Magnetic Fields, Turbulence and Cosmic Rays in Galaxy Clusters
Magnetic Fields, Turbulence and Cosmic Rays in Galaxy Clusters
Magnetic Fields, Turbulence and Cosmic Rays in Galaxy Clusters
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<strong>Magnetic</strong> <strong>Fields</strong>, <strong>Turbulence</strong> <strong>and</strong><br />
<strong>Cosmic</strong> <strong>Rays</strong> <strong>in</strong> <strong>Galaxy</strong> <strong>Clusters</strong><br />
Klaus Dolag (∗)<br />
A.Bonafede, J.Donnert, I.Zhuravleva, H.Kotarba, A.Geng <strong>and</strong> A.Beck<br />
(∗) Universitäts-Sternwarte München<br />
14/3/2011 – p. 1
The Cluster Bermuda-Triangle<br />
amplification<br />
B<br />
?<br />
v CR<br />
(turb)<br />
acceleration<br />
radio emission<br />
(e,p)<br />
14/3/2011 – p. 2
Where are we ?<br />
<strong>Magnetic</strong> Field<br />
Schlickeiser et al. 1987<br />
transport koefficient<br />
~ 0.1 * v * L<br />
turb<br />
turbulence (IGM/ICM)<br />
=> radio emission<br />
Burbidge 1958 (!!)<br />
14/3/2011 – p. 3
Problem 1: Orig<strong>in</strong> of B<br />
Orig<strong>in</strong><br />
• Primordial<br />
• Battery<br />
• Dynamo (<strong>Turbulence</strong>)<br />
• Stars<br />
• Supernovae<br />
• Galactic W<strong>in</strong>ds<br />
• AGNs, Jets<br />
• Rees 1994<br />
Shocks<br />
+ further amplification by structure formation<br />
- dissipation ?<br />
14/3/2011 – p. 4
Problem 2: <strong>Turbulence</strong><br />
Observed turbulece <strong>in</strong> clusters: (see talk by de Plaa, ...)<br />
Ddiff = 0.1 × vturb × λturb , vturb(l) ∝ λ (1/3)<br />
turb<br />
Schuecker et al. 2004<br />
14/3/2011 – p. 5
Problem 2: <strong>Turbulence</strong><br />
Simulations: Simulated turbulece <strong>in</strong> clusters (I):<br />
SPH ENZO<br />
log(E turb)[erg]<br />
62.0<br />
61.5<br />
61.0<br />
60.5<br />
60.0<br />
13.4 13.6 13.8 14.0 14.2 14.4 14.6<br />
log(M merg)[M sun]<br />
Dolag et al. 2005 / Vazza et al. 2006 Vazza et al. 2010 Iapich<strong>in</strong>o et al. 2009/2010<br />
Dolag et al. 2005 (see also Iapich<strong>in</strong>o et al. 2008/2009, Vazza et al. 2006/2009/2010, ...)<br />
Need to dist<strong>in</strong>guish bulk <strong>and</strong> turbulent motions.<br />
⇒ strongly depend on operational def<strong>in</strong>itions !<br />
Orig<strong>in</strong> (<strong>in</strong> cosmological context):<br />
• Beh<strong>in</strong>d shocks (mostly beyond core radius)<br />
• Passage of gas rich substructure (whole cluster)<br />
• Passage of dm substructure (mostly cluster core)<br />
14/3/2011 – p. 5
Problem 2: <strong>Turbulence</strong><br />
Simulated turbulece <strong>in</strong> clusters (II):<br />
(Dolag et al 2005, Vazza et al 2009, Maier et al 2009, ...)<br />
(Gadget)<br />
(Enzo)<br />
SGS (Fearless)<br />
see talk by I.Zhuravleva<br />
14/3/2011 – p. 5
Problem 3: Low B<br />
Please:<br />
(numbers are from private communication)<br />
Cluster Pthermal B 2 /8π β<br />
Coma 1.02e-10 1.63e-12 1.6<br />
A2255 5.016e-11 2.487e-13 0.5<br />
A400 1.927e-11 1.681e-12 8.7<br />
A119 3.63e-11 1.204e-12 3.3<br />
A2382 1.21e-11 3.581e-13 3.0<br />
Note on <strong>Turbulence</strong>:<br />
10% (Observed, Coma)<br />
10-20% (Simulations)<br />
14/3/2011 – p. 6
Problem 3: Low B<br />
Observed B <strong>in</strong> clusters: (Bonafede et al. 2010, ...)<br />
B(r) = B0<br />
Decl<strong>in</strong>ation<br />
1 + (r/rc) 2 −1.5η , |Bk| 2 ∝ k −n , (km<strong>in</strong>,kmax)<br />
29:00:00.0<br />
30:00.0<br />
28:00:00.0<br />
30:00.0<br />
27:00:00.0<br />
500 kpc<br />
5C4.152<br />
5C4.127<br />
5C4.114<br />
5C4.85<br />
5C4.81<br />
2 Mpc<br />
5C4.74<br />
04:00.0 02:00.0 13:00:00.0 58:00.0 12:56:00.0<br />
Right ascension<br />
5C4.42<br />
Bonafede et al. 2010<br />
14/3/2011 – p. 6
Problem 3: Low B<br />
B(r) = B0<br />
1 + (r/rc) 2 −1.5η , |Bk| 2 ∝ k −n , (km<strong>in</strong>,kmax)<br />
• S(dx,dy) = [RM(x,y) − RM(x + dx,y + dy)] 2<br />
• A(dx,dy) = 〈RM(x,y) × RM(x + dx,y + dy)〉<br />
• 〈|RM|〉 scale , 〈σRM〉 scale<br />
η<br />
2<br />
1.5<br />
1<br />
0.5<br />
0<br />
−0.5<br />
2 4 6 8 10<br />
Β [µG]<br />
< 0 ><br />
⇒ constra<strong>in</strong>s on magnetic field strength !<br />
B [µG]<br />
8<br />
6<br />
4<br />
2<br />
Analytic profile<br />
Power spectrum<br />
fluctuations<br />
0<br />
0 500 1000<br />
r [kpc]<br />
1500 2000<br />
14/3/2011 – p. 6
Problem 3: Low B<br />
B(r) = B0<br />
1 + (r/rc) 2 −1.5η , |Bk| 2 ∝ k −n , (km<strong>in</strong>,kmax)<br />
⇒ A655: Inferred outer scale ≈450 kpc (Vacca et al. 2010) !<br />
• Depolarization <strong>in</strong>dicates truncation at small scales !<br />
⇒ No fluctuations at scales below ≈ (.1 − .5) kpc !<br />
Govoni et al. 2010, Vacca et al. 2010, Guidetti et al. 2010, Bonafede et al. 2010, Guidetti et al.<br />
2008, Govoni et al. 2006, La<strong>in</strong>g et al. 2006, Vogt & Enssl<strong>in</strong> 2005, Murgia et al. 2004,<br />
Ennsl<strong>in</strong> & Vogt 2003, ... , Tribble 1991.<br />
14/3/2011 – p. 6
Problem 3: Low B<br />
Govoni et al. 2010<br />
• Comb<strong>in</strong>ation of RM measured <strong>in</strong> many clusters.<br />
• How does B scale with cluster temperature ?<br />
• <strong>Magnetic</strong> Field <strong>in</strong> Radio quiet/active clusters ? 14/3/2011 – p. 6
Problem 4: Radio Emission<br />
Radio Relic<br />
Radio Halo<br />
1 Mpc<br />
Feretti 1999<br />
M<strong>in</strong>iati et al. 2001<br />
Dolag & Enssl<strong>in</strong> 2000<br />
Pfromer et al. 2007<br />
Dolag & Enssl<strong>in</strong> 2000<br />
Cluster wide diffuse synchrotron emission connected to<br />
merger events, periferal emission directly connected to shocks.<br />
• Radio halo: <strong>Turbulence</strong>, shocks, secondary ?<br />
• Relics: Primary from shocks or compressed radio plasma ?<br />
14/3/2011 – p. 7
The Big Picture<br />
see talk by I.Zhuravleva<br />
B [G]<br />
B [G]<br />
MHD Simulations<br />
Bonafede et al. 2011<br />
10 -5<br />
10 -6<br />
10 -7<br />
10 -5<br />
10 -6<br />
10 -7<br />
g1657050<br />
g4606589<br />
Coma<br />
100 1000<br />
R [kpc]<br />
100 1000<br />
R [kpc]<br />
η m =5<br />
η m =10<br />
η m =20<br />
Coma<br />
η m =5<br />
η m =10<br />
η m =20<br />
COMA<br />
B [G]<br />
(Gadget)<br />
(Enzo)<br />
SGS (Fearless)<br />
see talk by I.Zhuravleva<br />
10 -5<br />
10 -6<br />
10 -7<br />
g0016649 g0272097<br />
g1212639<br />
g1657050<br />
g3327821<br />
g4606589<br />
g5699754<br />
g1680241<br />
g3346905<br />
g1987669<br />
g3888703<br />
g6287794 g6348555<br />
Bonafede et al., work <strong>in</strong> progress<br />
g0272097<br />
g1483463<br />
g2980844<br />
g4425770<br />
g4915399 g5265133 g5503149<br />
g6802296<br />
5E-08 8E-07 2.66E-05 0.0043659<br />
g735 g7570 g7577<br />
g726<br />
Coma<br />
100 1000<br />
R [kpc]<br />
η m =5<br />
η m =10<br />
η m =20<br />
Schlickeiser et al. 1987<br />
Decl<strong>in</strong>ation<br />
29:00:00.0<br />
30:00.0<br />
28:00:00.0<br />
30:00.0<br />
27:00:00.0<br />
500 kpc<br />
5C4.152<br />
5C4.127<br />
5C4.114<br />
5C4.85<br />
5C4.81<br />
2 Mpc<br />
5C4.74<br />
5C4.42<br />
04:00.0 02:00.0 13:00:00.0 58:00.0 12:56:00.0<br />
Right ascension<br />
Bonafede et al. 2010<br />
Bonafede et al. 2010<br />
Schuecker et al. 2004<br />
14/3/2011 – p. 8
Cluster MHD simulations<br />
14/3/2011 – p. 9
Cluster MHD simulations<br />
DEC<br />
Observation<br />
3C449<br />
Feretti et al. 1999<br />
RA<br />
(RAD/M/M)<br />
Simulation<br />
RM<br />
(counts)<br />
684 Mpc<br />
684 kpc<br />
68.4 Mpc<br />
6.84 Mpc<br />
“Zoomed” cluster simulation (Dolag & Stasyszyn 2009). Movie: u,v 14/3/2011 – p. 9
Cluster MHD simulations<br />
Simulation<br />
Dolag et al. 2002<br />
ε(k) [erg cm -2 ]<br />
Simulation<br />
1e-10<br />
1e-11<br />
1e-12<br />
1e-13<br />
1e-14<br />
1e-15<br />
0.1 1 10<br />
k [kpc -1 ]<br />
REALMAF<br />
Vogt<br />
Observation<br />
Kuchar & Enssl<strong>in</strong> 2009<br />
Pakmor & Dolag 2006<br />
<strong>Magnetic</strong> field power spectra: predictions vs. observations.<br />
See also Brüggen et al. 2005, Xu et al. 2009<br />
14/3/2011 – p. 9
<strong>Magnetic</strong> Field buildup<br />
Simulations on galaxy scales ...<br />
M51 (Fletcher & Beck 2006) <strong>and</strong> a simulation us<strong>in</strong>g the MHD<br />
implementation <strong>in</strong> Gadget (Kotarba et al. 2009).<br />
14/3/2011 – p. 10
<strong>Magnetic</strong> Field buildup<br />
Simulat<strong>in</strong>g the magnetic field amplification dur<strong>in</strong>g galaxy<br />
mergers like <strong>in</strong> the Antennae system. F<strong>in</strong>al magnetic field<br />
strength <strong>and</strong> field configuration <strong>in</strong> broad agreement with<br />
observations.<br />
(Chyzy & Beck 2005 Kortarba et al. 2010)<br />
14/3/2011 – p. 10
<strong>Magnetic</strong> Field buildup<br />
F<strong>in</strong>al magnetic field close to equipartition with turbulent velocity<br />
component, largely <strong>in</strong>dependent of <strong>in</strong>itial field values.<br />
⇒ Hierarchical buildup of magnetic field<br />
(Kortarba et al. 2010)<br />
14/3/2011 – p. 10
<strong>Magnetic</strong> Field buildup<br />
y [kpc/h]<br />
y [kpc/h]<br />
y [kpc/h]<br />
y [kpc/h]<br />
100<br />
0<br />
-100<br />
100<br />
0<br />
-100<br />
100<br />
0<br />
-100<br />
100<br />
0<br />
-100<br />
-100 0 100<br />
x [kpc/h]<br />
t=982 Myr t=1483 Myr t=1984 Myr t=2486 Myr<br />
t=2987 Myr<br />
-100 0 100 200<br />
x [kpc/h]<br />
(A. Geng, work <strong>in</strong> progress)<br />
t=3488 Myr<br />
-100 0 100<br />
x [kpc/h]<br />
-100 0 100 200<br />
x [kpc/h]<br />
t=3989 Myr<br />
-100 0 100<br />
x [kpc/h]<br />
-100 0 100 200<br />
x [kpc/h]<br />
t=4490 Myr<br />
-100 0 100<br />
x [kpc/h]<br />
-100 0 100 200<br />
x [kpc/h]<br />
-25<br />
-26<br />
-27<br />
-28<br />
-29<br />
-7<br />
-8<br />
-9<br />
log < density [g cm -2 ] ><br />
log < |B| [G] ><br />
14/3/2011 – p. 10
<strong>Magnetic</strong> Field buildup<br />
Smaller merger less efficient <strong>in</strong> driv<strong>in</strong>g turbulence.<br />
(Geng et al., <strong>in</strong> prep)<br />
14/3/2011 – p. 10
DECLINATION (J2000)<br />
<strong>Magnetic</strong> Field buildup<br />
34 00 00<br />
33 59 30<br />
00<br />
58 30<br />
00<br />
57 30<br />
00<br />
56 30<br />
00<br />
55 30<br />
PLot file version 2 created 11-SEP-2009 16:13:17<br />
ICONT:SQ IPOL 4860.100 MHZ SQ 6.I.3<br />
22 36 10 05 00 35 55 50<br />
RIGHT ASCENSION (J2000)<br />
Cont peak flux = 9.4028E-03 JY/BEAM<br />
Levs = 9.000E-06 * (3, 5, 8, 12, 20, 30, 50, 80,<br />
120, 200, 300, 500, 800)<br />
Pol l<strong>in</strong>e 1 arcsec = 4.1667E-06 JY/BEAM<br />
Soida et al., <strong>in</strong> prep. Kortarba et al. 2010<br />
14/3/2011 – p. 10
<strong>Magnetic</strong> Field buildup<br />
Kortarba et al. 2010<br />
• Merg<strong>in</strong>g drives shocks, turbulence <strong>and</strong> star-formation<br />
• Star-formation drives w<strong>in</strong>ds<br />
• W<strong>in</strong>ds transport out magnetic fields<br />
14/3/2011 – p. 10
<strong>Magnetic</strong> Field buildup<br />
Comparison of magnetic growth <strong>and</strong> simple expectation for<br />
vturb = 100km/s <strong>and</strong> λ = 25kpc.<br />
A. Beck, diploma thesis<br />
14/3/2011 – p. 10
<strong>Magnetic</strong> Field buildup<br />
z=4<br />
z=0<br />
primordial<br />
galactic outflows<br />
Seed<strong>in</strong>g from galactic outflows (Donnert et al. 2009)<br />
14/3/2011 – p. 10
z=0<br />
<strong>Magnetic</strong> Field buildup<br />
dipole (10x)<br />
dipole<br />
quadrupole (10x) cont<strong>in</strong>uously seed<strong>in</strong>g<br />
Different w<strong>in</strong>d parameters (Donnert et al. 2009)<br />
dipole (1/10)<br />
primordial<br />
14/3/2011 – p. 10
<strong>Magnetic</strong> Field buildup<br />
⇒ Galactic seed<strong>in</strong>g models also reproduce observed RM<br />
profile with<strong>in</strong> galaxy clusters (Donnert et al. 2009)<br />
14/3/2011 – p. 10
Madgetic diffusion <strong>in</strong> clusters<br />
η = ηcoulomb + ηturb ≈ 0.1 × vturb × λvturb<br />
g0016649 g0272097<br />
g1212639<br />
g1657050<br />
g1483463<br />
g1680241 g1987669 g2980844<br />
g3327821 g3346905 g3888703 g4425770<br />
g4606589<br />
g4915399<br />
g5265133<br />
g5503149<br />
g5699754 g6287794 g6348555 g6802296<br />
g7263961<br />
g7358274 g7570066<br />
g7577931<br />
Selected 24 most massive clusters from a 1Gpc/h box.<br />
Bonafede et al. 2011<br />
0.00000 0.00003 0.00012 0.00028 0.00050 0.00078 0.00112 0.00153 0.00200 0.00253 0.00312<br />
14/3/2011 – p. 11
Madgetic diffusion <strong>in</strong> clusters<br />
B [G]<br />
B [G]<br />
10 -5<br />
10 -6<br />
10 -7<br />
10 -5<br />
10 -6<br />
10 -7<br />
g0272097<br />
COMA: best fit<br />
COMA: 3 σ profiles<br />
100 1000<br />
R [kpc]<br />
g4606589<br />
COMA: best fit<br />
COMA: 3 σ profiles<br />
η m =5<br />
η m =10<br />
η m =20<br />
η m =5<br />
η m =10<br />
η m =20<br />
100 1000<br />
R [kpc]<br />
0.003534<br />
0.001773<br />
0.000889<br />
0.000442<br />
0.000220<br />
0.000109<br />
0.000052<br />
0.000025<br />
0.000010<br />
0.000004<br />
0.000000<br />
0.00592<br />
0.00297<br />
0.00149<br />
0.00074<br />
0.00037<br />
0.00018<br />
0.00009<br />
0.00004<br />
0.00002<br />
0.00001<br />
0.00000<br />
B [G]<br />
B [G]<br />
10 -5<br />
10 -6<br />
10 -7<br />
10 -5<br />
10 -6<br />
10 -7<br />
g1657050<br />
COMA: best fit<br />
COMA: 3 σ profiles<br />
η m =5<br />
η m =10<br />
η m =20<br />
100 1000<br />
R [kpc]<br />
COMA: best fit<br />
g6802296<br />
COMA: 3 σ profiles<br />
100 1000<br />
R [kpc]<br />
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<br />
η m =5<br />
η m =10<br />
η m =20<br />
0.01473<br />
0.00739<br />
0.00371<br />
0.00184<br />
0.00092<br />
0.00045<br />
0.00022<br />
0.00010<br />
0.00004<br />
0.00001<br />
0.00000<br />
0.002587<br />
0.001298<br />
0.000651<br />
0.000323<br />
0.000161<br />
0.000080<br />
0.000038<br />
0.000018<br />
0.000008<br />
0.000003<br />
0.000000
Madgetic diffusion <strong>in</strong> clusters<br />
B [G]<br />
10 -5<br />
10 -6<br />
10 -7<br />
g0016649<br />
g1212639<br />
g1483463<br />
g1680241<br />
g1987669<br />
g2980844<br />
g3327821<br />
g3346905<br />
g3888703<br />
g4425770<br />
g4915399<br />
g5265133<br />
Bonafede et al. 2011<br />
g5503149<br />
g5699754<br />
g6287794<br />
g6348555<br />
g7263961<br />
g7358274<br />
g7570066<br />
g7577931<br />
g0272097<br />
g1657050<br />
g4606589<br />
g6802296<br />
η m =20<br />
100 1000<br />
R [kpc]<br />
⇒ Profiles of 24 Coma-like galaxy clusters<br />
14/3/2011 – p. 11
Madgetic diffusion <strong>in</strong> clusters<br />
B [G]<br />
10 -5<br />
10 -6<br />
10 -7<br />
Bonafede et al. 2011<br />
COMA: best fit<br />
Dianoga set<br />
η m =20<br />
100 1000<br />
R [kpc]<br />
⇒ Profiles of 24 Coma-like galaxy clusters<br />
14/3/2011 – p. 11
Madgetic diffusion <strong>in</strong> clusters<br />
B 0 [µG]<br />
10<br />
8<br />
6<br />
4<br />
2<br />
Bonafede et al. 2011<br />
Coma<br />
1.0 1.5 2.0<br />
M [10<br />
v<br />
2.5 3.0<br />
15 M h<br />
sol -1 ]<br />
⇒ Central B of 24 Coma-like galaxy clusters<br />
14/3/2011 – p. 11
Radio emission of cluster<br />
⇒ Solve Fokker-Planck equation for CRe population<br />
+ H(p)n + Q(t)<br />
∂n<br />
∂t<br />
= ∂<br />
∂p<br />
Dpp ∂n<br />
∂p<br />
− n<br />
T(t)<br />
• 10% turbulent energy <strong>in</strong> fast mhd modes <strong>and</strong> reacceleration<br />
by those only<br />
• Momentum Diffusion Coefficient<br />
Dpp ∝ v 4 turb /hsml/csound<br />
• cool<strong>in</strong>g with <strong>in</strong>verse compton, synchrotron <strong>and</strong><br />
bremsstrahlung<br />
• See also Cassano & Brunetti 05, Brunetti & Lazarian 2007<br />
• 1% CRp as seed for CRe (hadronic background)<br />
Donnert et al. 2011<br />
14/3/2011 – p. 12
Radio emission of cluster<br />
Idealized 1:4 merger, solv<strong>in</strong>g Fokker-Planck equation for all<br />
particles. (2x128 3 ). (Donnert et al. 2011)<br />
14/3/2011 – p. 12
Radio emission of cluster<br />
Synthetic radio emission, smoothed to coma observation by<br />
Deiss et al. 1996 (right). (Donnert et al. 2011)<br />
14/3/2011 – p. 12
Radio emission of cluster<br />
Evolution of vturb (black), B (green) <strong>and</strong> P1.4 (red).<br />
Donnert et al. 2011<br />
14/3/2011 – p. 12
Radio emission of cluster<br />
P1.4<br />
Lx<br />
10x<br />
Evolution of the spectrum of the radio emission <strong>and</strong><br />
the Lx-P1.4 relation (<strong>in</strong>lay). Donnert et al. 2011<br />
14/3/2011 – p. 12
Conclusions<br />
Zhuravleva (see poster)<br />
B [G]<br />
10 -5<br />
10 -6<br />
10 -7<br />
(Gadget)<br />
(Enzo)<br />
SGS (Fearless)<br />
see talk by I.Zhuravleva<br />
Bonafede et al. 2011<br />
COMA: best fit<br />
Dianoga set<br />
Kulpa−Dybel et al. 2011<br />
η m =20<br />
100 1000<br />
R [kpc]<br />
MHD Cluster Simulations<br />
Schlickeiser et al. 1987<br />
Decl<strong>in</strong>ation<br />
29:00:00.0<br />
30:00.0<br />
28:00:00.0<br />
30:00.0<br />
27:00:00.0<br />
500 kpc<br />
5C4.152<br />
5C4.127<br />
5C4.114<br />
5C4.85<br />
5C4.81<br />
2 Mpc<br />
5C4.74<br />
5C4.42<br />
04:00.0 02:00.0 13:00:00.0 58:00.0 12:56:00.0<br />
Right ascension<br />
Bonafede et al. 2010<br />
Bonafede et al. 2010<br />
Donnert et al. 2011<br />
Schuecker et al. 2004<br />
14/3/2011 – p. 13
Conclusions<br />
Observations (RM & Radio probes µG)<br />
• Measurement of magnetic field power spectra<br />
• Clear <strong>in</strong>dication of magnetic field shape<br />
• Indications for m<strong>in</strong>imum/maximum length scale<br />
Simulations (hydro):<br />
• Motions with<strong>in</strong> the ICM are unavoidable (> 100 km/s)<br />
• Overall good agreement with (rare) observations<br />
• Overall good agreement between different simulations<br />
Simulations (MHD):<br />
• Overall good agreement with observed magnetic fields<br />
• Detailed comparison reveal dissipative processes<br />
Simulations (Radio Halo):<br />
• Turbulent re-acceleration reproduce on/off <strong>and</strong> spectra<br />
• Secondary floor emission at best at 10% level<br />
14/3/2011 – p. 13