A representative survey of the dynamics and energetics of FRII radio galaxies

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by  Judith Ineson

MNRAS000,1–17(2016) Preprint23January2017 CompiledusingMNRASLATEXstylefilev3.0
A representative survey of the dynamics and energetics of FRII
radio galaxies
J. Ineson,1⋆ J. H. Croston,1 M. J. Hardcastle,2 and B. Mingo3
1SchoolofPhysicsandAstronomy,UniversityofSouthampton,SouthamptonS171BJ,UK
2CentreforAstrophysicsResearch.SchoolofPhysics,AstronomyandMathematics,UniversityofHertfordshire,Hatfield,HertfordshireAL109AB,UK
7 3DepartmentofPhysicsandAstronomy,UniversityofLeicester,UniversityRoad,LeicesterLE17RH,UK
1
0
2 AcceptedXXX.ReceivedYYY;inoriginalformZZZ

n
a
J ABSTRACT
9 We report the first large, systematic study of the dynamics and energetics of a representa-
1 tive sample of FRII radio galaxies with well-characterized group/cluster environments. We
used X-rayinverse-Comptonandradio synchrotronmeasurementsto determinethe internal

] radio-lobeconditions,andthese werecomparedwithexternalpressuresactingonthelobes,
A
determinedfrom measurementsof the thermalX-ray emission of the group/cluster.Consis-
G tentwithpreviouswork,wefoundthatFRIIradiolobesaretypicallyelectron-dominatedby
. asmallfactorrelativetoequipartition,andareover-pressuredrelativetotheexternalmedium
h
in their outer parts. These results suggest that there is typically no energetically significant
p
protonpopulationinthelobesofFRIIradiogalaxies(unlikeforFRIs),andsoforthispopula-
-
o tion,inverse-Comptonmodellingprovidesanaccuratewayofmeasuringtotalenergycontent
r andestimatingjetpower.WeestimatedthedistributionofMachnumbersforthepopulation
t
s ofexpandingradiolobes,findingthatatleasthalfoftheradiogalaxiesarecurrentlydriving
a strongshocksintotheirgroup/clusterenvironments.Finally,wedeterminedajetpower–radio
[
luminosity relation for FRII radio galaxies based on our estimates of lobe internal energy

1 andMachnumber.Theslopeandnormalisationofthisrelationareconsistentwiththeoretical
v expectations, given the departure from equipartition and environmentaldistribution for our
2 sample.
1
6 Keywords: galaxies:active,galaxies:clusters:intraclustermedium,galaxies:jets
5
0
.
1
0 1 INTRODUCTION formationthatispredictedbyevolutionarymodelsbutnotseenin
7 observations(e.g.Dunn&Fabian2006;Raffertyetal.2006).
1 Thejetsofradio-loudAGNconsistofplasmadrawnatrelativistic
Thedynamicsofthelobesofradio-loudAGNaredependent
: speedsfromthecentralregionsoftheAGN.Theplasmaistrans-
v ontheirpressurerelativetothatofthesurroundingICM(Scheuer
portedintothesurroundinggalaxygrouporclusterwhereitforms
Xi intolobes,whichdisplacetheintra-clustermedium(ICM).Cavities 1974). In Scheuer’s models A and B the lobes are highly over-
pressuredand soexpand atsupersonic rates;inmodel Ctheyare
r carvedintheICMbythelobeshavebeenobservedinclustersout
a toredshiftsgreaterthan0.5(Hlavacek-Larrondoetal.2012),while nearpressurebalanceandsoexpandmoregentlyandarecapable
ofbeingmouldedbytheICM.Thelattermodelismoreinkeeping
detailed studies of local sources have shown complex substruc-
withobservedlobeshapes,butthetipmustremainover-pressured
turesintheICM(e.g.Karovskaetal.2002;Fabianetal.2003)and
forthelobetocontinuetogrowandsotheremaystillbesupersonic
shockfrontsdrivenbythelobeexpansion(e.g.Crostonetal.2009;
movementoutthroughtheICM.
Shelton2011).Thesefeaturesprovidedirectevidencethatthera-
dio jets are disturbing the ICM on a large scale and transferring If the expansion is supersonic, the lobes will input en-
energyfromtheAGNtotheICM.Estimatesoftheenergyrequired ergy through shocks as well as through gas displacement (e.g.
tocreatethecavitiesaroundthelobes,andhenceoftheenergytobe Bîrzanetal. 2004; Hlavacek-Larrondoetal. 2012). Lobe shocks
dissipatedintotheICM,varywiththemethodused(e.g.Gittietal. have been seen in some observational studies, and estimates of
2012),butenthalpiestendtoliebetween1055and1061ergdepend- their Mach numbers range from 1.2 to 8.4 (e.g. Wilsonetal.
ingontherichnessofthecluster(e.g.Bîrzanetal.2004).Thishas 2006; Bîrzanetal. 2008; Crostonetal. 2009; Sheltonetal.
beenestimatedtobesufficienttooffsettheICMcoolingandstar 2011; Crostonetal. 2011; Worralletal. 2012; Kraftetal. 2012;
Nulsenetal.2013).However,inmanycasestheuncertaintiesinthe
methodsusedtoestimateMachnumbersmeanthatthesearelikely
tobelowerlimitsandsothetruevaluescouldbehigher.Therate
⋆ E-mail:[email protected] of lobe expansion is therefore important in determing heat input
(cid:13)c 2016TheAuthors
2 J. Inesonet al.
intotheICM.Sanders&Fabian(2007)havemadeadetailedstudy surements of external and internal conditions along the jet show
ofripplespropagatingthroughthePerseuscluster,andsuggestthat thatthesearemostlikelytocomefromentrainment.
20–40 per cent of thecavitypower goesintosound waveswhich FRII sources tend to be more distant so there are fewer
carrytheenergyoutwardsfromthecavitiesandheattheICM.For detailed studies, but they also appear under-pressured with re-
themorepowerfulFRIIlobes,estimatesoftheenergyinputtothe spect to the environment when the pressure is estimated assum-
environmentthatarebasedoncavityvolumearelikelytounderes- ing equipartition (e.g. Hardcastle&Worrall 2000). Unlike FRI
timatethetotalenergyinputmuchmoreseverelyandsotheusual lobes, however, many FRII lobes show X-ray emission indica-
pV estimatesofcavitypowershouldbetakenaslowerlimits(e.g. tive of IC and when this used to better model the electron en-
Gittietal.2012;Hardcastle&Krause2013;Peruchoetal.2014). ergy density in the lobes (assuming that the lobes are electron-
dominated), the lobes tend to appear close to pressure balance
Therelativisticleptonsintheradiojetsemitsynchrotronradi-
with their environment (e.g. Hardcastleetal. 2002; Crostonetal.
ationacrossarangeofradiofrequencies.Thetotalenergyemitted
2004;Kataoka&Stawarz2005;Crostonetal.2005;Belsoleetal.
depends onboth theparticleand magnetic fieldenergies, andwe
2007). This suggests that the assumption that the lobes are pre-
cannotseparatethesefactorsanddeterminetheinternallobecon-
dominantly populated by relativistic electrons is likely to be rea-
ditions from just the radio flux observations (e.g. Longair 2011,
sonable;theremaystillbesomelowerenergybaryonspresentbut
Section 16.5). We can however calculate the lobe conditions re-
theycanonlyaccountforasmallamountoftheenergybudget(e.g.
quiredtoproducetheobservedfluxbyassumingthatthetwofac-
Hardcastle&Croston2010).
torsmakesimilarcontributionstothetotalenergy–theassumption
There are however two major assumptions made in the syn-
ofequipartition.Thisissimilartotheminimumenergyconditions
chrotron and IC calculations that we cannot resolve from ob-
requiredtoproducetheobservedfluxandsowecanobtainalower
servations – that the dominant relativistic particles are elec-
limitontheinternallobepressure(Burbidge1956).
trons/positrons, and the proportion of the lobe that is filled
AsecondsourceofemissionisinverseCompton(IC),where
by the particles. As discussed by Hardcastle&Worrall (2000);
the relativistic particles boost photons in the lobes to X-ray fre-
Hardcastleetal.(2002)andCrostonetal.(2005),iftheseassump-
quencies and above, and this can be seen in X-ray observations
tions are incorrect then, assuming that the synchrotron-emitting
of the lobes of many FRII sources. The dominant photon field is
leptons are interspersed with non-radiating particles, the internal
fromCMBphotonsinthebodyofthelobes,withasmallcontribu-
pressuresofthelobesarelikelytobeunder-estimated.Thiswould
tion from synchrotron self-Compton (SSC) (e.g. Hardcastleetal.
resultinlobesthataremorehighlyover-pressuredwithrespectto
2002). SSC is stronger at lobe hot-spots, in the knots of FRI
theirenvironment.
jets and very occasionally in small, compact lobes where photon
As described above, lobe-tip shocks have been observed in
densitiesand electron energiesarehigher (Hardcastleetal.2004;
somestudies,butthetemperaturevariationsacrosstheshock can
Kataoka&Stawarz 2005; Hardcastle&Croston 2010). Some IC
only be isolated for strong, nearby sources. Mach numbers can
emission from nuclear photons has also been observed in a few
however be estimated from the ratio between internal and exter-
lobesandwhenstrongthiscould makeanimportant contribution
nal lobe pressure (e.g. Worrall&Birkinshaw 2006).Thismethod
totheICemission.3C207,forexample,hasmuchstrongerX-ray
doeshoweverneglecttherampressure,soMachnumbersobtained
emissionnearthenucleusthanintherestofthelobe(Brunettietal.
in this way should be regarded as lower limits, but, importantly,
2002). However, in other potential examples of nuclear emission
theyallowlimitstobesetontheenergyinputfromthelobes.
theeffectisnotsoclearlyvisibleandanycontributiontotheover-
InthispaperwereporttheinitialresultsofaninverseComp-
allX-rayfluxinthelobeisthoughttobesmall(e.g.Crostonetal.
ton study of FRII radio lobes in which we look at theradio lobe
2004;Belsoleetal.2004;Crostonetal.2005).
dynamics, look for evidence of energy being input into theICM,
If IC emission isobserved across the lobe, this allows us to and see whether the ICM in its turn has an effect on the devel-
estimatetheelectrondensityandsogainabetterestimateofinter- opmentofthelobes.InInesonetal.(2013,2015)wemodelledthe
nallobeconditionsthantheassumptionofequipartition.Anumber large-scaleenvironmentsoftwosamplesofradio-loudAGNatred-
ofobservational studiesandsimulationshaveconsidered howthe shifts∼0.5and∼0.1,andhereweusethesemodelstocalculatethe
internalconditionsoflobesdifferfromequipartition;theirinferred ICMpressuresaroundtheradiolobesoftheFRIIgalaxiesinthose
particlecontent;howtheirinternalpressurecompareswiththatof samples.WethenuseradioandX-rayobservationstomeasurethe
theICM;andhowenergyistransferredfromthelobetotheICM. synchrotron and IC fluxes in the lobes. These allow estimates of
ICX-rayemissionhasnotbeendetectedfromFRIlobesand internallobepressuresandlobetipMachnumberstobemadefor
sotheirlobepressuresaregenerallycalculatedassumingequipar- alarge,representativesampleofFRIIlobesforthefirsttime.
tition.Thesepressureestimatestendtobelessthanthatofthesur- ThroughoutthispaperweuseacosmologyinwhichH0=70
roundingICM(e.g.Hardcastleetal.1998c;Worrall&Birkinshaw kms−1 Mpc−1,Ωm=0.3andΩΛ=0.7.Unlessotherwisestated,
2000;Dunnetal.2005)whichindicatesthepresenceofapopula- errorsarequotedatthe1σlevel.
tionofnon-radiatingparticlestoboostthepressure.Crostonetal.
(2008) looked at the morphologies of a sample of FRI galaxies
and found that those where the jets were in direct contact with
2 SAMPLE
the ICMshowed a larger pressure deficit, suggesting that the ad-
ditional particles are likely to come from entrainment of mate- ThesampleconsistsofthelobesoftheFRIIgalaxiesinthesamples
rial from the ICM. Some detailed studies of local sources (e.g. ofradio-loudAGNatredshifts∼0.5and∼0.1usedinInesonetal.
Hardcastle&Croston 2010; Croston&Hardcastle 2014) use X- (2013,2015).Table1liststheFRIIgalaxiesusedinthisstudy,and
rayobservations toobtainupper limitsonthelobeICfluxwhich theirbasicproperties.Thetablesarearrangedwiththez∼0.1sub-
placeslimitsonthepopulationofrelativisticleptons.Thispopula- sampleprecedingthez∼0.5subsample,andwithinthesesubsam-
tionisinsufficienttoprovidetherequiredlobepressures,suggest- plesthesourcesintheindividual radiosurveysarelistedinorder
ing there must also be a significant population of baryons. Mea- ofRA.
MNRAS000,1–17(2016)
Thedynamicsand energeticsof FRIIradiogalaxies 3
Thetwosubsamplesareasfollows: We used radio maps to define the shapes of the radio lobes,
sothat wecould measure theradio and X-ray fluxfrom the syn-
• The ERA sample (0.4 < z < 0.6) is a subset of the sam-
chrotronandICemissionandestimatelobevolume.Again,these
ple used by McLureetal. (2004), which was taken from the
mapswereusedbyInesonetal.(2013,2015),andTable3contains
3CRR (Laingetal. 1983),6CE (Ealesetal. 1997; Rawlingsetal.
detailsoftheradiomaps,includingreferences.
2001), 7CRS (Lacyetal. 1999; Willottetal. 2003), and TexOx-
1000 (Hill&Rawlings 2003) radio surveys. It contains 21 FRII
sourcesrangingfrom3.5×1025 to4.8×1027 WHz−1 sr−1 inra-
4 ANALYSIS
dio luminosity. Of these, 15 are High Excitation radio Galaxies
(HERGs)and6areLowExcitationradioGalaxies(LERGs). Theaimoftheanalysiswastoinvestigatethelobedynamicsand
• The z0.1 sample (0.01<z<0.2) was taken from the 3CRR particlecontentbycomparingtheobservedandminimum(equipar-
survey (Laingetal. 1983) and the subsample of the 2Jy sur- tition)lobepressures,andthentousetheseresultstocomparecon-
vey (Wall&Peacock 1985; Tadhunteretal. 1993) defined by ditionswithintheradiolobeswiththoseofthesurroundingICM.
Dickenetal.(2008).Itcontains 32FRIIsources(23 HERGsand We needed therefore to find the internal lobe pressures, compare
9 LERGs), with radio luminosities between 1.2×1025 and 3.3× them with ICM pressures, and estimate a lower limit on the ad-
1026WHz−1sr−1. vancespeedsofthelobetips.
Tofindtheinternallobeconditions,weneededtoestimatethe
Anumberoflobeswereexcludedfromtheanalysisforprac-
lobevolume,radioflux(fromthesynchrotronemission)andX-ray
ticalreasons:becausethelobeimageswereincomplete–partially
flux(fromtheICemission).
off the chip or lying across chip boundaries; because they were
small in angular extent and masked by nuclear emission or by a
richICM;becausetheICMwasstrongandhighlydisturbedsothe
4.1 LobeshapesandICMpressures
resultswerehighlydependentonchoiceofbackground;orbecause
themapwasofpoorqualityorlowresolutionandthelobeshapes WeusedtheradiomapslistedinTable3tofindthepositionsofthe
couldnotbedefinedwithsufficientaccuracy.Inonecasethelobes lobetips,themid-point ofthelobesandestimatethelobeshapes
wereso largethat theyextended wellbeyond both themaximum andvolumes.Weexcluded thenucleus, jetsandhot-spots(which
detectedICMradiusandtheR overdensityradius,makingesti- willhavedifferent electrondensitiesand magneticfieldstrengths
200
matesoftheICMpressureproblematic.Table2liststhelobesthat from the lobes) and background X-ray sources. Where possible,
wereexcluded,andthepossibilityofbiasesinourconclusionsasa wemadeseparatefluxmeasurementsandvolumeestimatesforthe
resultoftheseexclusionsarediscussedinSection5.7.6below.This individuallobes.FortheERAsample,however,theX-rayfluxwas
left atotal sample of 37 FRIIgalaxies, 14from theERA sample generallyverylowsoweusedfluxesforthecombinedlobes.Also,
(11HERGs,3LERGs)and23fromthez0.1sample(19HERGs,4 forsomesourcestherewasnocleardivisionbetweenthetwolobes,
LERGs). soagainwecombinedthelobes.Detailsofthelobesarelistedin
Oneofthesourcesexcludedbecauseitliesinadisturbeden- Table5.
vironment,PKS2211−17(3C444),hasasurfacebrightnessdrop As can be seen from Table 3, we did not have a consistent
around the lobes. A detailed study of the source (Crostonetal. set of radio maps for the sources in the samples. When possi-
2011) shows cavities and a temperature drop corresponding to a ble,weusedmapsatthelowestavailablefrequency todefinethe
Machnumberof∼1.7.Wehaveincludedthissourceinthesection lobeshapes, volumesand excluded regions. However, ifthelow-
where we consider Mach numbers (Sections 5.3) but not in any frequencymapswereoflowresolution,weusedhigherfrequency
analysisbasedonlobeinternalconditions. maps to define the shapes, but checked with the low resolution
PKS0625−53wasclassifiedasanFRIIgalaxyinInesonetal. mapstoseeiftherewereanyregionsofextendedfluxmissingfrom
(2015). It was originally classified as having a Wide Angle Tail thehigherfrequencymaps.
morphology(Morgantietal.1999),andconsequentlyislikelytobe WethencalculatedtheICMpressures.InInesonetal.(2013,
anFRIgalaxy,butwaslaterlistedasanFRII(Dickenetal.2008). 2015), we fitted the ICM surface brightness profiles with ei-
WehavefollowedMingoetal.(inpreparation)andrevertedtothe ther single β models (e.g. Cavaliere&Fusco-Femiano 1976;
FRIclassification and soPKS0625−53 has not been included in Jones&Forman1984)or,whenthehostgalaxyextendedbeyond
thecurrentsample. thePSFfromthenucleus, double β modelswhich takealine-of-
Wherepossible,weanalysedthetwolobesfromeachsource sight projection of the single β models fitted to the two compo-
separately. However, as discussed inSection 4.1, thiswasnot al- nents(Crostonetal.2008).Hereweusedthosemodelstofindthe
ways possible so for some sources we combined the lobes. The electrondensityatthelobetipsandmid-points.Pressurewasthen
totalnumberoflobesinthesamplewas47.14werefromtheERA obtained following the methods of Birkinshaw&Worrall (1993)
sample(11HERGs,3LERGs)and33werefromthez0.1sample andCrostonetal.(2008),byconvertingtheelectrondensitytogas
(26HERGs,7LERGs). densityandapplyingtheidealgaslaw–forthisweusedtheICM
temperatures from Inesonetal. (2013, 2015) (Table5). The ICM
mid-lobeandlobetippressuresarelistedinTable5.
ThesepressuresaredependentontheICMtemperaturemea-
3 OBSERVATIONSANDDATAPREPARATION surementsandtheβ-modelfits.Sincepressurescaleswithtempera-
ture,errorsinthetemperaturewouldproduceproportionallysimilar
3.1 X-rayandradiodata
errorsinthepressure.Thetemperatureswereobtainedwherepos-
WeusedX-rayobservationstomeasurethefluxproducedbyICin siblebyspectralanalysis.Forthez0.1sample,thesehave1σerrors
theradiolobes.TheobservationscamefromChandraandXMM- thataremostlylessthan20percentofthecalculatedtemperature,
Newtonandwereprocessed duringprevious studies(Inesonetal. withthehighestbeing∼50percent.TheerrorsfortheERAsample
2013,2015).ObservationdetailsarelistedinTable3. tendtobelarger,with5sourcesat∼50−70percentandonesource
MNRAS000,1–17(2016)
4 J. Inesonet al.
(3C427.1)withanuppererrorof∼1.6timesthecalculatedtem- possible,weusedarectangleofthesamelengthasthelobe,start-
perature.Forsourceswherewecouldnotobtainatemperaturefrom ingatthesamedistancefromthenucleusasthelobeandextend-
thespectrum,weestimatedthetemperatureusingthetemperature- ing radially out from the nucleus. This method was suitable for
luminosityscalingrelationofPrattetal.(2009).Whenthespectral well-definedlobesindentednearthenucleus.Forsmalllobesand
temperaturewasknown,theestimatewasusuallycompatiblewith lobes where the emission spread about the nucleus, we modelled
itsotheestimatedtemperaturesareunlikelytobemuchinerror. thebackgroundusinganellipsesurroundingthelobe.
For the majority of the sources, the β-models are a good fit We modelled the IC emission in XSPEC, using a power law
to the surface brightness profiles. Thus if the electron density is coreectedforGalacticabsorption(WABS(POWER)).Wealsotried
being estimated within themaximum detected radius of theICM tofitathermalmodel(APEC)incasetherewasacontributionfrom
then it is likely be accurate. This is the case at mid-lobe for all theshockedICM,butthisonlygaveanimprovedfitforonesource
but 7 lobes, and 3 of those are less than 10 per cent beyond the –3C452.ThissourcehasbeenstudiedindetailbySheltonetal.
detectedradius.11lobeshavethelobetipbeyondtheICMdetected (2011)usinganXMM-Newtonobservation;weobtainedcompati-
radius (although 4 of these are less than 15 per cent beyond the bleresults.Wethenobtainedthefluxdensityat1keVbyrefitting
detectedradius).Thusthemajorityofthedensityestimatesshould themodelusingtheCFLUXcomponent convolvedwiththepower
beestimatedwellfromthesurfacedensityprofile. lawmodel.
Forthelobesexteningbeyondthemaximumdetectedradius, Weassumedforallsourcesthattheelectrondistributionfol-
thedensityestimatesdependonthequalityofthefitoftheβ-model lowedapowerlawwithanelectronenergyindexδ=2.4(spectral
extrapolation.Ifthisispoorthenthedensitycouldbeconsiderably indexα=0.7)andminimumandmaximumenergiesdefinedbythe
inerror.For9oftheselobes,thelower1σerrorboundiscloseto Lorentzfactorsγmin=10andγmax=105.Theseassumptionsare
zero.Theworstcaseis3C321,whichhassmalllobeswiththemid- discussedinSections5.7.2and5.7.3.
lobe position at nearly threetimesthe maximum detected radius, Forsomeofthesourceswithlowcounts,wecouldgetanac-
andisalsoinasparseICMwithasteepβ-modelwhichhaserrors ceptable fit from either a power law or a thermal model, but the
on both β and the core radius that cover most of their expected temperaturefromthethermalfitwasalwayslow–usuallylessthan
ranges.Ifwereplacetheβ-modelparametersfor3C321withthe theICMtemperature–sowasunlikely tobeacontributionfrom
medianvalues,whichgiveamuchlesssteepβ-model,thedensity shockedgas.Inthesecasesweusedthepowerlawfit.Itispossible
estimateisinceasedbyafactorof∼7. thattherecouldbeathermalcontributionfromtheICMduetoin-
Tosummarise,sincethemajorityofthelobesinoursamplelie completebackgroundsubtraction,particularlyforthesourceswith
withinthemaximumdetectedradiusoftheICM,theerrorsintro- lobe emission around the nucleus. Neglecting this could result in
ducedbyuncertaintiesintheICMtemperatureanddensityshould the power law normalisation being too high, leading to high flux
besmall.However,ICMpressureestimatesforthefewlobeslying andinternalpressureestimates.Wethereforelookedatthequality
wellbeyondthedetectedradiuscouldbesubstantiallyinerror. ofthebackgroundsubtractionforaselectionofsourceswithgood
powerlawfits,andfoundonlytwosourcesforwhichwecouldfit
alowtemperaturebackgroundcontribution–oneoftheselowered
4.2 Radioflux thefluxbyslightlymorethanthe1σerror;theotherhadamuch
smaller effect. This suggests that our background modelling was
Wemeasuredtheradiofluxdensitywithinthedefinedlobeshape
ingeneralgoodanderrorsinthemodellingshouldnothavemuch
withthenucleus,jetsandhot-spotsexcluded.Forthebackground,
effectonthelowcountsources.
weselectedaregionofsimilarlengthtothelobeinanareaofthe
Formanysources,therewereinsufficientcountstogetagood
mapclosetothelobebutoutsidethelobeemission.
fitforthepower law.ForthesewefollowedCrostonetal.(2005)
Since the the commonest map frequency was 1.4 GHz, we
in assuming a photon index of 1.5. If the photon index from the
usedmapsatthisfrequencywhenavailabletoobtaintheradioflux
fit was much different from this we fixed it at 1.5 and fitted the
density.Whenweonlyhadhigherfrequencymaps,weusedpub-
modeltoobtainthenormalisation.Iftherewereinsufficientcounts
lishedfluxdensitymeasurementsat408MHzfromtheMolonglo
ReferenceCatalogofRadioSources1 orat178MHzfromtheon- to fit the model, we used an unbinned spectrum with the photon
line3CRRcatalogue2.Nuclearandhot-spotemissionhasnotbeen indexagainfixedto1.5.Finally,ifthenetcountsinthelobewere
lessthanthreetimesthebackgrounderrorweusedthreetimesthe
excluded fromthesemeasurements, but thefluxmeasurements at
frequencies below ∼500 MHz are expected to be dominated by backgrounderrorasanupperlimitonthecountsandagainuseda
photon index of 1.5toobtain thenormalisation. Table6contains
lobe emission for the LERGs and NLRGs. We split the low flux
the radio and X-ray flux densities for the sources, together with
density measurements between the lobes in the same ratio as the
detailsofthepowerlawfitsfortheX-rayemission.
fluxdensitiesfromthehigherfrequencymeasurementsaswasdone
Inall,weobtainedagoodfitforthephotonindexfor23ofthe
by Crostonetal. (2005). The frequencies used for the radio flux
47lobes,andobtainedanormalisationwithanindexof1.5for18
densitymeasurementsaregiveninTable6.
lobes.WedidnotdetectX-rayemissionintheremaining6lobes.
4.3 X-rayflux
4.4 Internallobeconditions
To obtain the X-ray flux densities, we generated spectra for the
WeusedtheradioandX-rayfluxdensities,togetherwiththelobe
lobesusingSPECEXTRACT.Forthebackground,weneededtosam-
volumes,toobtaintheequipartitionandobserved(inverseComp-
pleregionsoftheX-raybackgroundandICMrepresentativeofthe
ton)magneticfieldsandelectronenergydensities.Forthiswefol-
loberegion,andinsomecases,thewingsoftheAGNPSF.Where
lowed the method described by Crostonetal. (2005), using the
SYNCH code (Hardcastleetal. 1998a) to find the magnetic and
1 http://vizier.cfa.harvard.edu/viz-bin/VizieR?-source=VIII/16 electronenergydensitieswithinthelobes.SYNCHmodelsthepop-
2 http://3crr.extragalactic.info/ ulationofrelativisticelectronsexpectedfromtheinputradiospec-
MNRAS000,1–17(2016)
Thedynamicsand energeticsof FRIIradiogalaxies 5
trum,calculatingtheequipartitionconditionsandtheICX-rayflux inTable7–thevalueforeachsourceisthesumoftheindividual
expectedfromthesynchrotronandCMBphotonfields.Havingde- jetpowersforthatsource.Theerrorswereobtainedbypropagating
finedtheequipartitionconditions,theusercanthenmodifythelobe theinternallobepressureandtheMachnumbererrors.
magneticfield,iteratinguntilthepredictedX-rayfluxmatchesthe ThelobetipMachnumbervariesduringthelifetimeofthera-
observed flux within the lobe. The electron density from SYNCH diojets–thisisdescribedbrieflyinSection5.3andinmoredetail
then gives the magnetic field strength and internal lobe pressure. in, for example, Hardcastle&Krause (2013) – so the timescales
Themodelassumesthattheparticlecontentofthelobesisdomi- calculatedhereareestimates.Moreaccurateestimatescouldbeob-
natedbyrelativisticelectrons:thisassumptionisdiscussedinSec- tainedbytakingintoaccount howtheMachnumbersvaryduring
tion5.1. thelifetimeofthesource.
Table 7 contains the equipartition and observed magnetic
fieldsandpressureswithinthelobes.Thequotederrorsontheob-
served fieldand pressure are derived from theX-ray flux density
error,sodonotincludethesystematicerrorsdiscussedbelow(Sec- 5 RESULTSANDDISCUSSION
tion5.7).
5.1 Deviationfromequipartition
Figures 1 and 2 show the ratio between the observed (IC) and
4.5 Lobe-tipMachnumber
equipartitionmeasurementsofthemagneticfieldstrengthsandof
Wethenusedacomparisonoftheinternalandexternallobepres- the total internal energies for the sample, with and without the
sures at the tip to estimate the lobe tip Mach number M using upper limits. The observed magnetic field strength is lower than
theRankine-Hugoniotconditions,whicharederivedfromthecon- theequipartitionfieldstrengthfor allsources, suggesting thatthe
servationofmass,momentumandenergyacrossthediscontinuity lobescontainelectronenergydensitiesgreaterthanwouldbeim-
(e.g.Worrall&Birkinshaw2006).Usingtheequationforthespeed plied by the minimum energy condition. All lobes are however
of sound inanideal gas, assuming equal pressurethroughout the within one order of magnitude of equipartition in terms of field
lobeinterior,andassumingthattheshockedshellsurroundingthe strengthwithamedianratioofobservedtoequipartitionfieldsof
lobe isinpressure balance withthelobe sothat the internal lobe 0.4.Hardcastleetal.(2002)andCrostonetal.(2005)foundsimilar
pressurecanbeusedasaproxyfortheshockedgaspressure,this results;wehavenowconfirmedthesewithalarger,morerepresen-
gives tativesample.
Similarly, the observed internal energy is higher than the
equipartition internal energy for all sources and all the observed
1 P
M2= (Γ+1) i −(1−Γ) (1) energiesarewithinoneorderofmagnitudeoftheequipartitionen-
2Γ Po ! ergies.Themedianoftheratioofobservedtoequipartitioninternal
whereΓistheadiabaticindex(5/3foramonatomicgas),andP and energies is 2.4. As with all the calculations in this chapter, these
i
Po arethepressuresinsideandoutsidethelobe.Asnoted above, resultsassume that there are no protons inthe lobes and that the
thejetrampressureisnotincludedinthecalculationsoM willbe lobesarecompletelyfilledwithsynchrotron-emittingparticles.As
alower limit–thisisdiscussed inSection5.7.9. Inaddition, the discussed by Crostonetal. (2005), the relativelyclose agreement
lobe internal pressure calculations assume that there are no non- betweentheequipartitionandobservedmagneticfieldscalculated
radiatingparticles(e.g.protons)inthelobes.Iftherewereasignif- assumingthelobesaredominatedbyrelativisticelectronssuggests
icantprotonpopulation,thiswouldalsoincreasetheinternalpres- thatthelobesarenotenergeticallydominatedbyprotons.Ifthere
sureandconsequentlytheMachnumber. wereprotons inthe lobes, the observed internal energy would be
TheMachnumbersareincludedinTable7.Theerrorswere higherthanthevaluescalculatedhereandthelobeswouldbemore
obtained by propogating the internal and external lobe pressure over-pressuredrelativetotheexternalenvironment.
errors, which in their turn come from the X-ray flux density er-
rors and the Bayesian estimates of the ICM β-model parameters
(Inesonetal.2015)respectively.
5.2 Lobepressurebalance
Wehaveexcluded sources withupper limitsfor theexternal
ICMpressurePo.Notethatbecausenearlytwo-thirdsofthelowlu- Figure3showstheobservedpressureplottedagainsttheexternal
minosityLERGsinouroriginalsamplesareFRIsources,wehave pressureatthelobetipandatmid-lobe.Pressurebalanceisshown
Machnumbersforonly6LERGsources(9lobes,including2with as a dotted line. If the lobes are growing they should be over-
upperlimitsforP). pressured atthetip,andthisisthecaseforall thesources inour
i
sampleexcept 3C 326(whichhasthelargestlobesinour sample
byseveralhundredkpc,sotheexternalpressureisfromanextrap-
4.6 Jetpower olatedβ-model).Sincetheeffectsofthejetrampressurehavenot
been included, the internal lobe-tip pressure will be higher than
Having obtained the Mach number, we calculated the speed of
the observed lobe pressure calculated here, and so the observed
soundintheICMusingcs= ΓmkT wherekistheBoltzmancon- pressures at the tip should be regarded as lower limits. The true
q
stant,andtheparticlemassmis0.6timesthemassofthehydrogen tippressure could plausibly beabove pressure balance forall the
atom (Worrall&Birkinshaw 2006). This then gives the advance sources.Ourmedianlobe-tippressureratioof4.3lieswellwithin
speedofthelobeand,fromthelengthofthejet,anestimateofτ, therangefoundinthesimulationsofHardcastle&Krause(2013);
theageofthejet.AssumingtheworkdoneindisplacingtheICM our spread is greater but we have a wider range of environments
issimilar totheinternal energy of thelobe(Hardcastle&Krause thanwereusedinthesimulations.
2013,2014),thetime-averagedjetpoweristhenQ ∼2E/τwhere Atmid-lobe,thelobesaredistributedaboutthepressurebal-
jet i
Ei istheinternalenergydensityofthelobe.Jetpowersarelisted ancelinewithamedianPobs/Pextof1.8–Crostonetal.(2005)and
MNRAS000,1–17(2016)
6 J. Inesonet al.
16 16
HERG HERG
LERG
14 14 Median
12 12
10 10
es es
c c
our 8 our 8
o. s o. s
N N
6 6
4 4
2 2
0 0
0.2 0.5 1 0.2 0.5 1
Observed/equipartition magnetic field Observed/equipartition magnetic field (no lower limits)
Figure1.Theratioofobserved(calculatedfromtheICemission)toequipartitionmagneticfieldstrengths,separatedintoexcitationclasses.HERGsareshown
insolidblack,LERGsshaded.Thedottedlineshowsthemedianratio.Thelefthistogramincludesallsources;therighthistogramexcludeslowerlimits.
16 16
HERG
LERG
Median
14 14
12 12
10 10
es es
c c
ur ur
o. so 8 o. so 8
N N
6 6
4 4
2 2
0 0
1 10 1 10
Observed/equipartition internal energy Observed/equipartition internal energy (no upper limits)
Figure2.Theratioofobserved(calculatedfromtheICemission)toequipartitioninternalenergiesforthelobes,separatedintoexcitationclasses.HERGsare
showninblack,LERGsshaded.Thedottedlineshowsthemedianratio.Thelefthistogramincludesallsources;therighthistogramexcludesupperlimits.
Belsoleetal.(2007)alsofoundFRIIlobestobenearpressurebal- contain non-radiating particles such as protons to provide addi-
anceatmid-lobe.Thelowestratioofobservedtoexternalpressure tionalpressure.However,althoughweusedthesameobservations
is0.18for3C326,whichalsohasthelowestlobe-tippressureratio. forthesesourcesasBelsoleetal.(2007),weobtainedlowerexter-
Thereareonlythreelobesmorethanoneorderofmagnitudeabove nalpressures,andalthoughthesetwoLERGsoccupyricherenvi-
pressurebalance. ThelowerlimitPKS0034−01 (Pobs/Pext=41) ronmentsthananyoftheHERGsinoursample,ourpressureratios
hassmalllobes(42kpclong)somaybeayoungsource.3C321, forthemdonotstandoutfromtherestofthesample.
which has very high pressure ratios of well over 100, has small Thelowestpressureratiolobesinoursamplearealsofroma
lobes(50and90kpclong) 280kpcfromthenucleus. Itismerg- LERG source (3C 326), although the pressure ratios of the other
ingwithaneighbouring galaxyandisinadisturbedenvironment LERG sources (except the lower limit PKS 0034−01 mentioned
(Evansetal.2008).Theβ-modelhassteep,poorlyconstrainedpa- above)liewithintherangeofresultsfortheHERGs.Themedian
rameters, giving very low ICM pressures at mid-lobe and so the pressureratiosare1.9and0.9fortheHERGsandLERGsrespec-
extrapolationofthemodeltoobtaintheexternallobepressuresis tively and a median test shows no evidence for a difference be-
likely tobe imprecise. Asdiscussed inSection 4.1, replacing the tween the HERG and LERG mid-lobe pressure ratios (χ2 =0.7,
β-model parameters withthe median model parameters increases p=0.4).Ourpressureestimatesassumethattheradiatingparticles
themid-lobeexternalpressureestimateconsiderably. inthelobesareleptons;thefactthatourLERGresultsdonotstand
Belsoleetal. (2007) had only two LERGs in their sample out from the HERG results suggests that the two types of radio
(3C427.1and3C200),butfoundthatbothoftheseappearedun- galaxyhavesimilarlobecontents,andthereforethattheapparent
derpressured at mid-lobe, giving the possibility that LERG lobes differenceinFRIandFRIIparticlecontentdiscussedinSection1
MNRAS000,1–17(2016)
Thedynamicsand energeticsof FRIIradiogalaxies 7
isrelatedtolarge-scalemorphologyandenvironmentalinteraction For example, the highest Mach number in the examples listed in
ratherthandifferencesincentralengine. Section1(8.4,Crostonetal.2009)comesfromtheinnerlobesof
Ourresultsthereforeshownoevidenceofasystematicdiffer- CentaurusA,whichareonlyafewkpclong.
encebetweenHERGandLERGlobes,butitshouldbenotedthat, Takingthesepointsintoaccount,itisunderstandablethatthe
sincethemajorityofFRIIgalaxiesinoursampleareHERGs,there Machnumbersforour matureFRIIsampleshouldhaveasimilar
areonly10LERGlobes(including3upper limits)inour sample rangetothoseobservedinlocalFRIgalaxies.
of44lobes.
5.3.2 HERG/LERGsubsamples
5.3 LobetipMachnumber OurHERGsubsamplehasawiderrangeofMachnumbersthanthe
LERGsubsample,andthemedianMachnumberfortheLERGsis
TheMachnumbersareplottedinFigure4.AsmentionedinSec-
lowerthanthatoftheHERGs.However,amediantestdoesnotre-
tion4.5,these Mach numbers neglect the jetram pressure. How-
jectthenullhypothesisthatthemediansarethesame(χ2=0.26,
ever,wediscussthepossiblemagnitudeoftherampressureinSec-
p=0.6),andasmentionedabove, thisgivesusnoreasontosup-
tion5.7.9andconcludethatitislikelytobesmallcomparedwith
pose that the lobes of the two types of radio galaxy should have
thelobeinternalpressure.WethereforeregardtheseMachnumbers
differentdynamics.ThedifferenceinrangeofMachnumbersprob-
asareasonableestimateofthetruevalue. Ourresultsfor3C452
ablyreflectsthedifferentdistributionofenvironments(Inesonetal.
aresimilartothoseofSheltonetal.(2011),whoobtainedaMach
2015).
numberof1.6forthecombinedlobesofthatsource.
The two lobes with Mach numbers greater than 10 are both
from 3C 321, which, as mentioned above, has very low, uncer-
5.3.3 Particlecontent
tain ICM pressures. Replacing the ICM pressures with pressures
estimatedusingthemedianβ-modelparametersreducestheMach As stated before, these Mach numbers assume that the lobes do
numbersofthetwolobesto∼5and∼7–stillhighbutnotunrea- not contain protons. Thepresence of asignificant proton popula-
sonable.Wehavenotincluded3C321inanyfurtherplots,butall tionsuchasisthoughttoexistinFRIlobeswouldincreasethelobe
statisticshavebeencalculatedwithandwithout3C321. internalpressuresubstantially.Wethereforelookedattheeffectof
Without 3C 321, themaximum Mach number is4.8and the aten-foldincreaseininternalpressureonourmedianMachnum-
medianis1.8,sotheresultsofourlargesampleliewithinthoseof ber andfound that thiswould raiseit to5.7–near thetopof the
theindividualandsmall-samplestudieslistedinSection1–ofthe range of Mach numbers found in the observational studies listed
eightexampleslistedthere,onlytwosourceshavelobesadvancing in Section 1. It is unlikely that our sample median would be so
atmorethanMach2.Ourmedianalsolieswithintherangeofsim- highcompared withtheMachnumbers calculated fromobserved
ulation results of Peruchoetal. (2014) for well developed lobes, shocks,whichwouldsuggest thatanyprotoncontentislowcom-
supportingtheirchoicesofconditions. paredwiththatofFRIlobes.
5.3.4 Machnumberandradioluminosity
5.3.1 MagnitudeoftheMachnumber
It would be useful if the lobe dynamics, and consequently ener-
Themajorityoftheexamples inSection1areFRIgalaxies, with
getic input could be inferred directly from the radio and/or envi-
twoofmixedmorphologyandonlyonepureFRII.Itmightbeex-
ronmentproperties.Asafirststepwesearchedforanyrelationship
pected that the more powerful FRII galaxies should have higher
between radio luminosity and Mach number (Figure 5). The plot
Mach numbers, but both backflowing plasma and changes in jet
shows no sign of acorrelation, and this isconfirmed by a gener-
direction would disperse the jet momentum over a wider region
alisedKendall’sτtest(Table8).
than thejet radiusand would reduce the Mach number fromthat
expected for a static jet. Evidence that the latter process is com-
monplaceisfoundinobservationsofmultiplehot-spotsandofoff-
5.3.5 MachnumberandICMrichness
setsbetweenthehot-spotsatdifferentfrequencies(e.g.Laing1981;
Hardcastleetal.2007),andMingoetal.(inpreparation),looking We then compared Mach number with ICM richness (Figure 7,
attheextendedemissioninthe2Jysources,foundseveralexamples left),usingtheICMX-rayluminositiesfromTable5.Inthiscase
inthesourcesusedinthisstudy. Machnumber appearstodeclinewithincreasingICMluminosity
WhencomparingthepropertiesofFRIandFRIIradiogalax- fortheHERGsubsample, whiletheLERGsourcesarelimitedto
ies,italsoneedstoberememberedthat,asmentionedinSection1, abandofICMluminositiesatlowMachnumber.Thegeneralised
FRIgalaxiesarethoughttoentrainmaterialfromtheICMwiththe Kendall’s τtests(Table 8) show astrong negative correlation for
amountofentrainmentbeingrelatedtotherichnessoftheenviron- boththefullsampleandtheHERGsubsample.Thecorrelationis
ment. Thisintroduces anon-radiating proton population, increas- weakened slightlywhentheuncertain 3C 321Mach numbers are
ingtheinternalpressureofthejetandresultinginanFRIgalaxy removed, but isstillstrong. There isquite substantial scatter –at
having a higher jet power than an FRII galaxy of the same radio leastsomeofthisislikelytobeduetosystematicerrorswhichare
luminosity.ThusitistobeexpectedthatFRIIMachnumberswill discussedinSection5.7below.
ingeneralbelowerthanthoseofFRIswithsimilarluminosities. ItmustbenotedhoweverthatICMexternalpressurewasused
Inaddition,theexpansionspeedofaradiolobewilldependon intheMachnumberestimates.Ascanbeseenfromtheright-hand
itsstageofevolution(e.g.Heinzetal.1998;Hardcastle&Krause plotinFigure7,lobe-tipexternalpressurecorrelatesverystrongly
2013).Thejetextendsrapidlyinitsearlystagesbeforeexpanding withICMluminosity.Sincebothfactorshaveadependenceonred-
sideways as the shocked material at the tip starts to spread. The shift,weusedapartialKendall’sτtesttoconfirmthatthecorrela-
Machnumber isthereforeexpectedtobehighforyoungsources. tionwasnotdrivenbyredshift(Table8).
MNRAS000,1–17(2016)
8 J. Inesonet al.
10−11 10−11
a) a)
P P
e ( e (
ur ur
ess10−12 ess10−12
pr pr
e e
b b
o o
C) l C) l
d (I10−13 d (I10−13
e e
v v
er er
Obs z0.1 LERG Obs z0.1 LERG
z0.1 HERG z0.1 HERG
10−14 EERRAA LHEERRGG 10−14 EERRAA LHEERRGG
LERG u/l LERG u/l
HERG u/l HERG u/l
Pext=Pobs Pext=Pobs
10−15 10−14 10−13 10−12 10−11 10−15 10−14 10−13 10−12 10−11
External lobe-tip pressure (Pa) External mid-lobe pressure (Pa)
Figure3.Internallobepressurevsexternal(ICM)pressure,atthelobetip(left)andatmid-lobe(right).EmptysymbolsareLERGs,withdiamondsshowing
thez0.1samplesourcesandcrossestheERAsources.BlacksymbolsareHERGswithcirclesshowingthez0.1sourcesandstarstheERAsources.Arrows
denoteupperlimits.
16
HERG z0.1 LERG
HERG u/l z0.1 HERG
14 LERG ERA LERG
LERG u/l ERA HERG
Median LERG u/l
HERG median HERG u/l
12 LERG median 10 z0.1 HERG
p
10 be ti
No. sources 8 number at lo
6 h PKS 2211-17
c
a
M
4
1
2
0
1 10 0 0.1 0.2 0.3 0.4 0.5 0.6
Mach no. at lobe tip Redshift
Figure4.Ontheleft,Machnumberatthelobetip.HERGsareshowninsolidblackandLERGsshaded,HERGupperlimitsaresolidgrey,LERGupper
limitsarewhite.TheHERGandLERGmedianMachnumbersareshownbydashedanddash-dottedlinesrespectively,andtheoverallmedianbythedotted
line.Ontheright,Machnumberatthelobetipplottedagainstredshift.SymbolsasinFigure3.ThetwoMachnumbersgreaterthan10arefromthelobesof
3C321,discussedinSection5.3
Itseemslikelythatlobe-tipexternalpressureisthefactordriv- Machnumberandenvironmentrichness,butmoreworkisneeded
ing the correlation between Mach number and ICM luminosity. toeliminatepotentialconfoundingfactors.
However, ICM temperature is related to ICM luminosity and is
also used in the pressure calculations so is a potential confound-
Thatthereshouldbesomedependenceoflobeadvancespeed
ing factor. Temperatures were obtained wherever possible from
onthedensityoftheenvironmentistobeexpectedandsoitseems
the ICM spectrum, but when there were insufficient counts they
reasonablethatalobeinaweakenvironmentshouldadvancemore
were estimated using the luminosity-temperature scaling relation
quicklythanoneinarichenvironment.However,theenvironment
of Prattetal. (2009). Wetherefore removed these estimated tem-
densityreduceswithdistancefromthecentreofthecluster.Inthe
peraturesfromthesampleincasetheybiassedtheresults;thecor-
simulations discussed in Hardcastle&Krause (2013), the jet ini-
relation between Mach number and luminosity was considerably
tiallyextendsrapidlyandthenslowsasitstartsforminglobes.Then
weakenedbutwasstillpresent(Table8).Thenwecheckedtosee
asthejettipreachesthesparserenvironmentbeyondtheICMcore
ifMachnumberwasrelatedtothespectrum-derivedICMtemper-
radiusitspeedsupagain.Thusevenifallotherfactorsremainthe
atures.AscanbeseenfromFigure6,thereisnosignofacorre-
sametheMachnumberwillnotbeconstantthroughoutthelifeof
lation.Thusitseemspossiblethatthereisarelationshipbetween
theradiogalaxy.Moreworkisthereforeneededtolookathowthe
Machnumbersofjetsinenvironmentsofdifferentrichnesschange
MNRAS000,1–17(2016)
Thedynamicsand energeticsof FRIIradiogalaxies 9
5 jet powers found by Bîrzanetal. (2008),Cavagnoloetal. (2010)
z0.1 LERG
z0.1 HERG andO’Sullivanetal.(2011),andhaveaverysimilarrangetothe
EERRAA LHEERRGG FRII sample of Godfrey&Shabala (2013) and the lower regions
LERG u/l ofthesampleofpowerfulFRIIsofDalyetal.(2012).Oftheseven
4 HERG u/l
sources we have incommon withGodfrey&Shabala (2013) and
p Dalyetal. (2012), we obtained similar Qjet estimates for all but
e ti onesource(3C321–seeSections5.2and5.3).
b
o 3
at l InFigure8(right)weshowtherelationshipbetweenjetpower
o. andradiopower.Acorrelationisexpectedasthetwoquantitiesare
n
ch not completely independent: thejet power estimateshave acom-
a
M 2 plicateddependenceonthemeasuredradiofluxandredshift.How-
PKS 2211-17 ever, weare interestedin comparing the jet power measurements
andtheslopeandnormalisationoftherelationwithothermethods.
Wefindastrongcorrelationinthepresenceofacommonrelation-
1 shipwithredshift(z=4.11,p<0.0001–Table8).Sincetherewere
onlytwoupperlimits,weexcludedtheseandcalculatedtheregres-
1025 1026 1027 sionlineusingtheBCESregressionmethod(Akritas&Bershady
Radio luminosity (W/Hz/sr)
1996) so that we could include the efect of the calculated errors.
ThisgaveQ =5×1039L0.89±0.09whereQ isinWattsandL
Figure5.Radio luminosityplotted againstMachnumber.Symbolsasin jet 151 jet 151
is the 151 MHz radio luminosity in units of 1028 W Hz−1 sr−1.
Figure3.
Willottetal.(1999),assumingtheFRIIlobeswereself-similarand
atminimumenergy,obtainedtherelation Q =3×1038f3/2L6/7
jet 151
where f is a factor expected to depend on the properties of the
z0.1
5 ERA sourceanditsenvironmentandpredictedtoliebetween1and20.
ThusourQ −L relationshiphasaverysimilarslopetothatob-
jet 151
tainedbyWillottetal.,butitrequires f ∼6.5tomatchthenormal-
isation.Dalyetal.(2012)foundafactorof f ∼4fortheirsample
4
of FRII galaxies, and Turner&Shabala (2015) found that a fac-
torof f =5wasneededtofittheirdynamicalmodelresultstothe
no. theoreticalmodel.
ch 3
a Since the equation derived by Willottetal. (1999) assumed
M
minimum energy conditions for the lobes, which give very simi-
lartotalinternalenergiestotheequipartitionconditions,wecalcu-
2 latedthejetpowersresultingfromanassumptionofequipartition
PKS 2211-17 andobtainedaregressionlineQ =2×1039L1.0±0.07.Thediffer-
jet 151
enceinthenormalisationsofourtworelationsiscompatiblewith
1 ourmedianratioofobservedtoequipartioninternallobeenergyof
2.38.Thenormalisationforourequipartitionequationishowever
1 10 stillhigherthanthatofWillottetal.byafactorof6.7(f ∼3.5).
Temperature (keV)
Another potential contribution to f comes from the viewing
Figure6.MachnumbervsICMtemperatureforthesourceswithtempera- angleofthelobes;assumingthisisrandomgivesameanfactorof
turescalculatedfromtheICMspectrum.Solidsquaresaresourcesfromthe ∼1.4(Willottetal.1999)andreducestheunexplainedcontribution
z0.1sampleandemptysquaresfromtheERAsample. to f to∼2.5.
At least some of this can be attributed to the environments
of the radio galaxies. Willottetal. (1999) use a sample of rela-
asthelobesgrowandage,andhowtheyareaffectedbyotherfac-
tivelydistantquasarswhichhaverelativelyrichenvironments;us-
torssuchasjetpower.
ing a particle density more typical of low redshift FRII galaxies
Ifthisnegativecorrelationisgenuine,itwillhavecontributed reducestheirestimateoftheageofthesystembyafactorof∼0.5,
to the lack of high Mach number LERGs – since ICM luminos-
thusincreasingthejetpowerbyafactorof2.Hardcastle&Krause
itycorrelateswithradioluminosityforLERGs(Inesonetal.2013,
(2013) report a similar dependency on environment in their sim-
2015)andthelowradioluminosityLERGsmostlyhaveFRImor-
ulations. Although the slope of their time/jet length relationship
phology,theLERGlobesremaininginthesampleareforthemost
eventually matches the slope of the theoretical relationship used
part in relatively rich environments and so would be expected to
by Willot et al, the normalisation is dependent on the properties
havelowMachnumbers.
oftheICM.Willottetal.useasimplepowerlawrelationshipfor
the change in ICM density with radius rather than the now more
commonly usedisothermal β-model, sotheir time/jet-lengthrela-
5.4 Jetpower
tionshipdoesnotincludetheeffectsofthechangesinICMdensity
Figure8(left)showsjetpower plottedagainst redshift.Sincethe profilearoundthecoreradius.Soforasourcewithβsimilartoour
sample istaken fromflux-limitedsurveys, thestrong redshift de- median(andtothevalueofβusedbyWillotetal.),Hardcastleand
pendence is expected. Our jet powers, being for FRII morphol- Krausseobtained sourceagesclosetothetheoreticalrelationship
ogysources, lieinandabove theupper partof theranges ofFRI fortheir80kpccoreradiusbuttheagewasreducedbyalmostone-
MNRAS000,1–17(2016)
10 J. Inesonet al.
5
z0.1 LERG z0.1 LERG
z0.1 HERG 10−11 z0.1 HERG
ERA LERG ERA LERG
ERA HERG ERA HERG
LERG u/l LERG u/l
HERG u/l HERG u/l
4
a)
e (P10−12
ur
Mach no. 3 be-tip press10−13
o
al l
2 n
PKS 2211-17 xter
E10−14
1
10−15
1041 1042 1043 1044 1045 1041 1042 1043 1044 1045
ICM luminosity (erg/s) ICM luminosity (erg/s)
Figure7.ICMX-rayluminosityplottedagainstMachnumber(left)andlobe-tippressure(right).SymbolsasinFigure3.
thirdfora40kpccoreradius–themedianforoursample–which ted in Figure 9. Note that 3C 321, which has two small lobes a
wouldraisethejetpowerbyafactorof1.5. great distance from thenucleus, hasbeen excluded –the ratioof
However, the normalisations obtained in the simulations in- lobe length to lobe tip distance for the rest of the sample ranges
cludetheeffectoftheinitialrapidgrowthofthejet,which,asdis- from0.18to0.25whereasthoseforthe3C321lobesare0.05and
cussedinHardcastle&Krause(2013),isnotmodelledaccurately, 0.08.
sothisfactorof1.5maynotbeaccurate.Butthesesimulationsdo Thereisaclear correlation betweenthetwofactors. Theer-
confirmthatthejetagesofFRIIgalaxiesinweakerenvironments rorsareunknownbutarepresentinbothfactors,sowecalculated
thanthoseusedbyWillottetal.(1999)arelikelytobeshorterthan Ordinary Least Squares (OLS) regression lines for both volume
theirtheoreticalpredictionandsowillcontributetoourhighernor- vslengthandlengthvsvolumeandtookthebisector (Isobeetal.
malisationoftheQ −L relationship.Also,sinceourcoreradii 1990) – this gives V ∝L2.51±0.02. The three regression lines are
jet 151
coverawiderange(seeTable4),thedifferencesinthedistancethat shown in Figure 9. They all have a slope of less than 3 which
thejettravelsbeforetheICMdensitydropswillcontributetothe suggeststhelobesdeviateslightlyfromself-similarity.Departures
scatterinourrelationship. fromself-similarityhavealsobeenreportedbyMullinetal.(2008),
OurestimatesofjetagearebasedonthecurrentMachnum- whofoundthattheaxialratioreduceswithincreasinglobelength.
berofthelobetipandsodonottakeintoaccounteithertheearly This result fits with our previous results showing that the lobes
growthofthejetorthevariationsduetotheICMdensityprofile. areonly partiallyover-pressured, and once again supports Model
Nevertheless,ourestimatesofjetpowerfromlobeinternalenergy C from Scheuer (1974). It also supports the simulation results of
andlobe-tipMachnumber producea Qjet−L151 relationshipthat Hardcastle&Krause(2013).
issimilartothetheoreticalrelationshipdevelopedbyWillottetal.
oncetheeffectsofthehigherelectronenergydensitiesandthedif-
ferentrichnessoftheICMenvironmentshavebeentakenintoac-
count.
5.6 Implications
We caution that radio luminosity isonly expected, from nu-
mericalmodelling,toberoughlyconstantwithtimeoncethesource As found by other researchers (e.g. Hardcastleetal. 2002;
hasgrowntoasizecomparabletothehostenvironmentcoreradius Isobeetal. 2002; Crostonetal. 2004; Isobeetal. 2005;
(e.g. Heinzetal. 1998; Hardcastle&Krause 2013; Englishetal. Kataoka&Stawarz 2005; Crostonetal. 2005), the internal
2016). During the early stages of a source’s evolution the radio energies and pressures of the lobes are near but slightly above
luminosity must necessarily depend on source age as well as jet equipartition, reflecting the contribution of a higher electron
power.Thenatureofourselectionmeansthatwearebiasedagainst density than required by the minimum energy conditions. If
small, young, faint sources and so we would expect to recover a there were a sizeable population of non-radiating particles in the
simplejetpower/radioluminosityrelationshipinoursample. lobes, as typically seen in FRI radio galaxies (e.g. Crostonetal.
2008),wewouldexpectalargerdeparturefromequipartition(e.g.
the electon energy densities in FRI lobes are typically a large
factorbelowequipartition).Thelobeswereallwithinonedecade
5.5 Lobevolumes
of equipartition, which suggests both that there is not a large
Finally, we compared the length and volume of the radio lobes. populationofenergeticprotonsandthatthefillingfactormustbe
If the lobes are self-similar, V ∝L3 where V is the lobe volume close to unity. Importantly, this means that (i) inverse-Compton
and Litslength(Kaiser&Alexander 1997);ifhowever thelobes analysisprovidesareliablemeasureofthetotalinternalenergyfor
arebeingpartiallymodifiedandconstrainedbytheICM,thenself- individual FRIIradiogalaxies, and(ii) for samplesof FRIIradio
similaritywouldbebroken(Hardcastle&Krause2013). galaxies without X-ray data, the total energy (and magnetic field
Theaveragelobelengthandvolumeforeachsourceareplot- strength)canbeestimatedreliablyfromradioobservationsalone,
MNRAS000,1–17(2016)