Table Of ContentJournal of The Korean Astronomical Society
37: 1 ∼ 5, 2004
Extragalactic Cosmic Rays and Magnetic Fields:
Facts and Fiction
Torsten Enßlin
Max-Planck-InstituteforAstrophysics,Karl-Schwarzschild-Str. 1,85741Garching,Germany
E-mail: [email protected]
(Received November 15, 2004; Accepted December 1,2004)
ABSTRACT
5
0 A critical discussion of our knowledge about extragalactic cosmic rays and magnetic fields is attempted. What
0 doweknowforsure? Whatareourprejudices? Howdoweconfrontourmodelswiththeobservations? Howcanwe
2 assessthe uncertaintiesinourmodelingandinourobservations? Unfortunately,perfectanswerstothesequestions
cannotbegiven. Instead,IdescribeeffortsIaminvolvedintogainreliableinformationaboutrelativisticparticles
n
and magnetic fields in extragalactic space.
a
J
Key Words : magnetic fields; cosmic rays; turbulence
7
1
1 I. What do we know? • cluster mergers: shock waves and turbulence
v (e.g., Miniati et al. 2000, 2001),
7 We know that cosmic rays and magnetic fields exist
3 inclustersofgalaxiesforseveralreasons. First,inmany • active galactic nuclei (e.g., Enßlin et al. 1997,
3 galaxy clusters we observe the so-called cluster radio 1998),
1 haloswithaspatialdistributionwhichisverysimilarto
0 • supernovae remnants (e.g., Vo¨lk et al. 1996),
that of the intra-cluster gas observed in X-rays. These
5
radio halos are produced by radio-synchrotron emit-
0 • galactic wakes (e.g., Jaffe 1980, Roland 1981,
tingrelativisticelectrons(cosmicrayelectrons=CRe)
/ Ruzmaikin et al. 1989),
h spiraling in magnetic fields. We do not have direct ev-
p idence of cosmic ray protons (CRp) probably due to • decaying/annihilating dark matter particles
- their much weaker radiative interactions. However, in (e.g., Colafrancesco & Mele 2001, Boehm et al.
o
r our own Galaxy the CRp energy density outnumbers 2004).
t the CRe energy density by two orders of magnitude,
s
a which makes the assumption of a CRp population in Furthermore,wehaveabasicunderstandingofrelevant
: galaxy clusters very plausible. physical processes, such as
v
Second,theFaradayrotationoflinearlypolarizedra-
i
X dioemissiontraversingtheintra-clustermedium(ICM) • particle cooling/radiationmechanisms,
r provesindependentlytheexistenceofintraclustermag-
a netic fields. It has been debated, if the magnetic fields • particle acceleration by shocks and turbulence,
seen by the Faraday effect exist on cluster scales in
• magneto-hydrodynamics.
the ICM, or in a mixing layeraroundthe radioplasma
whichemitsthepolarizedemission(Bicknelletal.1990,
In principle, we just have to put all these pieces to-
Rudnick & Blundell 1990). However, there is no valid gether in order to get an understanding of magnetic
indication of a source local Faraday effect in the dis- fields and cosmic rays in galaxy clusters. This is done
cussedcases(Enßlinetal. 2003),andtheFaradayrota- for the cosmic rays in a very schematic way in Fig. 1.
tionsignalexcessofradiosourcesbehindclusterscom- Theproblemwithsuchagenericapproachis,thatthere
pared to a field control sample strongly supports the are large uncertainties in the theoretical description of
existence of strong magnetic fields in the wider ICM the different plasma processes which do not allow to
(Clarke et al. 2001, Johnston-Hollitt & Ekers 2004). decide a priori which are the dominant processes are
ThedetailedmappingoftheFaradayeffectofextended within the complex network. Here, we will discuss two
radio sources reveals that the ICM magnetic fields are possibilities:
turbulent, with power on a variety of scales, and with
apower-spectrumwhichis Kolmogoroff-type(see Vogt • the relativistic electrons seen in cluster radio
& Enßlin, these proceedings). All these Faraday rota- halos are re-accelerated by cluster turbulence
tion measurements support magnetic field strengths of (e.g., Jaffe 1980, Roland 1981, Giovannini et
the order of several µG. al. 1993, Brunetti et al. 2001, 2004, Gitti et al.
The existence of ICM magnetic fields and cosmic 2001)
rays is not too surprising, since there are plenty of en-
ergy sources available, which could have contributed:
– 1 –
2 ENSSLIN
• the radio emitting CRe are secondaries from It can be seen, that the Faraday rotation based
hadronic interactions of a long-living CRp popu- fieldestimatescannotbeaccommodatedbysub-micro-
lation within the ICM gas. (e.g., Dennison 1980, Gauss field strength. For a typical cluster like Coma,
Vestrand1982,Blasi&Colafrancesco1999,Dolag 3−5µG are reproducing the Faraday signal if a mag-
& Enßlin 2000, Pfrommer & Enßlin 2004a) netic length-scale of 10 kpc is assumed. Lowering the
magnetic field strengthby one orderof magnitude – as
In order to have a chance to discriminate between suggested by the IC based field estimates (in the case
the different theoretical models, detailed information of the HEX excess) – would require an increase of the
on the electron spectrum would be very helpful, since magnetic length scale to ∼ Mpc in order to reproduce
the different scenarios exhibit different characteristics. the Faraday signal strength. But fields ordered on the
An attempt to collect such information is displayed cluster size would produce a nearly homogeneous RM
in Fig. 2. From the figure and the discussion in the signal,andnotexhibitthemanysignreversalsobserved
caption it becomes clear that the interpretation of the in clusters.
Extreme Ultraviolet (EUV) and High Energy X-ray
(HEX) flux reported for Coma as Inverse Compton (b) The origin of radio halos
scattered CMB photons would require magnetic fields
Also the origin of the relativistic electrons produc-
of1.4µG(EUV)orsignificantlyless(HEX).Suchweak
ing the cluster radio halos is controversially debated.
fieldstrengthsareanobviouscontradictiontotheFara-
There are the re-acceleration models, which are fa-
day method based estimates of several µG, especially
vored by some authors since they are able to repro-
if one compares magnetic energy densities or electron
ducenearlyeveryobservationalfeaturereportedsofar.
spectra as plotted in Fig. 2.
And then there are the hadronic models, which are fa-
voredbyothersnotonlybecauseoftheirsimplicity,but
II. What are our prejudices?
also since the necessary cosmic ray proton population
(a) Typical cluster magnetic field strength should be presentin the ICM because mostcosmic ray
acceleration mechanisms are believed to preferentially
Depending whom one asks, or which paper on clus- accelerate protons.
ter physics one consults, the assumption of the mag-
netic field strength differ significantly. Sub-micro- III. How to verify models?
Gaussfieldsareassumedwhenanemphasizeisgivento
the Inverse Compton scattering of CMB photons into It is often claimed that a model or theory is veri-
the EUV and HEX energy bands. Super-micro-Gauss fied. However, theories can only be falsified. To be a
fields are assumed in the context of the interpretation scientific theory, it has to be falsifiable (Popper). This
of Faraday rotation signals. means, it must be possible to derive from it unambigu-
Both methods of field estimates have their weak ous predictions for doable experiments such that, were
points. The inverse Compton argumentation can only contrary results be found, at least one premise of the
provide strict lower limits to magnetic fields strength. theory would have proven not to apply to nature.
The used observedEUV or HEX flux could have (par- Let us compare the different models for radio halos
tially) resulted from a different source or could be a in the light of this statement:
measurement artefact. Therefore, the number of rela-
tivistic electrons could be smaller than assumed in the (a) Hadronic model
estimate, requiring strongermagnetic fields in order to
The hadronic model is therefore a very good the-
providethesameamountofobservedsynchrotronemis-
ory in the sense of Popper, since it makes a number of
sion.
testable predictions.
Faraday rotation based field estimates are also not
straightforward,sincemagneticfieldreversalsalongthe
1. The hadronic model predicts gamma and neu-
line of sight partially cancel each other’s Faraday sig-
trino fluxes from clusters of galaxies.The gamma
nal. What is left as a typical cluster Faraday signal is
ray flux should be detectable with GLAST
the result of a random walk in rotation measure (RM)
(Pfrommer & Enßlinand also Reimer, these pro-
in the case of turbulent magnetic fields. The statisti-
ceedings),
calRMsignaldepends onthe statisticalmagneticfield
strengthtimesthesquarerootofthemagneticautocor- 2. The hadronic model can not explain very strong
relation length. The latter is unknown, and thus the spectralbending inthe radio,since evenamono-
Faraday based field estimates suffer from this uncer- energetic proton population injects a broad elec-
tainty. However, the statistical properties of Faraday tron spectrum, which produces an even broader
maps may allow to measure the magnetic autocorre- synchrotron spectrum.
lation length under relative reasonable assumptions of
statistical isotropy and homogeneity of the magnetic 3. Furthermore, the necessary energy budget of the
fields (see Vogt & Enßlin, these proceedings). hadronic model can exceed the available energy
Facts and Fiction 3
AGN cooling Torsten A. En β lin
Galaxies Radio Plasma Radio Ghosts
re−acceleration of
starburst
remnant electrons
driven Cluster Radio
winds Relics
Shock Particle
Waves Escape
Gas injection into
Motion the gaseous IGM p + p −> 2 N + π
Protons π+−−> e+ +− 3 ν pion (γd)ecay
Turbulent π0−> 2 γ
Cascade
> GeV
Coulomb Collisions
< GeV
injection of secondary nonthermal IC
electrons from hadronic (EUV,HEX, γ)
interactions
Electrons
Inverse Compton Radio
Cluster Merger > 150 MeV Synchrotron Emission Halos
& Accretion
< 150 MeV Bremsstrahlung
suprathermal
Coulomb Collisions
thermal
nonthermal X−rays
Acceleration Cooling (HEX)
Fig. 1.— Basictheorybuildingblockscoveringmostoftheproposedscenariosfortheproductionandmaintenance
of relativistic particle populations in galaxy clusters and their observational consequences. Nearly all theoretical
scenarios for cluster radio halos are summarized within this figure (e.g., re-acceleration model, hadronic model,
hybridhadronic-re-accelerationmodel,andmanymore). Redboxes: themainenergysources,yellowboxes: particle
populations (CRp, CRe), greenboxes: observables,white boxes: physicalprocesses/phenomenawhichare(nearly)
unobservable. The red cross indicates that the possibility that the reported non-thermal X-rays are generated by
Bremsstrahlung of a super-thermalelectron population runs into energetic problems due to strong Coulomb losses
of such electrons (Petrosian 2001).
sources, especially in the outer, low-density re- surement of extended radio halo luminosities in the
gions of clusters, where targets for an efficient vicinity of very strong point sources.
CRp to CRe conversionare rare. It was shown that at least the radio halos in the
Coma and Perseus clusters do not violate the energy
Some of these predictions seem to put already some constraints (Pfrommer & Enßlin 2004b). In order to
stress on the hadronic model. produce the observedradioemissionwithout toomuch
There is a strong spectralbreakreportedfor the to- energy in CRp, the hadronic models favor larger mag-
tal flux of the Coma cluster (Thierbach et al. 2003), netic field strength, in the range which are supported
whichwouldbetoostrongforthehadronicmodel. Ac- by the Faraday rotation measurements.
tually, this spectral break is too strong for any kind of The prediction of gamma rays could have not
synchrotron emission, indicating that there might be been tested by existing telescope sensitivities. Future
some problems with the spectral dataset of the Coma gamma ray telescopes have the potential to ultimately
radio halo compiled from the literature. The strong refutethehadronicmodel,sincethereisanunavoidable
spectral break might be partly explained by a con- minimum gamma ray flux of the order of the total ra-
taminationofthe highfrequency measurementsby the dio flux predicted for this class of models. If magnetic
Sunyaev-Zeldovich effect, however, it could also be an field strength are as low as 3µG or less, the predicted
artefact of the very difficult radio astronomical mea- gamma ray flux of the hadronic model has to be larger
4 ENSSLIN
Coulomb
losses
Beppo−Sax
thermal
electrons
EUVE
radio emitting
electrons
En β lin & Biermann 1998
Fig. 2.— Electron spectrum in the Coma cluster of galaxies (adopted from Enßlin & Biermann 1998). Red lines
indicate parts of the electron spectrum we know to exist: thermal electrons (left), and radio-synchrotronelectrons
(right). The exactspectrallocationofthe latter depends onthe unknownICMmagneticfield strength. The upper
limits result from physical processes, which would have produced photons in excess of observational constraints,
if more than the indicated electrons of a given energy were present in the ICM. One process is Inverse Compton
scatteringofknownbackgroundphotonfieldsintoobservationalbands. TheotherisBremsstrahlungfromenergetic
electrons with the ICM gas. Some of the used observations are actual claims of detections, and therfore could be
measurements of the electron spectrum. Green points indicate possible explanations of the reported high energy
X-ray (HEX) excess measured by Beppo-Sax (Fusco-Femiano et al. 1996, 2004, but see Rosetti & Molendi 2004,
who donotfinda significantsignal). Blue points indicate possible explanationsofthe reportedextremeultraviolet
excess measured by EUVE (e.g., Liu et al. 1996). However, some of the marked possibilities are unlikely (marked
by pink crosses): severe Coulomb losses would remove super-thermal and mildly relativistic electron populations
too quickly to be replenished (Petrosian2001,Enßlin, Lieu, Biermann 1999). The IC scattering of optical photons
into the HEX band wouldrequire too many relativistic electrons to be consistent with other upper limits resulting
from Bremsstrahlung.
than this minimum prediction. are many known, and maybe some unknown sources
of artefacts in radio astronomy, which can perturb the
(b) Re-acceleration models measured spectrum. To understand the meaning and
significance of features and spectra we need an end-to-
There-accelerationmodelhasnotmadeuniquepre-
end analysis of the data reduction process. This anal-
dictionswhichhavethe potentialtoallowtorefute the
ysis should go from the detector signal, through(self)-
model observationally. The model seems to be able to
calibration, to the map making, point source removal
fit anyyetreportedradioprofileandspectra due to its
and halo flux integration step. Without such an anal-
many poorly constrained parameters. Therefore, dis-
ysis it would be premature to claim that the hadronic
tinctive predictions of the re-accelerationmodel would
model is ruled out due to the reported spectral steep-
be very important, if they can be made at all (see
ening of the Coma radio halo.
Brunetti in these proceedings for first predictions of
AlsofortheFaradayrotationmeasurementssuchan
the re-accelerationmodel).
analysis would be highly desirable, in order to under-
stand if and how observational artefacts influence our
IV. How to access uncertainties?
fieldestimates. Inordertogointothisdirection,meth-
ods to quantify the levelofnoise andartefactsin Fara-
Reliable spectralinformation on radio halos has the
day maps were developed (Enßlin et al. 2003). They
potentialtorefute the hadronicmodel. However,there
Facts and Fiction 5
1e−11
Magnetic Power Spectrum of • the Faraday rotation observations, which point
towards turbulent fields strength of several µG
k E (k) Hydra A Cluster
[ergB/cm 3 ] Kolmogoroff strength: in the cool core region of the Hydra A
clusterafieldstrengthof7µGcorrelatedon3kpc;
spectrum
1e−12 in non-cooling flow clusters like Coma somewhat
lower fields (say 3µG) with a somewhat larger
correlation length (say 10-30 kpc).
1e−13 • the radio halo synchrotron emission of CRe in
B = (7.3 + 0.2 + 2) µ G Coma
l = (2.8 + 0.2 + 0.5) kpc • the EUV excess of the Coma cluster, which may
B
be understood as being inverse Compton scat-
1e−14
0.1 1 k [kpc− 1 ] 10 100 tered CMB light
TheFaradaymeasurementsprovideuswithvolumeav-
Fig. 3.— Magnetic power spectrum within the cool-
ing flow region of the Hydra A cluster of galaxies (for
eraged† magnetic energy densities, since the RM dis-
detailsseeVogt&Enßlin,theseproceedings). Thelast
persion scales as
data-point at large k-values is likely affected by map
noise and should be discarded. 2 2
hRM i∝hB iVol. (1)
The synchrotron emission is also (approximately) pro-
were used to verify the improved quality of Faraday
portionalto the magneticenergydensity, butweighted
mapsandeventheaccuracyofFaradayerrormapsgen-
with the CRe population around 10 GeV:
erated with the new Polarization Angle Correcting ro-
tation Measure Analysis (PACMAN) algorithm(Dolag 2
Lradio ∝hB nCReiVol. (2)
et al. 2004, Vogt et al. 2004). These maps were then
analyzed with a maximum likelihood power spectrum Finally, the inverse Compton flux is a direct measure-
estimator (Vogt & Enßlin, submitted), which is based mentofthe numberdensityofCRe(ofthe appropriate
onthecrosscorrelationofFaradaysignalsinpixelpairs, energy, see Fig. 2):
as expected for a given magnetic power spectrum and
galaxy cluster geometry (Enßlin & Vogt 2003, Vogt & LIC ∝hnCReiVol. (3)
Enßlin 2003).
The result of this exercise is not only a magnetic Combining the latter two measurements provides a
powerspectrum,whichiscorrectedforthecomplicated magnetic field estimate (for a given or assumed elec-
geometry of the used radio galaxy and of the Faraday tron spectral slope), which is weighted with the CRe
screen, but also an assessment of the errors, and even density:
thecrosscorrelationoftheerrors. Thepowerspectrum
of the Hydra A cluster cool core region, which is dis- hB2iCRe = hB2nCReiVol ∝ Lradio (4)
playedinFig. 3,exhibitsaKolmogoroff-likepowerlaw hnCReiVol LIC
on small scales, a concentration of magnetic power on
a scale of 3 kpc (the magnetic auto-correlationlength) (b) Reconciling the discrepant field estimates
and a total field strength of 7±2µG. The given error
The magnetic energy density derived from the com-
isthesystematicerrorduetouncertaintiesintheFara-
binationofsynchrotronandinverseComptonflux isat
day screen geometry. The statistical error is lower by
least one order of magnitude lower than the one de-
one order of magnitude.
rivedfromRM measurements. This discrepancymight
be reconciledifthereisasignificantdifferencebetween
V. Is a consistent picture possible?
volumeandCReweightedaverages. Thiswouldrequire
(a) Combining observational information
1. an inhomogeneous magnetic energy distribution,
Here, I am attempting to draw a consistent picture,
2. an inhomogeneous distribution of the CRe,
which may explain at least a significant subset of the
observational information∗ : tionalartefactsofthedifficileradioobservationanddatareduc-
tion plus some impact of the thermal Sunyaev-Zeldovich decre-
ment.
∗There are obviously some reported observations, which are not †Actually, itismoreanaverage withthe thermal electrondistri-
included in this subset: the HEX excess, since it’s significance bution. However, the latter varies slowly on scales over which
isdebated; thereportedspectral cut-offofthe Comaradiohalo the magnetic fields vary, so that it can be factorized out of the
emission, which may or may not be a combination of observa- signal.
6 ENSSLIN
3. an anti-correlationbetween these two. (e.g., Ruzmaikin et al. 1989, Sokolov et al. 1990, Sub-
ramanian 1999 and many others). The effective mag-
Therequiredconditionscouldbegeneratedifthereare netic Reynolds number (including turbulent diffusion)
physical mechanisms which reachesacriticalvalueofRc ≈20... 60. Themagnetic
fields should exhibit – more or less pronounced – the
a. produceinhomogeneousorintermittentmagnetic
following properties:
fields
A. The averagemagnetic energy density ε is lower
b. anti-correlatetheCRedensitywithrespecttothe B
magnetic energy density. εthBa≈n tεhkeintRurc−b1u.lent kinetic energy density εkin by
A very natural physical mechanism, which could pro-
B. The magnetic fluctuations are concentrated on a
videthisanti-correlationissynchrotroncoolingininho-
scalel,whichissmallerthanthehydrodynamical
mogeneousmagnetic fields. In caseofan injectionrate −1/2
of CRe which is un-correlated with the field strength, turbulence injection scale L by l ≈LRc .
the equilibrium electron density is
C. Correlations exist up to scale L, turn there into
nCRe ∝(B2+BC2MB)−1, (5) an anti-correlation, and quickly decay on larger
scales.
where BCMB ≈ 3.2µG describes the field strength
D. This maybe understood by Zeldovich’sflux rope
equivalent to the CMB energy density.
model, in which magnetic ropes with diameter l
Forillustration,weassumethatonlyasmallfraction
are bent on scales of the order L.
f =0.1ofthevolumeissignificantlymagnetizedwith
B
a field strength of 10µG, and the rest with only 1µG. E. Within flux ropes, magnetic fields can be in
WewillseelaterthatfB =0.1maybeaplausiblenum- equipartition with the average turbulent kinetic
ber. The volumeaveragewouldgivehB2i1/2 =3.3µG, energy density.
Vol
whereas the CRe average gives hB2i1C/R2e = 1.5µG. F. The magnetic drag of such ropes produces a hy-
These numbers are in good agreement with the corre- drodynamicalviscosityonlargescales,whichisof
sponding fieldestimates for the Coma clusterbasedon theorderof4%oftheturbulentdiffusivity(Long-
Faraday rotation and IC/synchrotron measurements, cope et al. 2003).
respectively. A larger ratio in magnetic field estimates
could even be accomodated since the EUV emitting (d) Confronting theory with observations
electrons are at energies below the synchrotron elec-
trons. Aspectralbumpofanoldaccumulatedelectron Turbulent magnetic dynamo theory predicts inter-
population at these energies is therefore possible, and mittent magneticfields,asfavoredbytheproposedex-
evenplausibleduetotheminimumintheelectroncool- planation of the discrepancy in the different magnetic
ing rate at these energies. field estimate methods. Let’s see if the other predic-
tions of the theory areinagreementwith observations.
The hadronic model would provide a CRe injection
rate which is not correlated with the magnetic field We assume, that Rc is in the range 20 to 60.
strength, as would be required by the above explana-
tion of the discrepancy of magnetic field estimates by A. The expected turbulent energy density in the
thetwomethodswouldwork. Incontrasttothis,inthe Hydra A cluster core is of the order of
re-acceleration model one would expect a strong pos- (0.3...1)10−10ergcm−3, which corresponds to
itive correlation of CRe and magnetic field strength, turbulent velocities of vturb ≈ (300...500)km/s.
since magnetic fields are essential for the CRe acceler- This is comparable to velocities of buoyantradio
ation. plasmabubbles(Enßlin&Heinz2002),whichare
expected to stir up turbulence (e.g., Churazovet
(c) Turbulent magnetic dynamo theory al. 2001).
It remains to be shown that there is also a natu- B. The expected turbulence injection scale in the
ral mechanism producing intermittent magnetic fields. Hydra A cluster core is of the order of (15...25)
The Kolmogoroff-like magnetic power spectrum in the kpc, again consistent with the radio plasma of
cool core of the Hydra A cluster indicates that the Hydra A being the source of turbulence. The
magnetic fields are shaped and probably amplified dynamical connection of the radio source length
by hydrodynamical turbulence (e.g., De Young 1992). scaleandthemagneticturbulencescalewouldex-
Therefore, we have to look into the predictions of the plain why the Faradaymap of Hydra A is conve-
theories of turbulent dynamo theories. nientlysizedtoshowusthepeakofthe magnetic
power spectrum.
It is generally found by a number of researchers
that the non-helical turbulent dynamo saturates in
a state with a characteristic magnetic field spectrum
Facts and Fiction 7
C. This prediction is hard to test since fluctuations ACKNOWLEDGEMENTS
onscaleslargerthantheradiosourcearenotmea-
Itisapleasuretothanktheconferenceorganizersfor
surable due to the limited RM map size. How-
the excellentmeeting,andthe verywarmhospitality. I
ever, the downturn of the magnetic power spec-
also want to thank Corina Vogt and Christoph Pfrom-
trum at small k-values is at least in agreement
mer for discussion and comments on the manuscript
with this prediction.
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