Magnetic Fields, Turbulence and Cosmic Rays in Galaxy Clusters

Magnetic Fields, Turbulence and
Cosmic Rays in Galaxy Clusters
Klaus Dolag (∗)
A.Bonafede, J.Donnert, I.Zhuravleva, H.Kotarba, A.Geng and A.Beck
(∗) Universitäts-Sternwarte München
14/3/2011 – p. 1

The Cluster Bermuda-Triangle
amplification
B
?
v CR
(turb)
acceleration
radio emission
(e,p)
14/3/2011 – p. 2

Where are we ?
Magnetic Field
Schlickeiser et al. 1987
transport koefficient
~ 0.1 * v * L
turb
turbulence (IGM/ICM)
=> radio emission
Burbidge 1958 (!!)
14/3/2011 – p. 3

Problem 1: Origin of B
Origin
• Primordial
• Battery
• Dynamo (Turbulence)
• Stars
• Supernovae
• Galactic Winds
• AGNs, Jets
• Rees 1994
Shocks
+ further amplification by structure formation
- dissipation ?
14/3/2011 – p. 4

Problem 2: Turbulence
Observed turbulece in clusters: (see talk by de Plaa, ...)
Ddiff = 0.1 × vturb × λturb , vturb(l) ∝ λ (1/3)
turb
Schuecker et al. 2004
14/3/2011 – p. 5

Problem 2: Turbulence
Simulations: Simulated turbulece in clusters (I):
SPH ENZO
log(E turb)[erg]
62.0
61.5
61.0
60.5
60.0
13.4 13.6 13.8 14.0 14.2 14.4 14.6
log(M merg)[M sun]
Dolag et al. 2005 / Vazza et al. 2006 Vazza et al. 2010 Iapichino et al. 2009/2010
Dolag et al. 2005 (see also Iapichino et al. 2008/2009, Vazza et al. 2006/2009/2010, ...)
Need to distinguish bulk and turbulent motions.
⇒ strongly depend on operational definitions !
Origin (in cosmological context):
• Behind shocks (mostly beyond core radius)
• Passage of gas rich substructure (whole cluster)
• Passage of dm substructure (mostly cluster core)
14/3/2011 – p. 5

Problem 2: Turbulence
Simulated turbulece in clusters (II):
(Dolag et al 2005, Vazza et al 2009, Maier et al 2009, ...)
(Gadget)
(Enzo)
SGS (Fearless)
see talk by I.Zhuravleva
14/3/2011 – p. 5

Problem 3: Low B
Please:
(numbers are from private communication)
Cluster Pthermal B 2 /8π β
Coma 1.02e-10 1.63e-12 1.6
A2255 5.016e-11 2.487e-13 0.5
A400 1.927e-11 1.681e-12 8.7
A119 3.63e-11 1.204e-12 3.3
A2382 1.21e-11 3.581e-13 3.0
Note on Turbulence:
10% (Observed, Coma)
10-20% (Simulations)
14/3/2011 – p. 6

Problem 3: Low B
Observed B in clusters: (Bonafede et al. 2010, ...)
B(r) = B0
Declination
1 + (r/rc) 2 −1.5η , |Bk| 2 ∝ k −n , (kmin,kmax)
29:00:00.0
30:00.0
28:00:00.0
30:00.0
27:00:00.0
500 kpc
5C4.152
5C4.127
5C4.114
5C4.85
5C4.81
2 Mpc
5C4.74
04:00.0 02:00.0 13:00:00.0 58:00.0 12:56:00.0
Right ascension
5C4.42
Bonafede et al. 2010
14/3/2011 – p. 6

Problem 3: Low B
B(r) = B0
1 + (r/rc) 2 −1.5η , |Bk| 2 ∝ k −n , (kmin,kmax)
• S(dx,dy) = [RM(x,y) − RM(x + dx,y + dy)] 2
• A(dx,dy) = 〈RM(x,y) × RM(x + dx,y + dy)〉
• 〈|RM|〉 scale , 〈σRM〉 scale
η
2
1.5
1
0.5
0
−0.5
2 4 6 8 10
Β [µG]
< 0 >
⇒ constrains on magnetic field strength !
B [µG]
8
6
4
2
Analytic profile
Power spectrum
fluctuations
0
0 500 1000
r [kpc]
1500 2000
14/3/2011 – p. 6

Problem 3: Low B
B(r) = B0
1 + (r/rc) 2 −1.5η , |Bk| 2 ∝ k −n , (kmin,kmax)
⇒ A655: Inferred outer scale ≈450 kpc (Vacca et al. 2010) !
• Depolarization indicates truncation at small scales !
⇒ No fluctuations at scales below ≈ (.1 − .5) kpc !
Govoni et al. 2010, Vacca et al. 2010, Guidetti et al. 2010, Bonafede et al. 2010, Guidetti et al.
2008, Govoni et al. 2006, Laing et al. 2006, Vogt & Ensslin 2005, Murgia et al. 2004,
Ennslin & Vogt 2003, ... , Tribble 1991.
14/3/2011 – p. 6

Problem 3: Low B
Govoni et al. 2010
• Combination of RM measured in many clusters.
• How does B scale with cluster temperature ?
• Magnetic Field in Radio quiet/active clusters ? 14/3/2011 – p. 6

Problem 4: Radio Emission
Radio Relic
Radio Halo
1 Mpc
Feretti 1999
Miniati et al. 2001
Dolag & Ensslin 2000
Pfromer et al. 2007
Dolag & Ensslin 2000
Cluster wide diffuse synchrotron emission connected to
merger events, periferal emission directly connected to shocks.
• Radio halo: Turbulence, shocks, secondary ?
• Relics: Primary from shocks or compressed radio plasma ?
14/3/2011 – p. 7

The Big Picture
see talk by I.Zhuravleva
B [G]
B [G]
MHD Simulations
Bonafede et al. 2011
10 -5
10 -6
10 -7
10 -5
10 -6
10 -7
g1657050
g4606589
Coma
100 1000
R [kpc]
100 1000
R [kpc]
η m =5
η m =10
η m =20
Coma
η m =5
η m =10
η m =20
COMA
B [G]
(Gadget)
(Enzo)
SGS (Fearless)
see talk by I.Zhuravleva
10 -5
10 -6
10 -7
g0016649 g0272097
g1212639
g1657050
g3327821
g4606589
g5699754
g1680241
g3346905
g1987669
g3888703
g6287794 g6348555
Bonafede et al., work in progress
g0272097
g1483463
g2980844
g4425770
g4915399 g5265133 g5503149
g6802296
5E-08 8E-07 2.66E-05 0.0043659
g735 g7570 g7577
g726
Coma
100 1000
R [kpc]
η m =5
η m =10
η m =20
Schlickeiser et al. 1987
Declination
29:00:00.0
30:00.0
28:00:00.0
30:00.0
27:00:00.0
500 kpc
5C4.152
5C4.127
5C4.114
5C4.85
5C4.81
2 Mpc
5C4.74
5C4.42
04:00.0 02:00.0 13:00:00.0 58:00.0 12:56:00.0
Right ascension
Bonafede et al. 2010
Bonafede et al. 2010
Schuecker et al. 2004
14/3/2011 – p. 8

Cluster MHD simulations
14/3/2011 – p. 9

Cluster MHD simulations
DEC
Observation
3C449
Feretti et al. 1999
RA
(RAD/M/M)
Simulation
RM
(counts)
684 Mpc
684 kpc
68.4 Mpc
6.84 Mpc
“Zoomed” cluster simulation (Dolag & Stasyszyn 2009). Movie: u,v 14/3/2011 – p. 9

Cluster MHD simulations
Simulation
Dolag et al. 2002
ε(k) [erg cm -2 ]
Simulation
1e-10
1e-11
1e-12
1e-13
1e-14
1e-15
0.1 1 10
k [kpc -1 ]
REALMAF
Vogt
Observation
Kuchar & Ensslin 2009
Pakmor & Dolag 2006
Magnetic field power spectra: predictions vs. observations.
See also Brüggen et al. 2005, Xu et al. 2009
14/3/2011 – p. 9

Magnetic Field buildup
Simulations on galaxy scales ...
M51 (Fletcher & Beck 2006) and a simulation using the MHD
implementation in Gadget (Kotarba et al. 2009).
14/3/2011 – p. 10

Magnetic Field buildup
Simulating the magnetic field amplification during galaxy
mergers like in the Antennae system. Final magnetic field
strength and field configuration in broad agreement with
observations.
(Chyzy & Beck 2005 Kortarba et al. 2010)
14/3/2011 – p. 10

Magnetic Field buildup
Final magnetic field close to equipartition with turbulent velocity
component, largely independent of initial field values.
⇒ Hierarchical buildup of magnetic field
(Kortarba et al. 2010)
14/3/2011 – p. 10

Magnetic Field buildup
y [kpc/h]
y [kpc/h]
y [kpc/h]
y [kpc/h]
100
0
-100
100
0
-100
100
0
-100
100
0
-100
-100 0 100
x [kpc/h]
t=982 Myr t=1483 Myr t=1984 Myr t=2486 Myr
t=2987 Myr
-100 0 100 200
x [kpc/h]
(A. Geng, work in progress)
t=3488 Myr
-100 0 100
x [kpc/h]
-100 0 100 200
x [kpc/h]
t=3989 Myr
-100 0 100
x [kpc/h]
-100 0 100 200
x [kpc/h]
t=4490 Myr
-100 0 100
x [kpc/h]
-100 0 100 200
x [kpc/h]
-25
-26
-27
-28
-29
-7
-8
-9
log < density [g cm -2 ] >
log < |B| [G] >
14/3/2011 – p. 10

Magnetic Field buildup
Smaller merger less efficient in driving turbulence.
(Geng et al., in prep)
14/3/2011 – p. 10

DECLINATION (J2000)
Magnetic Field buildup
34 00 00
33 59 30
00
58 30
00
57 30
00
56 30
00
55 30
PLot file version 2 created 11-SEP-2009 16:13:17
ICONT:SQ IPOL 4860.100 MHZ SQ 6.I.3
22 36 10 05 00 35 55 50
RIGHT ASCENSION (J2000)
Cont peak flux = 9.4028E-03 JY/BEAM
Levs = 9.000E-06 * (3, 5, 8, 12, 20, 30, 50, 80,
120, 200, 300, 500, 800)
Pol line 1 arcsec = 4.1667E-06 JY/BEAM
Soida et al., in prep. Kortarba et al. 2010
14/3/2011 – p. 10

Magnetic Field buildup
Kortarba et al. 2010
• Merging drives shocks, turbulence and star-formation
• Star-formation drives winds
• Winds transport out magnetic fields
14/3/2011 – p. 10

Magnetic Field buildup
Comparison of magnetic growth and simple expectation for
vturb = 100km/s and λ = 25kpc.
A. Beck, diploma thesis
14/3/2011 – p. 10

Magnetic Field buildup
z=4
z=0
primordial
galactic outflows
Seeding from galactic outflows (Donnert et al. 2009)
14/3/2011 – p. 10

z=0
Magnetic Field buildup
dipole (10x)
dipole
quadrupole (10x) continuously seeding
Different wind parameters (Donnert et al. 2009)
dipole (1/10)
primordial
14/3/2011 – p. 10

Magnetic Field buildup
⇒ Galactic seeding models also reproduce observed RM
profile within galaxy clusters (Donnert et al. 2009)
14/3/2011 – p. 10

Madgetic diffusion in clusters
η = ηcoulomb + ηturb ≈ 0.1 × vturb × λvturb
g0016649 g0272097
g1212639
g1657050
g1483463
g1680241 g1987669 g2980844
g3327821 g3346905 g3888703 g4425770
g4606589
g4915399
g5265133
g5503149
g5699754 g6287794 g6348555 g6802296
g7263961
g7358274 g7570066
g7577931
Selected 24 most massive clusters from a 1Gpc/h box.
Bonafede et al. 2011
0.00000 0.00003 0.00012 0.00028 0.00050 0.00078 0.00112 0.00153 0.00200 0.00253 0.00312
14/3/2011 – p. 11

Madgetic diffusion in clusters
B [G]
B [G]
10 -5
10 -6
10 -7
10 -5
10 -6
10 -7
g0272097
COMA: best fit
COMA: 3 σ profiles
100 1000
R [kpc]
g4606589
COMA: best fit
COMA: 3 σ profiles
η m =5
η m =10
η m =20
η m =5
η m =10
η m =20
100 1000
R [kpc]
0.003534
0.001773
0.000889
0.000442
0.000220
0.000109
0.000052
0.000025
0.000010
0.000004
0.000000
0.00592
0.00297
0.00149
0.00074
0.00037
0.00018
0.00009
0.00004
0.00002
0.00001
0.00000
B [G]
B [G]
10 -5
10 -6
10 -7
10 -5
10 -6
10 -7
g1657050
COMA: best fit
COMA: 3 σ profiles
η m =5
η m =10
η m =20
100 1000
R [kpc]
COMA: best fit
g6802296
COMA: 3 σ profiles
100 1000
R [kpc]
Subset of 4 Coma-like clusters with η = 1.5, 3, 6 × 10 27 cm 2 /s. (Bonafede et al. 2011) 14/3/2011 – p. 11
η m =5
η m =10
η m =20
0.01473
0.00739
0.00371
0.00184
0.00092
0.00045
0.00022
0.00010
0.00004
0.00001
0.00000
0.002587
0.001298
0.000651
0.000323
0.000161
0.000080
0.000038
0.000018
0.000008
0.000003
0.000000

Madgetic diffusion in clusters
B [G]
10 -5
10 -6
10 -7
g0016649
g1212639
g1483463
g1680241
g1987669
g2980844
g3327821
g3346905
g3888703
g4425770
g4915399
g5265133
Bonafede et al. 2011
g5503149
g5699754
g6287794
g6348555
g7263961
g7358274
g7570066
g7577931
g0272097
g1657050
g4606589
g6802296
η m =20
100 1000
R [kpc]
⇒ Profiles of 24 Coma-like galaxy clusters
14/3/2011 – p. 11

Madgetic diffusion in clusters
B [G]
10 -5
10 -6
10 -7
Bonafede et al. 2011
COMA: best fit
Dianoga set
η m =20
100 1000
R [kpc]
⇒ Profiles of 24 Coma-like galaxy clusters
14/3/2011 – p. 11

Madgetic diffusion in clusters
B 0 [µG]
10
8
6
4
2
Bonafede et al. 2011
Coma
1.0 1.5 2.0
M [10
v
2.5 3.0
15 M h
sol -1 ]
⇒ Central B of 24 Coma-like galaxy clusters
14/3/2011 – p. 11

Radio emission of cluster
⇒ Solve Fokker-Planck equation for CRe population
+ H(p)n + Q(t)
∂n
∂t
= ∂
∂p
Dpp ∂n
∂p
− n
T(t)
• 10% turbulent energy in fast mhd modes and reacceleration
by those only
• Momentum Diffusion Coefficient
Dpp ∝ v 4 turb /hsml/csound
• cooling with inverse compton, synchrotron and
bremsstrahlung
• See also Cassano & Brunetti 05, Brunetti & Lazarian 2007
• 1% CRp as seed for CRe (hadronic background)
Donnert et al. 2011
14/3/2011 – p. 12

Radio emission of cluster
Idealized 1:4 merger, solving Fokker-Planck equation for all
particles. (2x128 3 ). (Donnert et al. 2011)
14/3/2011 – p. 12

Radio emission of cluster
Synthetic radio emission, smoothed to coma observation by
Deiss et al. 1996 (right). (Donnert et al. 2011)
14/3/2011 – p. 12

Radio emission of cluster
Evolution of vturb (black), B (green) and P1.4 (red).
Donnert et al. 2011
14/3/2011 – p. 12

Radio emission of cluster
P1.4
Lx
10x
Evolution of the spectrum of the radio emission and
the Lx-P1.4 relation (inlay). Donnert et al. 2011
14/3/2011 – p. 12

Conclusions
Zhuravleva (see poster)
B [G]
10 -5
10 -6
10 -7
(Gadget)
(Enzo)
SGS (Fearless)
see talk by I.Zhuravleva
Bonafede et al. 2011
COMA: best fit
Dianoga set
Kulpa−Dybel et al. 2011
η m =20
100 1000
R [kpc]
MHD Cluster Simulations
Schlickeiser et al. 1987
Declination
29:00:00.0
30:00.0
28:00:00.0
30:00.0
27:00:00.0
500 kpc
5C4.152
5C4.127
5C4.114
5C4.85
5C4.81
2 Mpc
5C4.74
5C4.42
04:00.0 02:00.0 13:00:00.0 58:00.0 12:56:00.0
Right ascension
Bonafede et al. 2010
Bonafede et al. 2010
Donnert et al. 2011
Schuecker et al. 2004
14/3/2011 – p. 13

Conclusions
Observations (RM & Radio probes µG)
• Measurement of magnetic field power spectra
• Clear indication of magnetic field shape
• Indications for minimum/maximum length scale
Simulations (hydro):
• Motions within the ICM are unavoidable (> 100 km/s)
• Overall good agreement with (rare) observations
• Overall good agreement between different simulations
Simulations (MHD):
• Overall good agreement with observed magnetic fields
• Detailed comparison reveal dissipative processes
Simulations (Radio Halo):
• Turbulent re-acceleration reproduce on/off and spectra
• Secondary floor emission at best at 10% level
14/3/2011 – p. 13