Simulating Magnetic Fields in Clusters of Galaxies
Simulating Magnetic Fields in Clusters of Galaxies
Simulating Magnetic Fields in Clusters of Galaxies
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11/5/2010 – p. 1<br />
Cosmological Simulations<br />
Klaus Dolag<br />
Max-Planck-Institut für Astrophysik<br />
t = 0.38 Myr<br />
"Zoomed" Simulation <strong>of</strong> a galaxy cluster<br />
t = 13.7 Gyr<br />
Density<br />
Temperature<br />
275 Mpc<br />
−2 −3<br />
10 cm<br />
10 8 K<br />
~ µ G<br />
−7<br />
10 cm −3<br />
10 5 K<br />
< nG
11/5/2010 – p. 2<br />
Outl<strong>in</strong>e<br />
• <strong>Simulat<strong>in</strong>g</strong> <strong>Magnetic</strong> <strong>Fields</strong> <strong>in</strong> Galaxy <strong>Clusters</strong><br />
• Hierarchical Buildup <strong>of</strong> <strong>Magnetic</strong> <strong>Fields</strong><br />
• Applications to observational strategies<br />
• RM-galaxy correlation to measure cosmic<br />
magnetization<br />
• High temperature correction to RM signal<br />
• Questions on magnetic fields:<br />
• M<strong>in</strong>imal length-scale <strong>of</strong> cluster fields ?<br />
• Pr<strong>of</strong>ile <strong>of</strong> magnetic field ?<br />
• <strong>Magnetic</strong> field <strong>in</strong> different cluster ?<br />
F. Stasyszyn (MPA), J. Donnert (MPA) and A. Bonafede (IRA)
11/5/2010 – p. 3<br />
Orig<strong>in</strong> <strong>of</strong> <strong>Magnetic</strong> <strong>Fields</strong><br />
Orig<strong>in</strong><br />
• Primordial<br />
• Battery<br />
• Dynamo (Turbulence)<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 ?
Simulation Network<br />
Density<br />
Coma<br />
Virgo<br />
Centaurus<br />
Perseus<br />
−4.5 −4.0 −3.5 −3.0 −2.5 −2.0 −1.5<br />
2<br />
log( ρ ) [g/cm ]<br />
Temperature<br />
Hydra<br />
ICs (Cosmology)<br />
Structure Formation<br />
Star Formation ? Dissipation ?<br />
Feedback ?<br />
<strong>Magnetic</strong> Pressure<br />
Numerics ?<br />
AGN ?<br />
Resolution ?<br />
Coupl<strong>in</strong>g to Star Formation<br />
Compression<br />
Seed <strong>Magnetic</strong> Field<br />
<strong>Magnetic</strong> Field Evolution<br />
−5.0 −4.0 −3.0 −2.0 −1.0 0.0 1.0<br />
log( T )<br />
[keV]<br />
Shock Statistics<br />
Detection ?<br />
Numerics ?<br />
Turbulence<br />
Viscosity ?<br />
Numerics ?<br />
Sub−Grid Model ?<br />
<strong>Magnetic</strong> Field<br />
Observables<br />
Efficiency<br />
δ(M)<br />
Mechanism<br />
???<br />
−11<br />
−9.0<br />
−7.0 −5.0 −3.0<br />
log(|B|) [ µ G]<br />
−1.0<br />
1.0<br />
Coma<br />
Nuza, Dolag & Saro 2010<br />
Perseus<br />
Virgo<br />
Centaurus<br />
Hydra<br />
Cosmic Rays<br />
Description ?<br />
Diffusion ?<br />
X−ray SB<br />
−23.0<br />
−21.0 −19.0 −17.0 −15.0 −13.0<br />
2<br />
2<br />
log(Lx) [erg/cm /s/arcm<strong>in</strong> ]<br />
−11.0<br />
<strong>Galaxies</strong><br />
Dolag, Hansen, Roncarelli & Moscard<strong>in</strong>i 2005 Donnert, Dolag, Cassano & Brunetti 2009<br />
Dolag, Grasso, Spr<strong>in</strong>gel & Tkachev Coma 2004/2005<br />
CR−p<br />
CR−e<br />
Virgo<br />
Centaurus<br />
Hydra<br />
A3627<br />
Perseus<br />
Pavo<br />
thermal SZ<br />
−10.5<br />
−9.5 −8.5 −7.5 −6.5 −5.5 −4.5<br />
log(Y)<br />
γ−ray SB<br />
−23.0 −21.0 −19.0 −17.0 −15.0 −13.0<br />
log( λ γ ) [ γ/cm 2/s/arcm<strong>in</strong> 2 ]<br />
−11.0<br />
Radio SB<br />
−17.0 −15.0<br />
−11.0 −8.0 −5.0 −2.0 1.0<br />
2<br />
log(P ν ) [mJy/arcm<strong>in</strong> ]<br />
UHECR−Deflection<br />
11/5/2010 – p. 4
Cosmological MHD simulations<br />
684 Mpc<br />
68.4 Mpc<br />
DEC<br />
Observation<br />
Simulation<br />
684 kpc<br />
6.84 Mpc<br />
3C449<br />
Feretti et al. 1999<br />
RA<br />
RM<br />
(RAD/M/M)<br />
(counts)<br />
“Zoomed” cluster simulation (Dolag & Stasyszyn 2009). Movie: u,v<br />
11/5/2010 – p. 5
11/5/2010 – p. 6<br />
<strong>Magnetic</strong> field buildup<br />
<strong>Simulat<strong>in</strong>g</strong> 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 and field configuration <strong>in</strong> broad agreement with<br />
observations.<br />
(Chyzy & Beck 2005 Kortarba et al. 2010)
11/5/2010 – p. 6<br />
<strong>Magnetic</strong> field buildup<br />
<strong>Simulat<strong>in</strong>g</strong> 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 and field configuration <strong>in</strong> broad agreement with<br />
observations.
<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 <strong>of</strong> <strong>in</strong>itial field values.<br />
⇒ Hierarchical buildup <strong>of</strong> magnetic field<br />
(Kortarba et al. 2010)<br />
11/5/2010 – p. 6
<strong>Magnetic</strong> field buildup<br />
F<strong>in</strong>al magnetic field close to equipartition with turbulent velocity<br />
component, quasi <strong>in</strong>dependent <strong>of</strong> <strong>in</strong>itial field values.<br />
⇒ Hierarchical buildup <strong>of</strong> magnetic field<br />
(Kortarba et al. 2010)<br />
11/5/2010 – p. 6
<strong>Magnetic</strong> field buildup<br />
Seed<strong>in</strong>g from galactic outflows (Donnert et al. 2009)<br />
11/5/2010 – p. 6
<strong>Magnetic</strong> field buildup<br />
Different w<strong>in</strong>d parameters (Donnert et al. 2009)<br />
11/5/2010 – p. 6
11/5/2010 – p. 7<br />
RM-Galaxy correlation<br />
Stasyszyn et al. 2010<br />
Mean magnetic field as a function <strong>of</strong> density for various models.
RM-Galaxy correlation<br />
Centaurus<br />
Coma<br />
Perseus<br />
A3627<br />
Virgo<br />
−7.0 −5.0 −3.0<br />
log(|B|) [ µ G]<br />
−1.0<br />
1.0<br />
Hydra<br />
Stasyszyn et al. 2010<br />
Full sky maps for the local universe show<strong>in</strong>g the magnetic field<br />
and galaxy distribution.<br />
11/5/2010 – p. 7
11/5/2010 – p. 7<br />
RM-Galaxy correlation<br />
Taylor et al. 2009<br />
Model foreground based on HAMMURABI (Waelkens et al. 2009),<br />
cosmic signal and observational noise compared to observations.<br />
Same but smoothed by 8 degrees.<br />
Stasyszyn et al. 2010
Stasyszyn et al. 2010<br />
11/5/2010 – p. 7<br />
RM-Galaxy correlation<br />
Same as before, but with foreground removal.<br />
Reduced noise (1 rad/m 2 ) and zoom on several clusters.
RM-Galaxy correlation<br />
Correlation functions (based on 3072 RMs):<br />
(normalized)<br />
(unnormalized).<br />
Stasyszyn et al. 2010<br />
ω RM (θ) ≡ 〈∆n(θ)|RM|〉 ,<br />
¯n|RM|<br />
ξ RM (θ) ≡ 〈∆n(θ)|RM|〉 .<br />
¯n<br />
11/5/2010 – p. 7
11/5/2010 – p. 7<br />
RM-Galaxy correlation<br />
Influence <strong>of</strong> the different components onto the correlation signal:<br />
• Cosmological signal (CS)<br />
• Includ<strong>in</strong>g galactic foreground and apply<strong>in</strong>g removal<br />
• Add<strong>in</strong>g only noise (1 rad/m 2 ) to the signal (CS+N)<br />
• All effects together<br />
Stasyszyn et al. 2010
RM-Galaxy correlation<br />
Correlation signal from different model (Stasyszyn et al. 2010).<br />
11/5/2010 – p. 7
RM <strong>of</strong> high temperature ICM<br />
standard RM<br />
high temperature corrections<br />
2.5 Mpc<br />
−3 −2 −1 (counts) 0 1 2 3<br />
∆ RM [%]<br />
Ignor<strong>in</strong>g high temperature corrections (ICM ≈ 10 keV<br />
<strong>in</strong> massive clusters !) to Faraday Rotation can lead to ≈ 5%<br />
underestimation <strong>of</strong> magnetic field <strong>in</strong> a Coma like cluster !<br />
RM ∝ ∫ n e B ‖ dl ⇒ ∫ )<br />
n e B ‖<br />
(1 − 2T<br />
m e<br />
dl (e.g.<br />
c 2 Mirnov et al. 2007)<br />
11/5/2010 – p. 8
11/5/2010 – p. 8<br />
RM <strong>of</strong> high temperature ICM<br />
corrected us<strong>in</strong>g X−ray temperature map<br />
without hight temperature corrections<br />
X−ray temperature map<br />
But mak<strong>in</strong>g use <strong>of</strong> X-ray temperature measurements can reduce<br />
the bias below 1% !<br />
RM ∝<br />
∫<br />
n e B ‖ dl ⇒<br />
∫<br />
n e B ‖<br />
(<br />
1 − 2T<br />
m e c 2 )<br />
dl
Questions<br />
• Dissipation (Spitzer / Ohmic)<br />
• <strong>Magnetic</strong> fields <strong>in</strong> cool cores<br />
• Direct coupl<strong>in</strong>g <strong>of</strong> magnetic field seed<strong>in</strong>g to star formation<br />
• Cosmological, magnetized galaxy formation<br />
• Jets <strong>in</strong> realistic galaxy clusters environment<br />
11/5/2010 – p. 9<br />
Movie & Simulation by P. Mendygral
Questions<br />
DEC<br />
3C449<br />
10x<br />
130x<br />
220x<br />
3000x<br />
Feretti 1999 Dolag 2005 Dolag 2006 Dolag 2009 Dolag 2009<br />
RA<br />
−70<br />
(counts)<br />
70<br />
−3 3 −30 30 −70 70 −600 600<br />
(counts) (counts) (counts) (counts)<br />
(RAD/M/M)<br />
Observed and simulated RM maps up to the highest resolution<br />
simulation: 20 Million particles with<strong>in</strong> R vir ,<br />
m DM = 10 7 M ⊙ /h, ǫ Grav = 1kpc/h (Stasyszyn & Dolag, work <strong>in</strong> progress)<br />
11/5/2010 – p. 9
11/5/2010 – p. 9<br />
Questions<br />
Sim (10x)<br />
Sim (130x)<br />
Sim (220x)<br />
Sim (3000x)<br />
Sim (3000x,EP)<br />
Obs (3C449)<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)〉
Questions<br />
Sim (10x)<br />
Sim (130x)<br />
Sim (220x)<br />
Sim (3000x)<br />
Sim (3000x,EP)<br />
Obs (3C449)<br />
Structure functions derived from observed and simulated RM<br />
maps up to the highest resolution simulation: Indication for need<br />
<strong>of</strong> magnetic dissipation (Stasyszyn & Dolag, work <strong>in</strong> progress)<br />
11/5/2010 – p. 9
Questions<br />
Govoni et al., submitted<br />
• For new RM maps with<strong>in</strong> massive clusters.<br />
• How does B ⃗ scale with cluster temperature ?<br />
• Different B ⃗ <strong>in</strong> clusters with observed radio halo ?<br />
11/5/2010 – p. 9
11/5/2010 – p. 9<br />
Questions<br />
Bonafede et al., work <strong>in</strong> progress
Questions<br />
g1987669<br />
10 -5<br />
η m<br />
=1<br />
η m<br />
=5<br />
η m<br />
=10<br />
η m<br />
=20<br />
B [G]<br />
10 -6<br />
10 -7<br />
100 1000 10000<br />
R [kpc]<br />
Bonafede et al., work <strong>in</strong> progress<br />
d ⃗ B<br />
dt = (⃗ B · ⃗∇)⃗v − ⃗ B( ⃗ ∇ · ⃗v) + η ⃗ ∇ 2 ⃗ B<br />
11/5/2010 – p. 9
11/5/2010 – p. 10<br />
Conclusions<br />
Cosmological MHD simulations<br />
• Reproduce overall picture well.<br />
• Details need better understand<strong>in</strong>g <strong>of</strong> dissipative processes<br />
• Important to test observational strategies<br />
RM Galaxy correlation:<br />
• Even small signal can survive foreground<br />
• RM measurement error important<br />
• Foreground is critical<br />
Questions on magnetic fields:<br />
• M<strong>in</strong>imal length-scale <strong>of</strong> cluster fields ?<br />
• Pr<strong>of</strong>ile <strong>of</strong> magnetic field ?<br />
• <strong>Magnetic</strong> fields <strong>in</strong> different cluster ?
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