Table Of ContentSuper-Eddington accreting massiveblackholes aslong-livedcosmologicalstandards
Jian-Min Wang1,2,∗ Pu Du1, David Valls-Gabaud3,1,2, Chen Hu1, and Hagai Netzer4
1KeyLaboratoryforParticleAstrophysics,InstituteofHighEnergyPhysics,CAS,19BYuquanRoad,Beijing100049,China
2National AstronomicalObservatories of China, CAS,20A DatunRoad, Beijing100020, China
3LERMA,CNRSUMR8112, ObservatoiredeParis,61Avenuedel’Observatoire, 75014Paris,Franceand
4School of Physics and Astronomy and The Wise Observatory,
TheRaymondandBeverleySacklerFacultyofExactSciences, Tel-AvivUniversity,Tel-Aviv69978, Israel
3 (Dated:Received27August2012;accepted16January2013byPhysicalReviewLetters)
1
Super-Eddington accreting massive black holes (SEAMBHs) reach saturated luminosities above a certain
0
accretion ratedue to photon trapping and advection inslimaccretion disks. Weshow that these SEAMBHs
2
could provide a new tool forestimating cosmological distances ifthey are properly identifiedby hard X-ray
n observations, in particular by the slope of their 2–10 keV continuum. To verify thisidea we obtained black
a holemassestimatesandX-raydataforasampleof60narrowlineSeyfert1galaxiesthatweconsidertobethe
J
mostpromisingSEAMBHcandidates. Wedemonstratethatthedistancesderivedbythenew methodforthe
7 objectsinthesamplegetclosertothestandardluminositydistancesasthehardX-raycontinuumgetssteeper.
1 Theresultsallowustoanalyzetherequirementsforusingthemethodinfuturesamplesofactiveblackholes
andtodemonstratethattheexpecteduncertainty,givenlargeenoughsamples,canmakethemintoauseful,new
] cosmologicalruler.
O
C PACSnumbers:98.80.Es,98.54.Cm,98.62.Js,98.62.Mw,95.36.+x
.
h
p
ThediscoveryoftheacceleratingexpansionoftheUniverse ratherthanlinearly)totheaccretionrate[6,7],
-
o hasnowbeenestablishedthroughobservationsoftypeIasu-
r pernovae (SNe Ia) [1], and is likely to be confirmed further L• =ℓ0(1+alnm˙ 15)M• , (1)
t
as wlatiitohnnse,wwesataknldeanrsdinrgulaenrsdpcrlouvsitdeersdobfygbaalaryxoiensa[2co].usHtiocwoesvceilr-, whereℓ0 ≈5.29×1038 ergs−1M⊙−1,anda≈0.476[7].For
[ reference,atm˙ =15thesaturatedluminosityis 4.20L .
SNe Ia beyond z & 1.5 are rare [3] as there is no time for ∼ Edd
Thus, at a given black hole mass, SEAMBHs are radiating
1
theirprogenitorstoevolveinsubstantialnumbersgiventheir
v basicallyataconstantluminositywhich,asshownbelow,can
lowermetallicity[4].Tofurtherprobethedynamicsoftheac-
5 thereforebeusedtodeducecosmologicaldistances.
2 celeration,newdistanceindicatorsareneededatandbeyond InthisLetterweaddresstwoimportantissues:howtoiden-
2 theseredshifts.Basedonwell-understoodphysicsweshowin
tify SEAMBHs and how to test, observationally, Equation 1
4 thisLetterthatsuper-Eddingtonaccretingmassiveblackholes
and its uncertainties such that it can be used to derive reli-
1. (hereafterSEAMBHs)insomeactivegalacticnuclei(AGNs), ablecosmologicaldistances. WhileSEAMBHsarepredicted
0 thatarecharacterizedbya massof 106∼8M⊙, canprovidea tohaveuniqueoptical-UVspectralcharacteristics[5–7],their
3 new tool to estimate cosmologicaldistances at a wide range
use to identify such sources is hampered by the dilution of
1
ofredshifts,includingthehighredshiftUniverse.
: thediskemissionbystellarradiationfromthehostgalaxyat
v
long wavelengths, and by the Galactic and inter-galactic ab-
i
X Radiation pressure limits the spherical accretion rate onto sorption at short wavelengths. In fact, current observations
r black holes to M˙Edd = LEdd/ηc2, where LEdd = cannot identify such systems using only their spectra in the
a
4πGM•mpc/σT is the Eddington luminosity for a pure hy- optical-UV domain. Fortunately, X-ray spectroscopy allows
drogenplasma, η ( 0.1)isthemasstoradiationconversion such identifications for two reasons. First, there is a well-
∼
efficiency,σT istheThomsoncrosssection,mp istheproton knownpositivecorrelationbetweenthe2-10keVX-raypho-
mass, c is the speed of light, G is the gravitational constant ton spectral index (Γ) and the Eddington ratio (L /L )
Bol Edd
and M• is the black hole mass. However, super-Eddington [8]. In addition, higher LBol/LEdd sources emit a smaller
accretionontoblackholesisfeasibleinslimdiskswherethe fractionoftheirtotalradiation(fX = LX/L•) athardX-ray
radiation pressure-dominated regions (RPDR) are thermally energies[9]. Thesepropertiesareeasytomeasurewithmod-
stable due to the radial advection of the locally emitted ra- ern X-ray observations and are similar to those observed in
diation [5]. In such disks, the timescale of photon diffusion GalacticblackholesinX-raybinaries[10].
to thedisksurfaceis longerthanthatofthe radialmotionof ThegeneraltheorythatlinksX-rayemissiontotheoptical-
the accreting gas in the RPDR. The photons are trapped in- UVspectrumofaccretiondisksisbasedontheassumptionof
sidetheaccretionflowsandareadvectedintotheblackholes. ahotcoronaabovethediskthatisthesourceoftheX-rayra-
This advection dominateswithin the photontrapping radius, diation. TheX-rayemissionefficiencyoftheprocessesinthe
Rtrap ≈ 430m˙ 15Rg,wherem˙ 15 = m˙ /15,m˙ = M˙•/M˙Edd, corona depends on LBol/LEdd. In particular, the magneto-
M˙•isthemassaccretionrateandRg =GM•/c2[6]. Photon rotational instability is a key factor to produce the viscosity
trappingaffectsthetotalemittedradiationandresultsinasat- thathelpstransportingangularmomentumoutward[11]. The
uratedluminosity,L•,whichisproportional(logarithmically, processtakes place throughmagnetic buoyanttransportation
2
abovethecolddisk[12]whichleadstoa“corona-dominated” lines ([OIII]/Hβ < 3); 5) fast, large amplitude X-ray vari-
dissipationthroughhardX-rayemission.Theincreasesofthe ations [19]. The typical black hole mass in NLS1s (see be-
accretionratesresultintheweakeningofthetransportationof low) is considerably smaller than that in BLS1s of similar
magnetic tubes because of the inflation of the disk by radia- L which implies that many of them may be accreting at
Bol
tionpressurewhichyieldsareductionofthebuoyantvelocity. super-Eddingtonrates.
Theendresultoftheseprocessesistheradialadvectionofthe TotestobservationallyEquation1inNLS1s,wehavetoes-
emittedphotonsandthesuppressionoftherelativeX-rayflux timateM•. Blackholemassescan bemeasuredindividually
(f )ofthesystem[13]. using the reverberation mapping (RM) technique, which in-
X
The second effectof an increasing L /L ratio is the vokestheresponse(timelag)ofthebroademissionlineswith
Bol Edd
steepeningoftheX-rayphotonindexΓ. Therehavebeenvar- respect to changes in the continuum producedby the under-
iousattemptsatcalculatingΓinhotcoronaefrombasiccon- lyingdisk[20,21]. Initsmostdetailedversion,thevelocity-
siderationsoftheconditionsinaccretiondisks[12]. The2-10 resolvedreverberationmapping(VRRM),onecanderivethe
keVemissionismainlyduetotheComptonizationofphotons spatialdistributionofthelineemittinggas,anditsvelocity,at
fromthe colddisks(the X-rayreflectioncan beneglectedin everylocationaroundtheblackhole. Inprinciple,thisphase-
thisband[14]). IthasbeenshownthatfX M•−1/18m˙ −4/9 spacemappingenablesustodetermine,accurately,theblack
∝ holemass(thisisequivalenttodynamicalmethodswhichare
intheRPDR(seeequation13forf 1andFigure1inRef.
X
≪ used to measure the masses of black holes in normalnearby
[13])andthusoneexpectsthataluminosityfXL• isradiated
galaxies). Suchtwodimensionalmappingsareonlyavailable
by the coronae. Since Comptonization is the main cooling
for a handful of sub-Eddington sources and many details of
process, the balance between heating and cooling yields the
densityofhotelectronsn f andn m˙ −4/9. thetechniqueneedtobeimprovedforaccuratemeasurements
c X c
∝ ∝ (e.g.thecaseoftheBLS1Mrk50[21]).
Under the conditions discussed above, the X-ray photon
Fortunately,wecanuseasaproxythetightcorrelationbe-
index can be approximated by Γ 2.25y−2/9 [15], where
≈ tween the size of the broadline regions(BLR) (the time lag
y = 4θ τ (1+4θ )(1+τ ) is the Comptonizationparam-
e T e T times the speed of light) and the underlying continuum lu-
eter, θ = kT /m c2, T is the electron temperatureand τ
e e e e T minosity to obtain an empiricalrelationship, fora sample of
is the Thomson scattering optical depth. It is expected that
about35AGNs,thatcanbecombinedwiththeobservedline
y nγ m˙ −4γ/9, where γ = 1 for unsaturated Comp-
∝ c ∝ widthstoestimatetheblackholemassesinalargesampleof
tonization(τ < 1)andγ = 2forsaturatedComptonization.
T sources.Therelationshipisgivenby
Thisscenariois supportedbythe behaviorsofblackholeX-
ray binaries in very high states [10], showing that the 2-10 L α
keV emission is at the level of low/hard states, but the pho- RBLR =R0 1044e51r0g0s−1 , (2)
ton indexes are typically Γ > 2. Considering that hard X- (cid:18) (cid:19)
ray spectra have a cutoff of 50-100 keV (θe ∼ 0.1 − 0.2) where R0 ≃ 9 × 1016cm, α = 0.6 ± 0.1, and L5100 is
[16] and applying the above coronal model to AGNs, we the AGN continuum luminosity (λL at 5100 A˚ in units of
λ
haveΓ m˙ 8γ/81. Thispredictionagreeswith the observed 1044erg s−1) [20, 22]. We note that among the 35 AGNs
∝
Γ LBol/LEdd correlationof AGNs hostingstandard(opti- used to derive this correlations, eight are NLS1s and follow
−
callythickandgeometricallythin)accretiondisks[8]. thesametrendasothersources[23].
The simplest model for the slim disks of SEAMBHs Equation2enablesustoobtaintheblackholemassesbyas-
assumes a spherical hot corona with a characteristic size sumingavirialized(gravitationallybound)cloudsystemand
ℓ . The Comptonization of photons from the slim combining all the unknown geometrical factors, such as the
c
disk surface produces a hard X-ray luminosity LX = inclination to the line of sight, into a single constant fBLR.
4θeneσTc L•/4πℓ2cc 4πℓ3c/3 , giving rise to τT = Using this constant we can now write an expression for the
3f /4θ 0.8f θ−1,whereτ = n σ ℓ ,f = f /0.1 “reverberationmapping-basedvirialmassestimate”ofsuper-
andX θ e ≈=(cid:0) θ /00..11. 0(cid:1)T.1(cid:0)he coron(cid:1)aTe haviengTacCo0m.1ptonizXation massiveblackholesas
0.1 e
parameterof y 0.8, the SEAMBHsare thencharacterized
by Γ & 2.3y−2≈/9, where y = y/0.8. Obviouslythere are M• =fBLRG−1VF2WHMRBLR , (3)
0.8 0.8
uncertaintiesintheseparametersandtheresultingtheoretical where V is the FWHM of the broademission line (e.g.
FWHM
relationships,however,wecanusetheobservedΓtoidentify Hβ)thatwasusedtoderivethetimelagintheRMmeasure-
SEAMBHsindifferenttypesofactivegalacticnuclei. ment.Thefactorf iscalibratedbycomparingtheresultsof
BLR
The best group of AGNs where such processes have been theRMexperimentstodirectblackholemeasurementsbased
studiedarenarrowlineSeyfert1galaxies(NLS1s).Theseob- ontheM• σ∗ relation,whereσ∗ isthestellarvelocitydis-
−
jectsareseparatedfrombroadlineSeyfert1galaxies(BLS1s) persion in the bulge of the host galaxy. Such a comparison
byhavingthefollowingproperties[17,18]:1)thefull-width- isnowavailableforabout30outofthe35AGNsin theRM
half-maximum (FWHM) of Hβ profiles are narrower than sample. It shows that f 1.2 0.2 [24]. Noting that
BLR
2000kms−1;2)strongsoftX-rayexcess;3)unusuallystrong L• = κBL5100, where κB is≃a bolo±metric correction factor,
(relative to Hβ) optical iron emission lines; 4) weak [OIII] we obtain an expressionof L• in terms of fBLR and VFWHM.
3
FIG.1:Left:ResidualsoftheSEAMBHdistancemodulus(∆µ=µ•−µL).Theerrorbarsaretakenas∆µ•=1.17mag(seetextfordetails).Theassumed
cosmologicalparametersareH0 =71kms−1Mpc−1,ΩΛ =0.73andΩM =0.27.Middle: Thedistributionof∆µasafunctionofthehardX-ray(2-10
keV)photonindexΓ. Thenormalizedfrequencyisreferredtofractionstothepeaknumberofobjects. N isthetotalnumberofSEAMBHsselectedbyΓ.
Right:scatterofthe∆µdistributionswithΓ(bottom)andthedistributionofΓforthesampleofSEAMBHcandidates.Thedependenceofthedispersioninthe
residualsasafunctionofΓshowsasystematicdecreaseandtendstoσmin,indicatingtheefficacyoftheselectionasstandardcandles.
∆µ
SinceL =4π 2F ,whereF isthemeasuredcon- similar results in [7, 28]). The contaminationsby the stellar
5100 • 5100 5100
tinuumfluxinunitDsofergs−1cm−2at5100A˚ and • isthe light of the host galaxy were removed, prior to the estimate
D
luminosity distance of the black hole, we obtain the expres- ofF ,usingtheapproximationdescribedinMaterialsOn-
5100
sion line. We examined the L /L distribution in our NLS1
Bol Edd
sampleandfoundthat,indeed,manyofthemindicatesuper-
• = 1 l0(1+alnm˙ 15)fBLRR0 1/2(1−α) VF1W/(H1M−α). Eddingtonratios,upto5andevenmore. Thus,theselection
D √4π (cid:20) GκB (cid:21) F511/020 ofsourcesbyΓisindeedagoodwaytoidentifysuchsources.
(4) We calculate ∆µ for all sources, bin them into various
Thisexpressionstillinvolvestheunknownaccretionratem˙ groupsofdifferentΓ,andplottheminFigure1. Asshownby
15
which,assuggestedearlier, canbe estimatedfromtheX-ray thestandarddeviation(σ ),thescatterof∆µsystematically
∆µ
slopeΓ.However,thedependenceforΓ>2(whichistheone decreasesasΓincreases. FromEquation4),thisbehaviorcan
weareinterestedhere,seebelow)isweakenoughthatwecan beunderstoodintermsofthescatterexpressedby
ktuhnsaeotwthanneoaopbbpsjeerorcvxtaiimbslaeatsiSoaEnnAdm˙Mc1o5Bn=Hsta1bnyatsn.mdTeoahbsutuasri,innhDgav•iitnsfrgoΓmeisnttahdbeelxios,thhweeder ∆µ• = ln510"4((11+−aαl)n−m2˙a125)2 (cid:18)∆m˙m˙ (cid:19)2+∆µ2X#1/2,
haveawaytodirectlymeasureitsdistance. (5)
In the following we use the distance modulus, µ• = where ∆µ2X = 5i=1∆µ2i, ∆µi = Ai(∆Xi/Xi), Xi =
5log(D•/pc) − 5, and compare it with the one obtained fBLR, R0,κB, VFWPHM,F5100, Ai(i = 1,2,3) = 1/2(1−α),
from the standard luminosity distance L in the Friedman- A4 = 1/(1 α)andA5 = 1/2. ∆µ• convergesto ∆µX as
D −
Lemaˆıtre-Robertson-Walkermetricµ = 5log( /pc) 5. ∆m˙ /m˙ decreaseswithincreasingΓ.
L L
D −
The prediction is that comparing • and DL we will get Toillustratethetypicaluncertaintyonindividualpointswe
D
smaller residuals ∆µ = µ• − µL for larger Γ, since large assumethat∆fBLR/fBLR = 0.2 [24] (fromthe scatterin the
indices point to conditions closer to those predicted by the M• σ∗distribution),∆F5100/F5100 =0.2(fromtheknown
−
SEAMBHtheory. variationsintheopticalcontinuumandtheuncertaintyinthe
We now turn to the available samples of SEAMBH can- substraction of the stellar background), ∆V /V =
FWHM FWHM
didates. While the observedNLS1 propertiesmay all be re- 0.05(fromtheuncertaintyinfittingtheemissionlineprofiles
latedtothelargeEddingtonratio[18,25],notallNLS1shave andmeasuringV ),∆R /R =0.2and∆κ /κ =0.3.
FWHM 0 0 B B
super-Eddington accretion rates. It is thus necessary to use Theestimateduncertaintyofκ isthelargestandmostprob-
B
thehardX-rayspectratoidentifySEAMBHsamongNLS1s. lematicforseveralreasons. First, allourestimatesof κ are
B
We selected a large number of NLS1s from several hetero- derivedfromtheoreticalcalculationsofslimdiskspectra [7].
geneous samples [18, 26] with hard X-ray observations by These have not been verified observationally because of the
ASCA, XMM-Newton, Chandra and Swift [27]. All data and lackofextremeUVobservations,wheremostof theemitted
datareductiondetailsareprovidedintheSupplementaryMa- luminosityindisksaroundsmallblackholes(106 107M⊙)
−
terials Online. In short, we use the observed F flux and is emitted. Moreover, a factor of 10 increase in black hole
5100
theestimatedblackholemassM• toderiveκB andhenceL• mass results in a factor of 101/3 decrease in κB (from about
for each source (see also a somewhat differentapproach but 100in106M⊙toabout40in107M⊙blackholes).Theentire
4
rangeofblackholemassesinoursamplesuggestsaverylarge ence and futureobservations. Moreover,the accuracyof the
∆κB/κB. Fortunately, the individualmasses are knownand measuredM•canincreasesubstantiallyifnew,dedicatedRM
the uncertainty on massive black holes using the RM-based experimentsare carried out on a large numberof SEAMBH
virial method is only a factor of about 3 [29]. This and the candidates. This can reduce the uncertainty on f , F ,
BLR 5100
allowedrangeofspectralshapesandm˙ givesthequotedesti- V andR andconstrainαtobetheslopeforthispopu-
FWHM 0
mateon∆κ /κ . lationonly.AsFigure1shows,itisreasonabletoassumethat
B B
Combining all these uncertainties and assuming α = 0.6 foralargeenoughsampleofSEAMBHsatanarrowredshift
we obtain ∆µX = 0.54. This correspondsto ∆µ• 1.17 range,wecouldexpectascatteronthepopulationµ• thatap-
≃
mag since the first term in Equation 1 tends to vanish for proaches0.15mag,similartothecurrentaccuracyofSNeIa
largeenoughvaluesof Γ. ThisisnotsurprisinggivenEqua- method[3].
tion 1 and the known uncertainties on M• measured by the SEAMBHs,asanewtypeofcosmologicaldistanceindica-
RM-basedvirialmethod. Thisuncertaintyisestimatedto be tor,haveanumberofadvantagesoverothers[30]:(1)Thesat-
0.3–0.5dexwhichwouldsuggestasimilaruncertaintyonL•. urated luminosities are well understoodon physical grounds
Sinceµ 2.5logL•,wegetasimilaruncertaintyonindivid- and have no potentialcosmic evolution. (2) The objects can
∝
uallymeasuredpointstotheoneobtainedbythemoredetailed beefficientlyselectedbytheirX-rayoropticalproperties.(3)
calculations. From Figure 1, we find ∆µ• & σ∆mµin = 0.93 Theycanprobea largerangeof redshifts, as theyfollowthe
mag,whichclearlyshowsthattheselectedsamplehasasmall cosmic growth of massive black holes that are abundant at
scatterof∆m˙ /m˙ relatedtothisterm. high-z and are very luminous. (4) Unlike SNe Ia, repeated
The panels of Figure 1 illustrate both the convergence to observationscanbemadetoimprovetheobservationalaccu-
∆µ = 0 and the reduced scatter when using increasinglt racy.
h i
larger values of Γ. The central panel shows that for a suffi-
Several observational issues require careful attention: (1)
cientlysteepX-raycontinuum,acombinationofalargenum-
As mentioned before, the R L relation applied here is
ber of SEAMBHs gives, indeed, the correct distance with a BLR −
theoneobtainedforallAGNs. There-calibrationofthisre-
smallscatter.
lationshipinadedicatedNLS1sorSEAMBHsample,byob-
The systematic decrease of the dispersion in the subsam-
tainingbetterestimatesofR andαinEquation2,canreduce
ples with increasing Γ, while keeping a median with little 0
thescatterinthederivedmassandhenceκ . Obviously,the
variation, cannot be accounted by statistical fluctuations in B
estimatedM• involvesthedistancetothesourcewhichisthe
the subsamples. Consideringthat the subsamplesare notin-
quantitywe are attemptingto measure. However, we do not
dependent,we assessthestatisticalsignificanceusingMonte
expect large differences between and so this uncer-
Carlosimulationswith107GaussiansamplesofsizeN =60 DL D•
tainty, by itself, is very small. (2) The 2-10 keV luminosity
withthesamemeananddispersionastheobservedone.From
andslope are bothvariable[19] whichmay leadto misiden-
them,weselecteddistinct(i.e.,withnoreplacement)random
tification of SEAMBHs. Long-term averaged values can be
sub-samplesofthesamesizeastheonesselected(Figure1),
usedtoimprovetheaccuracy.
andestimatetheprobabilitiesthatthedifferencesinthemedi-
The prospects of building large samples of SEAMBHs to
ansandtheratioofthedispersionscorrespondtotheobserved
beusedastestsofthecurrentcosmologicalmodelarepromis-
ones. We findthat while the probabilitythatthe mediansdo
ing. We expectthat roughly20%of NLS1 with Γ 2 host
notdifferfromthe oneoftheunderlyingsample of N = 60
≥
SEAMBHs. As NLS1 constitute about 10% of all AGNs,
is always verylarge (above 80%), the probabilitythat the
∼ thereshouldbe104 105SEAMBHsamongSeyfert1galax-
dispersionsareassmallastheobservedoneisalwayssmaller
∼
ieswithz 0.3[31]. SEAMBHscouldbeevenmoreabun-
than3%. Theobservedtrendcannotthereforebeascribedto
≤
dantathigh-zalthoughthedefinitionofNLS1shouldbemod-
randomfluctuationsofsmallsamplesextractedfromthemain
ifiedinsuchcases[32]. Herewerequireblackholemassesti-
sample. In the sample used here, there are only 12 sources
with Γ [2.3,2.5] but future samples will be larger since matesthatarebasedonboththeHβandMgIIλ2798A˚ lines.
∈ X-ray spectra can be obtained by Nustar, by the upcoming
such objects can be observed to high redshift. We point out
eRosita and HXMT missions [33]. Given accurate observa-
that the Γ 2.3 and 2.3 Γ 2.5 panels are statistically
≥ ≤ ≤ tions of SEAMBHs at high redshift we will have a unique
indistinguishable because of the poor quality of the sources
chance to explore in-depth the dynamics of the accelerating
with Γ > 2.5. There are 11 sources in total with Γ > 2.5
Universeaswellasthenatureofdarkenergy.
listedinTable1intheSupplementaryMaterialOnline. Five
of them with hard X-ray observations have large error bars JMW thanks the hospitality of M. Ward and C. Done at
(∆Γ 0.37),makingtheΓ binninglesssignificantforthese Durham,wherethisworkwasinitiatedinearlyOctober2011.
≥ −
small samples. Five other objects are observed in the 0.5–8 L.C. Ho,Y.-Y.Zhou,Z.-W.Han,C.Jin, Y.-R.Li, S.-M.Jia,
keVbandbyChandra(Williamsetal. 2004in[26],seenotes J.-M. Bai and J.-C. Wang are acknowledged for useful sug-
inTable1),butthedataqualityonlyallowsustoapproximate gestions and discussions. The research is supported by 973
the 0.5–8keV spectral indexeswith the 2–8 keV proxy, and project (2009CB824800), NSFC-11173023, -11233003, and
the errorbarsof these sourcesremainverylarge(∆Γ & 0.3 -11133006. DVG was supported in part by the CAS with a
except one). The 2.3 Γ 2.5 panel is shown for refer- VisitingProfessorshipforseniorinternationalscientists.
≤ ≤
5
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