The quest for cosmic ray protons
in clusters of galaxies
“Astrophysical Seminar”
Universität Würzburg
Christoph Pfrommer (MPA)
[email protected]
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Outline
A.) Introduction and motivation
1.) cosmic rays in galaxies and clusters of galaxies
2.) cosmological implications
3.) hadronic cosmic ray proton interactions in the ICM
B.) Cosmic rays in nearby clusters of galaxies
1.) γ -ray emission induced by cosmic ray protons
2.) minimum energy criterion: preferred CR profiles
C.) Cosmic rays in the simulation code GADGET
1.) philosophy and description
2.) first results
D.) Conclusions
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Galactic cosmic rays
Galactic cosmic rays are dynamically important:
• the pressure contained in cosmic ray protons and
magnetic fields each contributes at least as much
pressure as the thermal gas
• escape time of cosmic rays from the galactic disc
∼ 107 years (radioactive clocks)
• energy losses:
CRe: synchrotron, inverse Compton, Coulomb
CRp: inelastic collisions, Coulomb
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Cosmic rays in clusters of galaxies
predictions for the CR pressure
span between 10% and 50% of
the cluster’s pressure budget
• escape of cosmic ray protons only
possible for energies
ECRp > 2 × 1016 eV
•
•
energy losses (for particles with
E ∼ 10 GeV):
Coma cluster: radio halo,
CRe: synchrotron, inverse
ν = 1.4 GHz, 2.5◦ × 2.0◦
Compton: τ ∼ 108 yr
(Credit: Deiss/Effelsberg)
CRp: inelastic collisions, Coulomb
losses: τ ∼ 1010 yr ∼ Hubble time
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Cosmological implications
cosmic rays provide an additional pressure component:
→ modifications of the hydrostatic mass estimates
→ additional heating of the ICM (cooling flow problem)
• the equation of state of cosmic rays is ‘softer’ than the
thermal component (γCRp ∼ 43 ):
→ effects on the baryonic halo profile
→ modification of the ICM evolution (entropy
distribution)
• the cosmic ray energy reservoir is cooling differently than
the thermal:
→ influence on energetic feedback and star formation
→ prevents the ICM from overcooling
•
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Hadronic cosmic ray proton interaction
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Gamma-ray source function
3 −1
−1
qγ (E γ ) n−1
GeV−1 ]
N Np [γ cm s
10-14
αp = 2.0
αp = 2.4
αp = 2.7
αp = 3.0
αp = 3.5
10-16
10-18
•
• π 0 -decay
induced γ -ray source
function qγ :
10-20
10-22
10-24
10-26
10-4
10-2
100
102
104
qγ ∝
E γ [GeV]
αp = 2.0
αp = 2.4
αp = 2.7
αp = 3.0
αp = 3.5
0.2
∆ qγ /qγ (E γ )
0.1
PSfrag replacements
CRp population: fCRp ∝ p−α
•
0.0
"µ
2 Eγ
mπ 0 c 2
¶δ
+
µ
2 Eγ
mπ 0 c 2
¶−δ #−α/δ
below: relative deviation of our
analytic approach to simulated
γ -ray spectra
-0.1
-0.2
10-4
10-2
100
E γ [GeV]
102
104
this and the following work:
Pfrommer & Enßlin 2003, 2004
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Cooling core clusters are efficient CRp detectors
ROSAT observation:
Perseus galaxy cluster
Credit: NASA/IoA/A.Fabian et al.
Chandra observation:
central region of Perseus
Credit: ROSAT/PSPC
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Cooling core cluster model of CRp detection
εCRp= X CRpε th
Perseus galaxy cluster
CRp
π
p
0
γ
Chandra observation:
γ
central region of Perseus
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Inverse Compton emission of secondary CRes (B = 0),
π 0 -decay induced γ-ray emission:
10-6
EGRET
dFγ /dE γ [XCRp
γ cm−2 s−1 GeV−1 ]
frag replacements
Gamma-ray flux of the Perseus galaxy cluster
αp = 2.1
αp = 2.3
αp = 2.5
αp = 2.7
10-7
10-8
10-9
10-10
10-11
10-12
10-13
0.001
0.010
0.100
1.000
10.000
100.000
E γ [GeV]
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Upper limits on XCRp using EGRET limits
Cool core cluster:
A85
Perseus
A2199
B = 10 µG
Centaurus
Ophiuchus
Triagulum Australis
Virgo
g replacements
Non-cool core cluster:
Coma
A2256
B = 1 µG
αp
αp
αp
αp
A2319
= 2.1
= 2.3
A3571
= 2.7
0
0.01
= 2.3, radio
0.10
1.00
10.00
XCRp = εCRp /εth
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Expected limits on XCRp using Čerenkov telescopes
Sensitivity: Fγ, exp (E > Ethr ) = 10−12 γ cm−2 s−1 (Ethr /100 GeV)1−α
Cool core cluster:
A85
Perseus
A2199
Centaurus
Ophiuchus
Triagulum Australis
Virgo
Non-cool core cluster:
Coma
rag replacements
A2256
αp
αp
αp
αp
= 2.1
= 2.3
= 2.5
= 2.7
A2319
A3571
0
0.001
0.010
0.100
1.000
XCRp = εCRp /εth
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HEGRA detection of γ-rays from M 87
HEGRA − M87: TeV CoG position
Image courtesy of NRAO/AUI and Owen et al.
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What is the origin of the M 87 γ-ray emission?
processed radiation of the relativistic outflow (jet):
e.g. IC up-scattering of CMB photons by CRes (jet),
SSC scenario (Bai & Lee 2001)
• dark matter annihilation or decay processes
•
(Baltz et al. 2000)
•
Hadronically originating γ -rays:
assuming a CRp power law
distribution and a model for the
CRp spatial distribution
→ measurement of the CRp
population of the ICM/ISM of
M87!
(Pfrommer & Enßlin 2003)
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Gamma-ray flux profile of M 87 (Virgo)
top:
HEGRA
γ cm−2 kpc−2 s−1 ]
fγ (r⊥ ) [10−12 XCRp
10-1
isobaric profile
10-2
10-3
10-4
10-5
10-6
10-7
0.1
1.0
10.0
100.0
1000.0
impact parameter r⊥ [h−1
70 kpc]
2
HEGRA
Fγ (θbin
) [10−12 XCRp
γ cm−2 s−1 ]
0.8
PSfrag replacements
HEGRA data
PSF: σ = 0.08◦
PSF: σ = 0.05◦
0.6
0.4
0.2
0.0
-0.2
-0.4
0.000
modeled γ -ray surface
flux profile
• normalized
to
the
HEGRA flux (> 730 GeV)
within the two innermost
data points
bottom:
• comparison of detected to
simulated γ -ray flux profiles which are convolved
with two different widths
of the PSF
•
0.010
0.020
0.030
0.040
squared impact parameter θ2 [deg]
0.050
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Radio (mini-)halos: Coma and Perseus
Coma radio halo, ν = 1.4 GHz,
largest emission diameter ∼ 3 Mpc
Perseus mini-halo, ν = 1.4 GHz,
largest emission size ∼ 0.5 Mpc
(Credit: Deiss/Effelsberg)
(Credit: Pedlar/VLA)
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Minimum energy criterion (MEC): the idea
• εNT = εB + εCRp + εCRe
¯
¯
∂ε
NT
→ minimum energy criterion:
∂ε ¯
B
•
•
!
jν
=0
classical MEC: εCRp = kp εCRe
−(αν +1)/2
hadronic MEC: εCRp ∝ (εB + εCMB ) εB
ε NT
defining tolerance
levels: deviation
from minimum by
one e-fold
εB
εB
min
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Classical minimum energy criterion
εCRp
XCRp (r) = ε (r),
th
XB (r) = εεB (r)
th
Coma cluster: classical minimum energy criterion
Perseus cluster: classical minimum energy criterion
0.0100
XCRemin
XBmin
XCRemin
XBmin
PSfrag replacements
XBmin (r), XCRemin (r)
XBmin (r), XCRemin (r)
0.0100
0.0010
0.0001
0.0010
PSfrag replacements
0.0001
10
100
r [h−1
70
1000
kpc]
1
10
r [h−1
70
BComa (0) = 1.1+0.7
−0.4 µG
100
kpc]
BPerseus (0) = 7.2+4.5
−2.8 µG
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Hadronic minimum energy criterion
εCRp
XCRp (r) = ε (r),
th
XB (r) = εεB (r)
th
Coma cluster: hadronic minimum energy condition
Perseus cluster: hadronic minimum energy condition
0.100
0.100
PSfrag replacements
XCRpmin
XBmin
XBmin (r), XCRpmin (r)
XBmin (r), XCRpmin (r)
XCRpmin
XBmin
0.010
0.001
PSfrag replacements
1
10
100
r [h−1
70
1000
kpc]
0.010
0.001
1
10
r [h−1
70
BComa (0) = 2.4+1.7
−1.0 µG
100
kpc]
BPerseus (0) = 8.8+13.8
−5.4 µG
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Cosmic rays in GADGET
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).
Cosmic ray GADGET - Collaboration: Enßlin, Jubelgas, Pfrommer, Springel
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Philosophy and description
Our model describes the CR physics by two 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-adiabatic processes are mapped into changes of the adiabatic
constants q0 and C0 .
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Cosmic rays in GADGET – flowchart
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Shock waves in galaxy clusters
1E 0657-56 (“Bullet cluster”)
Abell 3667
(NASA/SAO/CXC/M.Markevitch et al.)
(Radio: Australia Telescope Comp.
Array. X-ray: ROSAT/PSPC.)
The quest for cosmic ray protons in clusters of galaxies – p.23/31
Shock tube: thermodynamics
1.2
300
0.8
Velocity
Density
1.0
0.6
0.4
200
100
0.2
0.0
0
0
100
200
300
400
500
8•104
100
200
300
400
500
0
100
200
300
400
500
10
Mach number
6•104
Pressure
0
4•104
2•104
0
1
0
100
200
300
400
500
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Shock tube: statistics
duth
dt d log M
1•108
8•107
6•107
4•107
2•107
0
1
10
100
10
100
log M
1.5•108
duth
dt
1.0•108
ag replacements
5.0•107
0
1
log M
The quest for cosmic ray protons in clusters of galaxies – p.25/31
1.2
500
1.0
400
0.8
Velocity
Density
Shock tube (CRs & th. gas): thermodynamics
0.6
0.4
300
200
0.2
100
0.0
0
0
100
200
300
400
500
0
100
200
300
400
500
0
100
200
300
400
500
2.5•105
10
Mach number
Pressure
2.0•105
1.5•105
1.0•105
5.0•104
0
1
0
100
200
300
400
500
The quest for cosmic ray protons in clusters of galaxies – p.26/31
7•108
duth
dt d log M
6•108
5•108
4•108
3•108
2•108
1•108
0
1
10
100
10
100
log M
1•109
8•108
duth
dt
6•108
4•108
ag replacements
Shock tube (CRs & th. gas): statistics
2•108
0
1
log M
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Cosmological simulation
1011
2 #
z = 8.1
z = 7.5
z = 6.6
z = 5.6
z = 4.5
z = 3.4
z = 2.4
z = 1.5
z = 0.9
z = 0.4
z = 0.0
dEth
1010 M h−2 Gyr−1 km
s
dt d log M
1010
109
"
108
107
106
rag replacements
105
1
10
100
1000
10000
log M
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Cosmic ray effects on cluster physics
100.000
Test case:
resimulation of a cosmologically evolving
galaxy cluster with thermal gas, star formation (cooling processes and SN feedback) and
CRs (shock injection)
Pressure
10.000
1.000
0.100
0.010
NoCR
Shock
0.001
1
10
100
Radius [kpc]
1000
10000
Results:
• the composite gas (CRs & thermal gas) is
easier compressible and thus leads to stronger
radiative cooling processes
1.0
0.8
•
clusters with shock-injected CRs show
stronger matter concentration in central
regions at z=0
•
in dense regions, CRs represent an important pressure component (because thermal gas
cools down with high efficiency)
0.6
0.4
0.2
0.0
10-4
10-2
100
102
104
106
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Cosmic ray effects on galaxy evolution
Stellar mass as a function of time:
M* [ MO• ]
1010
108
Test case:
simulation of a collapse of isolated gas
spheres inside NFW dark matter profiles.
Results:
106
• global star formation efficiency
104
0
1
2
t [ Gyr ]
3
4
105
NoCR
Shock
dM / dt [ MO• yr-1 ]
10
4
is strongly dependent on the
total halo mass: faint galaxies
are strongly suppressed
103
• galaxy evolution in the hierarchi-
102
101
100
10-1
0
5
10
15
20
25
cal Universe: star formation rate
effectively suppressed at early
times (galaxy cluster simulation)
redshift
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Conclusions
A.) Cosmic rays in nearby clusters of galaxies:
1.) limits on CRps from γ-rays (EGRET):
ε
XCRp = εCRp < 20%
th
2.) M 87 γ-ray emission is consistent with hadronic scenario
3.) radio mini-halos (Perseus) seem to be of hadronic origin
B.) Cosmic rays in the simulation code GADGET
1.) huge potential and predictive power of cosmological
simulations → provides detailed γ-ray emission maps
2.) galaxy evolution: influence on energetic feedback, star
formation, and galactic winds
3.) additional entropy floor at the cluster centers (cooling flow
problem)
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