Fundamental Plane of Black Hole Activity in Quiescent Regime

0.43 MB·

by  Fu-Guo Xie

DraftversionJanuary24,2017
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
FUNDAMENTALPLANEOFBLACKHOLEACTIVITYINQUIESCENTREGIME
Fu-GuoXie1andFengYuan1
DraftversionJanuary24,2017
ABSTRACT
Acorrelationamongtheradioluminosity(L ),X-rayluminosity(L ),andblackholemass(M )inactive
R X BH
galacticnuclei(AGNs)andblackholebinariesisknowntoexistandiscalledthe“FundamentalPlane”ofblack
holeactivity. Yuan&Cui(2005)predictsthattheradio/X-raycorrelationindex,ξ ,changesfromξ ≈ 0.6to
7 X X
1 ξX ≈1.2−1.3whenLX/LEdddecreasesbelowacriticalvalue∼10−6. Whilemanyworksfavorsuchachange,
0 therearealsoseveralworksclaimingtheopposite. Inthispaper,wegatherfromliteraturealargestquiescent
2 AGN(definedasL /L .10−6)sampletodate,consistingof75sources.WefindthatthesequiescentAGNs
X Edd
followaξ ≈1.23radio/X-rayrelationship,inexcellentagreementwiththeYuan&Cuiprediction.Thereason
n X
forthediscrepancybetweenthepresentresultandsomepreviousworksisthattheirsamplescontainnotonly
a
J quiescentsourcesbutalso“normal”ones(i.e.,LX/LEdd &10−6).Inthiscase,thequiescentsourceswillmixup
withthosenormalonesinL andL . Thevalueofξ willthenbebetween0.6and∼1.3,withtheexactvalue
2 R X X
beingdeterminedbythesamplecomposition,i.e.,thefractionofthequiescentandnormalsources. Basedon
2
thisresult,weproposethatamorephysicalwaytostudytheFundamentalPlaneistoreplaceL andL with
R X
] LR/LEddandLX/LEdd,respectively.
E
Subjectheadings:accretion,accretiondiscs–blackholephysics–galaxies:active–methods:statistical
H
.
h 1. INTRODUCTION Yuan2016). Thescatterofthecorrelation,ontheotherhand,
p mayreflectsthe(combinationof)effectsofotherparameters,
Therearemanyobservationalevidencesinblackhole(BH)
-
e.g.,theintrinsicvariabilityinradioandX-rays,theBHspin
o X-raybinaries(BHBs)andactivegalacticnuclei(AGNs)for
r the coupling between the collimated relativistic jet and the (Milleretal.2009;Narayan&McClintock2012),thestrength
t of magnetic field (Blandford & Znajek 1977; Sikora et al.
s accretionflow. One such evidencecomesfromCorbeletal.
a (2003)andGalloetal.(2003),whodiscoveredaremarkably 2007), the Doppler beaming effect (Li et al. 2008, but see
[ van Velzen & Falcke 2013), the angular momentum of the
1 atitg,het.gc.o5rreolrat8i.o5nGbHetzw)eaenndrXad-rioay(m(aotn2o–c1h0rokmeVa;tihce,rLeRaft=erLνLXν) aFcaclcrektein2g01g3as).(Cao2016)andtheenvironment(vanVelzen&
v luminositiesinBHBsduringtheirhardstates(seeCorbeletal.
AfterthediscoveryoftheoriginalM03FP,severalnotable
3 2013forlatestsummary).Thiscorrelationwaslaterextended
complexitiesare revealedoverthe past decade. First, AGNs
4 toincludelow-luminosityAGNs(LLAGNs).Withtheimpact
with different radio loudness seem to follow relationships
1 of black hole mass M taken into account, Merloni et al.
BH thatare differentinbothnormalizationandcorrelationslope
6 (2003, hereafter M03) found that, logL = 0.6logL +
R X (e.g., Wang et al. 2006; Li et al. 2008; de Gasperin et al.
0 0.78logM +7.33, with a scatter of σ = 0.88dex. Here
. (and throuBgHhout this paper) the luminosRities and BH mass 2011). Secondly, long-term quasi-simultaneous monitoring
1 are, respectively, in units of ergs−1 and M . We refer on individual sources find that, some sources do not follow
0 ⊙
the slope predicted by the original M03 FP during their
7 thisrelationshipas the original/standardM03“Fundamental
fluctuations in luminosities, and they can be classified as
1 Plane” (hereafter FP) of back hole activity (for later work,
outliers (for BHBs, see e.g. Xue & Cui 2007; Coriat et al.
: see e.g., Falcke et al. 2004; Ko¨rding et al. 2006; Merloni
v 2011,andCorbeletal.2013forarecentsummary;forAGNs,
et al. 2006; Wang et al. 2006; Panessa et al. 2007; Li et al.
i see e.g. Bell et al. 2011; King et al. 2013;Xie et al. 2016).
X 2008;Gu¨ltekinetal.2009,hereafterG09;Plotkinetal.2012;
Theseoutliers,individually,seemtofollowahybridradio/X-
Younesetal.2012;Dong&Wu2015;Panessaetal.2015;Fan
r ray correlation, i.e. L ∝ L∼1.3 when L is high (see also
a &Bai2016;Liu,Han&Zhang2016;Nisbet&Best2016). R X X
Galloetal.2012;Dong,Wu&Cao2014;Panessaetal.2015;
Yuan, Cui & Narayan (2005) have proposed a coupled
Qiao&Liu2015),L ∝ L∼0 whenL ismoderatelylow,and
accretion–jet model for LLAGNs and BHBs (see Yuan & R X X
canrecovertheoriginalM03FPwhenL ismuchlower. The
Narayan2014forareview). Inthismodel,unlessthesystem X
hybridcorrelationismostevidentinBHBH1743–322(Coriat
is extremely faint, the thermalgas in a hot accretion flow is
etal.2011)andLLAGNNGC7213(Belletal.2011;Xieet
responsiblefortheX-rayemissionandtherelativisticpower-
al.2016).
lawdistributionelectronsinajetproducetheradioemission.
The third complexity, which is the focus of this work, is
Yuan & Cui (2005, hereafter YC05) show that the FP can
whether or not the AGNs with extremely low luminosities,
be explained naturally in this model (seel also M03; Heinz
i.e. theso-called“quiescent”AGNs(definedassourceswith
& Sunyaev 2003; Heinz 2004; Xie & Yuan 2016), i.e. it
is a directconsequenceof a tight relationshipbetween mass LX/LEdd .10−6,hereLEdd =1.3×1046 MBH/108M⊙ ergs−1
inflow/accretion rate and mass ejection rate (YC05; Xie & is the Eddington luminosity), follow the original M03 FP.
YC05 shows that the answer should be “no”. The reason
is that in the accretion–jet scenario, the origin of the X-ray
1KeyLaboratoryforResearch inGalaxies andCosmology, Shanghai
emission in quiescent AGNs is different to that of normal
Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan
Road,Shanghai200030,China;[email protected],[email protected] LLAGNs (defined as sources with L /L & 10−6), i.e.
X Edd
2 Xie&Yuan
it originates from jet instead of hot accretion flow (YC05). 2. THESAMPLEOFQUIESCENT/FAINTAGNS
Physically, this is because the both the hot accretion flow
Wegatherfromliteratureasampleofquiescent/faintAGNs
and the jet emit X-ray emission, but the dependence of X-
with measurements in their black hole mass, nuclei radio
rayradiationfromthehotaccretionflowontheaccretionrate
(at 5 GHz) and X-ray (2-10 keV) luminosities. Since most
is less sensitive compared to that from the jet. Thus with
of our targets are weak nuclei at the center of normal
the decrease of accretion rate (or equivalently luminosity),
galaxies, contamination of emission from their host galaxy,
the radiation from the jet will catch up with that from
i.e. the radio emission due to residual star formation or
the accretion flow and become dominant below a critical
supernovaeremnantsinthenucleiregionofthehostgalaxy,or
luminosity L /L ≈ 10−6 (see also Fender, Gallo &
X,crit Edd extended/elongatedradioemissionfrommini-lobesifthe jet
Jonker2003). Moreover,becauseofthechangeoftheX-ray
is spatially resolved (cf. discussions in Nyland et al. 2016),
originfromahotaccretionflowtoajet,YC05predictsthatthe
could be of vital importance. In order to discriminate these
quiescentaccretionsystemswillfollowasteeperrelationship
possible contaminations, we select data which are observed
between radio and X-rays (see also Heinz 2004; Gardner &
witharcsec(orevenhigher,e.g.,XMM-NewtonandChandra
Done2013),i.e.,theFPoffaintaccretionsystemsisrevised
for X-rays, and Very Large Array [VLA] for radio.) spatial
to (YYH09), logL = 1.23logL + 0.25logM − 13.45.
R X BH resolution. For sources that have several observations, we
HereafterwewillrefertothisrelationshipastheYC05FP.
prefer data with higher spatial resolution. Moreover, for
We note that the value of the critical luminosity L
X,crit sourceswithextendedradiomorphologies,weonlyconsider
depends on detailed parameters that control the properties
the nuclei component, i.e. the emission of the compact jet.
of accretion flow and/or jet. The L value obtained in
X,crit ConsideringthestrongfluctuationsinAGNactivity,weargue
YC05 is for the “general”sources. If for some reason (e.g.,
thatonlythiscompactradiocomponentrelatesdirectlytothe
Dopplerbeaming)theradiationfromthejetisverystrongin
current nuclei activity (shown in X-rays) of the AGNs. We
somesources,thecriticalluminositycanbecomesignificantly
alsonotethatfortheX-raysofNGC3115,onlythecompact
larger.Thisisthecaseofradioloudsources(e.g.,Wangetal.
componentisadopted(Wongetal.2014).
2006;Li et al. 2008;de Gasperin et al. 2011). In this work,
The BH mass in these systems is mostly derived based
weaimat“general”sources.
on the empirical M –σ relationship (cf. Kormendy & Ho
The YC05 predictions have been confirmed by many BH
2013 for review of various ways to estimate M ), whose
observational and theoretical works (see review by Yuan & BH
uncertainty is normally σ ≈ 0.3. More reliable M
Narayan 2014), both of AGNs (e.g., Pellegrini et al. 2007; M BH
measurements, such as those derived from kinematics or
Wu,Yuan&Ho2007;Wrobel,Terashima&Ho2008;Yuan,
reverberation-mapping,willbeadoptedifexist,cf.references
Yu & Ho 2009, hereafter YYH09; de Gasperin et al. 2011;
inTable1fordetails.Besides,inordertoconverttheobserved
Younes et al. 2012; Li, Yuan & Xie 2016) and BHBs (e.g.,
fluxtoluminosity,theluminositydistanced shouldbegiven
Pszota etal. 2008;Plotkin etal. 2013;Reynoldsetal. 2014; L
inadvance. Becauseoftheluminosityconstraint,mostofthe
Xie, Yang & Ma 2014; Yang et al. 2015a). For example, sources in our sample have d . 50 Mpc. Consequently,
YYH09didastatisticalanalysisbasedonasampleconsisting L
most of our sources have redshift-independent distance
of 22 quiescent AGNs. They found ξ = 1.22 ± 0.02, in
X measurements. For most of these sources, the distances
excellentagreementwithYC05prediction.
adoptedin this work are from Tully et al. (2013), where we
However,therearealsoclaimsinliteratureonanuniversal
select distances constrained through the surface brightness
FP extending down to quiescent systems, without any
fluctuation(SBF) method. Forthe restfewsourcesthatlack
steepening pattern. For example, the three BHBs with
redshift-independent distance measurements, we derive d
radio and X-ray observations during their quiescent states L
fromredshiftbasedonthePlanck2015flatcosmology(Planck
are claimed to follow the original M03 FP at low X-ray Collaborationetal.2016),withH =67.8kms−1Mpc−1and
luminosities (Gallo et al. 2006, 2014; Corbel, Koerding & 0
Ω =0.308.
Kaaret2008;Corbelet al. 2013). For AGNs, recently Dong M
The main selection criteria of our sample compilation
&Wu(2015,hereafterDW15)selectedfromtheflux-limited
comesfrom the X-ray luminosityconstraint, i.e. we require
Polmarsurveyasampleof73AGNs(SgrA*alsoincluded),
the X-ray Eddington ratio L /L . 10−6, a critical
and combine with a large sample of data points of BHBs, X Edd
luminositybelowwhichtheaccretion–jetmodelpredictsajet
toinvestigatetheFPjointlyfromsub-Eddingtontoquiescent
origin of the X-ray emission (YC05; YYH09). Considering
systems. They claim that those with L . L (24 AGNs
X X,crit the uncertainties in the measurements of M , practically
under a detailed definition of L , cf. DW15) seem to BH
X,crit this criteria is slightly weakened to L /L < 10−5.7
be roughly consistent the original M03 FP. As discussed in X Edd
(cf. the X-axis range of Fig. 1). There is one notable
detaillaterinSections5.3&5.4,wearguetheiranalysisand
exception – we exclude from our sample Sgr A*, whose
conclusionhavesomeproblems.
L /L ∼ 10−11 (in its quiescent state, cf. Fig. 6). High-
In this work, the FP of quiescent systems is re-examined. X Edd
resolution radio observations suggest the non-existence of
Because the aim is to check the YC05 prediction, following
elongated/collimated jet in this system during its quiescent
YYH09,weexcludenormalLLAGNsandfocusonquiescent
state(at∼ 10R level,whereR istheSchwardschildradius
AGNs only. In order to reduce the contamination of the s s
of BH, see e.g., Shen et al. 2005; Doeleman et al. 2008),2
host galaxy, we restrict ourselves to observations that have
andtheoreticallythelow-frequencyradioemission(e.g. at5
sufficientlyhighspatialresolutionandsensitivity. Thispaper
GHz) originates from the relativistic power-law distribution
isorganisedasfollows. Wedescribeoursamplecompilation
electronswithinthehotaccretionflowitself (Yuan,Quataert
(75 sources in total, to our knowledge the largest quiescent
& Narayan 2003), instead of the jet. Moreover, the X-
AGN sample to date) in Section 2. We then introduce the
statistical analysis method in Section 3. Subsequently we 2 Notethat,asanindependentapproach,thejetinquiescentstateofSgr
present the fitting results in Section 4. Sections 5 and 6 are A*isrecentlyruledoutbythereliablemeasurementoftheFaradayRotation
devotedtodiscussionsandabriefsummaryrespectively. Measureatsubmillimeterwavelength(Li,Yuan&Wang2014).
FundamentalPlaneofquiescentAGNs 3
ray emission in Sgr A* is dominated by diffuse gas around followingM03andG09.
∼105R (e.g.Baganoffetal.2003;Wangetal.2013),unlike
s 3. FITTINGMETHOD
thatinothernormalLLAGNswhereitoriginatesfromnuclei
< 50R regions(e.g.,Fabianetal. 2009;Emmanoulopoulos We consider the following linear (in logarithmic space)
s
etal.2014).DetaileddiscussiononSgrA*,includingitsflare relationship among three quantities, e.g., LR (in unit of
state,willbegivenlaterinSection5.3.2. ergs−1),LX (inunitof ergs−1)andMBH (inunitofM⊙),
logL =ξ logL +ξ logM +c. (1)
R X X M BH
For our statistical analysis, we adopt the Markov chain
MonteCarlo(MCMC)Bayesiananalysis(cf.e.g.Kelly2007;
Foreman-Mackeyet al. 2013, hereafter Bayesian approach.)
to derive the best-fit parameters and their corresponding
uncertainties(seee.g.,Plotkinetal.2012).Forthisapproach,
we take the Python routine Emcee (Foreman-Mackeyet al.
2013) ver. 2.2.1, which is based on the affine invariant
MCMC ensemble sampler method (Goodman & Weare
2010). Besides, we assume the intrinsic scatter of the FP is
of Gaussian distribution. Moreover, since L (or L /L ),
X X Edd
L (or L /L ) and M are symmetric physical quantities
R R Edd BH
during the modelling, we in practice set the model prior
probabilityfunctionp(ξ ,ξ ,c)to(VanderPlas2014),
X M
p(ξ ,ξ ,c)=(1+ξ2)−3/2(1+ξ2)−3/2 (2)
X M X M
Fig.1.—Distributionofblackholemass(inunitofM⊙)asafunctionofX- Wenotethatthemultivariatecorrelationcoefficientsshown
rayEddingtonratio(LX/LEdd).Thetworedsolidcurvesmarktheboundaries in several influential works (among others see e.g., M03
ofthe(quasi-)MBH-freesubsample, i.e. logMBH = 8.1,9.1,andtheblack
dashedcurve showsthe average BHmassofthis subsample, loghMBHi = andG09) are derivedthroughminimizationof the following
8.71.ThebluefilledcirclesrepresentsourceswithfirmdetectionsinLRand statistics(hereafterleastχ2approach),
LX,theorangeopencirclesandredarrowsshowsourceswhoseLRandLX
are,respectively, upperlimitconstraints. Thedarkgreyarrowsaresources (logL −ξ logL −ξ logM −c)2
warheolsaebeLllRedanindgLrXeeanr.ebothupperlimitconstraints. Severalnotablesources χ2 =Σ R σX2 +ξ2σX2 +Mξ2σ2 BH . (3)
R X X M M
Although this method can provide reasonable regression
As listed in Table 1 and shown in Fig. 1, our final
coefficients (cf. Fasano & Vio 1988), there are indeed
sample includes 75 sources, mainly selected from previous
some concerns (e.g., Plotkin et al. 2012). For the sake of
compilations, e.g., M03; Nagar, Falcke, & Wilson (2005);
direct comparison to those previous works, we also provide
Hardcastleetal.(2009);Ho(2009);Hoetal.(2009);YYH09;
resultsunderthisapproach,butourdiscussionswillbemainly
Pellegrini(2010);DW15andNylandetal.(2016).Asshown
based on results derived through the Bayesian regression
inFig.1,toourknowledgethisisthelargestquiescentAGN analysis. TechnicallyweusethePythonroutinekmpfit3of
sampletodate, inwhich5sourceshave L /L . 10−9. In
X Edd theKapteynpackagever. 2.3(Terlouw&Vogelaar2012),in
thissample,58sourceshavefirmdetectionsinbothradioand
which the C implementation of mpfit (Markwardt 2009) is
X-rays (blue filled circles in Fig. 1). 8 sources have upper
adopted.
limitconstrainsinradiobutfirmdetectionsinX-rays(orange
opencirclesinFig.1,andorangearrowsintherestfigures), 4. RESULTS
while 4 sourceshavefirm detectionsin radiobutonlyupper
In this section, we present the numerical results based
limit constrains in X-rays (red arrows in Fig. 1). The rest 5
on different approaches. Section 4.1 considers the sample
sourcesonlyhaveupperlimitconstrainsinbothradioandX-
consistingofallthequiescentAGNs(72sources),whereboth
rays(greyarrowsinFig.1).AsshowninFig.1,thisquiescent theBayesianandtheleastχ2methodsareadopted(cf.Section
AGNsamplecoversalargedynamicalrangeinbothradioand
3 above). Section 4.2 represents the results based on a sub-
X-ray Eddingtonratios, i.e. 10∼−14 < L /L < 10∼−7 (cf.
R Edd sample with similar black hole mass (42 sources). This is
Fig.6below)and10∼−10 < LX/LEdd <10∼−5.7. TheBHmass because we want to focus on the value of ξX so we hope to
ofmostsourcesisbetween10∼7.5M⊙and10∼9M⊙,withafew eliminateanypossiblecontaminationbytheblackholemass.
exceptions, e.g., MBH = 105.16 M⊙ for NGC 404 (Ho 2009) Wefindaconvergencyinbothmethods,i.e. ξX ∼1.2–1.4.
and M = 106.4 M forM32 (Kormendy& Ho 2013). We
BH ⊙
emphasisthatthenucleiofM31,withL /L = 10−14.0and 4.1. TheFPofquiescentAGNs
R Edd
LX/LEdd =10−10.2(Garciaetal.2010),representsthefaintest Hereweinvestigatethelinearrelationshipamonglog(LR),
(inEddingtonunit)sourceinoursample. log(L ) and log(M ), following the methodologies de-
X BH
With the fact that the LLAGNs are expected to vary scribed in Section 3. We first consider a sub-sample of 58
moderately on timescale of months to years (Ho & Peng sources, which have firm detections in both radio and X-
2001; Ho 2008), the uncertainties of the data mainly comes rays(hereafterfirm-detectionsubsample). We findthat,they
from the non-simultaneity between radio and X-rays (Note followaFPwithparametersconstrainedas,
thatadditionally,the time delaybetweenthe two wavebands
should be corrected, cf. Section 5.1). Considering the ξ =1.09+0.07, ξ =0.70+0.12, c=−11.61+2.19, (4)
X −0.07 M −0.11 −2.25
systematic and the observational uncertainties, we take
isotropic uncertainties with σ = σ = σ = 0.3 dex, 3https://github.com/josephmeiring/kmpfit
R X M
4 Xie&Yuan
Fig.2.—TheFundamentalPlaneofquiescentAGNs. TheredsolidanddashedcurvesrepresenttheBayesianregressionanalysisresult(cf. Eq.6)andits
scatter,respectively. Forcomparison,weshowtheoriginalM03FPbythetwogreylong-dashedcurves,withMBHfixedto109M⊙(upper)and108M⊙(lower).
ThemeaningofthesymbolsisthesameasthatinFig.1(notethattheorangearrowsherearethesameastheorangecirclesinFig.1).Severalnotablesources
arelabelledingreen.Additionally,SgrA*initsquiescentandflarestates,isshownbyblackasterisksforthepurposeofcomparison,seeSec.5.3.2fordetails.
WethenanalysethewholequiescentAGNsample. Under
theBayesianapproach,thefittingparametersread,
ξ =1.23+0.07, ξ =0.63+0.12, c=−16.53+2.11, (6)
X −0.07 M −0.12 −2.19
with the intrinsic scatter in logL to be σ = 0.81dex, and
R R
undertheleastχ2methodthefittingparametersread,
ξ =1.30+0.07, ξ =0.57+0.10, c=−18.53+2.19, (7)
X −0.07 M −0.10 −2.19
withtheintrinsicscatterinlogL tobeσ =0.82dex.
R R
Theradio/X-raycorrelationslopederivedabove(e.g. Eqs.
6&7)isclearlydifferent,at> 6σconfidencelevel,fromthat
of the original M03 FP, whose ξ ≈ 0.6 ± 0.1 (see also
X
Corbeletal.2013forsummaryofthisrelationshipinBHBs).
This FP is in good agreement (in ξ ) with the prediction of
X
YC05andtheresultofYYH09basedonalimitedquiescent
AGN sample. We show the Bayesian regression analysis
result (cf. Eq. 6) as the red solid curve in Fig. 2. The two
red dashed curves represent the intrinsic 1σ scatter of the
best-fit result. For comparison, we also show the original
M03 FP by the two black long-dashed curves, where the
blackholemassisfixedto108 M and109M ,respectively,
⊙ ⊙
for the lower and the upper curves. Fig. 3 shows one
and two dimensionalprojectionsof the posterior probability
Fig.3.— The one and two dimensional projections of the posterior distributions of Bayesian MCMC fitting parameters, where
probabilitydistributionsofthefittingparametersbasedonBayesianMCMC the three dashed curves mark the location of the best-fit
analysisofthewholequiescentAGNsample,cf. Eq.6. Thethreedashed
values,andthecorresponding1σuncertainties(cf. Eq.6).
curves mark the location of the best-fit value, and the corresponding 1σ
uncertainties. From Fig. 2, there are several points worth further
emphasis. First, considering the moderately large scatter in
undertheBayesianregressionanalysis,and
the observationaldata, the deviation to the originalM03 FP
ξ =1.12+0.07, ξ =0.82+0.11, c=−13.60+2.29, (5) (cf. thelong-dashedcurves)ismostevidentinM31(seealso
X −0.07 M −0.11 −2.29 Fig.5belowandWuetal.2013),whichhaslowest L /L
X Edd
under the least χ2 approach. Obviously the firm-detection and L /L in our sample. The other sources, on the other
R Edd
subsample shows a steeper radio/X-ray correlation slope hand, are in roughagreementwith the originalM03FP (see
comparedtothatoftheoriginalFP. also Fig. 5 below). In this sense, we urge to devote more
FundamentalPlaneofquiescentAGNs 5
efforts on sources whose X-ray Eddington ratio L /L . TABLE1 —Continued
X Edd
10−9.5. Thesesourcesareofcrucialimportanceinconfirming
the deviationto theoriginalFP, aswell asthe existenceofa Sources Log(MBH) Log(LR) Log(Lx) Refencesa
newYC05-typeFPinthesefaint/quiescentAGNs. Secondly, (M⊙) (ergs−1) (ergs−1)
theradio/X-raycorrelationslopeξ inquiescentAGNscanbe NGC4762 7.63 36.58 38.26 mrx:11
X NGC4772 7.57 36.48 39.30 mrx:14,17
constrained from a sample which includes quiescent AGNs
NGC5576 8.44 <35.50 38.88 mrx:12;x:30
only. If instead the sample also includes numerousbrighter NGC5638 7.60 <35.52 <38.33 mrx:12;x:30
sources,thenewsteepcorrelationwillbecomeinvisible. We NGC5813 8.75 37.49 38.79 mr:12;x:10
willdiscussthesetwoissuesfurtherinSection5.3. NGC5838 9.06 36.50 38.97 mrx:12;x:10
NGC5845 8.69 <35.46 39.05 mrx:12
NGC5846 8.43 36.62 39.54 mrx:14
TABLE1
NGC5866 7.81 37.04 38.57 mx:14;r:22
Table1.ObservationaldataofquiescentAGNs
NGC6109 8.56 39.44 40.35 m:1;rx:2
NGC6500 8.28 39.35 40.56 mrx:20;x:30
Sources Log(MBH) Log(LR) Log(Lx) Refencesa NGC7626 8.71 38.48 40.97 mrx:14,r:17
(M⊙) (ergs−1) (ergs−1) IC1459 9. 39.69 40.64 mrx:20
IC4296 9.1 38.72 40.24 mrx:20
3C31 8.70 39.48 40.70 m:1;rx:2
3C66B 8.84 40.00 41.13 m:1;rx:2
3C83.1B 9.01 39.49 41.16 m:1;rx:2 References. — (1)Wu,Cao,&Wang(2011);DW15;(2)Hardcastleet
3C338 8.92 39.47 40.34 m:1;r:3b;x:2 al.(2009);(3)Gentileetal.(2007);(4)Benderetal.(2005);(5)Garciaet
al.(2010);(6):vandenBosch&deZeeuw(2010);(7)Yangetal.(2015a);
3C449 8.54 39.11 40.38 m:1;rx:2
(8)Devereuxetal.(2003);(9)Milleretal.(2010);Kingetal.(2016);(10)
3C465 9.13 40.44 41.07 m:1;rx:2
Pellegrini(2010);(11)Nagar,Wilson,&Falcke(2001);(12)Nylandetal.
M31 8.14 32.25 36.06 m:4;rx:5
(2016); (13) Walsh et al. (2013); (14) Ho(2009); Ho et al. (2009); (15)
M32 6.40 32.36 36.00 m:6;rx:7
Brownetal.(2011);(16)Milleretal.(2012a);(17)Nagar,Falcke,&Wilson
M81 7.85 37.20 40.20 m:8;rx:9
(2005);(18)Wrobel&Nyland(2012);(19)Wongetal.(2014);(20)M03;
M84 8.97 38.54 39.50 mx:10;r:11,12
(21)Grieretal.(2011); (22)Filhoetal.(2004); (23)Laurent-Muehleisen
M87 9.5 39.70 40.82 m:13,rx:12
etal.(1997);(24)Ho(2002);(25)Akylas&Georgantopoulos(2009)(26)
NGC0404 5.16 33.5 37.02 mrx:14,1
Ho&Ulvestad (2001); (27)G09; (28)Wrobel, Terashima &Ho(2008);
NGC0474 7.73 <35.55 38.46 mr:12;x:10
(29)Nagaretal.(2002);(30)Terashima&Wilson(2003);(31)Milleretal.
NGC0507 8.91 37.67 40.66 mrx:14,1
(2012b).
NGC0524 8.94 36.75 38.57 mr:12;x:10
NGC0821 8.21 <35.40 <38.30 mrx:10,12 a thereferencesforblackholemass(labelled‘m’),LR(labelled‘r’)andLX
NGC1399 8.7 <38.03 <38.82 mx:10;r:15b (labelled‘x’).
NGC2768 8.82 37.50 39.77 mrx:12;x:16 bVLAobservedat1.4GHz;Thefluxisconverttothatat5GHzwithaflat
NGC2778 7.16 35.50 38.64 mrx:12;x:16
NGC2787 8.14 36.52 38.30 mx:14,1r:17 radiospectrumassumption,i.e.α=−0.4whereFν∝ν−α.
NGC2841 8.31 36.00 38.26 mx:14,r:17 c Only the compact component of Very Long Baseline Array (VLBA)
NGC3115 9.00 35.23 <37.50 mr:18;x:19 observation(at8.4GHz)isconsideredhere. Thefluxisconverttothatat
NGC3226 8.06 37.21 40.00 mx:14,r:17 5GHzwiththeassumptionα=−0.4.
NGC3245 8.21 36.94 39.25 mx:14,r:17
NGC3377 8.25 35.08 38.17 mrx:10
NGC3379 8.62 36.01 37.81 mrx:14,10 4.2. (Quasi-)MBH-freesubsample:theradio/X-ray
NGC3384 7.03 35.22 38.09 mr:12,15;x:10 correlationindexξ
NGC3414 8.67 36.65 39.92 mr:12;x:10 X
NGC3607 8.14 36.79 38.79 mr:12;x:10 Thekeypointof theYC05predictionis thechangeofthe
NGC3608 8.67 35.90 38.20 mr:12;x:10 radio/X-ray correlation index ξ . Therefore, the best way
NGC3610 8.09 <35.29 39.05 mr:12;x:16 X
to examine this prediction is to study the correlation only
NGC3627 7.24 36.37 38.30 m:20;r:11;x:21
NGC3628 7.24 36.40 38.51 mx:14;r:17c betweenLR and LX,withoutthepossible“contamination”of
NGC3675 7.1 <36.3 <38.1 mrx:14 blackholemassM . Thisisbecausewehavemorefreedom
BH
NGC3941 7.37 35.61 39.27 mx:14;r:17 inthefittingamongthreequantitiesL , L and M , thusit
NGC4143 8.16 37.11 39.97 mr:12;x:10 R X BH
isdifficulttodeterminethevalueofξ precisely.
NGC4168 8.13 37.44 <38.91 mrx:12 X
NGC4203 7.79 37.10 40.09 mrx:17,14 Following de Gasperin et al. (2011) and DW15 we create
NGC4216 8.09 36.58 38.91 mx:14;r:22c a subsample of sources with similar M , but has a large
BH
NGC4233 8.19 37.36 40.26 mrx:12 dynamicalrangeinX-rayluminosity(inEddingtonunit).For
NGC4261 8.72 38.62 41.12 mx:12;r:23
simplicity we name it a (quasi-)M -free subsample. As
NGC4278 8.61 38.35 40.04 mx:14;r:11 BH
NGC4365 9.01 <35.42 38.32 mr:12;x:10 shown in Fig. 1, we select sources with MBH in the range
NGC4459 7.82 36.04 38.82 mx:14;r:24 108.1−109.1M (onedexinM ,theboundariesareshownas
⊙ BH
NGC4472 9.40 36.60 <39.36 mrx:12 tworedsolidcurvesinthisplot). Theboundariesarechosen
NGC4473 7.95 <35.30 <38.10 mr:12;x:10
NGC4477 7.89 35.90 39.10 m:1;r:15b;x:25 so that the subsample will have largest dynamical range in
NGC4494 7.68 36.40 38.74 mx:12;r:15b LX/LEdd, i.e. 10∼−10 < LX/LEdd < 10∼−5.7. This MBH-free
NGC4501 7.79 36.28 38.89 mx:14;r:26 subsample includes 42 sources, among which 34 have firm
NGC4552 8.92 38.23 39.12 mx:12;r:10 detectionsin bothradioandX-rays. The averageblackhole
NGC4564 7.94 <35.13 38.52 mx:12;r:10
NGC4565 7.41 36.55 39.85 mx:14;r:17c massofthissubsampleishMBHi=108.71M⊙.
NGC4570 8.03 <35.23 38.13 mx:12;r:10 This MBH-free subsample can be used to explore the
NGC4594 8.46 37.85 40.2 mrx:27,14 radio/X-raycorrelation, and providedirect constrainson the
NGC4621 8.40 35.1 37.8 mrx:28 correlationslope ξ . A linear fit between logL and logL
NGC4636 8.33 36.4 <38.38 mr:12;x:20 X R X
ofthisM -freesubsampleundertheBeyesianmethodreads
NGC4649 9.07 37.48 38.10 m:14;rx:27 BH
NGC4697 8.31 35.00 37.30 mrx:28 (cf. Sec. 3, butnotethatthequantity MBH isomittedduring
NGC4698 7.57 35.59 38.69 mrx:14c themodelling.),
NGC4736 7.05 35.51 38.48 mx:14;r:29
NGC4754 7.76 <35.31 38.27 mrx:11 logL =1.36+0.07 logL −16.38+2.48, (8)
R −0.06 X −2.65
6 Xie&Yuan
5. DISCUSSIONS
5.1. Uncertaintiesoftheobservationaldata
Wefirstdiscusstheuncertaintiesoftheobservationaldata,
i.e. σ andσ .
R X
In quiescent AGNs (and normal AGNs also), emission
at different wavebands likely correlates with considerable
time delays. For one example, Bell et al. (2011) found a
∼40-d time delay of radio (at ∼5 GHz) to X-rays in the
LLAGNNGC7213.Thus,inordertoexplorethe“intrinsic”,
physically-connected FP, a correction of the radio/X-ray
timelag should be applied. However, in practice such
correctionisalmostimpossibleforAGNs,asitrequireslong-
term intense coordinated monitoring in radio and X-rays on
individual sources.4 Moreover, the monitoring should also
be able to capture at least one “outburst” in each AGN, in
order to have a reliable measurement of the timelag. With
soFliigd.4cu.—rveT,hweirthadξiXo/X=-r1a.y36c,orrereplraetsioenntsofththeefiMttiBnHg-forfeethsiusbssuabmsapmlep.lTe,hecfb.laEcqk. theseobstacles/challenges,todateveryfewAGNshavesuch
8.Forcomparison,wealsoshowtheξX=1.23FPofthewholesample(the intensemonitoring(seee.g. Belletal.2011;Kingetal.2013
reddashedcurve), andthe original M03FP(thegreylongdashed curve), for such monitoring in AGNs). The time interval between
bothofwhich have MBH fixedtohMBHi. Themeaning ofthesymbols is radioandX-raysforthedatashowninTable1istypicallyof
thesameasthatinFig.2. Inaddition,theredopentrianglesandthegreen
opensquaresarerespectively,the14normalLLAGNsselectedfromDW15 orderofmonthstoyears.
andthe10AGNsselectedfromM03,bothunderthesameMBH constraint. TheAGNsarevariable,withvariabilityamplitudepossibly
Theyareshownhereas representative ofnormalLLAGNsthat follow the as high as ∼ 100% on time-scales shorter than the time
shallowerM03FP.
intervalofobservations(Ho&Peng2001). Suchuncertainty
dominates over the actual observational uncertainties in the
andundertheleastχ2methodreads, fluxes(orluminosities; L and L )ofindividualobservation
R X
reported in literature. Admittedly different estimations will
logL =1.45+0.07 logL −19.59+2.83. (9)
R −0.07 X −2.83 result in somewhat different fitting results (Ko¨rding et al.
We show the Bayesian fitting result as the black solid curve 2006). There are several estimations on the systematical
in Fig. 4. Note that the radio/X-ray correlation slope here uncertainties of the observed fluxes (e.g. Ko¨rding et al.
is clearly different, at > 7σ confidence level, from that of 2006, DW15), and we adopt isotropic ones, following M03
theoriginalM03FP(blacklong-dashedcurveinFig.4,with and G09. DW15 adopted a slightly smaller scatter in radio
MBHsettohMBHi). Forcomparison,wealsoplotinFig.4the luminosities,i.e. σR = 0.2dex(Ho&Peng2001),compared
ξ = 1.23 FP of the whole quiescent AGN sample (the red to that in X-rays. With this modification to the whole
X
dashedcurve),with M alsofixedtohM i. Apparentlyits quiescent AGN sample, we carry out Bayesian regression
BH BH
differencetoEq.8isinsignificant. analysisandfindthat,
In Fig. 4, we additionally show 14 normal LLAGNs
(red open triangles) selected from DW15 and the 10 AGNs ξX =1.09+−00..0077, ξM =0.70+−00..1121, c=−11.61+−22..1295. (12)
(greenopensquares,hereaftertheM -selectedM03AGNs.)
BH Note that this result is consistent with a steeper radio/X-ray
selected from M03, both under the same M constraint.
BH correlation for quiescent AGNs (cf. Eq. 6), and disagrees
They are shown here as representative of normal LLAGNs
with the claim of a universalFP from sub-EddingtonAGNs
and normal AGNs that follow the shallower M03 FP. It is
toquiescentAGNs.
evidentfromthisplotthatquiescentAGNsfollowadifferent,
steeper, radio/X-ray correlation, compared to the normal
LLAGNsandnormalAGNs. 5.2. impactofFanaroff-RileyIsandthedimmestM31onthe
Because the physics of accretion and radiation is more FPderived
relevant to the quantities in Eddington unit rather than
It has been known for years that radio-loud sources
its absolute values (such as mass accretion rate and systematically follow a steeper radio/X-raycorrelation (e.g.,
luminosity), we further try to find a linear relationship
Li et al. 2008; de Gasperin et al. 2011; DW15). There
between log(L /L ) and log(L /L ) for this M -free
R Edd X Edd BH are 11 sources in our quiescent AGN sample that belong to
subsample. Assumingtheuncertaintyofeachquantityisstill Fanaroff-Riley (FR, Fanaroff & Riley 1974) Type Is, which
0.3dex,thefittingcanbereadas,
aregenerallyradio-loud. Oneconcernisthat,theFPderived
log(L /L )=1.35+0.07 log(L /L )+0.49+0.53 (10) above(cf.Eq.6)maybebiasedbythesesources.Toexamine
R Edd −0.07 X Edd −0.50 the impact of FR Is, we carry out a Bayesian regression
undertheBayesianstatistics,and analysis to a sub-sample (consist 64 sources) that excludes
thoseFRIs,andthefittingcoefficientsare,
log(L /L )=1.43(±0.08) log(L /L )+1.13(±0.57)
R Edd X Edd
(11) ξ =1.18+0.08, ξ =0.57+0.12, c=−14.06+2.48. (13)
underthe least χ2 approach. Finally a linear fitting between X −0.07 M −0.11 −2.59
log(L /L ) and log(L /L ) of the whole sample can be
R Edd X Edd 4 Note that, the radio/X-ray timelag is considerably small in BHBs.
derivedas,log(L /L )=1.48+0.07 log(L /L )+1.13+0.51,
R Edd −0.07 X Edd −0.51 Consequently, it is crucial to use (quasi-)simultaneous radio and X-ray
where the Bayesian approach is adopted. This result is observations to explore the radio/X-ray correlation in BHBs. Additional
consistentwiththatderivedbasedontheM -freesubsample. timelagcorrectionisusuallynotnecessaryfortheBHBcases.
BH
FundamentalPlaneofquiescentAGNs 7
Obviously, it is consistent with the YC05 FP, and disagrees in Sgr A* during its quiescent state (e.g. Shen et al. 2005;
withtheM03FP. Doeleman et al. 2008; Li, Yuan & Wang 2014), i.e. it does
Another concern is that, the FP derived in this work not satisfy the “existence of jet” prerequisite in the study of
is biased by the dimmest LLAGN in our sample M31 FP thus should be excluded from the sample. During the
(L /L ∼ 10−10), since the deviation to M03 FP is quiescentstate of Sgr A*, the low-frequencyradio emission
X Edd
insignificant for most of the sources in our sample, cf. likely originate from the non-thermal electrons of the hot
Fig. 2. We argue this is actually a misunderstanding, accretionflow,whiletheX-rayemissionisthebremsstrahlung
since the radio/X-ray correlation slope can already be radiationbydiffusegasaround∼ 105 R (seeBaganoffetal.
s
determined statistically by abundant other quiescent AGNs. 2003;Yuan,Quataert&Narayan2003;Wangetal.2013and
We demonstrate this by applying the Bayesian analysis to a referencestherein). As shownby the leftmostblackasterisk
subsample that further excludes M31 (63 sources in total). inFig.5,wefindthat,SgrA*initsquiescentstateagreeswith
Thecorrelationcoefficientsare, theM03FP(onlyacoincidencefromourpointofview),but
disagreeswiththenewξ ≈ 1.23FP,asitismorethanthree
ξ =1.12+0.08, ξ =0.61+0.12, c=−12.01+2.69, (14) X
X −0.08 M −0.12 −2.75 ordersof magnitudebrighterin L at the given L (see also
R X
consistentwiththeexpectationofaYC05FPinthesesystems. Markoff2005).
Sgr A* undergoes numerous flares, which are observed
5.3. Comparisonwithpreviousworks in sub-millimeter, infrared and X-rays (e.g., Baganoff et al.
2003;Neilsenetal.2013andreferencestherein).Theseflares
Mostoftheworkinliteratureonthefundamentalplaneof
usuallylast0.1–1hr(Yusef-Zadehetal.2006;Neilsenetal.
blackholeactivitybiastowardsmoderatelybrightersystems
2013),indicatingthattheyarefromnuclearregionsofSgrA*.
(e.g. M03; Falcke et al. 2004;Ko¨rdinget al. 2006;Li et al.
Duringtheseflares,theluminositiesareenhancedbyafactor
2008; G09; Fan & Bai 2016;Nisbet & Best 2016), thus are
as much as ∼ 10% in radio (e.g. at ∼20 GHz, e.g., Yusef-
irrelevanttothiswork. Inthissectionwediscusstherelation
Zadehetal.2006;Brinkerinketal.2015)and∼100(∼400in
ofourworktosomeoftherelatedworkspublishedinrecent
extremecases)inX-rays(2-10keV,e.g.,Baganoffetal.2003;
years,i.e. thoseincludethequiescentaccretionsystems.
Neilsen et al. 2013), compared to the quiescent “non-flare”
state. Wenotethat,interestingly,theseradioandX-rayflares
5.3.1. BHBsintheirquiescentstates:Galloetal.(2006,2014);
arelikelyproducedfromjet(Li,Yuan&Wang2016;Yusef-
Corbel,Koerding&Kaaret(2008)
Zadeh et al. 2006; Brinkerink et al. 2015). If this is indeed
In our work, we exclude from the sample data points of
the case, then Sgr A* in its flare state should be includedin
BHBsintheirquiescentstates.
ourquiescentAGNsample, andtheyarequalifiedtotestthe
CurrentlytherearethreeBHBswithreportedobservations
FP of quiescent AGNs. This is examined in Figs. 2 and 5,
in both radio and X-rays during their quiescent states, e.g.
where the flare state of Sgr A* is shown by the two black
A0620-00(Galloetal. 2006),V404Cyg(Corbel,Koerding asteriskswith L ≈ 1031.5 ergs−1 (10%thatofthequiescent
& Kaaret 2008)and XTE J1118+480(Gallo et al. 2014). It R
state) and L ≈ 1035.38 and ≈ 1035.98 ergs−1 (100 and 400
is claimed that these sources in their quiescent state follow X
timesthatofthequiescentstate), respectively. Hereweonly
the extensionofthe originalξ ≈ 0.6FP(Gallo etal. 2006;
X take the enhancedluminosities(comparedto the “non-flare”
Corbel, Koerding & Kaaret 2008; Gallo et al. 2014). We
quiescentstate) intoaccount,i.e. onlythesecomponentsare
argue that the claim of original FP down to quiescent states
ofjetorigin.Consistentwithourexpectation,wefindthatSgr
inBHBsisnotrobustasclaimed. Thereasonsareasfollows
A*initsflarestateagreesnicelywiththesteepYC05FP(cf.
(see also Yuan & Narayan 2014; Xie & Yuan 2016). First,
Eq.6andFig.2),butdisagreeswiththeoriginalM03FP(cf.
A 0620-00 only have observations in quiescent state, but
Fig.5).
lacks data in hard state. Secondly, V404 Cyg is still too
bright,with L ∼ 10∼−6.8L , toshowcleardeviationtothe
X Edd 5.3.3. Yuan,Yu&Ho(2009)(YYH09)
originalFP5. Finally,theradiodetectionofXTEJ1118+480
atL ∼10−8.5L isadmittedlymarginal,at3σlevel. YYH09isthefirstto discoverfromobservationaldatathe
X Edd existence of a new FP, with ξ ≈ 1.22, in well agreement
Moreover,wenotethatsince thecorrelationisestablished X
withthetheoreticalpredictionbyYC05. Duringtheirsample
in a statistical sense. Few individual sources that do not
compilation, YYH09 exclude data from normal LLAGNs,
follow the new correlationcan notbe taken to argueagainst
and only include data from quiescent AGNs. Besides, Sgr
the existence and correctness of the new relationship. For
A* is also excluded from their sample, for reasons listed
example,we notethattherealsoexistsome“outliers”ofthe
above. Our work is a natural extension of YYH09. The
originalcorrelation,asweintroduceinIntroduction.
main improvement to YYH09 is the sample size, which is
enlargedfrom22to75.Besides,theradioemissionofseveral
5.3.2. SgrA*inquiescentandflarestates
sources, e.g., M31 (Bender et al. 2005; Garcia et al. 2010,
For the AGN sample in literature, there is one source, i.e. L ∼10−10.2L )andM32(Yangetal.2015a),isnowfirmly
X Edd
Sgr A*, that deserves special discussion. This source, with detected,whileinYYH09theirradioemissiononlyhasupper
MBH = 4.30 × 106 M⊙ (Genzel, Eisenhauer & Gillessen limitconstraint.Themainconclusionremainsunchanged,i.e.
2010), has been included in most previous studies on FP. ourenlargedsampleconfirmsthediscoveryofYYH09.
However, as emphasised in Section 2, there are compelling,
independent pieces of evidence against the existence of jet 5.3.4. Dong&Wu(2015)(DW15)
DW15 recently select from the (nearly-)complete flux-
5Notethat,detailedmodellingonthequasi-simultaneousmultiband(radio
limited Polmar survey a sample of 72 AGNs, and combine
uptoX-rays)spectrum ofV404CygatsuchlowX-rayluminosityindeed
supportsthattheX-rayemissionatthequiescentstateisofjetorigin(Xie, withalargesampleofobservationaldatapointsofBHBs, to
Yang&Ma2014). investigatetheFPjointedlyfromsub-Eddingtontoquiescent
8 Xie&Yuan
Fig.5.—ObservationaldataofthecombinedsampleplotagainsttheM03FP(leftpanel,thegreylongdashedcurve)andtheξX =1.23YC05FPderivedin
thiswork(rightpanel,theredsolidcurve). HerethewholesampleincludesboththequiescentAGNsofthisworkandalsothenormalLLAGNs(28sources
fromDW15asrepresentatives;redopentriangles).Inbothpanels,symbolsandcurvesareofthesamemeaningtothoseinFig.2,withonemodification,i.e.the
quiescentsourcessharedbybothXYandDW15arenowshownasgreyfilledsquares. Inaddition,thegreydashedcurveshowsajointfittingtothiscombined
sampleinbothpanels,wheretheblackholemassisfixedto108.5M⊙. Inbothpanels,thegreenopensquaresarethe10MBH-selectedM03AGNs,cf. Fig.4,
andtheyaretakenasrepresentativeofbrighterAGNs.
systems. TheyclaimthosewithL . L (24AGNsunder somesourcesdonotfollowtheoriginalM03FP(e.g.,Lietal.
X X,crit
adetaileddefinitionofL )seemtofollowtheoriginalM03 2008;deGasperinetal.2011forAGNs,andCoriatetal.2011
X,crit
FP,whichdisagreeswiththiswork(andYYH09also). forBHBs. cf. Introduction). Consequently,theexactvalues
There are mainly two reasons on such discrepancy. First, of the fitting dependon bothsample selection and statistical
notable differences between their sample and ours are methods,asnotedinKo¨rdingetal.(2006)anddemonstrated
observed. Their sample includes the BHBs in their hard inSec.4.
and quiescent states, and also Sgr A* in quiescent state. We analysis the combined sample through the Bayesian
Moreover,becausetheirAGNsampleislimitedtodatafrom approach.Thecorrelationindexesnowreadas,
the Polmar survey, the quiescent AGN subsample of DW15
lack sufficient number of sources whose X-ray Eddington ξ =0.87+0.04, ξ =1.29+0.09, c=−8.05+1.48. (15)
ratios are sufficiently low. For the L /L < 10−8 regime, X −0.04 M −0.08 −1.50
X Edd
thereareonlythreesourcesintheirsample(exceptSgrA*), Notethatthevalueofξ isbetweentheresultofDW15and
X
whilethereare17sourcesinoursample.Severalnotablefaint thepresentworkshownin Section4. Thisindicatesthatthe
sourcesaremissed,e.g.,M31(Benderetal.2005;Garciaetal. valueofξ issomewhatsensitivetothefractionofquiescent
X
2010, L ∼ 10−10.2 L )andNGC3115(Wrobel&Nyland sources included in the sample, more fraction of quiescent
X Edd
2012; Wong et al. 2014, L < 10−9.5 L ). These faintest oneswillmakeitsvaluelargerandtheradio/X-raycorrelation
X Edd
sources,withpossiblylargestdeviationtotheoriginalFP,are slopesteeper. Thisisconsistentwithourexpectation.
ofcrucialimportancetorevealthenewtrend. Secondly,they Nowwe dothestatistical analysisbyanotherway. We fix
mainly provide a joint fitting of both normal LLAGNs and thevalueofξXandtesttwo-parameterfittingsofthecombined
quiescentAGNs6,whilewefocusonthequiescentAGNsonly sample.WefindthatboththeξX ≈0.6(M03-like)correlation
here. As illustrated below in Section 5.4, we argue that the and the ξX ≈ 1.23 (YC05-like) correlation could provide
smallnumberofquiescentsourcesintheirsampleandajoint almostequallygood(orbad)fitstothecombinedsample,i.e.
fittingarethereasonsforthediscrepancybetweentheirresult both of which leads to relatively similar reduced χ2 values.
andours. Consequentlyitisdifficulttojudgefromstatisticalinsteadof
physicalpointofviewwhichfittingisbetter.
Fig.5showsthedatapointsofthecombinedsampleplotted
5.4. DisadvantagesofajointfittingofbothnormalLLAGNs
against the M03 FP (left panel; cf. M03) and the YC05 FP
andquiescentAGNs
(right panel; cf. Eq. 6). For clarity, the quiescent sources
We here discuss the disadvantages of a joint fitting of a
sharedby bothXY and DW15 are now shownas greyfilled
sample that includes both normal LLAGNs and quiescent
squares.Forcomparison,weshowinthetwopanelsthefitting
AGNs,especiallywhenthesteepercorrelationisstatistically
ofthiscombinedsample(Eq.15)asgreydashedcurve,where
insignificantasthesamplelacksufficientnumberofdimmest
M issetto108.5 M . Basedontheabovefittingresultsas
sources. For this purpose, we consider a combined AGN BH ⊙
wellasthedirectcomparisonbetweenthetwopanels,wecan
sample, including not only the quiescent AGNs of this
understandthereasonforthediscrepancybetweenthiswork
work (hereby named as the XY sample) but also 28 normal
(andothersimilarones)andDW15(andothersimilarones).
LLAGNs of DW15 (red open triangles in Fig. 5. Note that,
The first reason has been pointed out already below Eq. 15,
except for Sgr A*, the rest 44 AGNs are selected into the
i.e.,thecorrelationindexwillbedeterminedbythefractionof
XY sample). We note that it has been known for years that
quiescentsources(orequivalentlynormalsources)whoseL
X
arefarawayfrom L includedinthesample. Thesecond
6Wenotethat,sincetheirquiescentsubsamplealsoincludesdatapoints reason is that, as shXo,cwritn in Fig. 5, because the luminosity
fromBHBsandSgrA*,afittingofsuchsubsample,asshowninthebottom-
scales as L ∝ L /L × M and the differences in
rightpanelofFig. 1inDW15,willbemisleadingalso. Indeed,asshownin R,X R,X Edd BH
theirFig.2,thesubsampleofquiescentAGNswithsimilarBHmassdohint MBH issufficientlylarge(by∼3ordersofmagnitude)inboth
onamuchsteeperradio/X-rayrelationship. quiescent and normal low-luminosity AGNs, the quiescent
FundamentalPlaneofquiescentAGNs 9
sources will mix up with those normal ones in L and L . writtenasL ∝ L 1.29M0.60.
X R R X BH
Consequently,quiescentsourcesthatare notdimenough(in
L /L ) will only contribute to the scatter of the original 5.5. ThedistributionofRadio-loudnessparameterR versus
X Edd X
M03FP,andtheYC05FPwillbeobscured. EddingtonratioinfaintAGNswithL /L .10−6
X Edd
It is widely known that LLAGNs tend to be radio-loud
systematically, and the radio-loudnessparameter, defined as
R = L /L ,scalesinverselywithEddingtonratiosL /L
X R X bol Edd
(amongothersseee.g.,Ho2008;Nylandetal.2016),where
L is the bolometric luminosity. We note that the FP can
bol
bere-writtenas,R ∝ LξX−1. IfL scalespositivelywithL
X X bol X
(likelyareasonableassumption),thentheYC05FP,withξ ≈
X
1.23>1,predictsthatquiescentAGNsfollowapositiveR –
X
L /L relationship,oppositetothosenormalLLAGNs.
bol Edd
Fig.6.—TheLR/LEdd–LX/LEddrelationshipofthecombinedsample.The
meaningofthesymbolsisthesameasthatinFig.5.Thesolidandthedashed
curvesrepresent,respectively,theYC05FP(cf.Eq.6)andtheoriginalM03
FP,wheretheblackholemassisfixedto108.5M⊙.
We argue that since the YC05 prediction is based on the
difference in L /L rather than L , the correct way to
X Edd X
examine this prediction is to investigate the sample only
consisting of sources with L /L . 10−6. This is also
X Edd
morephysicalsincetheunderlyingphysicsisdeterminedby
L /L instead of L . A M -free subsample (cf. Section
4.X2) wEdildl help to solvXe this prBoHblem. Indeed, fromthe MBH- ratFioig.L7b.o—l/LDEdidst,riwbuhteiroentohferbaodlioom-loeutrdicnelsusmpinaroasmityeteirsResXtimveartseudsaEs,ddLinboglto=n
selectedsample,thequiescentAGNsdofollowaradio/X-ray 16 LX. The meaning of the symbols is the same as that in Fig. 5. Note
correlationthatismuchsteepercomparedtothatfollowedby thatthoseblackopencircles aresourceswhoseLX and LR areupper-limit
thosenormal(LL)AGNs. ThisresultisclearlyshowninFig. constraints,i.e.theirRXisactuallyun-constrained.Thesolidandthedashed
curvesrepresent,respectively,theYC05FP(cf.Eq.6)andtheoriginalM03
4. FP,wheretheblackholemassisfixedto108.5M⊙.
Basedonthisconsideration,weproposethatabetterwayto
analyzethecorrelationistoreplaceL andL with L /L
R X R Edd Fig. 7 illustrates the distribution of radio-loudnessparam-
and L /L , and investigate the FP under a revised three-
X Edd eter R versus Eddington ratios for both quiescent AGNs
X
dimensional (log(L /L ), log(L /L ), log(M )) space.
R Edd X Edd BH and normal LLAGNs. For normal LLAGNs, we take those
Onenotableadvantageofthisnewspaceisthat,objectswith
from DW15 as representatives. Following Ho (2008), we
differentEddingtonratioswillbeseparatedautomatically.For
estimate the bolometric luminosity simply from the X-ray
a demonstration of this advantage, we show in Fig. 6 the luminosity, i.e. L = 16 L . Note that those black
bol X
L /L –L /L relationshipofthecombinedsample,with
R Edd X Edd open circles are sources whose L and L are upper-limit
X R
additional10 M -selected M03 AGNs. From this plot, we
BH constraints, i.e. their R is actually un-constrained. The
X
can see clearly that the correlation slope above and below
black solid and long-dashed curves, respectively, show the
LX/LEdd ∼ 10−6isdifferent. Thequiescentsourcesdofollow results derived from the YC05 FP and the original M03 FP,
asteeperradio/X-raycorrelationcomparedtothatofnormal where the BH mass is fixed to 108.5 M . From this figure,
⊙
LLAGNs, in agreement with YC05 and our finding in the the possible turnoverat Eddingtonratio L /L = 10∼−5.5
presentpaper. Thisnewparameterspacewillbeveryhelpful bol Edd
(or equivalently L /L = 10∼−6.5; see also Yang et al.
to the investigationof FP at differentluminosityregimes(in X Edd
2015b for this value, as constrained by the X-ray spectral
Eddingtonunit),whereachangeintheFPmaybeobserved,
properties in AGNs and BHBs.) is admittedly less evident.
as a consequence of the change in accretion mode at that
Moreobservationsof quiescentAGNswith L /L . 10−8
luminosity regime (e.g. Xie & Yuan 2012, 2016; Yuan & X Edd
(or Eddington ratio L /L . 10−7) are urged to examine
Narayan2014;Yangetal.2015b). bol Edd
thisnewtrendinfuture.
As a preliminary test, we consider our whole quiescent
AGNsample(theXYsample).Thescatterofeachquantityis
6. SUMMARY
fixedto0.3dex,forthesakeofsimplicity.UndertheBayesian
The Fundamental Plane provides a direct evidence on the
approachwefindthat,
disk-jet connection (e.g. M03; Falcke et al. 2004; Merloni
log(L /L )=1.29+0.07 log(L /L ) et al. 2006; YYH09). One remaining question under active
R Edd −0.06 X Edd
debate is whether or not those very faint accretion systems
+0.89+0.10 logM −7.61+0.87. (16)
−0.09 BH −0.89 (i.e., L /L below a critical value ∼ 10−6) follow the
X Edd
The scatter in L /L is 0.82 dex. This result can be re- original M03 FP or the steeper (in sense of the radio/X-ray
R Edd
10 Xie&Yuan
correlation slope) YC05 relationship. Many works favour is better. We thus argue this approach is not the best
the YC05 FP (e.g., Wu, Yuan & Ho 2007; Pellegrini et al. waytoexaminethecorrelationatquiescentregime. In
2007;Wrobel, Terashima& Ho 2008; YYH09; de Gasperin the traditional approach, unless the quiescent sources
et al. 2011; Younes et al. 2012; Reynolds et al. 2014), are extremely faint (in L /L ), we cannot separate
X Edd
while several others favour an universal FP extending down them from normalones, since they are mixed up with
to quiescent/faint systems (Gallo et al. 2006, 2014; Corbel, inL andL duetothelargerangeinblackholemass.
X R
Koerding&Kaaret2008;DW15).Inthisworkwere-visitthis Consequently,quiescentsourceswillonlycontributeto
problem.Forthisaim,thequalityofthedata(mainlytheradio thescatteroftheoriginalFP(theleftpanelofFig.5).
data)ofBHBsisnotsatisfactorythustheconclusionbasedon
thatisnotconvincing,asweargueinSection5.3.1.Therefore • Giventheabovereasons,weproposethatabetterway
we focus on quiescent AGNs, paying special attention to toinvestigatetheFundamentalPlaneistousearevised
the radio/X-ray correlation slope ξ . Compared to previous three-dimensional space spanned by log(L /L ),
X R Edd
studies, in our work we gather from literature as many faint log(L /L ), and log(M ). Physically, parameters
X Edd BH
AGNsaspossiblethusoursampleisthelargesttodate,with5 L /L and L /L have more directconnectionsto
R Edd X Edd
sourcesfainterthan10−9L inX-rays(Fig.1). Asweshow the accretion/jet physics. One notable advantage of
Edd
in the paper, these faint sources are crucial to discriminate thisnewspaceisthat,objectswithdifferentEddington
different correlations. Our main results are summarized as ratios (thus may relate to different accretion regimes)
follows, areseparatedautomatically.AsshownintheFigs.4&6,
there is clearly a “break” in the L /L – L /L
R Edd X Edd
• Based on our quiescent AGN sample, we find that correlation at a critical luminosity L /L ∼ 10−6,
X Edd
quiescentAGNsfollowasteeperFPcomparedtoM03 belowwhichthecorrelationissteeper, consistentwith
FP. The radio/X-ray correlation slope ξX ≈ 1.23, in YC05andYYH09.
goodconsistencywiththepredictionofYC05(Fig.2).
ACKNOWLEDGEMENTS
• To further focus on the radio/X-ray correlation but We thank Drs. Qingwen Wu and Ai-Jun Dong for
eliminateanypossiblecontaminationoftheblackhole helpful discussions and comments, and the referee for
mass, we create a sub-samplein which the black hole valuable suggestions that improve our analysis. FGX
mass is similar. For such a M -free sub-sample, we thanks Drs. Zhaoming Gan, Doosoon Yoon and Zhen
BH
findthatthevalueofξ ≈1.36(Fig.4). Yan for the help on Python, and Drs. Zhao-Zhou Li
and Shi-Yin Shen for the help on Bayesian regression
• We have further explored the reasons for the discrep- analysis. FGX andFY aresupportedinpartbythe National
ancy between the present result and some previous ProgramonKeyResearchandDevelopmentProjectofChina
ones. We find that, for the combined AGN sample (Grant Nos. 2016YFA0400804 and 2016YFA0400704),
that includes sources of both L /L . 10−6 and the Youth Innovation Promotion Association of Chinese
X Edd
L /L & 10−6, the value of ξ is ≈ 0.87 (Eq. 15), Academy of Sciences (CAS) (id. 2016243), the Natural
X Edd X
whichisbetween0.6and∼1.2–1.3. Itisexpectedthat Science Foundation of China (grants 11573051, 11633006
the exact value of ξ in general will be determined and 11661161012), the Key Research Program of Frontier
X
by the fraction of quiescent (or equivalently normal) Sciences of CAS (No. QYZDJ-SSW-SYS008). This work
sources in the sample. Put it in another way, we find has made extensive use of the NASA/IPAC Extragalactic
that the ξ ≈ 0.6 correlation and the ξ ≈ 1.23 Database (NED), which is operated by the Jet Propulsion
X X
correlationprovidealmostequallygood(orbad)fitsto Laboratory,CaliforniaInstituteofTechnology,undercontract
the combined sample, and it is difficult to judge from with the National Aeronautics and Space Administration
statisticalinsteadofphysicalpointofviewwhichfitting (NASA).
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