Gamma-ray probe of cosmic-ray pressure in galaxy clusters and cosmological implications

0.33 MB·English

by  Shin'ichiro Ando

Mon.Not.R.Astron.Soc.000,1–12(2008) Printed1February2008 (MNLATEXstylefilev2.2)
Gamma-ray probe of cosmic-ray pressure in galaxy clusters
and cosmological implications
Shin’ichiro Ando⋆ and Daisuke Nagai†
California Institute of Technology, Mail Code 130-33, Pasadena, CA 91125, USA
Accepted 19January2008; submitted19December 2007;inoriginalform16May2007
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ABSTRACT
2
Cosmic rays produced in cluster accretion and merger shocks provide pressure to the

n intraclustermedium(ICM)andaffectthemassestimatesofgalaxyclusters.Although
a direct evidence for cosmic-ray ions in the ICM is still lacking, they produce γ-ray
J
emission through the decay of neutral pions produced in their collisions with ICM
1
nucleons.We investigatethecapabilityoftheGamma-ray Large Area Space Telescope
2 (GLAST)andimagingatmosphericCˇerenkovtelescopes(IACTs)forconstrainingthe

cosmic-ray pressure contribution to the ICM. We show that GLAST can be used to
]
h place stringent upper limits, a few per cent for individual nearby rich clusters, on
p the ratio of pressures of the cosmic rays and thermal gas. We further show that it is
- possible to place tight (.10%) constraints for distant (z . 0.25) clusters in the case
o
of hard spectrum, by stacking signals from samples of known clusters. The GLAST
r
t limits could be made more precise with the constraint on the cosmic-ray spectrum
s
a potentiallyprovidedbyIACTs.Futureγ-rayobservationsofclusterscanconstrainthe
[ evolution of cosmic-ray energy density, which would have important implications for

cosmologicaltestswithupcomingX-rayandSunyaev-Zel’dovicheffectclustersurveys.
2
v Key words: galaxies: clusters: general — cosmology: miscellaneous — cosmic rays
8 — radiation mechanisms: non-thermal — gamma-rays:theory.
8
5
2
.
5
1 INTRODUCTION cisely based on accurate measurements of the density and
0
7 temperatureprofiles(Pointecouteau,Arnaud,&Pratt2005;
Clusters of galaxies are potentially powerful observational
0 Vikhlininetal.2006;LaRoqueetal.2006).However,theac-
probesofdarkenergy,thelargestenergybudgetintheUni-
: curacyofthehydrostaticmassestimatesiscurrentlylimited
v versecausingthecosmicacceleration(e.g.,Haiman,Mohr,&
bynonthermalpressureprovidedbycosmicrays,turbulence,
i Holder2001;Albrechtetal.2006).Mostofthecosmological
X and magnetic field in the ICM (Ensslin et al. 1997; Rasia
applications usingclusters rely on theestimates of theirto-
et al. 2006; Nagai, Vikhlinin, & Kravtsov 2007a, and ref-
r talvirialmass—quantitywhichisdifficulttomeasureaccu-
a erences therein). This nonthermal bias must be understood
ratelyinobservations.Clustersofferarichvarietyofobserv-
andquantifiedbeforetherequisitemassmeasurementaccu-
able properties, such as X-ray luminosity and temperature
racyisachieved.Comparisonswiththemassestimatesfrom
(e.g.,Rosati,Borgani,&Norman2002),Sunyaev-Zel’dovich
gravitationallensingcanprovidepotentiallyusefullimitson
effect (SZE) flux (e.g., Carlstrom, Holder, & Reese 2002),
this nonthermal bias (see e.g., Mahdavi et al. 2007). How-
gravitational lensing of distant background galaxies (e.g.,
ever,presentobservationsdonotyetconstrainthenonther-
Smith et al. 2005; Dahle 2006; Bradaˇc et al. 2006), and ve-
mal pressure in the regime in which it dramatically affects
locitydispersionofclustergalaxies(e.g.,Beckeretal.2007)
thecalibration of thehydrostaticmass estimates. Ifnot ac-
and proxies for cluster mass.
counted for, these nonthermal biases limit the effectiveness
One of the most widely used methods for measuring
of upcoming X-ray and SZE cluster surveys to accurately
cluster masses relies on theassumption of hydrostaticequi-
measuretheexpansion history of theUniverse.Detailed in-
librium between gravitational forces and thermal pressure
vestigationsofsourcesofnonthermalpressureinclustersare
gradients in the intracluster medium (ICM) (Sarazin 1986;
thus critical for using clusters of galaxies as precision cos-
Evrard, Metzler, & Navarro 1996). Current X-ray and SZE
mological probes.
observations can yield mass of individual clusters very pre-
There is growing observational evidence for the non-
thermalactivityinclusters.Forexample,radioandhardX-
⋆ E-mail:[email protected] ray observations of clusters suggest presence of relativistic
† E-mail:[email protected] electrons. This also implies presence of relativistic protons
(cid:13)c 2008RAS
2 S. Ando and D. Nagai
producedintheshockthatacceleratedtheseelectrons.How- rayprotonstheninteractwiththesurroundingICM(mostly
ever, the signature γ-ray emission due to decays of neutral nonrelativistic protons), producing neutral and charged pi-
pions produced in the collisions of cosmic rays with nucle- ons;theformerdecaysintotwophotons(π0 2γ)whilethe
→
ons in the ICM has not been detected. From non-detection latter into electrons, positrons, and neutrinos. The volume
of γ-ray emission from clusters with the Energetic Gamma emissivity of the π0-decay γ-rays (number per volume per
Ray Experimental Telescope (EGRET) in the GeV band unit energy range) at distance r from the cluster center is
(Reimer et al. 2003; but see also Kawasaki & Totani 2002; given as (e.g., Blasi & Colafrancesco 1999)
Scharf& Mukherjee2002), constraints havebeenplaced on
∞ ∞
thefractionofcosmic-raypressureinnearbyrichclustersat
q (E,r) = 2n (r)c dE dE
lessthan 20%(Ensslinetal.1997;Miniati2003,Virgoand γ H π p
∼ ZEπ,min ZEp,th(Eπ)
Perseus clusters) and less than 30% (Pfrommer & Enßlin
2th0e04W, ChoipmpalecClˇuesrteenr)k.ovSimteilleasrcocpoen∼sitnratihnetsTaerVe obbatnadin(ePdeurksiinngs × ddσEpπp(Eπ,Ep)√nEpπ2(E−pm,r2π)c4, (1)
et al. 2006). These measurements indicate that the cosmic
wherem andE isthemassandenergyoftheneutralpion,
π π
raysproviderelatively minorcontributiontothedynamical E =E+m2/4E is theminimum pion energy required
supportintheICM(e.g., Blasi 1999). However,thecurrent π,min π
to produce a photon of energy E, and similarly E (E )
p,th π
constraintsaretoolooseforthefuturecluster-basedcosmo-
is theminimum energy of protonsfor pion production. The
logical tests.
density of ICM, n (r), is very well measured by the X-ray
H
Thenextgenerationofγ-raydetectors,suchasGamma-
observationsofbremsstrahlungradiationfromthermalelec-
ray Large Area Space Telescope (GLAST) and imaging at-
trons, and the cross section of the proton–proton collision
mosphericCˇerenkovtelescopes(IACTs),willbeabletopro-
forpionproduction,dσ /dE ,canbecalibratedusinglab-
pp π
vide dramatically improved constraints on the cosmic-ray
oratory data. The distribution function of cosmic-ray pro-
pressure in clusters, and may even detect γ-ray radiation
tons n (E ,r) depends on the injection power, spectrum,
p p
fromseveralrichclusters(Andoetal.2007a, andreferences
and spatial distribution of cosmic rays. By specifying these
therein).TheGLASTsatellite,whichissoontobelaunched,
ingredients, we can predict the γ-ray fluxfrom a cluster.
is equipped with the Large Area Telescope (LAT) that en-
In practice, we use a fitting formula as well as cluster
ablesallskysurveywithGeVγ-rays.SeveralIACTsarecur-
parametersgiveninPfrommer&Enßlin(2004); forthefor-
rently working or planned for detecting TeV γ-rays, which
mer,webrieflysummarizeitinAppendixA.Inaddition,one
include HESS, MAGIC, VERITAS, and CANGAROO-III.
should also note that electrons and positrons produced by
Confronting therecentadvancesin γ-rayastronomy aswell π±decayscanscattercosmicmicrowavebackground(CMB)
as growing interests in dark energy studies, in the present
photons up to γ-ray energies. For a while, we neglect this
paper, we investigate the sensitivity of these detectors to
secondary process, butrevisit it in Section 6and showthat
high-energy γ-raysof cosmic-ray origin.
it is in fact negligible undermost of realistic situations.
We first show updated sensitivities of GLAST and
IACTsfornearbyrichclustersfollowingPfrommer&Enßlin
(2004).Inparticular,GLASTwouldbeabletoconstrainthe
cosmic-ray energy density in such clusters to better than a
few per cent of the thermal energy density, while IACTs
would be useful to constrain the cosmic-ray spectrum. We
thenconsiderstackingmanyγ-rayimagesofdistantclusters
2.1 Cosmic-ray power and spectrum
toprobetheevolutionofcosmic-raypressure.Weshowthat,
by stacking many massive clusters, the upcoming GLAST Thecosmic-raypressureP andenergydensityρ ,whichare
p p
measurements will have the statistical power to constrain thequantitiesthatwewanttoconstrain,aredirectlyrelated
thecosmic-ray pressure component to betterthan 10% of to the injection power of the cosmic rays. The cosmic-ray
∼
the thermal component for clusters out to z . 0.25. These spectrum is measured to be a power law with the index of
forthcoming measurements will be able to place stringent α = 2.7 in our Galaxy, but in the clusters it is perhaps
p
limits on the bias in the cluster mass estimates and hence harder, since they can confine cosmic rays for cosmological
provideimportanthandleonsystematicuncertaintiesincos- times (V¨olk, Aharonian, & Breitschwerdt 1996; Ensslin et
mologicalconstraintsfromupcomingX-rayandSZEcluster al.1997;Berezinsky,Blasi,&Ptuskin1997).Wethusadopt
surveys. harder spectrum with α = 2.1 and 2.4, but also use α =
p p
Throughout this paper, we adopt theconcordance cos- 2.7 as a limiting case.
mological model with cold dark matter and dark energy It is also possible that the injection of the cosmic rays
(ΛCDM), and use Ωm = 0.3, ΩΛ = 0.7, H0 = 100 h km andthustheirenergydensityρp areintermittent.Although
s−1 Mpc−1 with h=0.7, and σ8 =0.8. itisinterestingtoconstrainthesourcepropertybymeasur-
ing such γ-ray variability, this is not the primary focus in
the present paper. Instead, we concentrate on constraining
energydensityρ averagedoverGLASTexposuretime.For
2 γ-RAY PRODUCTION DUE TO p
thesensitivityofGLAST,weconsidertheresultofone-year
PROTON–PROTON COLLISIONS
all-sky survey, which corresponds to 70-day exposure to
∼
Cosmic-ray protons are injected in the ICM through the each source as the field of view is 20% of the whole sky.
∼
shock wave acceleration, and the momentum distribution Therefore, any time variability within this 70-day duration
follows the power law, p−αp with α 2–3. These cosmic- is smeared out.
p p
≃
(cid:13)c 2008RAS,MNRAS000,1–12
Cosmic-ray pressure in galaxy clusters 3
2.2 Radial distribution areacceleratedtorelativisticenergies(e.g.,Loeb&Waxman
2000;Miniati2002;Keshetetal.2003;Gabici&Blasi2003).
We define quantities X and Y as ratios of energy density
p p Unlikeelectronsthatimmediatelyloseenergiesthroughsyn-
andpressureof cosmicraystothoseofthermalgas, respec-
chrotron radiation and inverse-Compton (IC) scattering off
tively,i.e.,
CMB photons, protons are hard to lose energies, and they
X ρp , Y Pp . (2) are transported efficiently into the cluster center following
p ≡ ρth p ≡ Pth themotionofICMgas(Miniatietal.2001).Inordertopre-
dict the eventual profile of the cosmic-ray energy density,
Ingeneral,thesedependontheradius,buttheconcretede-
one needs to resort to numerical simulations. The recent
pendenceistotallyunknown.Variousmechanismssupplying
radiativesimulationsbyPfrommeretal.(2007) showsome-
the cosmic-ray protons have been proposed, which produce
whatjaggedshapefortheX (r)profile,whichimplieslarge
characteristic and diverse profiles of X and Y . We thus p
p p
clumpingfactor. Here, we model its global structurewith a
parameterize them using a simple power-law:
smoothprofilewithβ = 0.5,ignoringtheeffectsofclumpi-
r β ness. On the other hand−, they also performed nonradiative
X (r) = X (R ) ,
p p 500 R simulations which rather imply β =1 profile. Although the
„ 500«
r β lattermaynotberealistic,theeffectsofcoolingandheating
Y (r) = Y (R ) , (3) inclustersarealsosomewhatuncertain.Thus,westilladopt
p p 500 R
„ 500« thismodel, treating it as an extreme case.
where R (here ∆ = 500) is the radius at which the en-
∆
closed spherical overdensity is ∆ times the critical density
of the Universe at the cluster’s redshift,1 where the cluster 2.2.3 Central point source
mass M is traditionally defined with the X-ray and SZE
∆ A central powerful source such as active galactic nuclei or
measurements. We note that this approach ignores boosts
cD galaxy might bean efficient supplierof thecosmic rays,
in γ-rayfluxcaused byclumpiness. Theconstraintsderived
whichdiffuseoutfromthecentralregionafterinjection.The
using a smooth model hence provide a conservative upper profileofcosmic-rayenergydensityisr−1,buttruncatedat
limit on X and Y .
p p a radius that is far smaller than R for relevant energies
500
We first focus on X , and later discuss Y . The rela-
p p (Berezinsky et al. 1997; Colafrancesco & Blasi 1998). The
tion between γ-ray intensity and X is summarized in Ap-
p actualγ-raydetectionmightthereforecausesignificantover-
pendix A and that between X and Y is discussed in Sec-
p p estimateofthecosmic-raypressure;weaddressthisissuein
tion 5. We shall study the dependence of results on β, for
Section 3.2.
which we adopt 1, 0, and 0.5. Below, we outline several
− Numericalsimulationsofjetsfromactivegalacticnuclei
models that motivate these valuesof β.
suggest that temporal intermittency and spatial structure
might be complicated (e.g., O’Neill et al. 2005). Neither of
these,however,affectourresultsthatdependonglobaland
2.2.1 Isobaric model
time-averaged properties.
The simplest model is based on the assumption of β = 0,
i.e.,theenergydensityofcosmicrayspreciselytracesthatof
thermalgaseverywherein thecluster.Thelatterispropor-
3 COSMIC-RAY ENERGY DENSITY IN
tional to temperature times number density of the thermal
NEARBY GALAXY CLUSTERS
gas, both of which are very well measured with X-rays for
variousnearbyclusters.Thegasdensityprofileisnearlycon- 3.1 Constraints from entire region of clusters
stantwithinacharacteristiccoreradiusr ,beyondwhichit
c
decreasesasapowerlaw,whiletemperatureprofileisalmost We first discuss the case of the Coma cluster, focusing on
constant.Thecoreradiusandouterprofilearerc =300kpc, the region within R500 = 2.1 Mpc and assuming the iso-
r−2.3 (Coma), r = 200 kpc, r−1.7 (Perseus), and r = 20 baric distribution of thecosmic-ray energy density (β=0).
c c
kpc,r−1.4 (Virgo)(seeTable1ofPfrommer&Enßlin2004, Fig. 1 shows theintegrated γ-ray flux with photon energies
foramorecomprehensivelist).Thelattertwoclustershave above Emin, F(> Emin), for Xp = 0.1. This flux is to be
an even smaller ‘cool core’, but this structure gives only a compared with the sensitivities of GLAST and IACTs, for
minor effect on the γ-ray flux. which one has to take the source extension into account.
Indeed,theradialextensionoftheComaclusterR corre-
500
spondstoθ =1◦.2,whichathighenergiesexceedsthesize
500
2.2.2 Large-scale structure (LSS) shocks ofthepointspreadfunction(PSF),δθ (E).Weobtainthe
PSF
fluxsensitivityforanextendedsourcefrom thatforapoint
Theformationofgalaxyclustersisduetomergingoraccre-
source by multiplying a factor of max[1,θ /δθ (E )],
tion of smaller objects. When this occurs, the shock waves 500 PSF min
if the sensitivity is limited by backgrounds. On the other
are generated at the outskirts of the clusters, somewhere
hand,iftheexpectedbackgroundcountfrom theclusterre-
around 3Mpcfromthecenter,whereprotonsandelectrons
∼ gionissmallerthanone,whichisthecaseforGLASTabove
30 GeV, the sensitivities for a point source and an ex-
∼
1 We use R∆hE(z) = r5(Tspec/5 keV)η/3, where r5 = tendedsourceareidentical.Theregion∼2–30GeViswhere
0.792 h−1 Mpc and η =1.58 for ∆=500, r5 =0.351 h−1 Mpc theexpectedbackgroundcountissmallerthanonefromthe
and η = 1.64 for ∆ = 2500, and E2(z) = Ωm(1+z)3+ΩΛ for PSFareabutlargerthanonefromtheentirecluster.Weas-
theflatΛCDMcosmology(Vikhlininetal.2006). sumethatIACTsarelimitedbybackgroundovertheentire
(cid:13)c 2008RAS,MNRAS000,1–12
4 S. Ando and D. Nagai
Table1.SensitivitytoXp(R500)ofGLAST(Emin=100MeV)forvariousvaluesofspectralindexofcosmicraysαp,andisobaricand
LSS shock models forradial distribution or β. The limits onXp areset by the γ-rayflux from a regionwithin whichever of the larger
betweenthepointspreadfunction δθPSF(Emin)≈3◦ andthesourceextension θ500.
Xp,lim(R500)forβ=1 Xp,lim(R500)forβ=0 Xp,lim(R500)forβ=−0.5
Cluster θ500 αp=2.1 αp=2.4 αp=2.7 αp=2.1 αp=2.4 αp=2.7 αp=2.1 αp=2.4 αp=2.7
Coma 1◦.2 0.11 0.063 0.10 0.040 0.022 0.035 0.018 0.0098 0.016
Perseus 1◦.5 0.024 0.013 0.022 0.012 0.0068 0.011 0.0050 0.0027 0.0044
Virgo 4◦.6 0.076 0.042 0.067 0.041 0.022 0.036 0.016 0.0088 0.014
Ophiuchus 1◦.3 0.088 0.048 0.078 0.020 0.011 0.018 0.0064 0.0035 0.0056
Abell2319 0◦.6 0.048 0.027 0.043 0.057 0.031 0.050 0.032 0.018 0.029
for X = 0.1. In particular, the models with different val-
p
ues of α predict similar amount of γ-ray fluxes for low-
p
energy thresholds (E < 1 GeV); GLAST measurements
min
canthereforeprovideconstraintsonX ,almostindependent
p
of α . Non-detection with GLAST from these nearby clus-
p
ters is also very interesting as it provides very tight upper
limittothecosmic-rayenergydensityinclusters.Thefluxes
above 1 TeV, on theother hand,dependsvery sensitively
∼
on α ; IACTs will thusconstrain thespectral index.
p
In Table 1, we summarize the sensitivity to X (R )
p 500
forGLASTinthecaseofE =100MeV,forseveralvalues
min
of α and different models of radial distribution of cosmic-
p
rayenergydensity.Wealsoperformedthesameanalysisfor
other nearby rich clusters (Perseus, Virgo, Ophiuchus, and
Abell2319),andreporttheirresultsaswell.Thisindeedcon-
firmsthattheGLASTconstraintsonX dependonlyweakly
p
ontheassumedspectralindex.2Theconstraintsimprovefor
smaller valuesofβ.Forβ 60,theGLAST non-observation
can place tight upper limits on the cosmic-ray energy den-
sityatafewpercentlevel.Eveninthecaseofnonradiative
LSS shock model (β = 1) the constraint is still as good as
10% for the Coma. This is a dramatic improvement from
∼
theEGRETbounds(see,e.g.,Table3ofPfrommer&Enßlin
Figure1.Fluxofγ-rayemissionfromtheregionwithinR500 =
2004), by more than an order of magnitude.
2.1 Mpc of the Coma cluster, for the isobaric model with Xp =
0.1(labeled as ‘π0-decay’). Thespectral index of the cosmic-ray On the other hand, the IACT constraints on Xp (with
protons is αp = 2.1 (solid), 2.4 (dashed), and 2.7 (dot-dashed). Emin = 1 TeV) for the Coma cluster and β = 0 profile
The sensitivity curves of GLAST and IACTs are for a source are 0.37, 2.3, and 42 for αp = 2.1, 2.4, and 2.7, respec-
extendedbyθ500=1◦.2(correspondingtoR500),whilethepoint- tively. Thus, IACTs will therefore provide constraints on
sourcesensitivityofGLASTisalsoshownasashortdashedcurve. the spectral index, which is directly related to astrophysi-
FluxduetoICscatteringandnonthermalbremsstrahlungisalso calmechanismsofparticleacceleration. Asimilartrendcan
shown(dotted; fromReimeretal.2004).
befoundinTable6ofPfrommer&Enßlin(2004);however,
theauthorsappliedpoint-sourcefluxlimittothe(extended)
clustersandobtainedmuchmorestringentsensitivitiesthan
energy region, and we multiply the point source sensitiv- ours.
ity by θ /δθ with δθ = 0◦.1; this is consistent with
500 PSF PSF
Aharonian et al. (1997) for relevant energy regime. A more
detailedderivationofthissensitivityisgiveninAppendixC. 3.2 Direct constraint from large radii
Wealso show fluxof IC scattering and bremsstrahlung
So far, we treated all clusters but Virgo as point sources.
radiationsfromelectronsprimarilyacceleratedintheshocks
Although we showed that the dependence on the assumed
(Reimer et al. 2004). The authors suggested that these
radialprofilewasreasonablyweak,amoregeneralapproach
electron components would always be below the GLAST
wouldbetousetheresolvedimage.Thisisparticularlyuse-
and IACT sensitivities, based on constraints from radio,
ful,iftheradialprofilecannotbesimplyparameterized(see
extreme-ultraviolet (EUV),and hard X-ray observations. If
Section 2.2). Because we are interested in the cosmic-ray
this is the case, the γ-ray detection would imply existence
ofcosmic-rayprotons,andbeusedtoconstrainthepressure
from this component (see also, Enßlin, Lieu, & Biermann 2 Notethatthesensitivitypeaksatαp=2.5.Thisisbecausefor
1999; Atoyan & V¨olk 2001). We give more detailed discus- evenlargerαp,thecontributionfromlow-momentumprotons to
sions about IC mechanisms in Section 6. the energy density becomes more significant, while they do not
Fig. 1 shows that γ-raysfrom π0 decays are detectable produceγ-rays.
(cid:13)c 2008RAS,MNRAS000,1–12
Cosmic-ray pressure in galaxy clusters 5
pressure at R and the γ-ray yields would rapidly drop
500
with radius, we here consider constraints in a projected ra-
dial shell between θ and θ . We mainly focus on the
2500 500
Perseus, and assume α = 2.1; in this case, θ = 0◦.65.
p 2500
In order to resolve the inner region, we consider the en-
ergy threshold of 0.6 GeV, above which the GLAST reso-
lution becomes smaller than θ . The GLAST flux lim-
2500
its for the outer region and for E > 0.6 GeV correspond
to the following limits on the fractional energy density:
X (R ) = 0.099, 0.089, and 0.080, for β = 1, 0, and
p,lim 500
0.5, respectively, which are still reasonably small. In ad-
−
dition, these are much less sensitive to the assumed profile,
thus applicable to more general cases including the central
sourcemodel.Thesimilarprocedurepredictssensitivitiesfor
other clusters: X (R ) =0.42 (Coma), 0.14 (Virgo), 0.41
p 500
(Ophiuchus), and 0.55 (Abell 2319), in the case of β = 0
andα =2.1.Althoughitislimitedtonearbyclusters,such
p
analysis provides an important handle on the radial distri-
bution of cosmic-ray ions in clusters.
4 EVOLUTION OF COSMIC-RAY ENERGY
DENSITY
While we could obtain stringent constraints for individual
nearby clusters, these rapidly get weaker for more distant
clusters. In this case, however, one can stack many clusters
to overcome the loss of signals from each cluster. Reimer
et al. (2003) took this approach for the EGRET analysis,
andobtainedanimprovedupperlimittotheaveragefluxof
50 nearby clusters. Weargue that theflux is not a physical
quantitybecauseitdependsondistanceandthereforedistri-
bution of sources. We should instead convert this improved
flux limit to constraint on more physical quantities such as
γ-rayluminosity. Here,we examinethe GLAST constraints
on X (R ) obtained by stacking clusters from the whole
sky apnd i5n00several redshift intervals. As we consider rather Figure 2. (a) Cluster mass function as a function of M200 at
several redshifts. Threshold mass Mth corresponding to Tth =
distant clusters, they are all treated as point sources.
3, 5 keV is shown as vertical lines. (b) Cluster mass function
dnh/dlnM200 multiplied by M220.10(∝ FXp), in arbitrary units.
Linetypes arethesameasin(a).
4.1 Stacking γ-ray signals from galaxy clusters
4.1.1 Formulation and models
Thenumberofclusters withM >M betweenredshiftsz
th 1 WegivethethresholdmassM (z)intermsofthreshold
and z is given by th
2 temperature T based on the observed mass–temperature
th
z2 dV ∞ dn relation: M = 1015h−1M (T/8.2 keV)3/2E(z)−1 (Voit
Ncl = dzdz dMdMh(M,z), (4) 2005).This2i0s0becausetheeffi⊙ciencyoflarge-scale SZEclus-
Zz1 ZMth
ter surveys relies mainly on cluster temperature regardless
where dV is the comoving volume element, dn /dM is the
h of cluster redshifts. Note that this relation is between tem-
halo mass function (comoving numberdensityof dark mat-
peratureandmassM ,whichiswithinaradiusR .Here
200 200
terhalosperunitmassrange);theformercanbecomputed
weusetheprescriptionofHu&Kravtsov(2003)forthecon-
givencosmological parameters,andforthelatterweusethe
version of different mass definitions, M and M with
200 180m
following parameterization:
assumed concentration parameter c =3. Forthethreshold
v
dMdn18h0m =AJMΩ1m8ρ0mc exp −|lnσ−1+BJ|ǫJ ddMln1σ80−m1, (5) tthemepmearasstufruen,cwtieonadaospwteTlltha=s t3hraenshdo5ldkmeVa.ssFcigo.rr2e(sap)osnhdoiwngs
toT ,at various redshifts. In Table 2, welist values of N
ˆ ˜ th cl
where ρ is the critical density of the present Universe,
c afterintegratingequation(4),forseveralredshiftrangesand
σ(M ,z)isastandarddeviationfordistributionfunction
180m different T .
th
of linear over density, A =0.315, B = 0.61, and ǫ =3.8
J J J The average flux of γ-rays from these clusters is
(Jenkinsetal.2001).HerewenotethatM isdefinedas
180m
anenclosedmasswithinagivenradius,inwhichtheaverage F = 1 z2dzdV ∞ dMdnh(M,z)F (M,z), (6)
density is 180Ωmρc(1+z)3. st,Xp Ncl Zz1 dz ZMth dM Xp
(cid:13)c 2008RAS,MNRAS000,1–12
6 S. Ando and D. Nagai
Table 2. GLAST sensitivities to Xp(R500) and Yp(R500) by stacking Ncl clusters above threshold temperature Tth at given redshift
ranges,forαp=2.1,β=0,andEmin=1GeV.
Tth=3keV Tth=5keV
z Ncl Xp,lim Yp,lim Ncl Xp,lim Yp,lim
0.05–0.10 200 0.11 0.06 30 0.09 0.05
0.10–0.15 530 0.21 0.11 60 0.16 0.09
0.15–0.25 2500 0.29 0.16 290 0.23 0.13
0.25–0.40 7900 0.57 0.31 870 0.46 0.25
0.40–0.60 17000 1.3 0.72 1700 1.1 0.60
ing these three and assuming that X is independent of
p
mass, we obtain a scaling relation L X M2.1E1/3(z).
γ ∝ p 200
In Fig. 3, we show predicted γ-ray luminosity as a function
ofclustermass(inferredfromtemperature),forseveralwell-
measurednearbyclusters(takenfromtablesinPfrommer&
Enßlin 2004) with the parameters X =0.1, α =2.1, and
p p
β=0. TheL –M relation can indeed bewell fittedwith
γ 200
L (> 100 MeV) = 7.6 1044X (M /1015h−1M )2.1 erg
γ p 200
s−1 for clusters at z ×0, shown as a solid line i⊙n Fig. 3.
≈
Whenwecomputetheγ-rayfluxF (M z)(orequivalently
Xp |
luminosity) from clusters with a given mass M, we adopt
this mass–luminosity relation as a model for average clus-
ter, and scale as L E1/3(z) for high-redshift clusters.
γ
∝
Fig.2(b)showsthemassfunctionweighedbythemass
dependence of the flux (in arbitrary unit). This quantity
represents which mass scale dominates the average flux at
each redshift. From this figure, one can see that clusters
with M 3 1014M most effectively radiates γ-rays
200
in the low-r∼edsh×ift Unive⊙rse, but the distribution is rather
broadfor 1014–1015M .IfweadoptT =5keV,thenthe
th
clusters ar∼ound the thr⊙eshold mass are the more dominant
contributors tothe average flux.
Figure 3. Relation between γ-ray luminosity (above 100 MeV)
and cluster mass M200, for several nearby clusters and for the
parameters Xp =0.1, αp =2.1, and β =0. Filled(open) points 4.1.2 GLAST constraints on Xp
are for cooling flow (non-cooling flow) clusters. The solid line is
theLγ ∝M220.10 profilethatfitsthedataquitewell. Theaveragefluxofthestackedclusters(equation6)isthen
compared with thecorresponding GLAST sensitivity,
F
F = lim . (8)
st,lim √N
whereF (M,z)istheγ-rayfluxfrom aclusterofmassM cl
Xp
at redshift z, given Xp. The flux from each cluster above where Flim is the sensitivity to each cluster given as the
Emin is written as thick dashed line in Fig. 1 (for a point-like source). To de-
1+z ∞ rive constraints on Xp from the stacked image, we solve
FXp(M,z)= 4πd2 dVcl dE qγ(E,r|M), (7) Fst,Xp = Fst,lim for Xp. Throughout the following discus-
L Z Z(1+z)Emin sion, we adopt β =0, α =2.1 and E =1 GeV, around
p min
whered istheluminositydistance,dV representstheclus- which the γ-ray yields are maximized compared with the
L cl
ter volume integral, and q is the volume emissivity given point-sourcesensitivity(Fig.1).Inaddition,thepixelnum-
γ
by equation (1) or (A1). ber with this threshold (4π divided by PSF area; 6 104)
×
We then quantify the mass dependence of this flux is large enough to minimize the positional coincidence of
F (M,z).Inthecaseof theisobaric model(β=0)with a multiple clusters (compare with N ’s in Table 2).
Xp cl
fixed X , the γ-ray luminosity scales as ICM number den- We summarize the results in Table 2. We find that the
p
sity times energy density, i.e., L X n ρ X n2T. limits are as strong as X . 0.16 (0.23) for 0.1 < z < 0.15
γ ∝ p H th ∝ p H p
On the other hand, luminosity of X-rays due to the ther- (0.15 < z < 0.25). The sensitivities improve for larger T ,
th
mal bremsstrahlung process scales as L n2T1/2. There- because the smaller cluster number is compensated by the
X ∝ H
fore, there is a relation between γ-ray and X-ray lumi- strong mass dependence of the flux. The constraints on X
p
nosities as follows: L /L X T1/2. In addition, there degrades rapidly with redshift. Table 2 also shows GLAST
γ X p
∝
are empirical relations between X-ray luminosity and clus- sensitivities for Y , which is almost twice as stringent as
p
ter mass, L M1.8, and also between gas temperature thoseforX inthecaseofα =2.1.Wediscussimplications
and mass, TX ∝ M220/03E2/3(z) (Voit 2005). Thus, combin- of this resuplt for Y in Sectiopn 5 in details.
∝ 200 p
(cid:13)c 2008RAS,MNRAS000,1–12
Cosmic-ray pressure in galaxy clusters 7
ThecurrentX-raycatalogcoversclustersatz.0.2for
T =5keV(B¨ohringeretal.2001).TheGLASTdatacould
th
thus immediately be compared with this low-redshift cata-
log.Athigherredshifts,theSouthPoleTelescopewouldfind
manyclusterswithT &3keVusingSZE;butsinceitcovers
10% of the whole sky, the limits would become 3 times
∼ ∼
weaker than those in Table 2. The Planck satellite, on the
otherhand,wouldyieldall-skySZEcatalog ofverymassive
clusters;wefindthatthelimits for T =8keVclustersare
th
nearly identical to those for T =5 keV systems.
th
In addition toprobing its redshift evolution, thestack-
ing approach is also useful for studying cosmic-ray compo-
nentinnearbylow-massclusters,andthedependenceofX
p
onclustermass.Althoughindividualclustersarenotbright
enough,clustermassfunctionpredictsthatthereareanum-
berofsuchlow-massclusters,whichshouldhelpimprovethe
GLAST sensitivity.
4.2 Extragalactic γ-ray background
Another avenue to constrain the universal average of X
p
is to use the extragalactic γ-ray background (Sreekumar et Figure4.Relationbetweenratiosofpressure(Yp=Pp/Pth)and
al. 1998), because galaxy clusters would contribute to this energy density (Xp = ρp/ρth) plotted as a function of spectral
backgroundintensitytoacertainextent.Theircontribution index αp of cosmic rays (solid line). Dotted line is the linear fit
is quantified as Yp/Xp=0.5(αp−1).
∞ d2V ∞ dn
I = dz dM h(M,z)F (M,z), (9)
γ dzdΩ dM Xp
Z0 ZMth 5 X-RAY AND SZE CLUSTER MASS
ESTIMATES
which is quite similar to equation (6). Adopting the same
models for dnh/dM and FXp as in Section 4.1, and using Future γ-ray observations of galaxy clusters will have the
αp =2.1, β =0, and Emin=100 MeV, we obtain potentialtoplacetight constraintson thenonthermalpres-
I (>100 MeV)=4 10−7X cm−2 s−1 sr−1. (10) sureprovidedbycosmicrays.Theseforthcomingγ-raycon-
γ p
× straints will, in turn, provide important handle on system-
Even with X = 1, this is much smaller than the measure- atic uncertainties in the X-ray and SZE cluster mass esti-
p
ment by EGRET: 10−5 cm−2 s−1 sr−1 (Sreekumar et al. matesbasedonthehydrostaticequilibriumoftheICM.The
1998). This indicates that cosmic-ray processes in galaxy hydrostatic mass profile of a spherically-symmetric cluster
clusters are very unlikely to contribute to the γ-ray back- is given by
groundfluxsignificantly,especiallybecauseitrequiresavery
r2 dP dP
large value for X , which is already excluded by EGRET M(<r)= − th + nt , (11)
p Gρ dr dr
for some of nearby clusters. This result is consistent with g „ «
the previous studies such as Colafrancesco & Blasi (1998). where M(< r) is the mass enclosed within radius r, ρ is
g
Hence,weconcludethatthestackingmethodusingresolved the gas density, and P and P are the thermal and the
th nt
clustersintroducedinSection4.1wouldprovidemuchmore nonthermalcontributionsto thepressure. Thethermal gas,
stringent constraint on X than the approach using extra- measureddirectlywithcurrentX-rayandSZEobservations,
p
galactic γ-raybackground. providesasignificant fraction ofthetotalpressuresupport.
However, we here mention a few possibilities that may The contribution of the nonthermal pressure, on the other
render this approach more viable in the near future. Soon hand,iscustomarilyassumedtobesmall(.10%)outsideof
after launch, GLAST should start resolving many point aclustercore(seee.g.,Nagai,Kravtsov,&Vikhlinin2007b),
sources (mainly blazars) that are now contributing to the and it is often ignored in the hydrostatic mass estimates
background flux. Furthermore, using angular power spec- based on X-ray and SZE data. The cosmic-ray pressure, if
trum of the γ-ray background map might enable to dis- present, is a potential source of systematic bias in the hy-
entangle the origin (Ando & Komatsu 2006; Ando et al. drostaticmassestimatesofclusters(e.g.,Ensslinetal.1997;
2007b). In addition, there is a claim that the measured γ- Rasiaetal.2006;Nagaietal.2007a,andreferencestherein).
raybackgroundfluxisdominatedbytheGalacticforeground In equation (11), a directly relevant quantity is pres-
evenat high latitude,and that thereisno certain measure- suregradientratherthanenergydensityX thatwemainly
p
mentoftrulyextragalacticcomponent(Keshet,Waxman,& discusseduntilthispoint.Currently,itisnotpossibletoin-
Loeb2004).Inanyofthecasesabove,thecontributionfrom fer both pressureand its radial profile, and here,we simply
galaxy clusters might be found to be significantly smaller assume that the cosmic-ray pressure profile is the same as
than the current observed flux, which would be useful to that of thermal pressure. In this case, one needs to relate
constrain X at higher redshifts. X to Y . If the cosmic rays are dominated by relativistic
p p p
(cid:13)c 2008RAS,MNRAS000,1–12
8 S. Ando and D. Nagai
component, then equation of state would be P = ρ /3. magnetic fields are also potential sources of bias in X-ray
p p
On the other hand, for nonrelativistic thermal gas, it is and SZE cluster mass estimates. Recent numerical simula-
P = 2ρ /3. Thus, we expect P /P = (1/2)(ρ /ρ ) = tionsofclusterformationindicatethatsub-sonicmotionsof
th th p th p th
X /2.Moreprecisely,wecanobtaintheequationofstatefor gasprovidenonthermalpressureinclustersbyabout 10%
p
∼
cosmic-ray protonsbynumerically integratingthefollowing evenin relaxed clusters (e.g., Rasia et al. 2006; Nagai et al.
expressions: 2007a,andreferencestherein).Mostclusteratmospheresare
∞ also magnetized with typical field strengths of order a few
ρp = dp fp(p) p2+m2p−mp , (12) µG out to Mpc radii (Carilli & Taylor 2002; Govoni & Fer-
Z0 “q ” etti 2004), but this would only give negligible contribution
∞ p2 to thetotal pressure support.
P = dp f (p) , (13)
p p
3 p2+m2
Z0 p
where fp(p) p−αppis the differential number density dis- 6 INVERSE-COMPTON SCATTERING FROM
∝
tribution. In Fig. 4, we show a correction factor between NONTHERMAL ELECTRONS
the pressure ratio Y and X , as a function of spectral
p p
index α . This relation is well fitted by a linear formula 6.1 Secondary electrons from pion decays
p
Y /X = 0.5(α 1) as shown as a dotted line in Fig. 4;
p p p − Until this point, we have neglected the contribution to γ-
the deviation is only 0.3% at α = 2.7. As expected, for
∼ p raysfromrelativisticelectronsandpositronsproducedfrom
α closeto2,theratioisabout0.5.Therefore,theexpected
p decays of charged pions. Those charged pions are produced
sensitivityofGLASTforYp wouldbestrongerthanthatfor by the proton–proton collisions just as π0’s that decay into
X given in Table 1and asexplicitly shown in Table 2.For
p γ-rays. Thus, as long as the cosmic-ray protons exist, there
αp = 2.1, GLAST sensitivities to Yp based on the cluster should also be relativistic e± component associated with
stacking method are 5%, 9%, and 13% at 0.05 < z < 0.10,
them. GeV γ-rays would be produced by IC scattering of
0.10 < z < 0.15, and 0.15 < z < 0.25, respectively. Note,
CMB photons due to such a ‘secondary’ leptonic compo-
however, that the conversion between Y and X depends
p p nent. In this subsection, we show the expected IC flux to
on αp, for which IACTmeasurements would beessential. compareitwiththefluxfromπ0 decays,andarguethatthe
Observational constraints on X = ρ / ρ is also
p h pi h thi former is indeed negligible, justifying our earlier treatment.
sensitive to any non-negligible small-scale structure in the
Unlikeprotons,leptonscancoolquicklybysynchrotron
ICM.Whengasclumps,ithasdensityhigherthanthelocal
radiation and IC scattering. Energy distribution of these
average, ρ .Ifitisnotresolvedandmaskedout,thelocal
h thi electrons (positrons) after cooling is obtained as a steady-
inhomogeneity in the ICM boosts γ-ray surface brightness
state solution of thetransport equation, which is
by a factor of C ρ ρ / ρ ρ and X-ray surface
b(wrihgihcthniessslinbeyaCrlyXγp≡r≡o˙pρho2trhpt¸io/thnhiaρlththio2p,ρitwhh)htiuhlenialeffaevcitnegdSbZyEclusimgnpai-l ne(Ee,r)= |E˙e(E1e,r)|ZE∞e dEe′Qe(Ee′,r), (14)
ness. A joint γ-ray+X-ray constraints on X based on a
p whereQ isthesourcefunctionofinjectedelectrons.Forthe
e
smooth modelisgenerally biased byafactor Cγ/CX,which energy-lossrateE˙ ,thedominantinteractionwouldbesyn-
e
could be greater or less than 1 depending on the relative
chrotron radiation and IC scattering of CMB photons, i.e.,
size of Cγ and CX.3 A joint γ-ray+SZE constraint on Xp, E˙ (U +U )E2,whereU andU aretheenergy
on the other hand, is biased high by a factor C . Recent − e∝ B CMB e B CMB
γ densities of magnetic fieldsand CMB. If theinjection spec-
cosmological simulations ofclustersthatincludecosmic-ray trum is power law, Q E−αe, then equation (14) states
physics indicate jagged shape for the Xp(r) profile, which that the spectrum afteer∝cooeling would be n E−αe−1,
implies a large clumping C (Pfrommer et al. 2007). These e ∝ e
γ steeper byone power.
simulations are potentially useful for estimating the values
Once we know the electron distribution we can unam-
of C , which would be important for interpretation of X
γ p biguously compute the IC spectrum after scattering CMB
in case of detection of cluster signals with upcoming γ-ray
photons.Inaddition,inthecaseofthesecondaryelectrons,
experiments. In absence of these constraints, observational
wecancomputethesourceQ relativelywellgiventhespec-
e
constraints on X should be taken as an upper limit.
p trum of cosmic-ray protons. In Appendix B, we summarize
Recently, Mahdavi et al. (2007) performed a compari-
fittingformulathatweuse,givenbyDolag&Enßlin(2000)
sonbetweenmassesestimatedwithweakgravitationallens-
and Pfrommer & Enßlin (2004). Looking at equation (14),
ing and using the assumption of hydrostatic equilibrium,
in order to get the electron distribution after cooling, we
and showed that the latter masses are typically biased to
also need to know magnetic field strength B in theclusters
belower by20%. This result might indicatepresenceof the
that is relevant for synchrotron cooling. The estimates of
nonthermal pressure component. Upcoming γ-ray measure-
B range 0.1–10 µG(Clarke,Kronberg,&B¨ohringer2001;
ments of galaxy clusters could thus provide useful informa- ∼
Fusco-Femianoetal.2004;Rephaeli,Gruber,&Arieli2006),
tion on theorigin of thismass discrepancy.Turbulenceand
while the CMB energy density corresponds to equivalent
fieldstrengthofB =3.24(1+z)2 µG.Thus,unlessB is
CMB
larger than orcomparable toB everywherein theclus-
3 CurrentX-rayobservations withsuperbspatialresolutionand CMB
ter,thesynchrotroncoolingwouldnotbesignificant,asthe
sensitivity are capable of detecting the prominent clumps that
energy loss is proportional to B2+B2 . We here assume
contribute significantly to the X-ray surface brightness. A com- CMB
parisonofrecentX-rayandSZEmeasurementsindicatethatthe B=0 to obtain themaximally allowed ICflux.
X-ray clumping factor is very close to unity (1 < CX .1.1) in In Fig. 5(a), we show flux of IC γ-rays from secondary
practice(LaRoqueetal.2006). leptons, compared with direct γ-ray flux from π0 decays,
(cid:13)c 2008RAS,MNRAS000,1–12
Cosmic-ray pressure in galaxy clusters 9
tronsis 108 years,whichismuchshorterthantypicalclus-
∼
terage. By thesame reason and also comparing thespatial
intensity distribution, it is unlikely that synchrotron radia-
tion from these primary electrons is responsible for the ob-
served radio halo emissions (e.g., Blasi, Gabici, & Brunetti
2007).
It might still be possible to overcome these difficul-
ties if these electrons are continuously reaccelerated in situ
through the second order Fermi mechanism (Schlickeiser,
Sievers, & Thiemann 1987; Tribble 1993; Brunetti et al.
2001; Petrosian 2001). In this case, however, the spectrum
of electrons has typically a cutoff at the Lorentz factor of
.105.Thisproperty,whileexplainsspectrum ofradiohalo
ofComaquitewell(e.g., Reimeretal.2004), would restrict
the γ-ray flux in the GeV region due to the IC scattering
andbremsstrahlung.InFig.1,weshowtheupperboundon
these components in the case of Coma cluster as a dotted
curve,taken from Reimeret al. (2004).
In consequence, as long as X is more than a few
p
per cent, it would be unlikely that the primary electrons,
whethertheyaredirectlyinjectedorcontinuouslyreacceler-
ated, dominate the GeV γ-ray flux, at least in a large frac-
Figure 5. (a) Flux of γ-rays from π0 decays with Xp = 0.1 tion of clusters. Even though primary electron component
(dotted), IC scattering due to secondary electrons (dashed) as dominated the detected flux, the shape of γ-ray spectrum
a function of minimum energy Emin, for αp = 2.1, β = 0, and wouldbeverydifferentfromπ0-decaycomponentespecially
B = 0; total flux is indicated as a solid curve. (b) Fractional at low energies, which could be used as a diagnosis tool;
contribution of IC scattering to the total γ-ray flux, FIC/Ftot, thisdifferencecomesfrom thekinematicsofπ0 decays.The
forα=2.1(solid),2.4(dotted), and2.7(dashed). GLAST energy band ranges down to 20 MeV, which is
∼
especially important characteristic for that purpose. More-
over, observations in lower frequency bands such as radio,
EUV, and hard X-rays, are also important, because these
assuming X = 0.1, α = 2.1, and β = 0. Fig. 5(b) shows
p p
emissions are understood as synchrotron radiation (for ra-
the fractional contribution of the IC processes for various
dio)andICscattering(forEUVandhardX-rays)fromnon-
valuesofα .Thesefiguresshowthateveninthecaseofvery
p
thermal electrons.
weekmagneticfieldstoreducetheelectronenergylosses,the
ICprocessesgiveonlysub-dominantfluxintheGeVenergy
range relevant for GLAST. The fractional contribution of
theICemissiontothetotalγ-rayflux,whichisindependent
of X , is smaller than 20% for E = 100 MeV and α =
p min
2.1. Forasteeperproton spectrum (α>2.1), thefractional
contribution become considerably smaller. Bremsstrahlung
processduetothesameelectronsandpositronsisevenmore
suppressed (Blasi 2001). We thusconclude that the IC and 6.3 Secondary leptons from ultra-high energy
bremsstrahlung γ-ray emission by secondary electrons are cosmic-ray interactions
sub-dominant for therealistic range of parameters.
If protons are accelerated up to ultra-high energies such as
&1018 eVin galaxy clusters, which maybeplausible, these
protons are able to produce e± pairs through the Bethe-
6.2 Primary electrons by shock acceleration HeitlerprocesswithCMBphotons:pγ pe+e−.These
CMB
Whenevertheshocksaregenerated,bothionsandelectrons high-energye±pairsthenICscattertheCM→Bphotons,pro-
areaccelerated.Thus,oneexpectsthattheICscatteringoff ducingGeV–TeVγ-rays(Aharonian 2002; Rordorf,Grasso,
theCMBphotonsduetosuchprimary electronswouldalso &Dolag2004;Inoue,Aharonian,&Sugiyama2005).Inthis
contribute to the GeV–TeV γ-ray flux to a certain extent case,theICphotonsmightdominatetheπ0-decayγ-raysby
(Loeb&Waxman2000; Totani&Kitayama2000; Waxman many orders.
&Loeb2000;Gabici&Blasi2004).Ifthisprocessdominates However, this mechanism is extremely uncertain, de-
theπ0 decaysinγ-rayenergyband,thentheconstraintson pending heavily on the maximal acceleration energy of the
X will be directly affected in case of detection. However, protons. This is especially because the threshold energy of
p
there are difficulties for this mechanism to work efficiently the Bethe-Heitler process is 1017–1018 eV, and it is un-
∼
in many clusters. clear whetherthemagnetic fieldsare strongenough tocon-
Aselectronslosetheirenergiesviaradiationmuchmore finetheseultra-highenergyprotonsforclusterages.Evenif
rapidly than protons, clusters would be bright with this the detected γ-rays are dominated by this mechanism, the
mechanism duringonlya limited period after injection. For spectrumwould bequitedifferentfrom the π0-decayγ-rays
example, the radiative cooling time scale for 10 GeV elec- andshouldbeeasilydistinguishable(e.g.,Inoueetal.2005).
(cid:13)c 2008RAS,MNRAS000,1–12
10 S. Ando and D. Nagai
7 CONCLUSIONS ACKNOWLEDGMENTS
We investigated the capability of the current and future γ- WethankChristoph Pfrommer, Julie McEnery,and Steven
ray detectors such as GLAST and IACTs for constraining Ritzforusefulcomments.ThisworkwassupportedbySher-
thecosmic-ray pressurecontribution to theICM. man Fairchild Foundation.
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