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Mon.Not.R.Astron.Soc.000,1–6(2015) Printed6March2015 (MNLATEXstylefilev2.2) Hadronic models of blazars require a change of the accretion paradigm Andrzej A. Zdziarski1 and Markus Bo¨ttcher2,3 5 1CentrumAstronomiczneim.M.Kopernika,Bartycka18,PL-00-716Warszawa,Poland 1 2CentreforSpaceResearch,North-WestUniversity,Potchefstroom2520,SouthAfrica 0 3AstrophysicalInstitute,DepartmentofPhysicsandAstronomy,OhioUniversity,Athens,OH45701,USA 2 r a Accepted2015March5.Received2015March3;inoriginalform2015January24 M 5 ABSTRACT Westudyhadronicmodelsofbroad-bandemissionofjetsinradio-loudactivegalacticnuclei, ] andtheirimplicationsfortheaccretioninthosesources.Weshowthatthemodelsthataccount E for broad-band spectra of blazars emitting in the GeV range in the sample of Bo¨ttcher et H al. have highly super-Eddington jet powers. Furthermore, the ratio of the jet power to the . radiativeluminosityoftheaccretiondiscis 3000onaverageandcanbeashighas 105. h ∼ ∼ p Wethenshowthatthemeasurementsoftheradiocoreshiftforthesampleimplylowmagnetic - fluxesthreadingtheblackhole,whichrulesouttheBlandford-Znajekmechanismtoproduce o powerfuljets. These results require that the accretion rate necessary to power the modelled r jets is extremelyhigh, and the averageradiativeaccretion efficiencyis 4 10 5. Thus, if t − s the hadronic model is correct, the currently prevailing picture of accre∼tion×in AGNs needs a tobesignificantlyrevised.Also,theobtainedaccretionmodecannotbedominantduringthe [ lifetimesof the sources, as the modelledveryhigh accretionrates wouldresult in too rapid 2 growthofthecentralsupermassiveblackholes.Finally,theextremejetpowersinthehadronic v modelareinconflictwiththeestimatesofthejetpowerbyothermethods. 4 2 Keywords: accelerationofparticles–galaxies:active–galaxies:jets–ISM:jetsandoutflows– 1 quasars:general–radiationmechanisms:non-thermal. 6 0 . 1 0 1 INTRODUCTION efficiently.Still,thosehadronsintheleptonicmodelsusuallydom- 5 inatethekineticluminosityofjets(e.g.,Ghisellinietal.2014). 1 : The most commonly considered models of broad-band emission Sikoraetal. (2009) and Sikora (2011) have shown that the v ofradio-loudjetsinAGNsutilizeemissionofrelativisticelectrons hadronicprocessesareveryinefficient.Thisimpliesthat,iftheto- i X andpositronsviasynchrotronandComptonprocesses.Theselep- taljetpowerisapproximatelylimitedbytheEddingtonluminosity, tonicmodelshavebeenhighlysuccessfulinreproducingthespec- thehadronicmodel canberuledout inmanycases. Ontheother r a traandtimevariabilityofblazarsandradiogalaxies,thoughthere hand, Bo¨ttcheretal.(2013)(hereafterB13) havesuccessfully ap- aresomephenomena,suchastheirextremelyshortvariabilitytime pliedhadronicmodelstoasampleofradio-loudAGNscircumvent- scales,insomecasesdowntoafewminutes(Aharonianetal.2007; ing this constraint by allowing the jet power to be highly super- Albertetal.2007),thatarenotreadilyexplainedbythem. Eddington.Herewediscussconsequencesofthissupposition. Thealternative,andquitepopular,modelisbasedonhadronic (or lepto-hadronic) processes (e.g.,Mannheim&Biermann1992; Mu¨cke&Protheroe2001;Aharonian2000).Itutilizesemissionof 2 ANALYSISOFTHESAMPLEOFB13 extremely relativistic ions, mainly due to proton-synchrotron and Westudyherethesampleof12blazarsofB13.Theirbroad-band photo-pionproductionprocesses,toexplainthehigh-energyemis- spectrawerefittedbythembyleptonicandhadronicmodels,and sionfromjet-dominatedAGNs.Thelatterprocessgivesrisetocas- weconsiderherethejetpowersobtainedbyB13forthelatter.B13 cadesofelectronsandpositrons,alsoemittingviathesynchrotron provide the redshifts, z, the apparent superluminal velocity, β , andComptonprocesses.Thepeakofthehigh-energyemissionof app andtheaccretionluminosity,L ,seeTable1.Sixofthoseobjects thebroadbandspectralenergydistributionofblazars,at 0.1–10 acc ∼ werealsopresentinthesampleofZamaninasabetal.(2014)(here- GeV,isthenduetotheseprocesses,mostlyprotonsynchrotron. after ZCST14), for which those authors provide estimates of the Westressthatthename’hadronic’refersonlytotheemission black-holemass, M,β ,and L basedonliterature.Thevalues app acc processes,andthe’leptonic’jetsinAGNmodelsalsocontainions, ofβ agreewellbetweenZCST14andB13,whilethevaluesof app thoughwithrelativelylowenergies,preventingthemfromradiating L agreetowithinafactor of 2,which isasatisfactory agree- acc ∼ c 2015RAS (cid:13) 2 A. A. Zdziarski& M. Bo¨ttcher 3.0 1.0 2.5 PL@(cid:144)DlgjE 112...050 @DΦlgBH 00..05 -0.5 0.5 a 0.0 -1.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 lg@Lacc(cid:144)LED lg@Lacc(cid:144)LED 5.0 Figure2.Thedimensionless magnetic fluxφBH asafunction oftheEd- 4.5 dingtonratio.ThedashedlineshowthegeometricaverageofφBH 1.9. 4.0 Themodelofefficientjetformationviablack-holespinenergyextr≃action LDacc 3.5 (Blandford&Znajek1977)predictφBH > 50(Tchekhovskoyetal.2011; P@(cid:144)gj 3.0 McKinneyetal.2012),whichismuchhig∼herthantheobtainedvalues. l 2.5 2.0 b equation of state can be described by an adiabatic index of 4/3), 1.5 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 seeTable1.Weneglectapossiblecontributionofcoldprotons,and lg@Lacc(cid:144)LED consideronlythoseinthepower-lawdistributionassumedtogive risetotheobserved spectrum, following thefitsofB13. Wethen Figure1.Theratioofthetotaljetpowerto(a)theEddingtonluminosity compareP tobothL (calculatedforanHfractionofX=0.7)and and(b)theaccretion luminosityasfunctions oftheEddingtonratio.The j E L inFig.1. Wefind P/L 85, P/L 2660, withthe dashedlinesshowthegeometricaverages. acc h j Ei ≃ h j acci ≃ standarddeviationscorresponding tofactorsof 10and 8.4,re- ≃ ≃ spectively.(Hereafterthesymbol . denotesageometricaverage, hi mentgiventhenecessaryapproximatecharacterofthoseestimates. i.e.,averageoflogarithms,andthegivenstandarddeviationcorre- However, theexception isW Comae, for which the L estimate spondstoamultiplicativefactor.)ExceptforWComaeandOJ287, acc usedbyB13is40timeshigherthanthatgiveninZCST14,which thedistributionof Pj/LE isrelativelyuniform.Asaconsequence, is the upper limit of Ghisellinietal. (2010), hereafter G10. B13 thereisananti-correlationbetweenPj/LaccandLacc/LE,butallthe usedtheestimateofXieetal.(2008),whoreferinturntotwoother obtainedvaluesarestillveryhigh,spanningPj/Lacc∼50–105.Fur- papers,whichdonotseemtogivethatinformation.Thus,weuse thermore,someofourvaluesofLaccareupperlimits,andthecor- herethevalueofG10.B13quoteanestimateof Lacc ofXieetal. respondingtruevaluesofPj/Lacccanbeevenhigher. (2008)forOJ287,whichis7timeshigherthantheupperlimitof In general, we can write Pj = ǫjM˙c2, where M˙ is G10;hereweusethelatter.Fortwoobjects(S50716+714and3C the accretion rate and ǫj < 1.5, the ratio of the jet 66A), B13giveno estimatesof L , andweusetheupper limits power to the available accreti∼on power, which we will call acc givenbyG10.Inthecaseof3C66A,thereisalsoanuncertainty here the jet formation efficiency. The approximate maxi- ofitsredshift,andB13usedanestimatedredshiftofz=0.3based mum corresponds (Tchekhovskoy,Narayan&McKinney 2011; onEBL-correctedSEDmodelling(Abdoetal.2011),whichisalso McKinney,Tchekhovskoy&Blandford 2012) to efficient extrac- marginallyconsistentwiththespectroscopicallydeterminedlower tionof theblack-hole spin energy (Blandford&Znajek1977),in limitontheredshiftbyFurnissetal.(2013).Sinceweusetheesti- which case the jet power may exceed M˙c2. However, attaining matesofthejetpowerfromB13,weadopttheirredshiftvalueand such a high jet formation efficiency requires the accretion flow rescaletheupperlimitofL ofG10,whousedz= 0.444,bythe to possess a strong poloidal magnetic field (Tchekhovskoyetal. acc ratioof D2, where D isthe luminosity distance. We assume the 2011; McKinneyetal. 2012), namely to form a magnetically ar- L L samecosmological parameters asB13, Ω = 0.7, Ω = 0.3 and rested disc(MAD, Narayan,Igumenshchev&Abramowicz 2003; Λ m H =70km/(s Mpc). see also Bisnovatyi-Kogan&Ruzmaikin 1976). The required en- 0 FortheobjectsnotinthesampleofZCST14,wefindmasses- ergy density corresponds then to the magnetic flux threading a timatesfromtheliterature,inparticularfromG10.Insomecases, rapidlyspinningblackholeofΦBH =φBH(M˙c)1/2rg,withφBH ≃50, thereisaconsiderableuncertainty.ForOJ287,weuse6.2 108M whichcorrespondstothemagneticfieldstrengthatthehorizonof fromWang,Luo&Ho(2004).However,ifthesystemis×indeed⊙a B2/8π ∼ 100m˙mpc2/(σTrg),where m˙ = M˙c2/LE,rg = GM/c2 is binary black-hole system, the massof the lessand more massive thegravitationalradius,mpistheprotonmass,andσTistheThom- component is estimated as 1.4 108M and 1.8 1010M , re- soncrosssection.Sincethemagneticfluxisconserved inthejet, spectively (Valtonen,Ciprini&×Lehto 20⊙12). Accre×tion wou⊙ld be itcanbemeasuredatlargescales,e.g.,throughtheradio-coreshift dominatedbythemoremassiveblackhole.Theadoptedvaluesof effect (Lobanov 1998; Hirotani 2005). Values of φBH ∼ 50 were L andMforallsourcesstudiedherearegiveninTable1. foundforalargesampleofblazarsandradiogalaxiesbyZCST14 acc B13givethejetpower1estimatedusingtheenergycontentand assuming M˙c2 = Lacc/ǫr fortheiradoptedaccretionradiativeeffi- fPor,oisnethjeeteonnthlya,lpsyeefltuhxeir(ee.qgu.,atLioenvsin(s3o–n5)2.0H06o)w,eavnedr,tthheecjeotupnotewrjeert, mcieondceylooffBǫr1=3,0w.4e.hHavoweetoveers,tgimivaetnetMh˙atinPsjte≫adLfraoccminththeejehtapdorowneirc, j should beincluded intheenergy budget. Thus,wemultiply their stronglydominatingtheenergybudget,i.e.,M˙c2 ≃Pj/ǫj≫Lacc/ǫr. valuesby8/3,assumingtheprotonsarerelativistic(andthustheir TocalculatethevaluesofφBHimpliedbythehadronicmodel, we use the radio core shift, ∆θ, measurements between 8 and 15 GHz for the sources in our sample from Pushkarevetal. (2012), 1 TheentryforLp (thepowerinprotons)ofOJ287inB13isatypo,it whichwegiveinTable1.WeapplyacorrectionofZdziarskietal. shouldbe0.083ratherthan8.3. (2015)tothepowerofthe(1+z)factorintheformulaforthemag- c 2015RAS,MNRAS000,1–6 (cid:13) Hadronicmodelsof blazars 3 Table1.Themainparametersofthesample.FSRQ-flatspectrumradioquasar,LBL,IBLandHBLrefertoblazarswhichsynchrotronspectrumhasthepeak atlow,intermediateandhighfrequencies,respectively;νandνFνgivetheestimatedpositionofthepeakoftheGeVspectrumapproximatedasapowerlaw, andPjisthetotaljet+counterjetpowerinthehadronicmodelofB13.SeeB13fortheremainingparametersofthesources. Object type z Lacc M Lacc/LE ∆θ ν νFν γmin γmax Pj ergs−1 M mas 1022Hz 10−10ergcm−2s−1 109 1048ergs−1 ⊙ 00223159++146248((A3CO)66A) LIBBLL 00.9.34 34..4800×11004434 44×110088 8.01.×001507−4 00..007036 1300 17 11 14..23 32.72 0420-014(PKS) FSRQ 0.914 3.02×1046 2.5×7 108 0.97 0.256 5 1 103 0.43 1.4 0528+134(PKS) FSRQ 2.07 1.70×1047 1.07×109 1.07 0.150 5 2 1 1.1 117 0716+714(S5) LBL 0.31 1.80×1044 1 ×108 0.012 0.125 70 1 1 2.7 0.69 0851+202(OJ287) LBL 0.306 1.50×1044 6.2× 108 0.0016 0.051 5 0.5 1 1.0 0.23 1219+285(WComae) IBL 0.102 1.50×1043 5 ×108 2.0 10 4 0.047 80 0.5 1 1.9 0.059 1226-023(3C273) FSRQ 0.158 1.30×1047 6.5×9 109 0×.13− 0.017 2 10 103 0.43 67 1253-055(3C279) FSRQ 0.536 2.00×1045 8 ×108 0.017 0.051 10 1 103 0.63 9.3 1510-089(PKS) FSRQ 0.36 1.12×1046 1.5×8 108 0.48 0.151 8 5 103 1,1 6.7 2200+420(BLLac) LBL 0.069 1.51×1045 1.70×108 0.060 0.052 10 0.3 1 1.9 26 2251+058(3C454.3) FSRQ 0.859 7.24×1046 4.90×108 1.00 0.159 10 10 103 1.1 96 × × neticfieldstrengthat1pc,B ,andthenusetheformulaforthejet tribution,andassumethejetLorentzfactor,Γ,tobeone-halfofthe 1 magneticflux,Φ,ofequation(5)ofZCST14.FromΦ =Φ we Dopplerfactor,δ,whileΓ=δfortheinclinationanglei=1/Γ,as j j BH obtainφ ,whichweplotinFig.2forǫ = 1andthedimension- favouredonstatisticalgrounds.Thus,forcomparisonwiththere- BH j lessblack-holeangularmomentumof1.Wefind φ 1.9with sultshere,theirjetpowersneedtobemultipliedbyafactorof32/3. h BHi≃ thestandarddeviationofa(multiplicative)factorof 5.Thesere- Still,wedonotexcludethatasub-Eddingtonjetpowerscanbeob- ≃ sultcanbecomparedtoanotherformulaforΦ ofZdziarskietal. tainedforsomeobjects,asitis,e.g.,thecaseforWComaeinour j (2015),whichtakesintoaccounteffectsduetothesmalljetopening sample.Generally,duetothesubstantiallylowertotalluminosities anglesintheradio-emittingregion(andtheconsequent lowvalue andatleastequallylarge(ifnotlarger)black-holemassesofHBLs of the magnetization parameter), and due to transverse averaging comparedtolow-frequencypeakedblazars(especiallyFSRQs),it ofthemagneticfield.Thatformulayieldsvalueslowerbyapproxi- seems less problematic to produce hadronic model fits with sub- mately √2fromthoseabove.Thus,ourresultsappeartogiverobust EddingtonjetpowersforHBLs. approximateestimatesofthemagneticflux(undertheassumption of the hadronic jet model). Given this and that all objects in the samplehaveφ 50,wecanruleouttheefficientversionofthe BH ≪ 3 THEMINIMUMJETPOWERINTHE modelofBlandford&Znajek(1977)forthesample.(Wenotethat PROTON-SYNCHROTRONMODEL thismodelislikelytoworkforthestudiedsourcesiftheleptonic modelisadopted,asinZCST14.) Theaboveresultsareforthemodel fitsofB13which,duetothe Inotherjetformationmodels(e.g.,Blandford&Payne1982; largenumberofparameters,maygenerallynotbetheonlypossible Coughlin&Begelman 2014), the jet formation efficiency has to hadronicmodelrepresentationofthechosenSEDs.Wemaythere- be < 1, and it is usually ǫ 1. Thus, the accretion pro- fore ask whether another set of fits of the hadronic model could j ≪ cess is even more highly super-Eddington. For such accretion, have lower total power. We can answer this question by finding Coughlin&Begelman(2014)makearoughestimateof ǫ = 0.1, theminimumpossiblepowerforagivenprotonsynchrotronflux, j whichwealsoadopt.Then, M˙c2/L 103,i.e.,theaccretionis found todominate theoverall model spectra of theobjectsinthe h Ei ∼ indeedhighlysupercritical.Theradiativeefficiencyoftheaccretion sample,seefig.9ofB13.WeusethemethodofZdziarski(2014) discinthiscaseisverysmall, L /M˙c2 4 10 5. (hereafterZ14),whocalculatedtheminimumjetpowerforagiven h acc i≃ × − Afterthecalculationspresented inthispaper hadbeencom- electron synchrotron flux. Wecan adapt those calculations to the pleted, Cerrutietal. (2015) presented an analysis of 5 high- proton synchrotron case by replacing the electron mass, m , by e frequencypeakedBLLacobjects(HBLs),whoseγ-raypeakislo- m intherelevantformulaeofZ14(includingphysicalconstants). p catedaround 1TeVratherthanat 1GeVastypicalforLBLsand Equivalently,σ ,thecriticalmagneticfield,B ,thedimensionless ∼ ∼ T cr IBLsconsideredinB13andinthiswork.Cerrutietal.(2015)found photon energy in the jet frame, ǫ , and the jet-frame flux, L (in thatitispossibletofindhadronic-modelfitswithsub-Eddingtonjet thenotationofZ14)needtobemu′ltipliedby(m /m ) 2,(m /m′ǫ′ )2, p e − p e powersforthoseparticularobjects.Adetailedanalysisofthoseob- (m /m ) 1 andm /m ,respectively.Correspondingly,theconstant p e − p e jects is outside the scope of this Letter, but we briefly address a a ofequation(33)ofZ14needstobemultipliedby(m /m )3/2,and e p e fewissues.Cerrutietal.(2015)tookintoaccountsecondaryprod- thepowerinrelativisticparticles,P ,andintherestmass,P,need e i uctsofhadronicprocessesinmoredetailthanB13.However,they tobemultipliedby(m /m )5/2andm /m ,respectively.Themini- p e p e assumedsteadystateprimaryprotonandelectrondistributionsas mumtotaljetpowerandthecorrespondingmagneticfieldstrength fixed power laws and followed the evolution of particle spectra, ofequation(36) inZ14needtobemultipliedby(m /m )10/7 and p e usingtherespectivekineticequations,onlyforthesecondarypar- (m /m )5/7,respectively. p e ticles,whileB13usedtheelectronandprotonkineticequationsfor The method of Z14 assumes a local synchrotron spectrum allparticles,whichistheself-consistentapproach.Itisnotclearto which can be well represented by a power law in some range of ushowthismightaffectthejetpowers.Also,thejetpowersgiven frequencies, and it uses one monochromatic measurement of the inCerrutietal.(2015)areforonejetonly,neglectthepressurecon- flux.Here,weuseanestimateofthefluxaroundthemaximumof c 2015RAS,MNRAS000,1–6 (cid:13) 4 A. A. Zdziarski& M. Bo¨ttcher 4 ASTROPHYSICALIMPLICATIONS 0.0 PDB13 -0.2 Ionf BSe1c3tioexnce2e,dwtehefiorurnadditahtiavtethluemjeintopsoitwieesrsbyofvtehrey AlaGrgNe fsaacmtoprlse, P(cid:144)est -0.4 withP/L 50–105 and P/L 3000.Then,weshowedin @lg Sectionj 3atchca∼t thevalues ofhthjejaectcipo∼wer obtained byB13inthe -0.6 a hadronic model cannot be significantly reduced by changing the -0.8 fitparameters,astheyare,onaverage,withinafactorofafewof -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 lg@Lacc(cid:144)LED theminimumjetpowersestimatedusingtheobservedγ-rayspec- tra for the radiative mechanism dominant in this model, namely 0.0 proton synchrotron. These findings imply that the jet formation PDest -0.5 eisffiaclireenacdyygqrueiatetlyhiegxhce(esdees,the.agt.,foGuhnidseilnlinlieepttoanl.ic20m1o4d).elWs,ewhhaicvhe (cid:144)min -1.0 alsofoundthatthemostefficientjetformationmechanismknown, P @lg based on the Blandford-Znajek mechanism extracting black-hole -1.5 b spinwithamagneticallyarresteddisc(Tchekhovskoyetal.2011; -2.0 McKinneyetal.2012),isruledoutbythemagneticfieldsmeasured -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 atthepcdistancescale.Sincethejetpowerhastobethenderived lg@Lacc(cid:144)LED entirelyfromaccretion,theimpliedaccretionratesarehugeandthe Figure3.(a)Theratioofthetotaljetpowerestimatedusingthemagnetic radiativeefficienciesoftheaccretiondiscmustbetiny. fieldstrengthsofB13andthemethodofZ14tothecorrespondingpower At the inferred accretion rates, M˙c2/L 103, accre- giveninB13,asafunctionoftheEddingtonratio.Thedashedlinecorre- h Ei ∼ tionissupercritical(rulingoutoptically-thinradiativelyinefficient spondstoequalpowers.(b)Theratiooftheminimumpowertothatcalcu- models, which can correspond only to M˙c2/L 1, see, e.g., latedusingthemethodofZ14withthemagneticfieldstrengthsofB13.The E ≪ Yuan&Narayan 2014). The angle-averaged accretion-disc lumi- dashedlinecorrespondstothegeometricaverage. nosity in this case is small, corresponding to L L and a ra- ∼ E diative efficiency is 10 3 (Sikora 1981; Sa¸dowskietal. 2014). − ∼ However, most of that luminosity emerges through axial funnels, wheretheobservedfluxissuper-Eddington,correspondingtoL ∼ 10L (Sikora1981;Sa¸dowskietal.2014).Oursampleconsistsof E blazars seen close to on-axis, on average at i 1/Γ, and the ∼ j accretion-disc-emission funnels have opening angles greater than theνF spectrum,usingspectralplotsinfig.9ofB13.Welistour ν that (Sa¸dowskietal. 2014). Thus, we would expect to see super- adoptedvaluesinTable1.Thisimpliesthattheparametere of max Eddington accretion-disc luminosities, while, in fact, they are all Z14is= 1.However,wemodifythemethodinordertotakeinto < L , with 8 out of 12 objects having L < 0.1L . Thus, the E acc E accountthatγminisspecifiedinthemodelofB13.Inthecaseofion h∼adronicemissionmodelforthejetsisincons∼istentwiththestan- acceleration,onewouldnaturallyexpectγ 1,unlikethecase min ∼ dardaccretiontheory. ofelectrons,whichcanbepreheatedto γ 1(withacceler- h mini ≫ The inferred extreme accretion rates present also a major ationonlyproceedingoutofthisdistribution).However,B13used γ = 103 forsomeobjects,seeTable1.Toaccount forthis,we problem in light of results of studies of supermassive-black-hole min definee =Bγ2 /(B m2ǫ )(cf.Z14).SinceBisitselfcalculated growth. The e-folding time by which the black-mass would in- min min cr p ′ creaseduetoaccretion, M/M˙,is 4 105 yrat M˙c2/L 103 bytheminimization,thisrequiresasimpleiterativecalculation. ≃ × h Ei ≃ foundinSection2.Thisisaveryshorttimecomparedtoestimated Wefirstcheckhowwelltheabovemethodreproducesthejet lifetimesofactivephasesofradiosources,e.g., 2 108yrforFR powersgiveninB13.Forthis,weusethevaluesofBgiveninB13 ≃ × IIs(Antognini,Bird&Martini 2012andreferences therein).Cor- instead of those corresponding to the minimum power. We show respondingly, the average radiative accretion efficiency we found theresultsinFig.3(a).Somedisagreementisexpectedgiventhat (undertheassumptionsofthehadronicmodel)of L /M˙c2 4 inthepresent estimatewetake intoaccount onlytheproton syn- h acc i≃ × 10 5is thantheaverageaccretionefficiencyof 0.1–0.3(Sołtan chrotronemissionandneglectcooling.Theadiabaticcoolingis,in − ≪ ∼ 1982; Marconietal. 2004; Silvermanetal. 2008; Schulzeetal. fact,dominantinAO0235+164andWComae,inwhichcasethe 2015). Thus, blazars radiating via the hadronic emission mecha- proton-synchrotron estimate gives values 200 and 50 times too ∼ nismhavetorepresentatmostasmallfractionofaccretingsuper- low, respectively. Apart from this, the overall agreement isgood, massiveblackholesand/or suchextremeaccretionepisodesmust withinafactorof2for7fortheremainingobjects,seeFig.3(a). be extremely short-lived, representing only a duty-cycle of order WethenapplytheminimizationmethodtothesampleofB13. 10 4 (whichisinconflict withthefact that thestudied objects We have found the minimum powers are on average lower by a ∼ − havequiteaverageproperties). factoroffewcomparedtothecorrespondingestimatesabove,with thegeometricaveragebeing 0.23,seeFig.3(b).Thisreduction Finally, the obtained extreme powers are in conflict ≃ isduetotheminimumcorresponding toanequipartitionbetween with studies of the jet power based on radio lobes and thepowerintherelativisticions,P,andinthemagneticfield,P , X-ray cavities (Merloni&Heinz 2007; Cavagnoloetal. 2010; i B whichmaynotbeabletoproduceafittotheentireSED.Indeed, Nemmenetal.2012;Russelletal.2013;Godfrey&Shabala2013; B13 found P P in most of their fits. This departure from Shabala&Godfrey 2013). Those studies indicate jet powers at i ≫ B equipartition naturally resultsinhigher total jet powers. Still,the mostmoderatelyexceedingtheEddingtonluminosity,andevenin overallpossiblereductionofthejetpowerduetochangingthefit themostluminoussourcestheyexceedtheaccretion-discluminos- parametersisbyatmostafactorofafew. ityonlybyafactorof<10.Ontheotherhand,thosepowersarein ∼ c 2015RAS,MNRAS000,1–6 (cid:13) Hadronicmodelsof blazars 5 anoverallagreementwiththepowersestimatedinleptonicmodels, REFERENCES see,e.g.,Ghisellinietal.(2014). 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Bo¨ttcher Zdziarski A.A.,SikoraM.,Pjanka, P.,Tchekhovskoy A.,2015, MNRAS,submitted,arXiv:1410.7310 c 2015RAS,MNRAS000,1–6 (cid:13)