR electrons in inelastic collisions
of CR protons with the ambient gas (Dennison 1980, Vestrad
1982, Miniati 2001, Pfrommer 2004)
C. Pfrommer
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Cluster radio halos
Energetically preferred CR pressure profiles
CR pressure influences SZ effect
Hadronic cosmic ray proton interaction
C. Pfrommer
Cosmological shock waves in SPH simulations
Cluster radio halos
Energetically preferred CR pressure profiles
CR pressure influences SZ effect
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Energetically preferred CR pressure profiles
Coma cluster: hadronic minimum energy condition
XBmin (r), XCRpmin (r)
0.100
PSfrag replacements
XCRpmin
XBmin
0.010
0.001
1
ε
XCRp (r ) = εCRp
(r ),
th
10
100
1000
r [h−1
70 kpc]
B (r )
XB (r ) = εεth
C. Pfrommer
→
BComa, min (0) = 2.4+1.7
−1.0 µG
Cosmological shock waves in SPH simulations
Cluster radio halos
Energetically preferred CR pressure profiles
CR pressure influences SZ effect
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Compton y parameter in radiative cluster simulation
1.0
0.5
1.0
1.0
0.5
0.5
0.0
-0.5
Compton y
y [ h-1 Mpc ]
10-6
0.0
0.0
-0.5
-0.5
10-7
-1.0
-1.0
-1.0
-1.0
-1.0
-0.5
-0.5
0.0
0.5
1.0
-0.5
0.0
x [ h Mpc ]
0.5
1.0
-1
C. Pfrommer
Cosmological shock waves in SPH simulations
Cluster radio halos
Energetically preferred CR pressure profiles
CR pressure influences SZ effect
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Compton y difference map: yCR − yth
10-5
10-6
0.5
0.5
10-7
y [ h-1 Mpc ]
10-8
0.0
0
0.0
0.0
Compton-y difference map: yCR - yth
0.5
-10-8
-0.5
-10-7
-0.5
-0.5
-10-6
-0.5
0.0
0.5
-0.5
0.0
x [ h Mpc ]
0.5
-1
C. Pfrommer
-10-5
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Cluster radio halos
Energetically preferred CR pressure profiles
CR pressure influences SZ effect
Simulated CBI observation of yCR − yth
(with Sievers & Bond)
20
40
60
80
100
120
140
160
180
200
220
20
40
60
80
100
C. Pfrommer
120
140
160
180
200
220
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Cluster radio halos
Energetically preferred CR pressure profiles
CR pressure influences SZ effect
Pressure profiles with and without CRs
100.000
PCR, Pth [Code units]
10.000
1.000
0.100
0.010
0.001
10
100
R [ h-1 kpc ]
C. Pfrommer
1000
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Cluster radio halos
Energetically preferred CR pressure profiles
CR pressure influences SZ effect
Phase-space diagram of radiative cluster simulation
2
1
104
2
1
log[ PCR / Pth ]
0
-1
-2
probability density [arbitrary units]
103
0
102
-1
-2
101
-3
-4
-3
-4
-2
0
-2
0
2
4
2
4
log[ 1 + δgas]
C. Pfrommer
6
8
6
8
100
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Summary
Understanding non-thermal processes is crucial for using
clusters as cosmological probes (high-z scaling relations).
Radio halos might be of hadronic origin as our simulations
suggests → tracer of structure formation
Dynamical CR feedback influences Sunyaev-Zel’dovic
effect
Outlook
Galaxy evolution: influence on energetic feedback, star
formation, and galactic winds
Huge potential and predictive power of cosmological CR
simulations/Mach number finder → provides detailed
γ-ray/radio emission maps
C. Pfrommer
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Cosmological statistics: resolution study
Differential 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 waves
Cosmic rays in galaxy clusters
Summary
Cosmological statistics: resolution study
in higher resolution simulations structure forms earlier
more energy is dissipated in shocks internal to collapsed
structures than in external shocks of pristine gas
integrated Mach number distribution converged
C. Pfrommer
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic rays in galaxy clusters
Summary
Idea of the Mach number finder in SPH
SPH shock is broadened to a scale of the order of the
smoothing length h, i.e. fh h, and fh ∼ 2
approximate instantaneous particle velocity by pre-shock
velocity (denoted by υ1 = M1 c1 )
Using the entropy conserving formalism of Springel &
Hernquist 2002 (A(s) = Pρ−γ is the entropic function):
A2
A1 + dA1
fh h dA1
P2 ρ1 γ
=
=
=1+
A1
A1
M1 c1 A1 dt
P1 ρ2
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 waves
Cosmic rays in galaxy clusters
Summary
Minimum energy criterion (MEC): the idea
What is the energetically least expensive distribution of
non-thermal energy density εNT given the observed
synchrotron emissivity?
εNT = εB + εCRp + εCRe
!
→ minimum energy criterion: ∂εNT = 0
∂εB jν
ε NT
defining tolerance
levels:
deviation
from minimum by
one e-fold
εB
εB
min
C. Pfrommer
Cosmological shock waves in SPH simulations
Cosmological shock waves
Cosmic 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

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