Cosmological shock waves in SPH simulations

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


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



Summary

Cosmic rays in GADGET


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.



Summary



Cosmic rays in GADGET– flowchart



Summary



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



Summary



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.)



Summary



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



Summary



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



Summary



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

⟩



Summary



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

⟩



Summary



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



Summary



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



Summary



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



Summary



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



Summary



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



Summary



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



Summary



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



Summary



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



Summary

Cluster radio halosEnergetically preferred CR pressure profilesCR pressure influences SZ effect

Radio halos as window for non-equilibrium processes

Coma radio halo, ν = 1.4 GHz,

largest emission diameter ∼ 3 Mpc

(2.5◦ × 2.0◦ , credit: Deiss/Effelsberg)

Coma thermal X-ray emission,

(2.7◦ × 2.5◦ , credit: ROSAT/MPE/Snowden)



Summary


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 emission

Re-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, Vestrad

1982, Miniati 2001, Pfrommer 2004)



Summary


Hadronic cosmic ray proton interaction



Summary


Energetically preferred CR pressure profiles

1 10 100 1000

0.001

0.010

0.100

PSfrag replacements

r [h−170 kpc]

XB

min(r

),X

CR

p min(r

)XCRpmin

XBmin

Coma cluster: hadronic minimum energy condition

XCRp(r) =εCRpεth

(r), XB(r) = εBεth

(r) → BComa, min(0) = 2.4+1.7−1.0µG



Summary


Compton y parameter in radiative cluster simulation

10-7

10-6

Com

pton

y

-1.0 -0.5 0.0 0.5 1.0-1.0

-0.5

0.0

0.5

1.0

-1.0 -0.5 0.0 0.5 1.0x [ h-1 Mpc ]

-1.0

-0.5

0.0

0.5

1.0

y [ h

-1 M

pc ]

-1.0 -0.5 0.0 0.5 1.0-1.0

-0.5

0.0

0.5

1.0



Summary


Compton y difference map: yCR − yth

-10-5

-10-6

-10-7

-10-8

0

10-8

10-7

10-6

10-5

Com

pton

-y d

iffe

renc

e m

ap: y

CR

- y th

-0.5 0.0 0.5

-0.5

0.0

0.5

-0.5 0.0 0.5x [ h-1 Mpc ]

-0.5

0.0

0.5

y [ h

-1 M

pc ]

-0.5 0.0 0.5

-0.5

0.0

0.5



Summary


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

120

140

160

180

200

220



Summary


Pressure profiles with and without CRs

10 100 1000R [ h-1 kpc ]

0.001

0.010

0.100

1.000

10.000

100.000P

CR

, Pth

[Cod

e un

its]



Summary


Phase-space diagram of radiative cluster simulation

100

101

102

103

104

prob

abili

ty d

ensi

ty [a

rbitr

ary

units

]

-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

2

log[

PC

R /

Pth

]

-2 0 2 4 6 8-4

-3

-2

-1

0

1

2



Summary

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→ tracer of structure formation

Dynamical CR feedback influences Sunyaev-Zel’doviceffect

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



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



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



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



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



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.


Documents

Cosmological shock waves in SPH simulations