Cosmic rays in galaxy clusters and cosmological shock ... · Cluster non-equilibrium processes Cosmic rays in GADGET Cosmological shock waves Summary Outline 1 Non-equilibrium processes

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



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




Outline








Outline








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





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









































Coma cluster: optical emission





Coma cluster: infra-red emission





Coma cluster: X-ray emission





Coma cluster: radio synchrotron emission





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)





Hadronic cosmic ray proton interaction





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)





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





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





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





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:





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)





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





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





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




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).





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.





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.





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.





Cosmic rays in GADGET– flowchart




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





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.)





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





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





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!





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





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⟩





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





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⟩





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





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





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:





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]





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





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





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





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





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




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.




Summary






Summary






Summary




Documents

Cosmic rays in galaxy clusters and cosmological shock ... · Cluster non-equilibrium processes Cosmic rays in GADGET Cosmological shock waves Summary Outline 1 Non-equilibrium processes