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Magnetic Fields in Clusters of Galaxies
Dongsu Ryu (UNIST, Korea)
November 2, 2017 CHEA Collaboration Meeting UNIST, Korea
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Faraday rotation measure
Hydra North
(Vogt & Ensslin 2005)
(Ryu et al 2008)
The large-scale structure of the universe
observed and simulatedgalaxy distributions
simulated matter distributionclustersfilaments void regions
the cosmic web
where most matters resideNovember 2, 2017 CHEA Collaboration Meeting UNIST, Korea
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Clusters of galaxies
aggregates of galaxies, which are the largest known gravitationally bound objects to have arisen thus far in the process of cosmic structure formation
Hubble space telescope image mostly star light
the intraclustermedium (ICM)
the superheated plasma with T ~ a few to several keV, presented in clusters of galaxies
optical (Hubble, white)
X-ray (Chandra, blue) hot gas
radio (VLA, red) cosmic rays
MACSJ0717MACSJ0717
November 2, 2017 CHEA Collaboration Meeting UNIST, Korea
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Perseus cluster: X-ray
Coma cluster: X-rayICMs are dynamical:- turbulent flow motions
- large-scale flow motions
- magnetic fields
- cosmic-rays
- shock waves
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Faraday rotation measure
Hydra North
(Vogt & Ensslin 2005)
CIZA J2242.8+5301 Sausage relic
(van Weeren et al 2010)
Coma clusterRelic halo
(Brown & Rudnick 2011)
Magnetic fields in galaxy clusters appears in observations
(Clarke et al 2004)
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(Govoni & Feretti 2004)
modeling of synchrotron of the Sausage relic B1 ~ 2 – 2.5 G modeling of synchrotron of the Toothbrush relic B1 ~ 1 – 1.5 G
(Kang & Ryu 2015)
(Kang, Ryu, & Jones 2017)
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Fluid quantities in ICM outskirts
baryon number density
gas temperature
magnetic fields
flow velocity
gas kinetic energy
gas thermal energy
cosmic-ray energy
magnetic energy
size of clusters
plasma beta is high with β ~ 50 - 100
magnetic
thermal
magnetic
thermal
3E
2E
P
Pβ
flows are subsonic (Ms ~ 0.5) but super-Alfvenic (MA > 1)
Lcluster ~ a few Mpc ~ 1025 cm
n ~ 10-3 cm
v ~ severalⅹ100 km/s
T ~ 108 K (8.6 keV) cs ~ 1,500 km/s
B ~ a fewⅹμG cA ~ 100 km/s
Ethermal ~ a fewⅹ10-11 erg/cm3
Ekinetic ~ a fewⅹ10-12 erg/cm3
Emagnetic ~ a fewⅹ10-13 erg/cm3
ECR <~ a fewⅹ10-13 erg/cm3 (Ethermal / 100)
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large-scale structure formation
shocks in the LSS of the Univ
gravitational collapse, mergers, & flow motions
stretching and compression
development into turbulence
amplification of magnetic fields
Turbulence dynamo model for magnetic fields in clusters of galaxies
generation of vorticity
small-scale or turbulent dynamo
(e.g., Ryu et al 2008)
shock dissipation
seed fields
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Observation of shocks in clusters: X-ray
The Bullet Cluster
Cluster A665
shock
cold front
6.03XM
(Dasadia et al. 2016)
(no associated radio relic)
5.2XM(Shimwell et al.
2015)
0.3XM
(Markevitch 2006)
(no associated radio relic)
cold front
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Observation of shocks in clusters: radio relics
PLCKG287.0+32.9
Sausage relic
‘Giant Gischt Relic’
Abell3411-3412
(van Weeren et al. + Ryu 2017)
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weak inreacluster shocks with M<4 (orange)
Shock waves in a simulated clusters of
galaxies
strong accretion shocks with M>10 (green)
Shock waves induced during the formation of the large-scale structure of the universe
(Vazza et al + Ryu)
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preshock density
postshock density
preshock flow speed
unit normal to shock surf.
curvature radius of surf.
Vorticity generated at cosmological shocks
R
nU
12
2
12cs
)(~
1
2
U
R
n
at shocks
- directly at interacting and curved shocks
- by the baroclinic term
p
2bc
1
constant ρ
constant p
baroclinity
due to entropy variation induced at shocks
Magnitude of vorticity or enstropy (e) enhanced by stretching and compression increases during the development of turbulence
div(v) ω
interacting shocks
(Porter, Jones, Ryu 2015)
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the spectrum of Kolmogorov turbulence
a schematic representation of the turbulent energy cascade from large to small scales
Kolmogorov's theory for incompressible hydrodynamic turbulence: it is based on the notion that that large eddies can feed energy to the smaller eddies and these in turn feed still smaller eddies, resulting in a cascade of energy from the largest eddies to the smallest ones.
on dimensional grounds, the only way of writing ε (energy transfer rate) in terms of V (velocity) and l(scale) is power spectrum of velocity!
Theory of turbulence
3/5
3/1
3
~
~
~
kP
lV
l
V
k
e ~ constant2
t
V~
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Turbulence in high resolution simulations of galaxy clusters
curl(v) in the plane through the cluster center(Miniati 2013)
in simulations, turbulence exists in all over the clusters!
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Turbulence energy of in the ICM
assuming that turbulence is contained in vorticalmotions
Mturb ~ 1(transonic turbulence)
in filaments
Mturb < ~1(subsonic turbulence)Eturb/Etherm ~ 0.1 – 0.3
inside and outskirtsof clusters
clusters
(Ryu et al 2008)November 2, 2017 CHEA Collaboration Meeting UNIST, Korea
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at the core of the Perseus cluster, the estimated
turbulence velocity ~ 165 km/s, (while the expected
value ~ 500 km/s)
(Hitomi Collaboration 2016)
X-ray spectrum of the core of the Perseus cluster
Evidences for turbulence in clusters
observations of turbulence in clusters are mostly around core regions!
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data n = 2 n = 11/3
- RM in Abell 119 for comparison with simulation
- turbulent cluster magnetic fields with power-low slope n=2 give a good fit (Kolmogorov n=11/3)
Murgia et al. (2004)
patchy Faraday rotation measure (RM) in clusters observed with radio galaxies
an evidence for turbulence in cluster outskirts?November 2, 2017 CHEA Collaboration Meeting UNIST, Korea
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Turbulence in astrophysical environments with magnetic fields
oB
BBpt
4
11
Fluid and magnetic fields interact with each otherfluid drags magnetic fieldmagnetic field exerts tension and pressure fluid and magnetic field moves together (“frozen”)
with large magnetic Reynolds number
B
t
B
Turbulence + magnetic field
Magnetohydrodynamic turbulence
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Origin of magnetic fields in clusters
- generation of seed fields
- amplification of seed fields by turbulent flow motions
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Suggestions include:
- generation in the early universe (e.g., see Widrow, Ryu et al 2012 for review)
e.g.) during the electroweak phase transition (t~10-12sec)
during the quark-hadron transition (t~10-5sec)
uncertain but maybe challenging (?)
- generation before the formation of the LSS of the universe
through plasma physical processes (e.g., see Ryu et al 2012 for review)
e.g.) Biermann battery or Weibel Instability at shocks(Kulsrud, Cen, Ostriker, & Ryu 1997) (Medvedev & Loeb 1999)
instabilities, thermal fluctuations, photo-ionization and etc …
weak (~ 10-20 G) and some at small scales, yet most promising(?)
- astrophysical processes
e.g.) magnetic fields from the first stars
maybe not the first magnetic field
Origin of seeds for comic magnetic fields is uncertain!
Seed magnetic fields in the large-scale structure (LSS) of the universe
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Small-scale dynamo of MHD turbulence with weak initial field
at saturationEmag/Ekin ~ ½ - 2/3
Ekin
Emaglinear
growth
saturation
growth of magnetic energy
exponentialgrowth
(Jo & Ryu, unpublished)
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exponential growth
linear growthinverse cascade
1
Evolution of magnetic field power spectrum at early stages(From J. Cho)
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Power spectrum at saturation
Ekin
Emag
(Jo & Ryu, unpublished)
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Bω
A model for magnetic fields in galaxy clusters
- vorticity generated at shocks and also due to baroclinity
- further enhanced by stretching and compression
- developed into turbulence- magnetic field produced by
turbulence dynamo
(Ryu et al 2008)
The model may reproduce the observed strength of magnetic field!
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CIZA J2242.8+5301 (sausage radio relic)
(van Weeren et al 2010)
Can Mpc-scale magnetic fields in outskirts , “if real”, be explained by turbulence dynamo?
Large-scale magnetic fields in cluster outskirts ?
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The growth time of magnetic fields in turbulence dynamo
Emag
Ekin
time evolution of energies(Porter, Jones, & Ryu, 2015)
10 t / teddy
teddy ≡ Linjection / vturb
In clusters, if turbulence is driven mainly by major mergers,
Linjection ~ 500 kpc (clump size)
vturb ~ 500 km/s
teddy ~ 1 Gyrs ~ 1/10 tage
or tage ~ 1/10 teddy
(tage the age of the universe)
There seems to be enough time for the growth of B!
It takes t ~ severalⅹteddy to reach
Emag ~ 1/10 Ekin
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Pmag(k)
Pkin(k)
power spectrum at saturation(Porter, Jones, & Ryu, 2015)
(Cho & Ryu 2009)
The scale of magnetic fields in turbulence dynamo
~3 t / teddy
At t ~ 10 teddy,the peak of Pmag(k) is ~ 1/3 Linjection
the peak of kPmag(k) is ~ 1/10 Linjection
If Linjection ~ 500 kpc,
the peak of “kPmag(k)” (the peak scale of magnetic energy) ~ 50 kpc, too small?
November 2, 2017 CHEA Collaboration Meeting UNIST, Korea
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in clusters- turbulence is driven “sporadically”- the medium is “stratified”
(Vazza et al + Ryu, 2016)
In clusters of galaxies, the turbulence is driven “sporadically”, mostly by “mergers”.
(Coma cluster)
Intracluster media are highly “stratified”, i.e., high density at cores and low density at outskirts.
turbulence energy dissipation rate in a cluster formed in a simulation for the formation of the large-scale structure of the universe
Turbulence dynamo in clusters
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Simulations of turbulence “sporadically” driven in “staratified” clusters
clusters of T = 108 K (cs = 1,500 km/s) described the beta model with β = 1 and rc = 300 kpc in a box of Lsize = 4 Mpc
4 Mpc
~tageturbulence of Mturb ~ ½ , driven for 4 times (that is, forcing on for Δt = 0.1 tage and off for Δt = 0.15 tage) during the age of the universe, tage, with the peak of forcing at Linjection = 500 kpc
(Roh, Ha & Ryu, preliminary)
November 2, 2017 CHEA Collaboration Meeting UNIST, Korea
Amplification of B up to Emag ~ Ekin /10 would be OK.
How about the scale of B?
29/36
The power spectra of velocity and magnetic field at t = 5 (~ tage)
stratified medium, constant forcing
uniform medium, constant forcing uniform medium, sporadic forcing
stratified medium, sporadic forcing
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Power spectra of turbulence in stratified medium with sporadic forcing
- Pkin(k) shows large-scale (scales up to the box size) powers- Pmag(k) has a broad peak over ½ kinjection – 2 kinjection
- kPmag(k) has a peak at ~ 2kinjection
or if Linjection = 500 kpc, the peak scale of magnetic energy ~200 - 300 kpc
Pmag(k)
Pkin(k)
kinjection
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log(Emag)
|curl(v)| div(v)
- less concentration of Ekin and Emag than ρ
- higher flow activities at outskirts
November 2, 2017 CHEA Collaboration Meeting UNIST, Korea
can this reproduce the observed polarization properties of radio relics?32/36
log(Ekin)log(ρ)
Slice images through the cluster center at t = 4.54 Mpc
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Shocks and magnetic fields
B on the top of div(v)
(|B| on the log scale)
zoomed regions showing perpendicular shocks (B and shock normal are perpendicular)
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Summary
- Magnetic field is ubiquitous in the large-scale structure of the universe including in clusters of galaxies.
- Magnetic fields of ~ a few μG in cluster outskirts could be explained by turbulence dynamo.
- The existence Mpc-scale magnetic fields in cluster outskirts need to be established in observation.
- Explaining large-scale magnetic fields of ~ Mpc scale, if they exist, would remain challenging in the picture of turbulence dynamo.
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Thank you !
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