Evidence for AGN Feedback in Galaxy Clusters and Groups

24 Pages·2012·2.74 MB·English

HindawiPublishingCorporation
AdvancesinAstronomy
Volume2012,ArticleID950641,24pages
doi:10.1155/2012/950641
Review Article
Evidence for AGN Feedback in Galaxy Clusters and Groups
MyriamGitti,1,2,3FabrizioBrighenti,4andBrianR.McNamara2,5,6
1INAF-OsservatorioAstronomicodiBologna,ViaRanzani1,40127Bologna,Italy
2Harvard-SmithsonianCenterforAstrophysics,60GardenStreet,CambridgeMA02138,USA
3INAF-IstitutodiRadioastronomiadiBologna,ViaGobetti101,40129Bologna,Italy
4DipartimentodiAstronomia,Universita`diBologna,ViaRanzani1,40127Bologna,Italy
5PhysicsandAstronomyDepartment,UniversityofWaterloo,200UniversityAvenueWest,Waterloo,ON,CanadaN2L2G1
6PerimeterInstituteforTheoreticalPhysics,31CarolineStreetNorth,Waterloo,ON,CanadaN2L2Y5
CorrespondenceshouldbeaddressedtoMyriamGitti,[email protected]
Received29July2011;Accepted14September2011
AcademicEditor:AngelaBongiorno
Copyright©2012MyriamGittietal.ThisisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense,
whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
ThecurrentgenerationofflagshipX-raymissions,ChandraandXMM-Newton,haschangedourunderstandingoftheso-called
“cool-core”galaxyclustersandgroups.Insteadoftheinitialideathatthethermalgasiscoolingandflowingtowardthecenter,the
newpictureenvisagesacomplexdynamicalevolutionoftheintraclustermedium(ICM)regulatedbytheradiativecoolingandthe
nongravitationalheatingfromtheactivegalacticnucleus(AGN).Understandingthephysicsofthehotgasanditsinterplaywith
therelativisticplasmaejectedbytheAGNiskeyforunderstandingthegrowthandevolutionofgalaxiesandtheircentralblack
holes,thehistoryofstarformation,andtheformationoflarge-scalestructures.Ithasthusbecomeclearthatthefeedbackfrom
thecentralblackholemustbetakenintoaccountinanymodelofgalaxyevolution.Inthispaper,wedrawaqualitativepictureof
thecurrentknowledgeoftheeffectsoftheAGNfeedbackontheICMbysummarizingtherecentresultsinthisfield.
1.Introduction Based on observational evidence and theoretical mod-
elling,theprimarysourceoffeedbackhasbeenidentifiedin
The physics of the intracluster medium (ICM) of clusters
theoutburstsandaccompanyingenergyinjection,likelyin-
and groups of galaxies is complex. The current generation
termittent, from the active galactic nucleus (AGN) of the
of X-ray satellites, Chandra and XMM-Newton, has shown
dominant cD galaxies (e.g., [6] and references therein),
indeed that it is regulated by yet poorly understood non-
which host the most massive black holes in the local Uni-
gravitationalprocessesbeyondsimplegravity,gasdynamics,
verse. AGNs manifest as central radio sources, which are
and radiative cooling usually considered in the standard
commonly observed in cool-core clusters [7]. Most of the
cold dark matter cosmological scenario [1]. In particular,
cool-coresystemshavehighlydisturbedX-raymorphologies,
animportantdiscoveryfromhigh-resolutionX-rayobserva-
and radio observations clearly show that AGN jets are the
tionswasthattheamountofthermalgasradiativelycooling
cause of many of the structures revealed by the X-ray tele-
to low temperatures is much less than what is predicted by
scopes.Suchsurfacebrightnessfeatures,includingapparent
thestandard“coolingflow”model(see[2–5]andreferences
depressions or “cavities” in the X-ray images and sharp
therein), thus radically changing our understanding of the
so-called “cool-core” systems. The implication is that the density discontinuities interpreted as shocks, indicate a
central gas must experience some kind of heating due to a strong interaction between the central AGN and the intra-
feedback mechanism that prevents cool cores from estab- clustermedium(ICM).Theincidenceandvarietyofcavities,
lishing cooling flows at the rates predicted by earlier, low- shocks,andripplesobservedbothintheradioandinX-rays
resolutionX-rayobservations.Establishingthesourceofthis in the hot ICM provides direct evidence of the widespread
heating,andunderstandingwhenandhowittakesplace,has presenceofAGN-drivenphenomena(e.g.,[8,9]forsample
becomeamajortopicofstudyinextragalacticastrophysics. studiesofclustersandgroups,resp.).
2 AdvancesinAstronomy
Such AGN feedback has a wide range of impacts, from sensitivetothespecificcosmologicalscenario(e.g.,[20]and
theformationofgalaxies,throughtotheexplanationofthe references therein). Therefore, if one builds the so-called
observedrelationbetweentheblackholemassandthebulge “clustermassfunction”n (M),thatis,thenumberdensity
M
velocity dispersion (which indicates a causal connection or ofclusterswithmassgreaterthanM inacomovingvolume
feedback mechanism between the formation of bulges and element and determines its evolution with redshift, it is
theircentralblackholes,e.g.,[10]),totheregulationofcool possibletoconstrainthemaincosmologicalparametersfrom
cores which explains why cooling and star formation still the comparison between the observations and the theory
proceedatareducedrate.Ontheotherhand,thedetailsof predictions. A complete understanding of the details of
howthefeedbackloopoperatesarestillunknown.Feedback the process of hierarchical merging would require accurate
is also required to suppress the overproduction of massive numericalsimulations.However,manyfundamentalaspects
galaxies predicted by dark-matter-only simulations and to canbeillustratedbysphericallysymmetric,simplifiedmod-
breaktheself-similarityofclusters(e.g.,[11–13]).Thenature els of cluster formation. In particular, the combination of
of this feedback is therefore vital to our understanding of spherical top-hat collapsemodels with the growth function
galaxyevolution([14]andreferencestherein). forlinearperturbations(assumedtobegaussian)hasledtoa
After a brief discussion of the importance of galaxy varietyofsemianalyticalmethodstoexpresstheclustermass
clusters and their scaling relations for the study of cosmic function in terms of cosmological parameters (the seminal
evolution(Section2),weoverviewtheroleofAGNfeedback workinthisfieldisby[21]).
instructureformation(Section3)andthebasicpropertiesof Therefore,thecomparisonbetweenthetheoreticalmass
clustersinX-raysemphasizingthehotintraclustermedium function and the mass function determined from obser-
(Section4). We then focus on the observational evidence vations allows one to constrain the main cosmological
of AGN feedback in action in galaxy clusters and groups parameters,althoughwithadegeneracybetweenthematter
(Section5)andfinallygiveourconclusions(Section6).The density parameter, Ω , and the power spectrum normal-
M
presentpaperdoesnotintendtobeacomprehensivereview,but ization of the perturbations within a comoving sphere of
aimsinsteadatdrawingaqualitativepictureoftheimpactof radius 8h−1Mpc, σ . Such a degeneracy can be broken by
8
the AGN feedback on the ICM addressed particularly to the studyingtheredshiftevolutionofthemassfunction,which
novices in this field. General reviews of clusters from an X- ishighlysensitivetoΩ ,bytakingintoaccounttheevolution
M
rayperspectiveweregivenbySarazin[15]andmorerecently of the observables (see the reviews by [18, 20, 22] and
byMushotzky[16]andArnaud[17].Areviewofclustersas referencestherein).Theaccuracyofthecosmologicalparam-
cosmologicalprobeswasgivenbyVoit[18],andcoldfronts eter measurements is currently limited by uncertainties in
andshocksassociatedwithclustermergerswerereviewedby the relations between cluster masses and the observable
MarkevitchandVikhlinin[19].Anexhaustivereviewofthe properties that trace these masses, such as luminosity or
issues of AGN heating in the hot atmospheres was recently temperature.Inordertomeasurethemassfunctionfroma
givenbyMcNamaraandNulsen[6]. largesampleofclustersisindeednecessarytolinkthemass
ThroughoutthepaperweassumeacosmologywithH = tothesequantitieswhichareeasilyobservable.
0
70kms−1Mpc−1 andΩM = 1−ΩΛ = 0.3,wherenotspeci- In this context are very useful the so-called “self-similar
fiedotherwise. scaling relations,” derived naturally by considering that the
cosmological structures originate from scale-free density
2.ClustersofGalaxiesasCosmologicalProbe perturbations and that the thermodynamical properties of
the ICM are determined by scale-free gravity only [23].
The existence of clusters of galaxies and of other cosmic Undertheseassumptions,galaxyclustersofdifferentmasses
structures demonstrates that the Universe is not perfectly may be considered as a scaled version of each other. The
homogeneous.ThematterdensityoftheprimordialUniverse density of each dark matter halo, ρ , is proportional to
DM
must have been slightly inhomogeneous, with overdense the critical density of the Universe at the cluster’s redshift,
perturbations which deviate from the mean density. In the ρ , through the so-called “overdensity” Δ = ρ /ρ ,
c,z DM c,z
so-called “Concordance Model” largely accepted today as where ρ = 3H2/8πG, and the expression for the Hubble
c,z z
thestandardcolddarkmattercosmologicalscenario,cosmic constant(cid:2)atredshiftzinaflatΛCDMUniverseis(e.g.,[24]):
structures like galaxies and clusters of galaxies originate Hz =H0 Ωm(1+z)3+ΩΛ ≡H0E(z).Therefore,allclusters
fromthegravitationalinstabilityoftheseprimordialdensity shouldhavethesamepropertieswhenrescaledbyΔ.
fluctuations.Theformationofstructuresfromperturbations
IfwedefinethemassMasthemassMΔinsidetheradius
in the density distribution of cold dark matter is a hierar- RΔatagivenoverdensityΔ,weobtain:MΔ ∝ρc,z·Δ·R3Δ ∝
cdheivciaaltepfrroocmesst.heSmHaulblbsluebflcoluwm,ptoscoofllmapastetearndarteotehxepefirrisetnctoe ρc,0·E(z)2·Δ·R3Δ,andthuswegettotheM-Rrelationinthe
form
gravitational relaxation because the density perturbations
have larger amplitudes on smaller mass scales. These small R∝M1/3·E(z)−2/3. (1)
objects then undergo a merging process to form larger and
largerstructures,uptotheclustersofgalaxies[1]. During cluster formation, the gravitational collapse of
Galaxyclusterstracethehigh-densitytailoftheprimor- the diffuse gas in the potential well of the dark matter halo
dial field of dark matter density perturbations, and their heatsthegasitselfatthevirialtemperatureofthepotential
numerical density as a function of redshift, z, is highly well that confines it: T ∼ GMμm /kR ∼ 108K, where M
vir p
AdvancesinAstronomy 3
isthetotalmass,kistheBoltzmannconstant,μ∼0.6isthe simulationsofcosmologicalstructureformationthatinclude
mean molecular weight and R is the virial radius. The gas the hydrodynamics of baryons and the radiative cooling
isthusheated toX-rayemitting temperaturesand becomes processes predict that (cid:2)20% of the baryons should have
a plasma in hydrostatic equilibrium whose emissivity is condensedintogalaxies,butonly(cid:3)10%havebeenobserved
proportionaltothesquareofitsdensity(seeSection4).The in the form of stars (e.g., [35]). In particular, simulations
virial temperature of an isothermal sphere of mass M is that include only gravitational heating predict an excessive
kT ∝ M/R ∝ M2/3 ·E(z)2/3, leading to the M-T relation cooling of baryons that results in a population of galaxies
intheform: which are too massive and too bright with respect to the
ones observed, thus failing to reproduce the truncation of
M∝T3/2·E(z)−1. (2)
the high-luminosity end of the galaxy luminosity function
From these relations it is possible to derive the relation [11,36].
betweentemperatureandluminosityemittedbythehotgas Instead of residing in the cD galaxies as predicted by
through bremsstrahlung emission: L ∝ ρ2 ·Λ·V, where simulations, most baryons are observed in the hot ICM.
X
ρ is the average gas density and Λ is the cooling function, This problem may find a solution in the nongravitational
thatinthebremsstrahlungregimeis∝ T1/2 (seeSection4). heating supplied by supernovae (SN) and active galactic
Assuming that the gas distribution traces the dark matter nuclei (AGN). Supernovae are essential in the process of
distribution,ρ∝ρ ∝ρ ,weobtain:L ∝ρ·T1/2·M∝ enrichment of the ICM to the metallicity level observed
DM c,z X
ρ ·E(z)2·T1/2·M∝E(z)2·T1/2·T3/2·E(z)−1,thusderiving [37,38],andfromtheheavy-elementabundancesinclusters
o
itisestimatedthatduringaclusterhistorytheysupplyatotal
theL-Trelationintheform:
amount of energy of the order of 0.3–1keV/particle (e.g.,
LX ∝T2·E(z). (3) [39, 40]). This is not enough energy to quench cooling in
massivegalaxies[38],astheenergyinputrequiredtoexplain
BycombiningtheM-Trelation(2)withtheL-Trelation
the mass-observable relations is ∼1-2keV/particle [41–43].
(3), we can finally derive the M-L relation that links
Energetically, AGN heating appears to be the most likely
the mass directly to the observable luminosity: L ∝
X mechanismtoseverelyreducethesupplyofgasfromthehot
[M2/3E(z)2/3]2E(z),finding
ICMinmassivegalaxiesandtoexplaintheobservedentropy
M∝L3/4·E(z)−7/4. (4) profiles [11, 18, 44–46]. AGNs are powered by accretion of
X material onto a black hole (BH), which is located at the
In principle, once calibrated with simulations and/or centerofeachstellarspheroid(bothbulgeswithinspiralsand
observations,thesescalingrelationsprovideamethodtolink ellipticals).Matterfallingontoablackholereleasesanenergy
themassofclusterstoobservablesundertheassumptionthat oftheorderofE = (cid:2)Mc2,where(cid:2) ≈ 0.1istheefficiency.
BH
theprocessofstructureformationisguidedbygravityalone. For supermassive black holes (SMBHs) of masses ∼109M(cid:6),
Ontheotherhand,deviationsfromtheserelationstestifythe the amount of energy released during their formation and
presence of physical processes more complex than gravita- growth is of the order of E ∼ 2 × 1062ergs−1. Even a
BH
tional dynamics only, which modify the thermodynamical tinyfraction((cid:3)1%)oftheenergyreleasedwithinthebulge
propertiesofthediffusebaryonsandthereforetherelations could heat and blow away its entire gas content in small
between observables and cluster masses. In particular, a systemsandpreventcooling,thusexplainingthelackofstar
number of observational measurements seems to indicate formation in bulges. An extraordinary discovery obtained
that the L-T relation is steeper than that predicted by self- recently in astrophysics is the correlation between the mass
similar models and is in the form L ∝ T2.5−3 (e.g., [25– of the central black hole (M ) and the velocity dispersion
BH
30], see also Section5.6). This observed breaking of the (σ) of the galaxy’s bulge used to estimate the mass of the
scaling relation has been ascribed to the presence of some bulgeitself[10].This“Magorrianrelation”M -σ suggests
BH
excessentropyinthegasduetoprimordialnongravitational that the large-scale properties of the galaxy and the small-
heatingbeforetheclustervirialization[31,32]andisoneof scale properties of the black hole are related. In particular,
thestrongestevidencefornongravitationalprocessesacting eachmassivegalaxyseemstohostacentralblackhole,whose
intheICM. mass is ∼0.1–0.2% of the bulge stellar mass [47–49]. Such
The main source of uncertainty in the determination a correlation may arise from the fact that the central black
of cosmological parameters from studies of cluster samples hole is able to regulate the amount of gas available for
arisesthenfromtheuncertaintyinthenormalization,shape, star formation in the galaxy. The formation of black holes
and evolution of the relationships that relate the cluster and the formation of bulges are closely linked. Therefore
masses to the observables. In order to understand better supermassive black holes can have a profound influence on
suchrelations,itisessentialtoinvestigatehowthestructure theformationandevolutionofgalaxies.Thephysicalprocess
formationandAGNfeedbackaffecttheevolutionofwhatwe regulatingthesephenomenahasbeencalled“feedback,”and
canobserve,thatis,thebaryonsinclusters. theunderstandingofhowitactsindetailisoneofthemain
openissuesinextragalacticastrophysics.
3.RoleofAGNFeedbackinGalaxyEvolution ClustersofgalaxiesaretheonlylocationsintheUniverse
where we can find an almost complete census of the inter-
Oneofthemainproblemsofthecurrentcosmologicalmodel galacticbaryonsandaverygooddescriptionoftheirthermo-
iswhysofewbaryonshaveformedstars[33,34].Numerical dynamicalstatusandoftheirenrichmentinheavyelements.
4 AdvancesinAstronomy
Therefore, X-ray observations of the ICM can provide us protons) would each have Maxwellian distribution,
with new important insights into the processes of cooling but generally at different temperatures, respectively,
andfeedbackwhichregulategalaxyformation. T and T. The time scale for the electrons and
e i
ions to reach equipartition T = T is t (p,e) ≈
e i eq
(m /m )t (e,e), and for typical values of the ICM
4.ClustersofGalaxiesinX-Raysand p e eq
temperatureanddensityist (p,e)(cid:3)6×108yr.Since
ThermalICM eq
this is shorter than the age of the clusters or their
large-scale cooling time (although it is comparable
Clustersofgalaxiesarethelargestvirializedstructuresinthe
Universe, with typical sizes of ∼2–4Mpc and total gravita- to or longer than the cooling time in the cores of
tional masses of ∼1014–1015M(cid:6). They are luminous X-ray clusters,see(21)below),theintraclusterplasmacan
sources,withtypicalluminositiesrangingfromafew×1043– generally be characterized by a single kinetic tem-
1046ergs−1.AsfirstsuggestedbyFeltenetal.[50],theX-rays peratureT = Te = Ti,whichdeterminestheratesof
allexcitationandionizationprocesses.Itisimportant
fromclustersareprimarilythermalbremsstrahlungemission
fromthediffuseICMwhichfillsthedeeppotentialwellsand tonotethatthemeanfreepaths,thatis,
isheatedtotemperaturesof∼108K(wherekT = 1keVfor (cid:3) (cid:4) (cid:3) (cid:4)
T =1.16×107K)duringtheprocessofclusterformation. λ =λ ≈23kpc Te 2 ne −1, (7)
e i 108K 10−3cm−3
4.1.PhysicalPropertiesofHotDiffusePlasma. Thesimpleas-
are generally much shorter than the length scales of
sumptionswhicharegenerallymadeinthestudyoftheioni-
interestinclusters(≈1Mpc),andthereforetheICM
zationstateandX-raylineandcontinuumemissionfroma
canbetreatedasacollisionalfluid,satisfyingthehy-
low-densityhotplasmaarebrieflyreviewedbelow[15].
drodynamicequations.
(1)ThetimescaleforelasticCoulombcollisionsbetween
(2)At these low densities, collisional excitation and de-
particlesintheplasmaismuchshorterthantheage
excitation processes are much slower than radiative
or cooling time of the plasma, therefore the free
decays,thereforeanyionizationorexcitationprocess
particles are assumed to have a Maxwell-Boltzmann
isassumedtobeinitiatedfromthegroundstateofan
distributionatthetemperatureT.Thisfollowsfrom
ion. Three (or more) body collisional processes are
considerationsonthemeanfreepathsofparticlesina
ignoredbecauseofthelowdensity.
plasmawithoutamagneticfield.Themeanfreepath
λe foranelectrontosufferanenergyexchangewith (3)Stimulated radiative transitions are not important,
another electron via Coulomb collisions is given by sincetheradiationfieldintheICMissufficientlydi-
[51]: lute.
33/2(kT )2 (4)At these low densities, the gas is optically thin and
λe = 4π1/2n e4elnΛ, (5) the transport of the radiation field can therefore be
e
ignored.
where T is the electron temperature, n is the elec-
e e
tronnumberdensity,andΛistheratiooflargestto Under these conditions, ionization and emission result
smallestimpactparametersforthecollisions(lnΛ≈ primarily from collisions of ions with electrons, and colli-
38). Equation (5) assumes that the electrons have sionswithotherionscanbeignored.Thetimescalesforion-
a Maxwellian velocity distribution at the electron izationandrecombinationaregenerallyconsiderablyshorter
temperature T . However, it can be demonstrated thantheageoftheclusteroranyrelevanthydrodynamictime
e
that if a homogeneous plasma is created in a state scale, therefore the plasma is assumed to be in ionization
inwhichtheparticledistributionisnon-Maxwellian, equilibrium(e.g.,[53]).Theequilibriumionizationstateof
elasticcollisionswillcauseittorelaxtoaMaxwellian adiffuseplasmadependsonlyontheelectrontemperature:
distribution on a time scale determined by the sinceinnearlyallastrophysicalplasmasmostoftheelectrons
mean free paths [51, 52]. Electrons will achieve originateinhydrogenandheliumatoms,andthesearefully
this equilibrium on a time scale given roughly by ionized under the conditions considered here, the ICM is
t (e,e) ≡ λ /(cid:7)v (cid:8) , where (cid:7)v (cid:8) is the rms elec- generallytreatedasafullyionizedplasma.
eq e e rms e rms
tronvelocity=(3kT /m )1/2: By indicating with X, Y, Z the mass fraction of hydro-
e e
gen, helium, and heavier elements, respectively, the corre-
(cid:3) (cid:4) (cid:3) (cid:4)
T 3/2 n −1 spondingatomnumberdensitiescanbewrittenintheform:
teq(e,e)≈3.3×105yr 108eK 10−3cem−3 . (6) nH = np ≡ ρX/mp, nHe = ρY/4mp = npY/4X, nz =
ρZ/Am = n Z/AX,whereρisthegasdensity,m thepro-
p p p
The time scale for Coulomb collisions between ton mass and A the mean atomic mass number (i.e., the
protons to bring them into kinetic equilibrium is numberofnucleons)ofheavierelements.Assumingthatthe
about t (p,p) ≈ (m /m )1/2t (e,e), roughly 43 gas pressure p = nkT is contributed only by electrons and
eq p e eq
times longer than that for electrons.After this time, protons,thusneglectingnuclei(n=n +n ),itispossibleto
e p
the electrons and ions (generally assumed to be derivetheelectrondensityn intermsoftheprotondensity
e
AdvancesinAstronomy 5
n .Fromtheexpressionofthenumberofparticlescontribut- The frequency-integrated total emissivity at a tempera-
p
ingtothepressure,n=2n +2n +(1/2)An ,oneobtains tureT canbewrittenas:
H He z
(cid:3) (cid:4)
n= 2+ 1Y + 1Z n , (8) JX(T)=Λ(T)nenpergs−1cm−3, (12)
2X 2X p
whereΛ(T)isthecoolingfunction,whichdependsuponthe
which for solar abundances (X = 0.71, Y = 0.265,
mechanismoftheemissionandcanberepresentedas:
Z =0.025)leadston ∼1.2n .Itisalsopossibletocalculate
e p
the mean molecular weight in amu, μ, such that the total Λ(T)=lTα, (13)
numberdensityofparticles(electrons,protonsandions)is
n=ρ/μmp.Fromtheexpressionn=2nH+3nHe+((1/2)A+ where −0.6 (cid:3) α (cid:3) 0.55; for thermal bremsstrahlung it is
1)nz,intheapproximationA(cid:9)1,oneobtains l∼2.5×10−27andα=1/2[62].Thegeneralbehaviourofthe
(cid:3) (cid:4) coolingfunctionwascalculatedanddiscussedbySutherland
3 1 −1
μ= 2X+ Y + Z , (9) andDopita[63].
4 2 The projection on the sky of the plasma emissivity
whichforsolarabundancesleadstoμ∼0.6. givestheX-raysurfacebrightness:inordertoconstrainthe
physicalparametersoftheICM,theobservedsurfacebright-
nesscanbeeithergeometricallydeprojectedor,moresimply,
4.2. X-Ray Emission from the ICM. The X-ray continuum
fitted with a model obtained from an assumed distribution
emissionfromahotdiffuseplasma,suchastheICM,isdue
ofthegasdensity.
primarily to two processes: thermal bremsstrahlung (free-
free emission) and recombination (free-bound) emission.
4.3. Hydrostatic Models for ICM Distribution. From the ex-
Processes that contribute to X-ray line emission (bound-
bound radiation) from a diffuse plasma include collisional pressionforthesoundspeedcs2 = γkT/μmp,whereγ = 5/3
foramonatomicgas,thetimerequiredforasoundwavein
excitation of valence or inner shell electrons, radiative and
theICMtocrossaclusterisgivenby:
dielectric recombination, inner shell collisional ionization,
andradiativecascadesfollowinganyoftheseprocesses. (cid:3) (cid:4) (cid:5) (cid:6)
T −1/2 D
Atthehightemperatures,typicalofclusters(inparticular t ≈6.6×108 yr, (14)
at kT (cid:2) 2.5keV), thermal bremsstrahlung is the predomi- s 108K 1Mpc
nantX-rayemissionprocess.Thebremsstrahlungemissivity
atafrequencyν(definedastheemittedenergyperunittime, whereDistheclusterdiameter.Sincethistimeisshortcom-
pared to the likely age of a cluster (in first approximation
frequency, and volume) of a plasma with temperature T,
assumed to be ∼1010yr), the gas is generally thought to be
electrondensityn andiondensityn isgivenby(e.g.,[54]):
e i in hydrostatic equilibrium in the gravitational potential of
Jbr(ν,T)=6.8×10−38Z2neniT−1/2e−hν/kTg(ν,T), (10) the cluster: ∇p = −ρ∇φ, where p = ρkT/μmp is the gas
pressure, ρ is the gas density, and φ is the gravitational po-
where the Gaunt factor g(T), which corrects for quantum tential of the cluster. Under the assumptions that the ICM
mechanical effects and for the effect of distant collisions, is is locally homogeneous and the cluster is spherically sym-
a slowly varying function of the parameters [55, 56]. If the metric,thehydrostaticequilibriumequationreducesto
ICM is mainly at a single temperature, then (10) indicates
thattheX-rayspectrumshouldbeclosetoanexponentialof 1dp =−dφ =−GM(r), (15)
thefrequency,asisgenerallyobserved. ρ dr dr r2
The total power per unit volume emitted by thermal
wherer istheradiusfromtheclustercenterandM(r)isthe
bremsstrahlung is obtained by integrating (10) over fre-
totalclustermasswithinr.Ifthegasself-gravityisignored,
quency,obtaining:
thenthedistributionoftheICMisdeterminedbythecluster
J (T)=1.4×10−27n nT1/2Z2g(T), (11) potential φ(r) and the temperature distribution of the gas
br e i
T(r), and (15) is a linear equation for the logarithm of the
where g(T) is a frequency average of g(ν,T) and is in the gasdensity.Undertheseassumptions,thegravitationalmass
range1.1to1.5(choosingavalueof1.2willgiveanaccuracy M ofagalaxyclustercanbewrittenas:
tot
intheestimateofJbr(T)towithinabout20%,[54]).Forsolar (cid:7) (cid:8)
abundances, the emission is primarily from hydrogen and kTr dlnρ dlnT
M (<r)=− + . (16)
helium. tot Gμm dlnr dlnr
p
Compilations of the different emissivities for X-ray
lines and continua can be found in the literature (e.g., This expression is commonly used to estimate the gravita-
[57, 58]). Early detailed calculations of the X-ray spectra tionalmassofgalaxyclustersandgroupsfromX-rayobser-
predictedbydifferentmodelsoftheICMhavebeengivenby vations, through the measurements of the radial profiles of
Sarazin and Bahcall [59] and Bahcall and Sarazin [60, 61]. temperature and density (e.g., [64–67]). However, we note
In these models most of the X-ray emission is thermal that (16) neglects the contribution of possible additional,
bremsstrahlungcontinuum,andthestrongestlines(highest nonthermal pressure that, if present, should be included in
equivalentwidth)areinthe7keVironlinecomplex. the estimate of the total mass. In particular, recent results
6 AdvancesinAstronomy
from numerical simulations indicate that the total mass of 4.4.CoolCoresandCoolingFlowProblem. TheX-raysemit-
simulated clusters estimated through the X-ray approach tedfromclustersofgalaxiesrepresentalossofenergyofthe
is lower that the true one due to gas bulk motions (i.e., ICM. The resultant cooling time is calculated as the time
deviationfromthehydrostaticequilibrium)andthecomplex takenforthegastoradiateitsenthalpyperunitvolumeH
v
thermalstructureofthegas[68,69].Possibleobservational usingtheinstantaneouscoolingrateatanytemperature:
biasesinthederivationofX-raymassesarealsodiscussedin
PiffarettiandValdarnini[70]. t ≈ Hv = γ kT , (21)
cool n n Λ(T) γ−1μXn Λ(T)
e H e
4.3.1.Theβ-Model. CavaliereandFusco-Femiano[71]stud- whereγ=5/3istheadiabaticindex;μ≈0.6isthemolecular
ied the X-ray emission by the hot plasma in galaxy clusters weight; X ≈ 0.71 is the hydrogen mass fraction; Λ(T) is
anddevelopedahydrostaticmodelbasedontheassumption the cooling function. In the central region, the cooling rate
thatthegasandthegalaxiesareinequilibriuminthesame of the ICM is sufficiently high that the particles lose their
gravitational potential φ (see, e.g., [15, 72] for a recent energy via radiation, as inferred from X-ray images of the
commentary on this model). By further assuming that the cores of many clusters which show strongly peaked surface
galaxydistributioniswelldescribedbyKing’sapproximation brightnessdistributions.Thedensityofthegasthenrisesto
to the isothermal sphere [73], the expression for the ICM maintainthepressurerequiredtosupporttheweightofthe
distributionmaybewrittenas[71]: overlyinggasintherestofthecluster,causingaslowsubsonic
(cid:7) (cid:3) r (cid:4)2(cid:8)−(3/2)β itnatflivoewpoicftumreatdeersiaclribtoewsathrdespthhyesiccsluosftetrhecepnrtoecre.sTshkinsoqwunalai-s
ρ(r)=ρ 1+ , (17)
0 r a cooling flow (see [2] for a review of the standard model,
core
and [74] for a quantitative description of the evolution of
and the surface brightness profile observed at a projected cooling flows). The steady cooling flow is confined within
radiusb,I(b),isintheform[71]: the region in which t is less than the time for which the
cool
(cid:7) (cid:3) b (cid:4)2(cid:8)1/2−3β saycstoeomlinhgasflboewe)n.rTehlaixsecdoo(ltihnugsraelglioowninisgdtheleimesittaebdlibshymtheentsoo-f
I(b)=I 1+ . (18)
0 rcore called cooling radius rcool, which is usually defined as the
radiusatwhicht isequaltothelook-backtimetoz = 1,
cool
Theparameterβisdefinedas that is, ∼7.7 × 109yr in the concordance cosmology. The
fractionofclusterswithacentralsurfaceexcesswithrespect
β= σr2 , (19) to a β-model, the so-called cool cores, is large. Cool core
kT/μmp clusters are about 90% of X-ray-selected clusters with total
mass Mtot (cid:3) 1014M(cid:6), and about 50% of X-ray-selected
where σr is the line-of-sight velocity dispersion and repre- clusters with total mass Mtot (cid:2) 1014M(cid:6) [75]. Cool cores
sentstheratioofspecifickineticenergiesofgalaxiesandgas.
arealsocharacterizedbystrongenhancementsinthecentral
This self-consistent isothermal model, called the “β-
abundance(e.g.,[76,77])anddecliningtemperatureprofiles
model,”iswidelyusedintheX-rayastronomytoparametrize
towardthecentralregion(e.g.,[78–80]).
the gas density profile in clusters of galaxies by fitting their
In the standard model, the “magnitude” of a cooling
surfacebrightnessprofile.Oneoftheadvantagesofusingaβ-
flow is measured from the amount of matter which crosses
modeltoparameterizetheobservedX-raysurfacebrightness r and flows towards the center, that is, M˙, the mass in-
cool
is that the total mass profiles can be recovered analytically
flow rate. The mass inflow rate, due to cooling, can be esti-
andexpressedbyasimpleformula:
mated from the X-ray images by using the luminosity L
cool
(cid:7) (cid:8) associated with the cooling region and assuming that it is
kr2 3βrT dT
M (<r)= − . (20) all due to the radiation of the total thermal energy of the
tot Gμmp r2+rc2 dr gas plus the pdV work done on the gas as it enters rc:
L =dE/dt,wheredE=dE +pdV =(γ/γ−1)pdV,and
Equation(17)statesthatthegasdensityrisestowardsthe cool th
pdV =(ρkTdV)/(μm )=(dMkT)/(μm ),withγ=5/3.By
cluster center. Since the bremsstrahlung and line emission p p
substitutingoneobtainstheexpressionforL :
dependonthesquareofthegasdensity (12),inthecentral cool
regions of clusters the loss of energy by X-ray emission 5 M˙
representsanimportantprocessforthethermalparticlesin Lcool= 2μm kT, (22)
p
theICM.Inparticular,ifthegasdensityreacheshighenough
values,largeamountsofgascoolandflowintothecentersof where T is the temperature of the gas at r . L ranges
cool cool
clusters,formingtheso-calledcoolingflows.Incoolingflow from ∼1042 to >1044ergs−1 and generally represents ∼10%
clusters,thesingleβ-modelisfoundtobeapoordescription ofthetotalclusterluminosity[2].ValueofM˙ ∼100M(cid:6)yr−1
of the entire surface brightness profile: a fit to the outer arefairlytypicalforclustercoolingflows.
regions shows a strong excess in the center as compared to However, the current generation of X-ray satellites,
themodel(seeSection4.4).Conversely,thecentrallypeaked Chandra and XMM-Newton, has radically changed our un-
emission is a strong indication of a cooling flow in relaxed derstanding of cooling flow systems. Albeit confirming the
cluster. existence of short cooling times, high densities and low
AdvancesinAstronomy 7
temperatures in the cluster cores, the arrival of high-reso- many clusters, including shocks, ripples, and sharp density
lutionX-rayspectraldatahasshowntheabsenceorweakness discontinuities.Thecomparisonwithradioimagesobtained
ofthesoftX-raylineFeXVII,indicatingthattheamountof at similar angular resolution has revealed that AGN jets
gascoolingradiativelybelowaboutone-thirdofitsoriginal are the cause of many of these disturbances. The most
temperatureistentimeslessthanexpected(e.g.,[3,4,81]). typical configuration is for jets from the central dominant
The lack of evidence for central gas cooling to very low elliptical of a cluster to extend outwards in a bipolar flow,
temperaturesattheratespredictedinthehotatmospheresof inflating lobes of radio-emitting plasma. These lobes push
galaxyclustersandgroupsrepresentsanopenquestionwhich asidetheX-rayemittinggasoftheclusteratmosphere,thus
isoftenreferredtoasthesocalled“coolingflowproblem”(see excavating depressions in the ICM which are detectable
[5,6,82]forreviews). as apparent “cavities” in the X-ray images. The brightness
Historically,twomainapproacheswereadoptedtosolve depressions observed in X-rays, which are mostly found in
this problem. As the gas radiates but does not appear pairs, are∼20–40% below the level of the surrounding gas,
to cool, either the normal signatures of radiative cooling consistently with the expected decrement along an empty
below 1-2keV are somehow suppressed, or there must bubbleimmersedinaβ-modelatmosphere[106–110].The
be an energy-injection mechanism into the ICM which cavitiesareoftensurroundedbybrightshells,orrims,which
compensatescooling.Differentpossibilitiesconsideredinthe are typically found to be cooler than the ambient medium
former hypothesis include absorption [3, 83], inhomoge- [106–109, 111]. This is likely due to the compression of
neousmetallicity[83,84],andtheemergingofthemissing thecentral,low-entropygasintothebrightshellduringthe
X-rayluminosityinotherbands,likeultraviolet,opticaland cavityrisingandexpansionintothehotatmosphere.
infrared due to mixing with cooler gas/dust [83, 85, 86]. X-ray cavities are present in (cid:2)70% of cool-core clus-
Proposed heating mechanisms in the context of the latter ters [112], but this fraction could be underestimated due
approach include, for example, processes associated with to the limitation of cavity detectability [113]. Identifying
relativisticAGNoutflows[87–93],electronthermalconduc- radio galaxies as a primary source of feedback in the hot
tion from the outer regions of clusters [94–97], continuous atmospheres of galaxy clusters and groups has been one
subcluster merging [98], contribution of the gravitational of the major achievements of the current generation of X-
potential of the cluster core [99], and feedback from ray observatories (for a comprehensive review see [6] and
intraclustersupernovae[100].Amongallthese,feedbackby referencestherein).Well-studiedexamplesofcavityclusters
thecentralAGNappearstobethemostpromisingsolution. are Perseus (e.g., [104, 106, 114, 115]), Hydra A (e.g., [4,
107, 116–120]), M 87 (e.g., [89, 121–125]), A 2052 (e.g.,
[108,126–128]),RBS797(e.g.,[111,129–131]),A133(e.g.,
5.X-RayCavitiesandShocks: [132, 133]), A 262 (e.g., [126, 134]), and MS 0735+7421
AGNFeedbackinAction (e.g., [135, 136]). In-depth analyses of individual objects,
which are now numerous in the literature, combined with
Itwasalreadyknownintheearly90sthatcentraldominant studiesofcavitysamples[8,112,137–140]haveenabledusto
(cD) galaxies of cool core clusters have a high incidence of identifytheglobalpropertieswhicharecommonamongthe
radio activity, showing the presence of central FR-I radio cavities,thussheddinglightofthefeedbackmechanism.The
galaxies in 70% of the cases [7, 101, 102]. Their behaviour emergingpictureisthatbipolaroutflowsemanatingfromthe
differsfromthatofquasar:inmanylow-accretion-rateAGNs BCG core inflate large bubbles while driving weak shocks,
almostallthereleasedenergyischanneledintojetsbecause heattheICMandinduceacirculationofgasandmetalson
the density of the gas surrounding the black hole is not scalesofseveral100skpc.Weakshockshavebeenobservedas
high enough for an efficient radiation (e.g., [103]). In fact, ripple-likefeaturesintheICMinthedeepestX-rayimagesof
the importance of these objects has been underestimated PerseusandA2052[115,128].
for a long time due to their poor optical luminosity. The However, the differences between groups and clusters
importance of radio galaxies in cool cores began to emerge imply that the existing studies on cavities in clusters tell us
afterthediscovery,withtheX-raysatelliteROSAT,ofdeficits little about how feedback operates in groups. With respect
in the X-ray emission of the Perseus and Cygnus A clusters to rich galaxy clusters, the observation of cavities in galaxy
which are spatially coincident with regions of enhanced groups and ellipticals is complicated by the lower X-ray
synchrotron emission [104, 105]. With the advent of the surfacebrightness,whichlimittheirdetectioninshallowX-
newhigh-resolutionX-rayobservationsperformedwiththe ray images. On the other hand, there are several examples
currentgenerationsofX-raytelescopes,ChandraandXMM- of AGN-ICM interaction just a few tens Mpc away from
Newton, it became clear that the central radio sources have us, which allow us to probe regions closer to the central
a profound, persistent effect on the ICM. In particular, black hole. In particular, low mass systems with cavities
Chandra images, which are obtained at the superb angular whichnowhavedeepChandraimagesareM84[141,142],
resolution of ∼1(cid:11)(cid:11), showed that the Perseus and Cygnus A NGC4636[143–145],NGC5044[146–149],HCG62[150–
clusters are not isolated cases—indeed the central hot gas 153],andNGC5846[154].Performingin-depthindividual
in many cool core systems is not smoothly distributed, but studies and sample studies of the lower-energy outbursts
isinsteadcavitatedonscalesoftenapproximatelycoincident in these smaller systems is of major interest because the
with lobes of extended radio emission. These observations relationship between AGNs and hot gas can significantly
also reveal highly disturbed structures in the cores of influencegalaxyevolutioninthegroupenvironment,which
8 AdvancesinAstronomy
100kpc 20kpc
(a) (b)
10kpc 10kpc
(c) (d)
Figure1:(a)Thegreencontoursoutliningthe330MHzradioemissionfromLaneetal.[164]areoverlaidontothe0.5–7.5keVChandra
imageofthegalaxyclusterHydraA(z=0.0538).Theextendedradiolobesfillalarge-scalesystemofX-raycavitiesandaresurroundedby
a“cocoon”shock.SeealsoSections5.6and5.8.adaptedfromNulsenetal.[116].(b)VeryLargeArray(VLA)radiocontoursoverlaidonto
the0.5–7.0ChandraimageofthegalaxyclusterRBS797(z=0.35).Thesubarsecresolutionradioimageshowsthedetailsoftheinnermost
4.8GHzradiojets(bluecontours),whichclearlypointinanorth-southdirection.Remarkably,theseinnerjetsarealmostperpendicularto
theaxisofthe1.4GHzemissionobservedat1(cid:11)(cid:11)resolution(greencontours),whichiselongatedinthenortheast-southwestdirectionfilling
theX-raycavities.AdaptedfromGittietal.[130].(c)0.3–2keVChandraimageofthegalaxygroupNGC5813(z=0.0066)with1.4GHz
VLA(blue)and235MHzGiantMetrewaveRadioTelescope(green)radiocontoursoverlaid.Theimageshowstwopairsofcavities,plusan
outercavitytothenortheast,twosharpedgestothenorthwestandsoutheast,andbrightrimsaroundthepairofinnercavities.Adapted
fromRandalletal.[157].(d)235MHzGMRTcontoursoverlaidonthesmoothed0.5–2.0keVChandraimageofthecompactgroupHCG
62(z = 0.0137).Theradiosourceshowsadisturbedmorphologywithinnerlobesclearlyfillingthewell-definedX-raycavities,butwith
outerlobeshavingnoassociatedX-raycavities(seealsoSection5.4).AdaptedfromGittietal.[153].
isthelocusofthemajorityofgalaxiesintheUniverse[155]. the other hand, in clusters there must be also the action
Duetotheshallowergrouppotential,theAGNoutburstcan of rare, powerful outbursts [163], although more extensive
have a large impact on the intragroup medium in terms of theoreticalworkisrequiredtoreachfirmconclusions.
altering the thermal history and spatial distribution of the Examples of well-studied cavity systems in clusters and
intragroupmedium,asthemechanicaloutputbyradioAGN groupsareshowninFigure1.
is of the same order of magnitude as the binding energy
of groups [156]. Such investigations have been undertaken 5.1.CavityHeating. Theheatingisthoughttooccurthrough
only recently for individual objects (e.g., NGC 5813: [157], the dissipation of the cavity enthalpy and through shocks
AWM4:[158,159])andforgroupsamples[9,160–162],and driven by the AGN outburst. The energy required to create
are rapidly improving our understanding of these systems. acavitywithpressure pandvolumeV isthesumofthe pV
However, this observational effort is still awaiting detailed workdonebythejettodisplacetheX-rayemittinggaswhile
theoretical work in order to corroborate the observational it inflates the radio bubble, and the internal energy of the
findings. Recent detailed simulations indicate that groups lobes,thatis,theenthalpygivenby:
are not simply a scaled-down version of clusters, as there
γ
mayberemarkabledifferencesbetweenhowAGNfeedback Ecav≡H =Eint+pV = γ−1pV, (23)
operatesingalaxygroupandingalaxyclusterenvironments
[163]. In particular, AGN heating in groups seems to act where γ is the ratio of the specific heats of the cavity con-
throughpersistent,gentleinjectionofmechanicalenergy.On tent. If the lobes are dominated by the magnetic field, by
AdvancesinAstronomy 9
nonrelativisticgas,orbyrelativisticplasma,Hcanvaryfrom fromthemeasurementsofE andt byapplying(23).The
cav cav
2pV and4pV.Inparticular,typicallyitisassumedthatthe cavitypower,P ,whichisameasureoftheenergyinjected
cav
internalcompositionofthecavityisdominatedbyrelativistic intothehotgasbytheAGNoutburst,canthenbecompared
plasma, therefore γ = 4/3 and H = 4pV. The product directly with the gas luminosity inside the cooling radius,
of pressure and volume can be estimated directly by X-ray L ,whichrepresentstheluminositythatmustbecompen-
cool
observations through measurements of the cavity size and sated for by heating to prevent cooling. The gas luminosity
of the temperature and density of the surrounding ICM. inside the cooling radius is estimated as the bolometric X-
A potential issue is represented by the uncertainties in the rayluminosityderivedfromadeprojectionspectralanalysis.
measurementofthecavityvolume.Thecavitysizeisusually In Figure2(a) is shown a quantitative comparison between
estimated through a visual inspection of the X-ray images. P =4pV/t andL calculatedfortheextendedsample
cav buoy cool
ThismethodisthereforedependentonthequalityoftheX- discussedinO’Sullivanetal.[165],whocombinednewdata
raydataandalsosubjecttothearbitrarinessoftheobserver. of9galaxygroupswiththeclustersampleofBˆırzanetal.[8]
Thecavitysizeandgeometrymeasuredbydifferentobservers andwiththeellipticalsampleofCavagnoloetal.[169].
mayvarysignificantlydependingontheapproachadopted, This plot follows those presented in Figure2 of Bˆırzan
leadingtodifferencesbetweenestimatesofuptoafactorofa et al. [137] and in Figure6 of Rafferty et al. [139]. As al-
fewin pV (e.g.,[131,153,165]). ready noted by these authors, it is evident that the cavity
Systematic observational studies of samples of X-ray powerscalesinproportiontothecoolingX-rayluminosity,
cavities show that their enthalpies measured from (23) lie althoughwithabigscatter.Ingeneral,itappearsthatthehigh
between∼1055erg(inellipticals,groups,andpoorclusters) mass(correspondingtohighL )systemsneedanaverage
cool
and (cid:2)1061erg (in rich clusters). On the other hand, simu- of4pV percavitytocountercooling.Ontheotherhand,if
lations indicate that pV varies with time during the cavity werecalculateP as1pV/t allthepointsintheplotwill
cav buoy
evolution and may be an inaccurate measure of the total shiftdownbyafactor4,andonlythelowermasssystemswill
energyreleased[166,167].Cavitypowerestimateswithina still lie around the line P = L . These systems require
cav cool
factoroftwoofthesimulatedvaluesseempossibleprovided 1pVpercavitytooffsetcoolingatthepresenttime.Afewlow
the inclination angle of the jets is known accurately [168]. mass systems will even still be above the equality line, thus
Bearingthiscaveatinmind,whendividedbythecavityage, indicating that the total mechanical power of the AGN far
t ,theobservationalmeasurementsgiveanestimateofthe exceedstheradiativelossesandtheiratmospheresarebeing
cav
so-called“cavitypower,”P .Sinceshocksareverydifficult heated. Although this extended sample is not a complete
cav
todetectandarecurrentlyknownonlyinafewsystems(e.g., sample and therefore is not representative of the whole
HydraA[116],MS0735+7421[135],HCG62[153],NGC populationofclusters,groups,andellipticals,itisinteresting
5813 [157]), for consistency, the usual approach in sample to consider the mean values of heating and cooling to see
studiesisthatofconsideringonlythecavitypower.P thus how they compare. We estimated a mean cooling power
cav
providesalowerlimit(andbest-availablegauge)tothetrue of 4.09 × 1044ergs−1, and a mean cavity power of 6.18 ×
total mechanical power of the AGN, that is, the jet power: 1044ergs−1. In order to quantify properly the contribution
P (cid:2)P =E /t . ofAGNfeedback,overthesystemlifetime,intheenergetics
jet cav cav cav
AsproposedbyBˆırzanetal.[137],thecavityagecanbe ofcoolingflow,itisimportanttodeterminethe“duty-cycle”
estimatedinthreeways:(1)byassumingthatthe(cid:2)cavityrises of AGN. Many studies have attempted such calculation by
thehotgasatmosphereatthesoundspeedc = γkT/μm adopting different approaches, for example, by considering
s p
theluminosityfunctionofradiogalaxies[170],thefraction
inthiscasethecavityreachestheprojecteddistanceRfrom
the(cid:2)cluster center in the sound crossing time ts = R/cs = o17f1c]l,utshteerfsreqthuaetnccyonotfabinubbbulebrbelqesuiraenddtocapvriotideusce[1s1u2ffi,c1ie3n8t,
R/ γkT/μm ;(2)byassumingthatthecavityisbuoyantand
p (cid:2) heating[172],theprevalenceofradio-loudAGN[101,173].
moveoutwardsattheterminalvelocityv = 2gV/SC,where In particular, by considering the cavities as tracers of the
t
g = GM /R2 is the gravitational acceleration at the cavity feedbackmechanism,thatis,byassumingthatthefeedback
<R
positionR,Visthevolumeofthecavity,Sisthecross-section isactiveandefficientaslongasthecavitiesarevisible,wecan
ofthecavity,andC=0.75isthedragcoefficient[8(cid:2)9]:inthis correct the mean cavity power by the fraction of cool core
casethecavityageisthebuoyancy-timet ∼R/ 2gV/SC; clusters with cavities, estimated by Dunn and Fabian [112]
buoy
oftheorderofatleast70%.Theratioofmeancavitypower
(3) by considering the time required for gas to refill the
tocoolingflowpoweristhusveryclosetounity.Themean
displaced volume of the cavity(cid:2)as it rises: in this case the
values for the whole sample are only indicative and do not
cavityageisestimatedastref∼2 r/g,whereristheradiusof reflectthedifferentbehaviourofgroupsandellipticalswith
thecavity.Typically,theageestimatesagreetowithinafactor respecttoclusters.Inparticular,suchmeanpowersmissthe
of 2, with the buoyancy times lying in between the sound pointthatinordertocountercoolingthelowmasssystems
crossingtimeandtherefilltimes.Mostsamplestudiesadopt require outbursts with relatively less total energy, lower
thebuoyancytime,whichfortypicalvaluesgivescavityages powers,andrepeatingmorerapidlythanhighmasssystems.
oftheorderoffew107yr(e.g.,[139]). Thisissupportedbyrecentnumericalsimulationsofgalaxy
groups which show that, in contrast to galaxy clusters, the
5.2. The Relationship between Jet Power and L . Once a AGNself-regulatedfeedbackmustactthroughaquasi-con-
cool
cavityisdetected,itisrelativelysimpletoestimateitspower tinuousgentleinjectionwithsubrelativisticoutflows,rather
10 AdvancesinAstronomy
104 104
103
103
−P421(10ergs)cav 110021 −P421(10ergs)cav 110021
100
100
10−1
10−1
10−2
10−2 10−1 100 101 102 103 104 10−4 10−3 10−2 10−1 100 101 102 103
Lcool(1042ergs−1) Lradio(1042ergs−1)
Birzanetal.(2008) Birzanetal.
O’Sullivanetal.(2011) O’Sullivanetal.
Cavagnoloetal.(2010)
(a) (b)
Figure2:(a)CavitypowerofthecentralAGN,P ,versustheX-rayluminosityoftheICMinsidethecoolingregion,L .Thecavity
cav cool
poweriscalculatedassuming4pV ofenergypercavityandthebuoyancytimescale.Differentsymbolsdenotesystemsindifferentsamples
presented in the literature: green triangles: Bˆırzan et al. [8], red squares: Cavagnolo et al. [169], blue circles: O’Sullivan et al. [165]. 1σ
uncertaintiesoncavitypowerareindicatedbyerrorbars(see[165]fordetails).ThediagonallinedenotesP = L .CreditO’Sullivan
cav cool
(privatecommunication).(b)CavitypowerofthecentralAGN,P ,versusintegrated10MHz–10GHzradiopower,L ,forthesystems
cav radio
inthesampleofBˆırzanetal.(greytriangles)andthegroupsinthesampleofO’Sullivanetal.(blackcircles).Thesolidfitlineindicatesthe
regressionfittothedatapointscalculatedbyO’Sullivanetal.[165].ThedottedlineindicatestherelationfoundbyBˆırzanetal.[8].Adapted
fromO’Sullivanetal.[165].
thanthroughrareandpowerfulepisodes[163].Anattempt from the thermal ICM are balanced by mechanical heating
to produce more meaningful averages could be that of fromthecentralAGNoverthesystemlifetime.Althoughthis
dividing the sample plotted in Figure2(a) in two subsets. scenarioisnolongerindoubt,itisstillnotclearhowheating
In fact, by doing this we find that the ratio of mean cavity canactpreservingatthesametimetheobservedtemperature
power to cooling power for the groups and ellipticals is gradientandthecoolcore(e.g.,[174]).
7.94 (samples of Cavagnolo et al. [169] and O’Sullivan
etal.[165]), compared to a ratio of 1.51 calculated for 5.3. The Relationship between Jet Power and Radio Power.
clustersonly(sampleofBˆırzanetal.[8]).Ifthedutycycleof Studies of cavity samples allow to derive the relationship
lowmasssystemsisthesameas(ornotlowerthan)highmass between the mechanical power and radio emission of AGN
systems [112, 173], the relative ratio of heating to cooling jets and lobes. Such a relationship is of great interest
appearstobeafactor(cid:2)5higherinlowmasssystems.Inother because it helps to understand the physics of AGN jets
words,groupsandellipticalsseemtohavefivetimesasmuch (e.g., [165, 175]), and because it provides an estimate of
poweravailabletocountercoolingthanrichclusters. the energy available from AGN based directly on the radio
A study of a complete unbiased sample including data (e.g., [101]), thus avoiding the problem of cavity
both cool-core and non cool-core systems is necessary to detectabilityinshallowX-rayimages.Bˆırzanetal.[8]studied
derive definite constraints on the balance between heating a sample dominated by galaxy clusters and derived the
and cooling. However, it seems plausible that the time- relationbetweencavitypowerand327MHzradiopower,as
averagedAGNfeedbackbalancesradiationlossesoftheICM. well as between cavity power and the integrated 10MHz–
Therefore, the general picture emerging from the observed 10GHz radio luminosity, extending to lower frequencies
trend between X-ray luminosity and bubble mechanical their previous work [137]. While many of the observed X-
luminosity, together with the existence of short central ray cavities are filled with 1.4GHz radio-emitting plasma,
cooling time, is that the AGN is fueled by a cooling flow some are undetected at this high frequency and have been
thatisitselfregulatedbyfeedbackfromtheAGN.Thebasic referred to as “ghost cavities.” These may result from the
ideaofthisAGN-coolingflowscenarioisthataself-regulated aging of the relativistic particle population or may have
equilibrium may be achieved, in which the radiative losses beeninflatedbyeventswhichproducedonlyparticlesoflow