Supermassive black holes do not correlate with dark matter halos of galaxies

0.61 MB·English

by  John Kormendy

Nature Letter, 20 January 2011, 000, 000–000
Supermassive black holes do not correlate with dark
matter halos of galaxies
6
Figure 1 updates the plot that was used to claim a BH–DM
correlation. The reliable original data are shown in black;
John Kormendy1,2,3 & Ralf Bender2,3
points measured with low velocity resolution were omitted as
documentedinSupplementaryTable1. Motivatedbytheabove
8
Supermassiveblackholeshavebeendetectedinallgalaxies discussion, we measured velocity dispersions in six Sc–Scd
thatcontainbulgecomponentswhenthegalaxiesobserved galaxiesthathavenuclearstarclusters(“nuclei”)butessentially
were close enough so that the searches were feasible. no bulges. They are shown by red points. Other color points
Together with the observation that bigger black holes live show additional published data on bulgeless galaxies that were
1inbiggerbulges1–4,thishasledtothebeliefthatblackhole measured with enough spectral dispersion to resolve nuclear σ.
1growth and bulge formation regulate each other5. That is, Figure1showsthatbulgelessgalaxies(colorpoints,NGC3198)
0blackholesandbulges“coevolve”. Therefore,reports6,7of show only a weak correlation between Vcirc and σ. This is
20
2asimilarcorrelationbetweenblackholesandthedarkmatter expected, because bigger galaxies tend to have bigger nuclei .
halosinwhichvisiblegalaxiesareembeddedhaveprofound Butnotightcorrelationsuggestsanymorecompellingformation
nimplications. Dark matter is likely to be nonbaryonic, so physics than the expectation that bigger nuclei can be
athesereportssuggestthatunknown,exoticphysicscontrols manufactured in bigger galaxies that contain more fuel. The
J
blackhole growth.Here we show– based in part on recent

4measurements8ofbulgelessgalaxies–thatthereisalmost
2no correlation between dark matter and parameters that
measureblackholesunlessthegalaxyalsocontainsabulge.

]We concludethat black holes do not correlate directly with
A
dark matter. They do not correlate with galaxy disks,
Geither9,10. Thereforeblackholescoevolveonlywithbulges.
This simplifies the puzzle of their coevolution by focusing
.
hattentiononpurelybaryonicprocessesinthegalaxymergers
pthatmakebulges11.
-
o Theideaofcoevolution wasmotivatedbytheobservation that
rbigger black holes (BHs) live in bulges and elliptical galaxies
stthathavebiggervelocitydispersionsσ atlargeradiiwherestars
afeel mainly each others’ gravity and not that of the BH3,4.
[This correlation was compelling, because its scatter was small,
consistentwithmeasurementerrors. Thereducedχ2was0.79for
1 3
the highest-accuracy sample , and “the intrinsic scatter [in BH
vmass M• at fixed σ] is probably less than 0.15 dex.”4 The
0
scatter was so small that σ could be used as a surrogate for
5
M• for many arguments. More important was the implication
6
that a fundamental physical connection between BH and bulge
4 12
growthawaitsdiscovery,giventherealization thatevenatiny
1.fractionoftheenergyproducedinBHgrowthcould,ifabsorbed Figure1|OuterrotationvelocityVcircvs. near-centralvelocitydispersionσ.
0by protogalactic gas, regulate bulge formation. Small scatter ThedataarelistedintheSupplementaryInformation.Errorbarsare1sigma.
1willbeimportanthere,too.Tightcorrelationsmotivateasearch The original BH–DM correlation6 is shown in black symbols (circled if the
1for underlying physics. Loose correlations are less compelling: galaxy has a classical bulge) except that points have been omitted if the
:bigger galaxies just tend to be made of bigger galaxy parts. σ measurement had insufficient velocity resolution. For example, the
v Thediscovery6,7 ofasimilarly tightcorrelation betweenσ and bulgeless Scd galaxy IC342 (now the orange point, after correction) was
Xitohfegacliarcxuielas,rwrohtearteiognravveiltoyciitsiecsoVntcriorclleodfbgyasdianrkthmeaotutetrer(DpaMrt)s, tshheowmne6asautreσme=nt7175h±ad1l2owkmresso-l1u,ticoonn:stihseteinntstwruitmhetnhtealbvlealcokcitpyodinistsp.ersBiount
arItnhefraecfto,rietwwaasstsaukgegnesttoedim6ptlhyatthtahteDmMoraelsfuonrdeagmuleantetsalBcHorrgerloawtitohn. σLoinwstrre=so(rleustioolnutoioftnenFWreHsMul)t/s2.i3n5owvaesre6s1timkmatesd-1σ,s.imThilearstaomσesfoouunrcdeinlisItCs3σ42=.
istheonewithDM;i.e.,thatdarkmatterengineerscoevolution. 77kms-1forthenucleusofM33,whichhasσ=21 2kms-1asmeasured
TheproposedBH–DMcorrelationraisedtwoconcerns. First,it athighresolution16,17. Infact,ahighresolutionme±asurementofIC342was
wasknownthatBHsdonotcorrelatewithgalaxydisks9,whereas available18:atσinstr=5.5kms-1,σisobservedtobe33 3kms-1(orange
galaxydiskscorrelatecloselywithDM13,14. Itwasnotclearhow point). Wecorrectoromitblackpointsifσ <∼σinstr. We±addpoints(color)
BHsand diskscould separately correlate with DM without also forgalaxiesmeasuredwithσinstr<10kms-1,i.e.,highenoughresolution
correlating with each other. Second, the velocity resolution of toallowmeasurementofthesmallestdispersionsseeningalacticnuclei.The
some σ measurements was too low to resolve narrow spectral line(equationatbottom;velocitiesareinunitsof200kms-1)isasymmetric
lines; this problem is discussed in thecaption to Figure 1. least-squaresfit19totheblackfilledcirclesminusNGC3198.Ithasχ2=0.25.
If dark matter controls BH growth and bulges are essentially Thecorrelationcoefficientisr=0.95. Thiscorrelationisatleastasgoodas
irrelevant, then Vcirc should correlate tightly with σ even in M•–σ.Thecorrelationforthe+pointshasχ2=2.6andr=0.77.Incontrast,
galaxies that do not havebulges. Figure 1 performs thistest. thecorrelationforthecolorpointsplusNGC3198hasχ2=15.7andr=0.70.
1
DepartmentofAstronomy,UniversityofTexasatAustin,1UniversityStation,Austin,TX78712-0259,USA
2
Max-Planck-Institutfu¨rExtraterrestrischePhysik,Giessenbachstrasse,D-85748Garching-bei-Mu¨nchen,Germany
3
Universita¨ts-Sternwarte,Scheinerstrasse1,D-81679Mu¨nchen,Germany
Nature, 20 January 2011, 000, 000–000 2
scatter is much larger than the measurement errors, χ2 = 15.7. Bulgesdissipatemorethandisks. Theconsequencesareshown
Noteinparticularthatgalaxieswithσ 25kms−1spanalmost in Figures S1andS2in theSupplementaryInformation. Figure
thecomplete Vcirc range for thecolor≃points, 96 – 210 km s−1. S1 shows that Vcirc for the bulge Vcirc for the halo for the
8 ≈
Our measurements were made with the 9.2m Hobby-Eberly two highest-Vcirc galaxies whose points are circled in Figure1.
Telescope and High Resolution Spectrograph; σinstr=8kms−1 Figure S2 shows that the same equality holds reasonably well,
reliablyresolvesthesmallestvelocitydispersionsseeningalactic given the uncertainties in rotation curve decomposition, for all
nuclei. We easily confirm that σ = 19.8 0.7 km s−1 in M33 decompositions that we could find that included a bulge. It
± −1
and includethis value in Figure 1. holdsinjusttheVcircrange, 180–260kms ,wheretheblack
Two properties of our sample deserve emphasis. First, we circles in Figure1show a tight correlation. Because a bulgehas
observed NGC 5457 = M101 and NGC 6946, because these are Vcirc √2σ,acorrelationlikethatinFigure1isexpectedfrom
−1 ∼
amongthebiggestbulgelessgalaxies(Vcirc 210kms ). This FigureS2. Allgalaxiesthatparticipate inthetightcorrelation in
is important because Ferrarese concluded6≃that “the Vcirc–σ Figure 1 are included in Figure S2. And all of them have bulges
relation ... seems to break down below Vcirc 150 km s−1 or pseudobulges. We conclude that the correlation is nothing
[in ournotation, so] halos of mass smaller than ∼5 1011M⊙ morenorlessthanarestatementoftherotationcurveconspiracy
∼ ×
areincreasinglylessefficientatformingBHs.” Ourgalaxiesshow for bulges and DM. It is a consequence of DM-mediated galaxy
that Vcirc – σ breaks down already at Vcirc = 210 km s−1 if formation. The conceptual leap to a direct causal correlation
thegalaxy contains no bulge. between DM and BHs is not required bythe data.
Second,oursampleisintentionallybiasedagainstgalaxiesthat So far, we have discussed BH correlations indirectly using the
contain bulges. We even avoided substantial “pseudobulges”; assumption that σ is a surrogate for BH mass. We now check
i.e., “fake bulges” that were made by the internal evolution of this assumption and show that it is not valid for most of the
galaxy disks21 rather than by the galaxy mergers that make black pointsthatdefinethetightcorrelation in Figure1. Ifσ is
“classical bulges”. The pseudobulge-to-total mass ratios of our notameasureofM•,thenthisfurthershowsthatthecorrelation
galaxies are < a few percent; the bulge-to-total ratios are zero. is not a consequence of a BH – DMcoevolution.
∼
Therelevanceofpseudobulgesisdiscussedbelow. Wechosethese In Figure 2, we examine directly the correlations between M•
galaxiesbecause,asnotedearlier,we want to know whether DM and host galaxy properties for galaxies in which BHs havebeen
correlates with BHs in the absence of the component that we detected dynamically. All plotted parameters are published
22
know correlates with BHs. A study of a large galaxy sample elsewhere. The galaxy sample and plotted data are listed in
10
that is not biased against bulges results in similar conclusions: the Supplementary Information of the accompanying Letter .
Vcirccorrelatesweaklywithσ,especiallyatHubbletypeswhere The same galaxies are shown in all panels except: ellipticals do
galaxies contain classical bulges, but the scatter is large and not appear in panel (c) because they have no disk; bulgeless
“these results render questionable any attempt to supplant the galaxies donot appearin panel (a) becausetheyhavenobulge;
bulge with the halo as the fundamental determinant of the somebulgelessgalaxiesandpseudobulgegalaxieswithM• limits
central black hole mass in galaxies.22” Results from this study do not appear in panel (b) because σ is outsidethe plot range.
are included in Figure S3 in theSupplementary Information. The top panels correlate M• with the (a) luminosity and (b)
Figure 1 shows substantial overlap in Vcirc between the color velocity dispersion of the host-galaxy bulge. Ellipticals (black)
points that show little correlation and the black filled circles and classical bulges (red) show the (a) good and (b) better
thatshowagoodcorrelationwithσ. (Theblackpointsshownas correlations that we havecome to expect.
10
errorbarsareforgalaxieswithonlyopticalrotationcurves;they Figure2(c)shows thatgalaxydisksdonotcorrelatewithM•.
measure Vcirc less accurately, because they reach less far out Disksparticipateintherotationcurveconspiracy: theyandtheir
6
into the DM halo . They show a weak correlation that is not a DMhaloshavesimilarVcirc. Buttheirmasses–representedhere
compellingargumentforcoevolution.) Intheoverlaprange,180 by their K-bandluminosities – cannot be used to predict M•.
km s−1 <∼ Vcirc <∼ 220 km s−1, galaxies participate in thetight Figure 2 also distinguishes “classical bulges” (red points) and
Vcirc – σ shown by the black filled circles only if they contain “pseudobulges” (blue points). Classical bulges are essentially
bulges. Clearly baryons matter to BH growth. But baryons indistinguishable in structure and parameter correlations from
in a disk are not enough. DM by itself is not enough. M101 elliptical galaxies (black points). We believe that both formed
(top-left red point) has a halo that is similar to those of half by galaxy mergers (see below). Pseudobulges are high-density,
of the galaxies in the tight correlation, but that halo did not centralcomponentsingalaxiesthatsuperficiallyresemble – and
manufacture a canonical BH in the absence of a bulge. This often are mistaken for – classical bulges but that can be
suggests that bulges, not halos, coevolve with BHs. recognized because their properties are more disk-like than
Nevertheless, most black circles in Figure 1 show a correlation those of classical bulges. We now know that this results from
whose scatter is consistent with the error bars. We need to fundamentally different formation histories. Complementary to
26
understandthis. hierarchical clustering , a new aspect of our understanding of
21
We suggest that the tight correlation of black points in galaxy formation isthatisolated galaxydisksevolveslowly as
Figure 1 is a result of the well known conspiracy13,14 between nonaxisymmetriessuchasbarsredistributeangularmomentum.
baryons and DM to make featureless rotation curves with no Duringthisprocess,pseudobulgesaregrownoutofdiskmaterial.
distinction between the parts that are dominated by baryonic Bulge-pseudobulgeclassifications arelisted forall objectsin the
and nonbaryonic matter. This possibility was considered and sampleintheSupplementalInformationofreference(10). Panels
dismissed in reference (6). However, it is a natural consequence (a) and (b) of Figure 2 illustrate a conclusion from that Letter
of the observation that baryons make up 17% of the matter in which has consequences here: Pseudobulges show essentially no
galaxies23 andthat,tomakestars, theyneedtodissipateinside correlation between M• and σ. Baryons do not predict M• if
their halos until they are self-gravitating. This is enough to they are in a pseudobulge.
engineerthatVcircisapproximatelythesameforDMhalosand IfM• and σ donot correlate for pseudobulges,then σ is not a
fordisksembeddedinthem24,25. That partoftheconspiracy is surrogateforM• inFigure1,either. Bulgeclassificationsforthe
notshownbyFigure1because,absentabulge,disksreachVcirc Figure1galaxiesaregivenintheSupplementaryInformationof
atlargeradiithatarenotsampledbyσ measurementsofnuclei. thispaper,andtwogalaxieswithnopublisheddataareclassified.
Nature, 20 January 2011, 000, 000–000 3
Figure2|Correlationsofdynamicallymeasuredblackholemasseswithstructuralparametersofhostgalaxies.Panel(a)showsBHmassM•versustheK-band
absolutemagnitudeofthehostgalaxybulgewithdisklightremoved. Panel(b)showsM•versusthevelocitydispersionofthehostbulgeaveragedinsidethe
radiusthatcontainsone-halfofthebulgelight.Ellipticalgalaxiesareplottedinblack;classicalbulgesareplottedinred,andpseudobulgesareplottedinblue.
Greenpointsareforgalaxiesthatcontainneitheraclassicalnoralargepseudobulgebutonlyanuclearstarcluster. Thelowerpanelsshowtheanalogous
correlationsforthedisksofhostgalaxies. Panel(c)showsM•versustheabsolutemagnitudeofthediskwithbulgelightremoved,andpanel(d)showsM•
versusouterrotationvelocityVcirc.Panels(a)–(c)arefromaparallelpaper10;alldataplottedherearetabulatedthereintheSupplementaryInformation.Errors
barsare1sigma.Basedonthese,inpanel(a),classicalbulgesandellipticalstogetherhaveχ2=12.1andr=-0.82;thisisthewellknowngoodcorrelationand
isconsistentwithpreviousderivations27.Weassume1-sigmaerrorsinMKof 0.05mag.Similarly,in(b),theredandblackpointshaveχ2=5.0andr=0.89
implyinganintrinsicscatterinlogM•of0.26atfixedσtoreduceχ2to1.0.Thi±salsoisconsistentwithpreviousderivations19,27.Itisthegoodcorrelationthat
motivatesourideasaboutBH–bulgecoevolution. Incontrast,pseudobulgesdonotcorrelatewithM•;inpanel(a),thebluepointshaveχ2=63andr=0.27,
andinpanel(b),theyhaveχ2=10.4andr=-0.08. Similarly10,disksdonotcorrelatewithM•: inpanel(c),theredandbluepointstogetherhaveχ2=81and
r=0.41.Formally,M•anddiskluminosityanticorrelate,butthisisnotsignificant.Finally,inpanel(d),thebluepointshaveχ2=11andr=0.29:theyshowno
correlation. Incontrast,theredpointsforclassicalbulgesshowacorrelationthat,weargue,isarestatementoftherotationcurveconspiracy. Here,elliptical
galaxiesandsomeS0sareplottedinlightgrayandpink,respectively,becauseVcircisnotknown.Wethereforeplotthesurrogatequantity√2σ,anditagrees
withthecorrelationseenforbulgesthathaveVcircmeasurements.Panel(d)isadirectdemonstrationthat,absentbulges,BHsdonotcorrelatewithDM.
We find that only four black circles in Figure 1 correspond to Therefore,overthewholerangeofVcircvaluesassociatedwith
classical bulges, M31, NGC 2841, NGC 4258, and NGC 7331. darkmatter,i.e.,atleast50–2000kms−1,Figure2(d)showsa
Their points are circled. The others are for pseudobulges. For correlationwithM• onlyfrom200–400kms−1 plusNGC7457
these,thedemonstration ofatightVcirc–σ correlation isnota at 105 km s−1, butonlyif thegalaxy containsaclassical bulge.
demonstration that DM and BHs correlate. Thebulgecorrelation canbeunderstood asan indirectresultof
Instead,ifVcirccorrelateswithσ butσ doesnotmeasureM•, the rotation curve conspiracy. Even in the above Vcirc range,
then this supports our conclusion that the correlation results there is no correlation if the galaxy has only a pseudobulge or
from the rotation curve conspiracy. Also, the circled points for disk. Baryonsarenotirrelevant. Theyarenotevensufficient. To
classical bulges agree with the correlation for pseudobulges. It correlatewithM•,theymustbeinaclassicalbulgeorelliptical.
isimplausibletosuggestthatthecorrelationforcircledpointsis WeconcludethatBHsdonotcorrelatecausallywithDMhalos.
causedbyBH–DMcoevolutionwhereastheidenticalcorrelation Thereisnoreasontoexpectthattheunknown,exoticphysicsof
for theother points has nothingto do with BHs. non-baryonicdarkmatterdirectlyaffectsBHgrowth. EvenDM
Finally, Figure 2(d) shows directly that M• does not correlate gravity is not directly responsible for BH–galaxy coevolution.
with Vcirc and therefore with dark matter for pseudobulges. Rather,that coevolution appears tobeassimple as it could be:
An additional argument is given in 3 of the Supplementary BHscoevolveonlywithclassicalbulgesandellipticals. Wehave
§
Information. If DM Vcirc predicts M• independent of baryon a well developed picture of the their formation. Hierarchical
−1
content,thentheVcirc 1400kms DMinclustersofgalaxies clustering of density fluctuations in cold dark matter results
predictsBHsofmassM∼• 7 1011 M⊙ thatareimpossibleto in frequent galaxy mergers11,26,28. The products of roughly
∼ ×
hidein well studied clusters such as Coma. equal-mass mergers are classical bulges and ellipticals, because
Nature, 20 January 2011, 000, 000–000 4
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Supplementary Information
We expand on four issues: 1 explains the consequences
forthispaperofthe“conspira§cy”inthebiggestdiskgalaxies
that bulges, disks, and dark matter halos are arranged in
density and radius so that their combined, circular-orbit
rotation curves are almost flat. Section 2 reconstructs
Figure1fortherotationcurvesampleusedinSection1and
updates it with newer and more accurate measurements.
The result(Fig.S3)is that the strongVcirc– σ correlation
athighVcircinFigure1looksweaker. Section3presentsan
additional argument that dark matter does not predict M•
irrespectiveofthenatureandamountofitsbaryoncontent.
Finally, 4 documents the data used to construct Figure 1.
§
1. The Conspiracy Between Visible and Dark Matter
To Produce Flat, Featureless Rotation Curves
Figure S1 illustrates the rotation curve conspiracy13,14,31
inthe highest-andthird-highest-VcircgalaxiesinFigure1.
InNGC2841,inM31,andinhigh-Vcircgalaxiesingeneral,
bulges, disks, and DM halos are arranged in radius and
density so that their combined rotation curves are so flat
andfeaturelessthatonecannoteasilytellwhichcomponent
dominates at which radius. To understand rotation curves,
it is necessary to decompose them into the contributions
32
from each component . Rotation curve decompositions
likethoseillustratedinFigureS1areavailableforallofthe
galaxies in Figure 1 that have HI measurements of Vcirc.
A slightly oversimplified paraphrase of the conspiracy is
thateachcomponenthasapproximatelythesamemaximum FigureS1|RotationcurvedecompositionsfortwogalaxiesinFigure1that
Vcirc. But they reachthese maxima atdifferentradii– the haveclassicalbulgesandVcirc>200kms-1. Thestandardtechnique32is
bulgenearthecenter,thenthedisk(includinggas)andthen todeterminethebulgeanddiskrotationcurvesfromtheirradialbrightness
the DM at radii that are usually outside the visible part of distributionsviatheassumptionthattheirmass-to-lightratiosM/Lareconstant
thegalaxy(FigureS1). Theimportantconclusionisthis: If with radius. Generally (top) but not always (bottom), HI gas is explicitly
Vcirc,bulge Vcirc,halo (in obvious notation), then there takenintoaccount. Thetotalrotationcurveisthesuminquadratureofits
is no reason≃to believe that any Vcirc – σ correlation that components,i.e.,Vcirc2(r)=Vcirc,bulge2+Vcirc,disk2+Vcirc,gas2. This
remains at high rotation velocities in Fig. 1 is a correlation visible-matterrotationcurvefitsonlythecentralpartoftheobservedrotation
of σ and hence M• with DM. It may be no more than the curve,someofwhichisshownbythedatapoints.Oneofthestrongestpieces
correlationwith bulges that we already know about. ofevidencefordarkmatter34isthatthevisiblemattercannotexplaintheflat
In particular, three of the four highest-Vcirc galaxies in rotationcurveat largeradii. Outsidethevisible matter –i.e., well outside
Figure 1 contain classical bulges. They are, from top to themaximainVcircforvisiblecomponents–thetotalrotationcurveshould
bottom, NGC 2841, M31, and NGC 7331. The fourth is becomeKeplerian,Vcirc r-1/2. Thisisthebehaviorofthebulgerotation
∝
NGC4565,whichhasbothabigboxypseudobulge–i.e.,an curvesinFigureS1,becausemostradiishownareoutsidemostbulgemass.
edge-on bar – and a smaller “disky” pseudobulge33. Some Because thetotalrotationcurvestaysflatratherthanbecomingKeplerian,
ofthebiggestpseudobulgesareconsistentwiththeBH-host sufficientdarkmattermustliveatlargeradiisothatthenewsuminquadrature
galaxy correlations in the top panels of Figure 2. ofVcircforallcomponentsfitsthedata. Therearetwobiguncertaintiesin
Torephraseourconclusion: We suggestthatanyVcirc–σ measuringthisdarkmatter32,35.MostimportantaretheunknownM/Lvalues.
correlation that remains in Figure 1 is due to the rotation Aprocedurewithsubstantial36-41butnotbomb-proof32,42-44justificationis
curve conspiracy. Ferrarese6 considered but dismissed this the“maximumdiskassumption”inwhichbulgeanddiskM/Lvaluesareset
possibility. However, we can test our suggestion, because tothelargestvaluesthatdonotover-predictthecentralrotationcurve.Figure
bulges dominate the biggest galaxies and then disappear S1illustrates thesemaximumdisk=minimumhalomodels. Theunknown
as galaxy luminosity decreases. If we are correct, then valuesandradialdependencesofM/Lexacerbatethesecondproblem,which
we expect that any correlation in Figure 1 breaks down at is that the radialdensity distributionρ(r) ofthe darkmatter is notknown.
Vcirc values where bulges become unimportant. We show The usual practice is to assume a functional form for ρ(r) and then scale
in Figure S2 that this happens at Vcirc 200 km s−1. theparametersofthehalountilitaddsupwiththevisiblemattertofitthe
The key to our test is that the rotation≪curve conspiracy observed rotation curve. In this paper, we use decompositions based on
is not perfect31: it works best for intermediate-luminosity isothermaldarkhalosortheirequivalent41. Consistentuseofdifferenthalo
galaxies,butatlargeradii,“rotationcurvesriseforfaint[er] modelswouldleadtosomewhatdifferentdecompositionsquantitativelybut
galaxies,fallforbright[er]ones.” Rephrasedinthelanguage the same qualitative trendswith galaxy luminosityand outerVcirc. In the
of Figure S1, Vcirc for the central component(s) is smaller decompositions illustrated, we assume that the rotation curve of the dark
than that of the halo in the smallest galaxies and larger matterconvergestotheflatouterrotationvelocityobserved.Theconclusion
than that of the halo in the biggest galaxies. We illustrate fromthedecompositions–andourpointinthissection–isthat, foreach
this point in Figure S2 and then show why it is relevant to galaxy,themaximumVcircisapproximatelythesameforthebulge,thedisk,
our argument. andthedarkhalo.
Nature, 20 January 2011, 000, 000–000 6
Before we interpret Figure S2, there are selection effects
in the galaxysample thatwe shouldunderstand. The most
importantoneisthis:HIgasneedstohavebeendetectedto
large enough radii to see the rotation curve flatten. Many
rotation curve decompositions were not used because they
do not reach large enough radii. This requirement means
thatgasmustbeplentiful. SolateHubbletypesarefavored.
One result is that the sample of galaxies with bulges –
especially small ones – is not large. However, we were
able to find rotation curve decompositions for all of the
galaxies shown by filled black circles in Figure1; their
points are circled in Figure S2. Also, there are notably
many dwarf galaxies; this is a result of the emphasis put
on studying tiny galaxies that are dominated by DM. It
helps our analysis; it gives us the largest possible dynamic
rangeforaderivationoftheunderlyingrelationshipbetween
Vcirc,disk and Vcirc (black straight line). Finally, we
note again that we use maximum disk decompositions; if
disk M/L values were smaller than these maximum values,
then Vcirc,disk would be correspondingly smaller. E.g.,
statistical comparisons of vertical velocity dispersions in
face-on disks with vertical scale heights in edge-on disks
suggest that M/L may be 63% of the maximum-disk
value42,43. Then Vcirc,disk∼would get 20% smaller,
FigureS2|MaximumrotationvelocitiesofthebulgeVcirc,bulge(redpoints) ∼
anddiskVcirc,disk(blackpoints)giveninbulge-disk-halodecompositionsof Vcirc,bulgewouldgetveryslightlylarger,andVcircforthe
halo would necessarily remain unchanged. Our conclusions
observedrotationcurveswhoseouterrotationvelocitiesareVcirc.HereVcirc
would be unchanged, too.
isassumedtobethemaximumrotationvelocityofthedarkmatter.Thesparse
In agreement with previous work31, we conclude that the
dottedlineindicatesequalityofthevisiblematteranddarkmattermaximum
rotation curve conspiracy works best in the biggest disk
rotationvelocities.Everyredpointhasacorrespondingblackpoint,butmany
galaxies are sufficiently bulgeless so that only a disk was included in the galaxies. Most galaxies with Vcirc >∼ 200 km s-1 contain
decompositionandthentheplotshowsonlyablackpoint.Thisisuniversally a large bulge, and many of these bulges are classical.
trueforthesmallestgalaxies;theynevercontainbulges. Therotationcurve Independent of whether they are classical or pseudo,
conspiracy happens for galaxies with Vcirc 200 km s-1: this is where Vcirc,bulge Vcirc,disk Vcirc. At Vcirc 200 km s-1,
∼ ≃ ≃ ≪
Vcirc,bulge Vcirc,disk Vcirc for the halo. Thecorrelation for bulges bulges become unimportant as Vcirc decreases, partly
≃ ≃
issteeperthanthatfordisks;i.e.,bulgesdisappearrapidlyatlowerrotation because they are rarer (caution: the points in Figure S2
velocities. Thelinesareleast-squaresfitssuchthattheadoptedrelationy(x) are not necessarily representative) and partly because
isthemeanofaregressionofyonxandoneofxony,whereeachvariable Vcirc,bulge drops below the value for the halo. But these
hasfirstbeensymmetrizedapproximatelyarounditsmean19. Thesampleis smaller galaxies are the ones for which both Figure 1 and
22
small,buttheregressionshintthatVcirc,bulgetendstobebiggerthanboth previous work show no tight Vcirc – σ correlation that
Vcirc,diskandVcircinthebiggestgalaxies;thishelpstoexplainwhythese argues for BH – DM coevolution.
galaxieshaveoutward-fallingrotationcurves31. Similarly,Vcirc,disk<Vcirc We conclude that there is no compelling evidence for a
inthesmallestgalaxies;thisistheotherhalfoftheconspiracy’sbreakdown31. directcausalcorrelationbetweenBHsandDMbeyondwhat
Infact,thebaryoniccomponentsdisappearalmostentirelyatVcirc 45km is implied indirectly by the rotation curve conspiracy.
s-1; this is an illustration of the well known observation that the∼smallest
galaxiesarecompletelydominatedbydarkmatter41. Theimportantpointfor
thepresentpaperisthatVcirc>∼200kms-1isjustasmuchaparameterofthe
bulgeasitisaparameterofthedarkmatterhalo.Allgalaxiesrepresentedby
blackfilledcirclesinFigure1arealsoincludedinFigureS2(circledpoints).
Thereforeourconclusionsapplytothesegalaxies.
To check whether the results in Figure S1 are general and
to see how they depend on Vcirc, we plot in Figure S2
the results of rotation curve decompositions illustrated
in the literature32,45−72. The sample is from a study
41
of dark matter scaling laws augmented by more recent
papers. Selection criteria are as rigorous as practical; only
galaxies with HI rotation curves are used, and they need
to reach large enough radii to yield reasonably reliable
measures of Vcirc. (We can never be completely certain
of halo rotation velocities: it is always possible that
they increase again at large radii beyond the reach of
present measurements even when Vcirc appears to have
flattened out35.) Only maximum-disk or nearly-maximum-
disk decompositions and only those that are based on
isothermal halos or equivalent41 are used.
Nature, 20 January 2011, 000, 000–000 7
2. Reconstructing the Vcirc – σ Correlation 3. If Dark Matter Halos Predict BH Masses
Independent of their Baryon Content,
Figure S3 reconstructs Figure 1 for all galaxy samples Then the Halos of Galaxy Clusters
discussed in this paper. The large scatter in the Vcirc–σ Predict Giant Black Holes That Are Not Seen
correlation reported by Ho22 is shown by the gray points.
Superposed in black are results for all rotation curve Themaintextmentionsthisargumentbriefly.Wederiveithere.
decomposition galaxies plotted in Figure S2 for which σ TheoriginalVcirc –σ correlation6,reproducedtowithinerrors
measurements are available. They include (circled points) in our Figure 1 (key at the bottom), is
allFerrarese6 galaxiesinFigure1(blackfilledcirclesthere) logVcirc =(0.84 0.09) logσ+(0.55 0.19), (1)
that have HI rotation curves. With the best rotation ± ±
and dispersion measurements available now, their scatter Substitutingfor σ in the M• – σ relation6,
is largerthanit wasinFigure 1 andconsistentwith the Ho σ 4.58±0.52
8
phoosinttdse.tCecltaesdsicBaHlsbuarlgeeisnc(rluedd)edanfrdompsFeuigduorbeu2l.geTsh(ebyluael)sothaaret M• =(1.66±0.32)×10 M⊙ (cid:18)200 km s−1(cid:19) , (2)
consistent with the Ho points. Ho also includes 18 of the yields
23 Ferrarese galaxies that had optical but no HI rotation M• Vcirc 5.45
dFaintaal(lyb,laFcikguproeinSt3ssmhoawrkseidnognrleyenwitthheegrarloarxbieasrsfrionmFFigiugruere1)1. 108 M⊙ =0.169(cid:18)200km s−1(cid:19) (3)
thathavevirtuallynobulgeorpseudobulge;thedispersions in ournotation. Asacheckon previousarguments, Vcirc =210
are those of their stellar nuclei. For these, there can be no kms−1 forM101predictsM• 2.2 107M⊙,inconflictwith
confusionwithanyBH–(pseudo)bulgecorrelation,sothey the observed upperlimit8, M•≃<∼ (2.6× 0.5) 106 M⊙.
remain the best galaxies with which to look for a BH–DM Richclustersofgalaxies havehigherD±MVcir×c valuesthanany
correlation. None is seen. Figure S3 therefore supports our galaxy.Theytypicallyhavevelocitydispersionsσ 1000kms−1
conclusion that the rotation curve conspiracy is sufficient and can have velocity dispersions as high as ∼2000 km s−1.
∼
andthataconceptualleapfromaBH–bulgecorrelationto Whetherwecanusetheseclusterhalosinourargumentdepends
a BH–DM correlation is not compelled by the data. on whetherthedarkmatterisalready distributedin thecluster
orwhetheritisattachedonlytothegalaxies,withtheresultthat
thetotal mass is large but that individualhalos arenot. Large-
28
scale simulations of hierarchical clustering show that, while
substructure certainly exists, much of the DM in rich, relaxed
clusters is distributed “at large” in the cluster. In fact, the
hierarchical clusteringofDMissonearlyscale-freethat75 “it is
virtually impossible to distinguish [the halo of an individual
big galaxy from that of a cluster of galaxies] even though
the cluster halo is nearly a thousand times more massive”
(emphasis added). DM halos of mass 1015 M⊙ are not rare76.
A cluster of galaxies like Coma77 has σ 1000 km s−1 and
Vcirc √2σ 1400km s−1. Equation (3∼) then predicts that
∼ ∼
11
M• 7 10 M⊙ . (4)
∼ ×
SunktothecenterofNGC4874orNGC4889,suchaBHwould
haveasphere-of-influenceradiusr• GM•/σ2 34kpc=69′′.
∼ ≃ 78
This is bigger than the effective radius of both galaxies . But
both galaxies have σ 300 kms−1 and normal, linear, and
shallow logσ(logr) pro≃files78.
Therefore, if baryons do not matter – if the hypothesis is that
DM makes BHs independent of how baryons are involved (as a
galaxy,asagroupofgalaxies, ornotatall) –thenEquation(3)
predicts unrealistically large M• for rich clusters of galaxies.
Is this a fair argument? Does it miss some essential physics
FigureS3|ReconstructionofFigure1forallgalaxysamplesdiscussed in that DM requires in order to make BHs? After all, clusters are
thispaper.HereVcircistheouterrotationvelocityofthegalaxydisk,usually differentfromindividualgalaxies, evenifbothcontainDM.But
measuredusingobservationsofHIgas,andσisthecentralornear-central weemphasize: Anymissingphysicscannotinvolvetheformation
averagevelocitydispersion. Eachgalaxy isplotted onlyonce; parameters of bulges and ellipticals, because if those are necessary, then we
are taken preferentially from Figure 1, Figure 2, FigureS2, and Ho22. All are back to BH – bulge coevolution. The obvious candidate for
FerraresegalaxieswithHImeasurementsinFigure1(blackfilledcirclesthere) a missing ingredientis cold gas. Rich clustersaredominated by
126
areincludedherebutwiththebestcurrentlyavailableparameters.Errorbars X-ray gas. But thesame is trueof giant ellipticals , and they
areonesigma.TheblackstraightlineisFerrarese’sfittohercorrelation.Ho’s have manufactured thebiggest BHs known. Both M87 and the
fittothelightgraypointsisnotshownbutissimilar.Theredlinesarenotfits; Coma cluster are dominated by stars and hot gas that are only
theyshowVcirc=√2σ(lower)andVcirc=1.72σ,respectively. Thelatter minimally helpfulforcurrentBHgrowthandhalosthatcontain
relationwasderived73byfittingdynamicalmodelswithavarietyofvelocity some substructure but that are almost self-similar. Ferrarese
anisotropies to x-ray and optical spectroscopy measurements of elliptical (ref. 6) argues that more massive DM halos are more efficient
galaxies. Anintermediaterelation,Vcirc=1.52σ(notshown)wasderived74 at making BHs. The most massive halos are those of galaxy
fromadynamicalanalysisofhigh-dynamic-rangekinematicobservationsof clusters. Therefore the observation that they do not contain
ellipticals. Aslope=1fittotheblackfilledcirclesinFigure1(omittingNGC BHs in accord with Equation (3) is a powerful argument that,
3198)givesVcirc=1.43σ. absent a bulge, DM does not directly control BH growth.
1
Nature, 20 January 2011, 000, 000–000 8
TABLE1
RotationVelocitiesandVelocityDispersionsofGalaxiesinFigure1
Galaxy Type BulgeType BulgeType Vcirc Vcirc σ σinstr σ,σinstr Figure1
source (kms−1) source (kms−1) (kms−1) source symbol
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Ferrarese(2002)GalaxiesWithHIRotationCurves
MW SBb P 8,82,83 180±20 6 100±20 individualstars 98 •
IC342 SAB(rs)cd P,N 8,84,87 185±10 6 77±12 61 15 replaced
NGC224 SA(s)b C,N 8,85 240±20 6 146±15 115 99? •
NGC598 SA(s)cd N 21 135±13 6 27± 7 ? 100 replaced
NGC801 Sc P thispaper 216± 9 6 144±27 77 101 •
NGC2841 SA(r)b C 21,84,86,87 281±10 6 179±12 57 102 •
NGC2903 SB(s)d P 84,86,87 180± 4 6 106±13 ≥44 103 •
NGC2998 SAB(rs)c P thispaper 198± 5 6 113±30 77 101 •
NGC3198 SB(rs)c P 86 150± 3 6 69±13 51 93,104 replaced
NGC3198 SB(rs)c P 86 150± 3 6 48± 9 51,42 104,105 •
NGC4258 SAB(s)bc C 8,10,27 210±20 6 138±18 68 15 •
NGC4565 SB(r)b P 21,33 264± 8 6 151±13 100 106 •
NGC5033 SA(s)c P 87 195± 5 6 122± 9 ≥89 103 •
NGC5055 SA(rs)bc P 8,84,86,87 180± 5 6 103± 6 ≥44 103 •
NGC6503 SA(s)cd P,N 8,87 116± 2 6 48±10 34 107 replaced
NGC7331 SA(s)b C 21,87 239± 5 6 139±14 78 109 •
Ferrarese(2002)GalaxiesWithOpticalRotationCurves
IC724 Sa ... ... 302± 3 6 243±18 77 101 +
NGC753 SAB(rs)bc ... ... 210± 7 6 121±17 77 101 +
NGC1353 SA(rs)bc P 86 191± 6 6 92±12 77 101 +
NGC1357 SA(s)ab ... ... 259± 5 6 121±14 77 101 +
NGC1417 SA(r)b ... ... 240± 9 6 148±18 77 101 +
NGC1620 SAB(rs)bc ... ... 250± 4 6 123±20 77 101 +
NGC2639 (R)SA(r)A: ... ... 318± 4 6 195±13 77 101 +
NGC2742 SA(s)c ... ... 173± 4 6 63±28 ≥89 103 omitted
NGC2775 SA(r)ab C 84,86,87,88 270± 4 6 162±13 77 101 +
NGC2815 (R)SB(r)b ... ... 278± 3 6 199±20 45 108 +
NGC2844 SA(r)a: ... ... 171±10 6 113±12 77 101 +
NGC3067 SAB(s)ab ... ... 148± 1 6 84±29 78 109 +
NGC3145 SB(rs)bc ... ... 261± 3 6 166±12 77 101 +
NGC3223 SA(r)bc P 88 261±11 6 163±17 77 101 +
NGC3593 SA(s)0/a P 84,86,87 101± 4 6 56±15 77 101 omitted
NGC4062 SA(s)c P 86,88 154±13 6 90± 7 84 110 omitted
NGC4321 SAB(s)bc P 21,84,87,89 216± 6 6 83±12 77 101 omitted
NGC4378 (R)SA(s)a ... ... 308± 1 6 198±18 49 101 +
NGC4448 SB(r)ab P 84,86,87 187± 3 6 175±21 75 111 +
NGC4698 SA(s)ab ? 86,87,88 252± 5 6 131±19 78 109 +
NGC7217 (R)SA(r)ab C 87,88 241± 4 6 171±17 75 111 +
NGC7541 SB(rs)bc ... ... 179± 1 6 109±15 ? ? omitted
NGC7606 SA(s)b ... ... 240± 4 6 124±21 78 109 +
Essentially(Pseudo)BulgelessGalaxiesWithNuclei
IC342 SAB(rs)cd P,N 8,84,87 192± 3 92 33± 3 5.5 18 orange
NGC598 SA(s)cd N 16,21 135±13 6 19.8±0.8 8 8 red
NGC3338 SA(s)c P,N 8,86 186± 4 93 77.5±1.5 8 8 red
NGC3810 SA(rs)c P,N 8 152± 3 93 62.3±1.7 8 8 red
NGC5457 SA(rs)cd P,N 8,84 210±15 8 27± 4 8 8 red
NGC6503 SA(s)cd P,N 8,87 115± 2 95 40± 2 8 8 red
NGC6946 SA(rs)cd P,N 8,84 210±10 8 56± 2 8 8 red
NGC300 SA(s)d N 87,90 96± 2 96 13.3±2.0 3.4 90 green
NGC428 SAB(s)m N 90 104±11 97 24.4±3.7 3.4 90 green
NGC1042 SAB(rs)cd N 90 145±13 93 32.0±4.8 3.4 90 green
NGC1493 SB(r)cd N 90 115± 4 93 25.0±3.8 3.4 90 green
NGC2139 SAB(rs)cd N 90 136± 2 93 16.5±2.5 3.4 90 green
NGC3423 SA(s)cd N 90 127± 4 93 30.4±4.6 3.4 90 green
NGC7418 SAB(rs)cd N 90 154± 3 93 34.1±5.1 3.4 90 green
NGC7424 SAB(rs)cd N 90 82± 2 93 15.6±2.3 3.4 90 green
NGC7793 SAd N 90 96± 3 93 24.6±3.7 3.4 90 green
NGC1705 BCD,N N 91 78± 4 93 11.4±1.5 3.4 91 blue
Note. — ThegalaxiesinthefirsttwoblocksarefromTable1inreference6;parametersaretakenfromthereunlessotherwisenoted. Parametersforthethird
blockofgalaxiesarefromthesourceslistedinthesenotesorinthecolumnsindicated. Column(1): Galaxyname. Column(2): Galaxytype,fromreference
79 as listed in reference 80 except for NGC 170581. Column (3): Bulge classification: C = classical bulge; P = pseudobulge; N = nucleus, which can occur
togetherwithCorP.Column(4): SourcesofbulgeclassificationsColumn(5): OuterrotationvelocityVcirc. Column(6): SourcesofVcirc. Column(7): Adopted
velocitydispersionσ. Forthefirsttwoblocksofgalaxies,thesearereference(6)“bulgevelocitydispersionscorrectedtoanapertureofsizere/8”,wherere is
theradiusthatcontainshalfofthelightofthebulgecomponent. Notethatσ ismeasuredinthesamewaywhetherthebulgeisclassicalorpseudo. Column
(8): Instrumentalresolutionofthespectrographusedtodetermineσ expressedasaninstrumentalvelocitydispersionσinstr ≡FWHM/2.35,whereFWHMis
thefullwidthathalfofmaximumintensity(ordepth)ofσ=0emission(orabsorption)linesasbroadenedbytheinstrumentalresolution. Whenσ.σinstr,the
galaxylinesaredangerouslyunder-resolved;theusualresultisthatσisoverestimated. AquestionmarkinColumn(6)meansthatthesourcedidnotgivethe
instrumentalresolution. Alowerlimitmeansthatthesourcedidnotgivetheinstrumentalresolutionbutdidgivethepixelsize;then(2pixels)/2.35isalower
limitonσinstr. Forreference(111),wequotethe“resolutionwidth”W whichistreatedlikeaninstrumentalvelocitydispersionintheirEquation(1). Column
(9): Sourceofσmeasurements. Morethanhalfofthesourceslistedinreference(6)appeartobeincorrect–wecouldnotfindthegalaxylistedinthatpaper.
Wecorrectedthesourcesaswellaspossible,basedonfindingthepaperthatlistsσasgiveninTable1,column(7)ofreference(6). Aquestionmarkindicates
thatσinthesourceneverthlessdifferedfromσinreference(6). ForNGC2841,aσvalueessentiallyequaltothatinReference(6)wasfound102. Column(10)
identifieswhetherthismeasurementwasusedinFigure1. Caseswhereσwasunder-resolvedareomittedwhennobetterdataareavailable. Ifbetterdataare
available,thenColumn(8)indicatesthatthislineofthetablewasreplacedwiththenewvalueinthenextline(NGC3198)orinthethirdblockofgalaxies.
Nature, 20 January 2011, 000, 000–000 9
4. Data Table for Galaxies in Figure 1
Table 1 lists the plotted parameters and data sources for all NGC 2998 and NGC 801 are by far the most distant galaxies
galaxies included in Figure 1. The top two blocks of galaxies in the top group in Table 1. At D = 67 Mpc and 79 Mpc,
are taken directly from reference (6) with as few changes as respectively,theyare 4timesfartherawaythanthenextmost
∼
possible. If these points are included in Figure 1, they are distant galaxy. As a result, much less is known about them,
plotted in black. The bottom block of galaxies (color points in and in particular, bulge classifications havenot been published.
Figure1)includesonlyobjectswithnoclassicalbulge,withvery However, enough dataare available so that wecan estimate the
smallpseudobulges(e.g.,IC342,NGC5457,NGC6946)ornone bulge typeusing theshape of thesurface brightness profile.
at all (e.g., NGC 598 = M33), and with nuclear star clusters
whose velocity dispersions have been measured with very high
velocityresolution (Vcirc<10kms-1). Inpractice, thebiggest
8
pseudobulge-to-total luminsity ratios included in the bottom
group of galaxies in Table 1 are PB/T 0.03.
∼
Exceptfortwonewbulge-pseudobulgeclassifications discussed
below, all data in Table 1 are published. Column 6 lists the
sourceofVcirc;thisistakendirectlyfrom reference (6)–where
the original source is listed – for all galaxies from that paper.
The velocity dispersion σ listed by reference (6) is intended to
be an average inside re/8, where re is the radius that contains
halfofthelightofthebulge. Someofthesevaluesweremeasured
with instrumental resolution σinstr σ which is too low (see
Figure 1 caption). This is documen≃ted in Table 1: σinstr is
listedinColumn(8)asreportedinthepaperthatpublishedthe
measurements (Column 9). When the resolution was too poor,
the object was “omitted” (Column 10) if we had no better σ
value or “replaced” with a high-resolution measurement, if we
had one. In the latter case, the galaxy appears again, either in
the next line or in the bottom block of objects, along with the
high-resolution σ measurement and, when necessary, an update
on Vcirc. Many σ sources are given incorrectly in reference (6);
we list these sources in Column (9), corrected as well as we are
able(see Table Notefor furtherdetails). Column (10) identifies
thesymbol used for each galaxy in Figure 1.
Readersmayworrythatσismeasuredindifferentwaysforthe
variouskindsofcentralcomponentsincludedinFigures1andS3.
But in fact, velocity dispersions σ are defined and measured
in exactly the same way for pseudobulges (see below) as for Figure S4 | Color image of the Sc galaxy NGC 2998 constructed using
classical bulges. In general, the papers that measured re and σ the g-, r-, and i-band images from the Sloan Digital Sky Survey (courtesy
did not distinguish between classical and pseudo bulges. Nuclei http://www.wikisky.org).ThegalaxyisacloseanalogofM101,exceptthatitis
are typically only afew arcsec in diameter; theirσ refers to the fartheraway(D=67.4Mpcversus7.0MpcforM101)andmoreinclined. The
whole nucleus. In one case (NGC 598 = M33), measurements totalK-bandabsolutemagnitudeisMKT=-24.2(comparedwith-23.7forM101).
withtheHubbleSpaceTelescopeshow17 thatσisindependentof NGC2998hasVcirc=198±5kms-1(cf.210±15kms-1forM101).Wefinda
radius. Thenitdoesnotmatterwhetherσisaveragedinsidere/8 pseudobulge-to-totalluminosityratioPB/T=0.03±0.01(cf.0.027±0.008in
or not. For NGC 5457 and NGC 6946, which contribute more M101).TheM101parametersarefromreference(8).Errorbarsare1sigma.
than any other galaxies to our conclusion that DM halos with
Vcirc > 200 km s−1 do not contain big BHs if they do not also NGC 2998 is illustrated in Figure S4. It is very similar to the
containclassicalbulges,thenuclearσmeasurementalsoincludes Scd galaxy M101, which has no classical bulge at all, but only
an equal or larger contribution from the center of the galaxy’s a nuclear star cluster and a tiny pseudobulge that contributes
tiny pseudobulge8. In any case, nuclei are so small that, if big 0.027 0.008oftheK-bandlightofthegalaxy8. Wemeasured
±
DM halos manufactured big BHs, then those BHs would easily thebrightnessprofileofNGC2998toseewhetherthetiny,bright
be revealed by large σ values that are not seen. And velocity center is a classical or pseudo bulge. The results are shown in
dispersiongradientsareshallowenoughsothattheexactfraction Figure S5.
ofreinsidewhichσisaveragedisnotcritical. Sothecomparison Asin11o4thernormal galaxies, the outerdisk has an exponential
of colored and black pointsin Figure 1 is fair. profile and the central component is well fitted by a S´ersic
Some arguments in the main text depend critically on the function113, log I(r) r1/n,where nis the“S´ersic index.” The
distinction10,21 between classical and pseudo bulges in the top bestfithasn=1.77∝ 0.15(onesigma). Thisismarginallyless
block of galaxies–the ones that show a tight correlation in than 2. Much work h±as shown21,84,86−89,115−123 that classical
Fig. 1. Bulge classifications are less well known for the middle bulges have n >∼ 2 whereas most pseudobulges have n < 2. So
block of galaxies, but these are also less important, because our results are most consistent with a pseudobulge, although a
they do not show a tight Vcirc – σ correlation. Table 1 lists classical bulgeis not strongly excluded.
the bulge classification in Column (3) and the source of the NGC801isalsoclassifiedasanScgalaxy,butits(pseudo)bulge
classification in Column (4). For NGC 801 and NGC 2998, is brighter than that of NGC 2998. The galaxy is illustrated
published (pseudo)bulge classifications are not available; we in Figure S6. No HST image is available, but ground-based
discuss these galaxies next. photometry is collected intoa composite profile in Figure S7.
Nature, 20 January 2011, 000, 000–000 10
FigureS5|Major-axis,H-bandsurfacebrightnessprofileofNGC2998. The FigureS7|Major-axis,r-bandsurfacebrightnessprofile124,125ofNGC801.
filled circles are ourmeasurements of a Hubble Space Telescope NICMOS The dashed curves show a decomposition into a Se´rsic function and an
imageavailablefromtheHSTLegacyArchive,http://hla.stsci.edu/hlaview.html. exponential;.Theirsum(solidcurve)fitstheprofileinsidethefitrange(vertical
Theopencirclesareourmeasurmentsofthe2MASSH-bandimage112. The dashes)withanRMSof0.077magarcsec-2. TheSe´rsicindexofthecentral
dashedcurvesshowadecompositionoftheprofileintoaSe´rsicfunction113 componentisn=1.4 0.4(1sigma).Itcontributes 23%ofthegalaxylight.
± ∼
(pseudo)bulgeandanexponentialdisk. Theirintensitysum(solidcurve)fits
Ourphotometricdecomposition(FigureS7)givesaS´ersicindex
theaverageprofileinsidethefitrange(verticaldashes)withanRMSof0.07
magarcsec-2.TheSe´rsicindexofthecentralcomponentisn=1.77<2,sowe that is marginally less than 2. This is most consistent with a
pseudobulge, but a classical bulge is not excluded. At the large
concludethatthisisapseudobulge(seethetext). Thepseudobulge-to-total
distance of this galaxy, other information such as molecular gas
luminosityratioistiny,PB/T=0.03 0.01(onesigma).
± or star formation measurements in the central component are
not available. So we cannot apply other classification criteria.
Weprovisionally classify thebulgeaspseudobutrecognizethat
this is uncertain.
The pseudobulge classifications of NGC 801 and NGC 2998
are more uncertain than the others in the top block of Table 1,
becausetheyarebasedononlyoneclassificationcriterion. Also,
it is essentially certain that some galaxies have both a classical
andapseudobulgecomponent. Thisisunlikelyinmostgalaxies
in the top block, based on detailed studies. But it is hard to
investigate in NGC 801, because that galaxy is far away and
because we do not have Hubble Space Telescope images. (A
multicomponentbulgeisnotlikelyinNGC2998: PB/T 0.03.)
≃
However, we emphasize two points. First, if both of the above
classifications were wrong, then the tight correlation of black
filled circles in Figure 1 would consist of an equal number of
classical bulges and pseudobulges. Our arguments in the main
text would remain valid. Second, the criterion that we used to
classifyNGC801andNGC2998wasusedsuccessfullytoclassify
the pseudobulges that prove to show no σ – M• correlation10.
If the same classification criterion identifies a similar sample of
pseudobulges that show a tight σ–DM correlation in Figure1,
thanthatcorrelationisnotduetoBHcoevolutiondrivendirectly
by DM. We discuss NGC 801 and NGC 2998 here mainly for
completeness. Our conclusions do not depend on the resulting
(pseudo)bulge classifications.
Figure S6 | Color image of the Sc galaxy NGC 801 from the Palomar
ObservatoryandAnglo-AustralianObservatoryDigitalSkySurvey(courtesy
References
http://www.wikisky.org).ThespatialresolutionispoorerthaninFigureS4;the
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