Molecular gas in NUclei of GAlaxies (NUGA)-IV. Gravitational torques and AGN feeding

20 Pages·2005·1.26 MB·English

A&A441,1011–1030(2005) Astronomy
DOI:10.1051/0004-6361:20052900 &
(cid:1)c ESO2005 Astrophysics
Molecular gas in NUclei of GAlaxies (NUGA)
(cid:1)
IV. Gravitational torques and AGN feeding
S.García-Burillo1,F.Combes2,E.Schinnerer3,F.Boone4,andL.K.Hunt5
1 ObservatorioAstronómicoNacional(OAN)-ObservatoriodeMadrid,AlfonsoXII,3,28014Madrid,Spain
e-mail:[email protected]
2 ObservatoiredeParis,LERMA,61Av.del’Observatoire,75014Paris,France
e-mail:[email protected]
3 Max-Planck-InstitutfürAstronomie,Königstuhl,17,69117Heidelberg,Germany
e-mail:[email protected]
4 Max-Planck-InstitutfürRadioastronomie,AufdemHügel,69,53121Bonn,Germany
e-mail:[email protected]
5 IstitutodiRadioastronomia/CNR,Sez.Firenze,LargoEnricoFermi,5,50125Firenze,Italy
e-mail:[email protected]
Received18February2005/Accepted24June2005
ABSTRACT
Wediscusstheefficiencyof stellargravitytorquesasamechanismtoaccount forthefeedingof thecentralengines offourlow luminosity
ActiveGalacticNuclei(AGN):NGC4321 (HIInucleus/LINER), NGC4826(HIInucleus/LINER), NGC4579(LINER1.9/Seyfert 1.9)and
NGC6951(Seyfert2).ThesegalaxieshavebeenobservedaspartoftheNUcleiofGAlaxies–(NUGA)COproject,aimedatthestudyofAGN
fuelingmechanisms.Ourcalculationsallowustoderivethecharacteristictime-scalesforgasflowsanddiscusswhethertorquesfromthestellar
potentialsareefficientenoughtodrainthegasangularmomentumintheinner1kpcofthesegalaxies.Thestellarpotentialsarederivedusing
high-resolutionnearinfrared(NIR)imagesandtheaveragedeffectivetorquesonthegasareestimatedusingthehigh-resolution(∼0.5(cid:3)(cid:3)–2(cid:3)(cid:3))
COmapsofthegalaxies.ResultsindicateparadoxicallythatfeedingshouldbethwartedclosetotheAGNs:inthefourcasesanalyzed,gravity
torquesaremostlypositiveinsider ∼200pc,resultinginnoinflowonthesescales.Asapossiblesolutionfortheparadox,wespeculatethat
the agent responsible for driving inflow tostill smaller radii istransient and thus presently absent inthe stellarpotential. Alternatively, the
gravitytorquebarrierassociatedwiththeInnerLindbladResonanceofthebarsinthesegalaxiescouldbeovercomebyothermechanismsthat
become competitiveinduetimeagainstgravitytorques.Inparticular,weestimateonacase-by-case basistheefficiencyofviscosityversus
gravitytorquestodriveAGNfueling.Wefindthatviscositycancounteractmoderate-to-lowgravitytorquesonthegasifitactsonanuclear
ringofhighgassurfacedensitycontrastand∼afew100pcsize.
Weproposeanevolutionaryscenarioinwhichgravitytorquesandviscosityactinconcerttoproducerecurrentepisodesofactivityduringthe
typicallifetimeofanygalaxy.Inthisscenariotherecurrenceofactivityingalaxiesisindirectlyrelatedtothatofthebarinstabilitiesalthough
theactivephasesarenotnecessarilycoincidentwiththemaximumstrengthofasinglebarepisode.Thegeneralimplicationsoftheseresults
forthecurrentunderstandingoffuelingoflow-luminosityAGNarediscussed.
Keywords.galaxies:individual:NGC4321,NGC4579,NGC4826,NGC6951–galaxies:ISM–
galaxies:kinematicsanddynamics–galaxies:nuclei–galaxies:Seyfert–radiolines:galaxies
1. Introduction these massive black holes, very few are highly active. AGN
are foundin 10%of the localgalaxies(Hoet al. 1997); how-
The phenomenonof nuclearactivity is understoodto be a re- ever, this percentage is increased up to ∼44% if LINERs are
sult of the feeding of supermassive black holes (SMBHs) in
takeninto account.One of the presentchallengesis to under-
galactic nuclei. Observational evidence accumulated over the
stand how AGN can be fed during their lifetime. In the feed-
last decadeindicatesthatSMBH existinmostgalacticbulges
ing problem the gas supply must come from the whole disk
(e.g., Kormendy & Richstone 1995; Magorrian et al. 1998;
of the host galaxy at large distances compared to the radius
Ferrarese & Merritt 2000; Gebhardt et al. 2000). Among all
ofgravitationalinfluenceofthecentralengine.Thereforeitis
(cid:1) BasedonobservationscarriedoutwiththeIRAMPlateaudeBure expectedthatahierarchyofmechanismscombinetodrivevir-
Interferometer. IRAM is supported by INSU/CNRS (France), MPG tuallyallthegasfromthelarge∼kpcscalesdowntotheinner
(Germany)andIGN(Spain). ∼pc scales. The different spatial scales involved suggest that
Article published by EDP Sciences and available at http://www.edpsciences.org/aaor http://dx.doi.org/10.1051/0004-6361:20052900
1012 S.García-Burilloetal.:MoleculargasinNUcleiofGAlaxies(NUGA).IV.
thevariousmechanismsatworkhaveverydifferenttimescales characterizegravitationalinstabilitiesandtoconstrainthemod-
(Shlosmanetal.1989,1990;Combes2001,2003;Jogee2004). els. The NUclei of GAlaxies-NUGA-project, fully described
Recent observational and theoretical evidence indicates that by García-Burillo et al. (2003a,b), is the first high-resolution
the AGN lifetimes may be as short as ∼a few 107–108 yr (∼0.5(cid:3)(cid:3)–1(cid:3)(cid:3)) CO survey of 12 low luminosity AGN (LLAGN)
(Ho et al. 2003; Martini 2004; Wada 2004; Merloni 2004). includingthefullsequenceofactivitytypes(Seyferts,LINERs
Moreover, Wada (2004) finds evidence that mass accretion and transition objects from HII to LINER). In the case of
may not be constant even during the nominal duty cycle of LLAGN, the required mass accretion rates derived from the
108 yr, but composed of several shorter episodes with a du- typical bolometric luminosities of these objects range from
ration of 104−5 yr. This time-scale conspiracy could explain 10−2to10−5 M(cid:4)yr−1(fromSeyfertstoLINERs;e.g.,seecom-
the lackof successofobserversinfindinganycorrelationbe- pilation by Jogee 2004). Observations, carried out with the
tweenthepresenceof∼kpcscalenon-axisymmetricperturba- IRAMPlateaudeBureInterferometer(PdBI),havebeencom-
tions (e.g., large-scale bars and interactions) and the onset of pleted early 2004. NUGA surpasses in both spatial resolu-
activity in galaxies, except for very high luminosity objects tionandsensitivityongoingsurveysofnearbyAGNconducted
(QSOs)(Molesetal.1995;Mulchaey&Regan1997;Knapen at OVRO (MAIN: Jogee et al. 2001) and at NRO (Kohno
etal.2000;Krongoldetal.2001;Schmitt2001).Onthesespa- etal.2001).
tialscales,Hunt&Malkan(1999)havefoundasignificantcor- In this paper we focus on the study of gravitational
relationbetweenthedetectionrateofouterringsandtheonset torques in a subset of NUGA galaxies, which span the
ofactivity. range of the different activity classes within our sample:
The search for a universal feeding mechanism has been NGC4321(transitionobject: HII/LINER),NGC4826 (transi-
pursued by looking for morphological features in the cen- tion object: HII/LINER), NGC4579 (LINER 1.9/Seyfert1.9)
tral kpc of nearby AGN with high spatial resolution (∼a few and NGC6951(Seyfert 2). Information on the stellar poten-
100 pc), though with limited success. Nuclear stellar bars tials, obtained through available HST and ground-basedopti-
seem to be as common in AGN as in non-AGN (Regan & cal/NIRimagesofthe sample,is usedto determinethe gravi-
Mulchaey1999;Laineetal.2002).Furthermore,asimilarsce- tationaltorquesexertedbythederivedstellarpotentialsonthe
narioholdsfornuclearspirals:whileMartini&Pogge(1999) gaseous disk. The efficiency with which gravitational torques
andPogge&Martini(2002)initiallyfoundahighfrequencyof drain the angular momentum of the gas depends first on the
dustyspiralsintheHSTenhancedcolorimagesofSeyfertnu- strengthofthenon-axisymmetricperturbationsofthepotential
clei of their sample, more recently,Martiniet al. (2003) have (m > 0) but, also, on the existence of significant phase shifts
shown on a firmer statistical basis that these nuclear features between the gas and the stellar distributions. The estimate of
are not preferentially found in AGN. Similarly there is only these phase shifts necessarily requires the availability of im-
weakstatisticalevidencethatnuclearringsaremorefrequently agesofcomparablyhighspatialresolution(≤0.5(cid:3)(cid:3)inourcase)
foundinSeyferts(Knapen2005).Hunt&Malkan(2004)found showingthedistributionofthestarsandthegas.Inthispaper
evidenceforanexcessin type2 Seyfertsof kpc-scaletwisted wepurposelyneglecttheroleofgasself-gravityasasourceof
isophotes,thoughthecauseofsuchtwistsisunclear. non-axisymmetryinthegravitationalpotential.Nucleargalaxy
On the modeling front, significant progress has been diskswithahighgassurfacedensityandamostlyaxisymmet-
made in recent years on the study of the feeding effi- ric stellar potential can be prone to develop this kind of gas
ciency of different types of gravitational instabilities: nested self-gravitatingperturbation.We purposelydefer the study of
bars (e.g., Shlosman et al. 1989; Friedli & Martinet 1993; pure gas instabilities and their ability to drive gas inflow to a
Maciejewski & Sparke 2000; Englmaieret al. 2004), gas spi- forthcomingpublication.
ral waves (e.g., Englmaier & Shlosman 2000; Maciejewski We describe in Sect. 2 the observations used, includ-
et al. 2002; Maciejewski2004a,b), m = 1 perturbations(e.g., ing high-resolution CO maps and NIR images of NGC4321,
Shu et al. 1990; Junqueira & Combes 1996; García-Burillo NGC4826, NGC4579 and NGC6951. Section 3 interprets
et al. 2000) and nuclear warps (e.g., Schinnerer et al. 2000). themintermsofAGNfeeding.Section4computesfromNIR
However, the lack of high quality multi-wavelength observa- images the gravitational potentials and forces, and deduces
tionalconstraintsonthedifferentmodelshasthusfarmadethe fromtheCOmapstheeffectivetorquesappliedtothegas.From
choiceofasingleoptimalscenarioratherdifficult. thesetorques,itispossibletoderivetime-scalesforgasflows
The study of interstellar gas in AGN is essential to un- anddiscusswhethergravitytorquesaloneareefficientenough
derstand the phenomenon of nuclear activity in galaxies and to feed the AGNs. The general implications of these results
its possible link to circumnuclear star formation. As most of for the current understanding of AGN feeding are presented
the neutral gas in galactic nuclei is in the molecular phase, inSect.5.
CO lines are best suited to undertake high-resolution map-
pingofAGNhosts,withinterferometerresolutionof<100pc,
2. Observations
i.e., the scales on which secondary modes embedded in kpc-
scale perturbations are expected to take over. CO lines bet-
2.1.CONUGAobservations
ter trace the total gas column densities than dust extinction
probes obtained from HST NIR/optical color images. Most Observations of the circumnuclear disks of NGC4826,
importantly, CO maps provide the gas kinematics (velocity NGC4579 and NGC6951 were carried out as part of the
fieldsandvelocitydispersions).Thisinformationisessentialto NUGA survey with the PdBI between December 2000 and
S.García-Burilloetal.:MoleculargasinNUcleiofGAlaxies(NUGA).IV. 1013
Table 1. We list the position angle (PA), inclination (i), distance (D), spatial scale, coordinates of the dynamical center derived from CO
and/or from thelocus of theradio continuum source [(RA , Dec ); accurate to∼0.5(cid:3)(cid:3) on average] and systemic velocity(vLSR) derived
2000 2000 sys
fromCOforNGC4321,NGC4826,NGC4579andNGC6951usedinthispaper.ThespatialresolutionsoftheCOobservationsarelistedin
Cols.9,10.
Galaxy PA(◦) i(◦) D(Mpc) Scale(pc/(cid:3)(cid:3)) RA Dec vLSR(kms−1) CO(1–0)((cid:3)(cid:3)×(cid:3)(cid:3)) CO(2–1)((cid:3)(cid:3)×(cid:3)(cid:3))
2000 2000 sys
NGC4321 153 32 16.8 83 12h22m54.91s 15◦49(cid:3)19.9(cid:3)(cid:3) 1573±10 2.2×1.2 –
NGC4826 112 54 4.1 20 12h56m43.63s 21◦40(cid:3)59.1(cid:3)(cid:3) 413±10 2.5×1.8 0.7×0.5
NGC4579 95 36 19.8 97 12h37m43.52s 11◦49(cid:3)05.5(cid:3)(cid:3) 1469±10 2.0×1.3 1.0×0.6
NGC6951 134 42 19 93 20h37m14.12s 66◦06(cid:3)20.0(cid:3)(cid:3) 1441±10 1.4×1.1 0.6×0.5
March 2003. We used the ABCD set of configurationsof the ratio measured within the equivalent 1–0 beam at each posi-
array(Guilloteauetal.1992).Thisassureshighspatialresolu- tion, and subsequentlywe convertthem into N(H ) assuming
2
tion(<1(cid:3)(cid:3)atthehighestfrequency)butalsoanoptimumsensi- theXfactorreferredtoabove.
tivity to all spatial frequenciesin the maps. A previousset of We have estimated the percentageof CO(1–0)flux recov-
observationsofNGC4826,usingdatatakenwiththeBCDcon- eredinthePdBImapsbycomparingthesingle-pointfluxesde-
figurations,hasbeendiscussedinGarcía-Burilloetal.(2003b) tected bythe 30 m telescope(García-Burillo& Krips, private
(hereaftercalledPaperI).Wehaveobservedsimultaneouslythe communication) towards the nuclei of the four galaxies dis-
J =1–0andJ =2–1linesof12COinsinglefields.Table1lists cussedinthispaperwiththefluxesrecoveredinthePdBImaps,
thespatialresolutionoftheseCOobservationsaswellasother corrected by primary beam attenuation and convolved to the
sourcerelatedparameters.Theprimarybeamsizeis42(cid:3)(cid:3)(21(cid:3)(cid:3)) 30mresolutionatthisfrequency(21(cid:3)(cid:3)).Thefractionoftheflux
in allthe1–0(2–1)lineobservations.Asthebulkof therele- recoveredinsidethe21(cid:3)(cid:3) field-of-viewrangesfrom60%–65%
vantnucleardiskemissionariseswellinsidethecentral15(cid:3)(cid:3)in in NGC 6951 and NGC 4579to 75% in NGC 4321 and 90%
thefourgalaxiesdiscussedinthispaper,observationshavenot inNGC4826.Thecorrespondingvaluesforthe2–1lineofCO
beencorrectedforprimarybeamattenuation.Duringtheobser- arecomparable.Themissingzerospacingfluxinthesemapsis
vationsthespectralcorrelatorwassplitintwohalvescentered expectedtobefoundinlow-levelemissionarisingintheshape
atthetransitionrestfrequenciescorrectedfortheassumedre- ofsmoothextendedcomponents.AshasbeenshownbyHelfer
cessionvelocities.Thecorrelatorconfigurationcoversaband- etal.(2003),whoestimatedthepercentageoffluxrecoveryin
width of 580MHz for each line, using four 160MHz-wide BIMA SONG galaxies using the 12 m NRAO telescope, this
units;thisisequivalentto1510kms−1(755kms−1)at115GHz percentageisalwaysveryhighinthecentralregionsofgalax-
(230GHz).Visibilitieswereobtainedusingon-sourceintegra- ies(i.e.,thedomainofNUGAmaps).Thereasonisthattheve-
tiontimesof20minframedbyshort(∼2min)phaseandam- locitygradientislargestatthenuclearregions.COemissionis
plitudecalibrationsonnearbyquasars.Theabsolutefluxscale thusconfinedtomuchsmallerareasinindividualchannelmaps
in our maps was derivedto a 10% accuracybased on the ob- comparedtotheouterdiskregionswherethepercentageofflux
servationsofprimarycalibratorswhosefluxesweredetermined filtered out can be higher. Considering that the percentage of
fromacombinedsetofmeasurementsobtainedatthe30mtele- flux actually present in the PdBI maps over the total single-
scopeandthePdBIarray.Imagereconstructionwasdoneusing dishestimateismoderate-to-largeinthegalaxiesstudiedhere
standardIRAM/GAGsoftware(Guilloteau&Lucas2000).In (seeabove),wedonotexpectthatthemorphologyofthemaps
this work we use prior observations of the 1–0line of 12CO willsignificantlychangebytheadditionofaplateau-likecom-
ofNGC4321madeusingtheBCDconfigurationsofthePdBI ponent.Moreover,thegravitytorquecalculationdevelopedin
and previously published by García-Burillo et al. (1998) (see thispaperis based onazimuthalaveragesmade to infertime-
thispaperandTable1fordetails). scales for the gas flows in these galaxy nuclei. The approach
Depending on the resolution/sensitivity requirements, we followedmakesourresultsvirtuallyinsensitivetothepresence
ofaweakextendedcomponent:gravitytorquesonthistypeof
use either naturallyoruniformlyweightedline maps,as indi-
sourcedistributionwillbezero.Thereforewedonotexpectthe
catedthroughoutthepaper.Uniformweightinginthe2–1line
derivedtorquebudgettobesignificantlybiased.
enables us to achieve subarcsecond spatial resolution in the
mapsofNGC4826,NGC4579andNGC6951.Bydefault,all
velocitiesarereferredtothesystemicvelocities(vsys,listedin 2.2.Near-infraredandopticalobservations
Table1),asdeterminedfromthisworkandfromGarcía-Burillo
etal.(1998).Similarly(∆α,∆δ)offsetsarerelativetotheAGN We acquired from the HST archive1 broadband images
lociderivedfromourownestimates(Table1). of NGC4826, NGC4579 and NGC6951, including three
NICMOSimages(F110WandF160WforNGC6951;F160W
Molecular gas masses are derived from the CO(1–0) in-
forNGC4826)andfourWFPC2images(F450WandF814W
tegrated intensities assuming a CO-to-H conversion factor
2
X = N(H2)/ICO(1−0) = 2.2×1020 cm−2 K−1 km−1 s(Solomon 1 BasedonobservationsmadewiththeNASA/ESAHubbleSpace
&Barrett1991).Whenrequired,moleculargascolumndensi- Telescope, obtained from the data archive at the Space Telescope
tiesareinferredfromtheCO(2–1)integratedintensitymaps.In ScienceInstitute.STScIisoperatedbytheAssociationofUniversities
thiscaseCO(2–1)intensitiesarefirstcorrectedbythe2–1/1–0 forResearchinAstronomy,Inc.underNASAcontractNAS5-26555.
1014 S.García-Burilloetal.:MoleculargasinNUcleiofGAlaxies(NUGA).IV.
Fig.1.a)The12CO(1–0)integratedintensitymapobtainedwiththePdBI(contourlevelsfrom1.5to5instepsof0.5Jykms−1 beam−1 and
from5to10instepsof 1Jykms−1 beam−1)observed inthenucleus ofNGC4321. Thefilledellipseatthetoprightcorner representsthe
CO beam size.Thecentralr ∼ 1kpc molecular disk of NGC4321 consistsof two nuclear spiral armsconnected (e.g.,B component) toa
marginallyresolvedr∼150pcdiskof∼108 M(cid:4)ofmoleculargascenteredontheAGNlocus(highlightedbythestarmarker).(∆α,∆δ)-offsets
arewithrespecttothelocationoftheAGN[(RA ,Dec )=(12h22m54.91s,15d49m19.9s)].Thispositioncoincideswithintheerrorswith
2000 2000
a secondary radio continuum maximum measured at 6 cm by Weiler et al. (1981) and with a peak in the (J, H, K)-2MASS image of the
galaxy(Jarrettetal.2003).b)IllustratesthekinematicsofmoleculargasalongthestripatPA=127◦ (thicklineina).Levelsgofrom0.015
to0.14instepsof0.0125Jybeam−1.Velocitiesarerelativetothesystemicvelocity(vLSR =1573kms−1;determinedfromCOkinematicsby
sys
García-Burilloetal.1998)and∆xoffsetsarerelativetotheAGN.Themajoraxisorientationisshownbythedashedline.Gaskinematicsover
theemissionbridgeBdepartfromcircularrotation.
for NGC4826; F555W and F814W for NGC4579). The op- a prominent nuclear bar (detected in the K band by Knapen
tical imageswere combinedusing (crreject) to eliminate cos- et al. 1995; see also Fig. 5) and extends out to r ∼ 1.2 kpc.
mic rays, and calibrated accordingto Holtzman et al. (1995). There is also a central CO source coinciding with the AGN
TheNICMOSimageswerere-reducedwiththeSTSDAStask which is marginallyresolved (r ∼ 150 pc) by the ∼2(cid:3)(cid:3) beam.
calnicausingthebestreferencefiles,andtheimageswerecal- Thiscentralsourcecontainsamoleculargasmassof∼108 M(cid:4).
ibrated in the standard way. The “pedestal” effect (see Böker TheCO spiralarmsmostlylie atthetrailingedgesofthe nu-
et al. 1999) was removed with the van der Marel algorithm2. clearbar.Thisparticulargeometrydeterminesthefeedingbud-
Sky values were assumed to be zero since the galaxy filled getforthegasinthisregion(seeSect.4.2.1).Thespiralarms
the WFPC2/NICMOS frames, an assumption which makes andthecentralsourceareconnectedbyamoleculargasbridge
an error of ∼0.1 mag at most, in the corner of the images. whichisspatiallyresolvedNWofthenucleus,i.e.,atthelead-
A J − H color image of NGC 6951 was constructed from ingedgeofthenuclearbar(componentBinFig.1b).García-
F110W–F160WaccordingtothetransformationsbyOriglia& Burilloetal.(1998)interpretedtheseCOobservationsandtheir
Leitherer(2000).ForNGC4321,wehaveadoptedthe(ground- relationwithothergaseousandstellartracersusingnumerical
based)K-bandimagepresentedbyKnapenetal.(1995). simulations of the cloud hydrodynamics.They found that the
bestfitforthegasflowcorrespondstothenuclearbarbeingde-
coupledfromthelarge-scalebar.Thenuclearbarisfast,witha
3. Observationalevidenceofongoingfeeding patternspeedΩ ≥150kms−1kpc−1.Thispushescorotationof
p
3.1.NGC4321 thenuclearbarinward,likelyinsidetheouteredgesoftheCO
spiralarms.
The inner r ∼ 1.5 kpc of this galaxy was mapped by García-
Burillo et al. (1998) with the PdBI at moderate (∼2(cid:3)(cid:3)) spa- The kinematics of molecular gas are characterized by
tial resolution in the 1–0 line emission of 12CO. NGC 4321 streaming motions detected in the CO spiral arms (see dis-
has beenclassified as a transitionobject(i.e.,HII/LINER)by cussion in García-Burillo et al. 1998). Closer to the AGN
(r < 500 pc), we find that molecular gas also displays sig-
Ho et al. (1997). As can be seen in Fig. 1a, molecular gas in
nificantdeparturesfrom circular rotationat the location of B.
the nucleus of NGC4321 is concentrated in a two spiral arm
structure that starts at r ∼ 550 pc, near the end points of Figure1bshowstheposition-velocity(p−v)plotalongastrip
atPA=127◦,purposelyorientedtoillustratetheCOkinemat-
2 http://www.stsci.edu/marel/software/pedestal.html ics at B. The discontinuity in radial velocities at ∆x ∼ −4(cid:3)(cid:3)
˜
S.García-Burilloetal.:MoleculargasinNUcleiofGAlaxies(NUGA).IV. 1015
Fig.2.a)The12CO(2–1)integratedintensitymapobtainedwiththePdBI(contourlevelsfrom2.8to10instepsof0.9Jykms−1 beam−1)is
overlaidontheB−IcolorimagefromHST(greyscale)observedinthenucleusofNGC4826.Thefilledellipseatthetoprightcornerrepresents
the CO beam size. (∆α, ∆δ)-offsets are with respect to the location of the AGN (marked by the star): (RA , Dec )=(12h56m43.63s,
2000 2000
21d40m59.1s).TheAGNlocusisidentifiedbyabluepoint-likesourceintheB−Imap;italsocoincideswithanon-thermalradiocontinuum
peakmeasuredat6cmbyTurner&Ho(1994).The80pcradiuscircumnucleardisk(CND)ofNGC4826,with∼3×107 M(cid:4)ofmoleculargas,
showsalopsidedringeddiskmorphology;thediskisoff-centerwithrespecttotheAGN.b)Thekinematicsofthegas,heredisplayedalong
theminor-axis p−vplot(thicklineina),aresuggestiveofstrongstreamingmotionsatthecrossingoftheringedges(N,S).Levelsgofrom
0.025to0.19instepsof0.015Jybeam−1.Velocitiesarerelativetothesystemicvelocity(vLSR =413kms−1;determinedfromCOkinematics
sys
byGarcía-Burilloetal.2003b)and∆yoffsetsarerelativetotheAGN.
indicatesthatthemoleculargasflowisdecelerated,exactlyas of molecular gas in the CND is fully resolved; the CND ap-
expectedifgasflowsalongtheleadingedgesofthebar.Details pears in the new maps as an off-center ringed disk (Fig. 2a).
onthekinematicsofmoleculargasinthecentralcomponentare Thedynamicalcenterofthegalaxydeterminedfromtheseob-
hiddenduetotheinsufficientspatialresolutionoftheCOmaps. servationscoincideswithintheerrorswithabluepointsource
Wenoticehoweverthatmoleculargasemissionisasymmetric identifiedintheB−IHSTcolormapofFig.2a.Thisconfirms
withrespecttov :COemissionispreferentiallyblue-shifted. ourearlier findingsthatthe putativesuper massive blackhole
sys
Asisthecasefortheothertransitionobjectanalyzedinthis liesonthesoutheasterninnersideoftheoff-centerringeddisk.
paper(NGC4826),we havefounda largemoleculargascon-
The gas kinematics in the CND are characterized by the
centration(∼108M(cid:4))neartheAGNinNGC4321(r<150pc).
presenceofstreamingmotions.Afirstanalysisofthe2Dkine-
Theanalysisofgaskinematicsprovidesevidenceforgasfuel-
maticsperformedonthelowestresolutiondataofPaperIindi-
ingatpresentonintermediatescales:atr ∼ 200–300pcfrom
catedthattheinstabilitiesidentifiedin theCND (andthoseof
theAGN.However,thespatialresolutionoftheCOmapsdoes
the inner m = 1 spiral) may not favor AGN feeding. The in-
notallowustoprobecloserthan100pcfromtheAGN.
formationcontainedinthenewestimagesconfirmsthisresult.
Figure 2b shows the departures from circular motion of gas
3.2.NGC4826 velocities,identifiedatthe northernandsoutherncrossingsof
theCNDringalongtheminoraxis.Gasvelocitiesbecomesys-
The first NUGA maps of the transition object NGC4826 tematicallyredder(bluer)whenweapproachthenucleusfrom
were published in Paper I. The CO images showed already a the southern (northern)side of the ring along the minor axis.
large concentration of molecular gas (∼1600 M(cid:4)/pc2 ) in the Deprojectedontothegalaxyplane(Northisthenearside),this
∼160 pc-diameter circumnuclear disk (CND) of this galaxy. pattern indicates that the radial velocity component changes
The distribution of molecular gas in the inner CND is signif- fromaninflowsignature(outsidethering)intoanoutflowsig-
icantly lopsided with respectto the position of the AGN; this nature(insidethering).AsitisfullydiscussedinpaperI,this
suggeststhatm = 1instabilitiesmaybeatworkatradialdis- measured change of sign across the minor axis is compatible
tancesofr∼50–60pcfromthecentralengine.Withthenewest withthepatternexpectedforatrailingwaveoutsidecorotation
0.5(cid:3)(cid:3)(10pc)resolution12CO(2–1)observationsthedistribution (fast wave), i.e., the type of perturbation that would not help
1016 S.García-Burilloetal.:MoleculargasinNUcleiofGAlaxies(NUGA).IV.
Fig.3. a) The 12CO(2–1) integrated intensity map obtained with the PdBI (contour levels from 0.4, 0.7, 1.3, 2.0 to 11 in steps of
0.9 Jy km s−1 beam−1) is overlaid on the V − I color image from HST (grey scale) observed in the nucleus of NGC4579. The filled el-
lipseatthetoprightcornerrepresentstheCObeamsize.(∆α,∆δ)-offsetsarewithrespecttothelocationoftheAGN(markedbythestar):
(RA ,Dec )=(12h37m43.52s,11d49m05.5s).TheAGNlocusisidentifiedbyapoint-likecontinuumsourcedetectedat3mmand1mm
2000 2000
byGarcía-Burilloetal.(2005,inprep.).Twospiralarcsconcentratethebulkofthe∼3.2×108 M(cid:4)moleculargasmassinthecentral1kpcof
thegalaxy.Aclose-upviewoftheinner200pcregion(showninc),showsacentralringeddisk(highlightedbythedashedellipse)withthe
AGNlyingonitssouthwesternedge.Agasclumpof∼106 M(cid:4)(denotedasE)delimitsthedisktotheEast.b)Thekinematicsalongthemajor
axis(thicklineina)) revealhighlynon-circular motionsrelatedtotheEclump.Levelsgofrom0.006to0.09instepsof 0.006Jybeam−1.
Velocitiesarerelativetothesystemicvelocity(vLSR = 1469kms−1;determinedfromCOkinematicsbyGarcía-Burilloetal.2005,inprep.)
sys
and∆xoffsetsarerelativetotheAGN.d)Sameasb)butherealongthedeclinationaxis(dashedthicklineina))withlevelsgoingfrom0.006
to0.024instepsof0.006Jybeam−1.Highlynon-circularmotionsarerelatedtotheNclump.
todrainthegasangularmomentum.Thedrivingagentofthese García-Burillo et al. 2005, in prep.). The molecular gas dis-
“mainly”gaseousm = 1instabilitiesmaynotberelatedtothe tributionin the central∼1 kpcof NGC4579suggeststhatthe
stellarpotentialwhichisessentiallyfeaturelessandmostlyax- gas flow responds to the 9 kpc-diameter stellar bar identified
isymmetric(seeSect.4.2.2;anddiscussionofPaperI). in all the NIR images of this galaxy (e.g. Jarret et al. 2003).
BasedontheCOmapsofNGC4826wefindlittleevidence The12CO(2–1)mapofFig.3arevealsamassof3.2×108 M(cid:4)
of ongoingAGN feedingatscales r < 150pc fromthe AGN. ofmoleculargaspiledupintwohighlycontrastedspiralarcs.
While the molecular gas reservoir of NGC4826 is abundant TheCOlaneslieattheleadingedgesofthestellarbar,which
(>3 × 107 M(cid:4)) close to its central engine (r < 150 pc), the is oriented along PA = 58◦. The northernspiral is more con-
analysis of gas kinematicsprovidesno evidence that ongoing tinuous and better delineated than its southern counterpart; it
AGNfeedingisatworkinthistransitionobject. isalsoverywellcorrelatedwiththeredlaneseenNorthinthe
V −I colorHSTimageofthegalaxy,showninFig.3a.There
is little moleculargasat r < 100pc distance fromthe central
3.3.NGC4579 engineofNGC4579:theclosestgascomplexof∼106 M(cid:4) lies
The 12CO(2–1) emission in the S1.9/L1.9 galaxy NGC4579 East of the nucleus at r ∼ 150 pc (complex E in Figs. 3a,b).
hasbeenmappedat∼0.5(cid:3)(cid:3)resolution(seeFig.3aadaptedfrom There is no moleculargas emission coincidentwith the AGN
S.García-Burilloetal.:MoleculargasinNUcleiofGAlaxies(NUGA).IV. 1017
itselftoa3σdetectionlimitof∼afew105 M(cid:4).TheV−Icolor tracedforover180◦;thewindingspiralarmsendupasahighly
HST image of the galaxyhelpsto identify the eastern molec- contrastedpseudo-ringat r ∼ 350 pc. The spiral arms can be
ular complex as part of a structured disk of 150pc-diameter identified by their red color in the J − H HST image of the
and ring-like shape (Figs. 3a,c). The position of the AGN is galaxy,shown in Fig. 4a. This m = 2 gas instability contains
welldefinedbyitsradiocontinuumemissiondetectedatboth a significant gas reservoir of 3 × 108 M(cid:4) which is presently
1mmand3mmcomingfromapointsourcethatliescloseto feeding a nuclear starburst, also identified by its intense ra-
the southwestern edge of the central disk. This indicates that diocontinuumandHαemissions(Ho&Ulvestad2001;Rozas
them = 2point-symmetryofthegasflowdrivenbythebarof et al. 2002). The geometry of the molecular gas ridges likely
NGC4579breaksup atr < 200pc andletslopsidednesstake reflectsthe crowdingof molecularcloudsalongthe x family
2
over.Anindependentconfirmationofthispicturecomesfrom of orbits of the prominentstellar bar, detected in all NIR im-
the new HST image of the nuclear region of NGC4579 ob- agesofNGC6951(Márquez&Moles1993;Friedlietal.1996;
tainedwiththeACScameraat3300Å;thisimageresolvesthe Pérez et al. 2000). As shown in Fig. 4a, only a small amount
centraldiskintoawindingm=1spiralinstabilitythatmimics ofmoleculargashassucceededinmakingitswaydowntothe
aring(Contini2004). AGN:mostofthemoleculargasmassistrappedinthenuclear
The kinematics of molecular gas in the central 1 kpc of spiralarms, quite similar to the case of NGC4579(thoughin
NGC4579 are characterized by the presence of highly non- this galaxy molecular gas likely populatesboth x1 and x2 or-
circularmotionsdetectedoverthespiralarmsandmostnotably bits).Acompactunresolvedmolecularcomplex(denotedasG
over the central disk. Figure 3b shows the p-v plot along the inFigs.4a,b)of∼afew106M(cid:4)isdetectedatthepositionofthe
kinematicmajoraxisofNGC4579(PA = 95◦).Theradialve- centralengine.Thiscomponentcouldcorrespondtoamolecu-
locitiesofthegasinthecentralgasdiskdepartby>100kms−1 lartorus(of∼40–50pcsize).AsseeninFig.4a,lowlevelCO
fromtheexpectedpatternofcircularrotation:emissionofthe emissionhasbeententativelydetectedinsidethering,bridging
Eastern gascomplex(at ∆x ∼ 1.5(cid:3)(cid:3)) appearsat highly forbid- the “apparent” gap between the N spiral arm (running North
den negative velocities (i.e., v < v ). Assuming that the gas fromWest)andthecentralsource.Thebridgeisbetteridenti-
sys
flowsinsidethegalaxyplane,thereportedvelocitydeviations fiedinthe p–vplotofFig.4b.Themoleculargasmassofthis
measured at E would imply that gas is apparently counter- emissionbridgeismoreaccuratelyestimatedusingthenatural
rotating at a speed of v ∼ 150 kms−1. As it is discussed in weightedmap:thegasmassamountsto∼107 M(cid:4) (Schinnerer
García-Burillo et al. (2005), this could be qualitatively ex- etal.2005).Thiscouldbethenorthernmolecularcounterpart
plained by very eccentric m = 1 orbits. Alternatively, this ofthefilamentaryspiralstructureidentifiedinthe J −H HST
velocity pattern could be accounted for assuming that gas is map(Fig.4a).
flowing out of the galaxy plane, possibly entrained by an ex- Thekinematicsofmoleculargasinthenuclearspiralarms
panding shell. The expanding shell scenario is supported by reveal streaming motions (Schinnerer et al. 2005) also iden-
the observed kinematics of the gas close to the N side of the tified in the previous lower resolution CO and HCN maps of
central disk. Figure 3d shows the p − v plot taken along the NGC6951 (Kohno et al. 1999). Inside the ring (50 pc< r <
declination axis, i.e., very close to the orientation of the mi- 350pc), however,gaskinematicsare compatiblewith regular
nor axis. Molecular gas kinematics at the N complex (where rotation (Fig. 4b). Of particular note, this is in clear contrast
v−v < −75kms−1)canbeinterpretedeitherasgasflowing tothecaseofNGC4579.ThekinematicsoftheG-component,
sys
outwardinsidetheplanealongtheminoraxis(Northisthenear althoughcompatible with circular motions, cannot be studied
side),orasasignatureofoutoftheplanemotions(similarlyto indetailduetoinsufficientspatialresolution.
thecaseoftheEcomplex).IneithercasethisimpliesthatAGN Whilemostofthe3×108M(cid:4)moleculargasdiskisfeeding
fuelingispresentlythwartedonthesescales. a starburstepisodein the nuclearspiralarmsat r ∼ 350pc, a
Insummary,mostofthemoleculargascontentofthecen- smallamountofmoleculargas(∼afew106 M(cid:4))hasbeende-
tral1kpcofNGC4579istrappedinatwoarmspiralstructure tectedonthecentralengine.Thiscentralcomponentrevealsa
thatcanbe tracedfromr ∼ 1kpcdownto r ∼ 200pc.Some prior accretionepisode down to scales of r ∼ 50 pc. It is un-
moleculargas(106 M(cid:4))isdetectedatr≤150pcfromthecen- clearwhethermoleculargasdetectedinthebridgecomponent
tralengineofNGC4579,butnotonthepositionofthecentral isfallingintothenucleusormigratingoutward:thegasflowis
engineitself(<afew105 M(cid:4)).Thefirst-orderinterpretationof fullycompatiblewithregularcircularmotionsfromr = 50pc
thecomplexgaskinematicsatr<150pcprovidesnoevidence tor=350pc.
ofongoinginflowfromthesescalesdowntotheAGN,buton
thecontrary,itindicatesoutflowmotions.
4. GravitationaltorquesandAGNfueling
3.4.NGC6951 To explore more precisely the efficiency of feeding, we have
estimatedthegravitationaltorquesexertedbythestellarpoten-
NGC6951 is a prototypical Seyfert 2 galaxy for which sub- tials(derivedfromtheNIRimages)ontheirmolecularcircum-
arcsecond resolution 12CO(2–1) maps have been completed nucleardisks(asgivenbytheNUGACOmaps).Afterestimat-
within the NUGA project (Fig. 4a adapted from Schinnerer ingtheroleofstellargravitationaltorques,wewillinvestigate
et al. 2005, in prep.). The molecular gas distribution in the whetherothermechanismsarerequiredtoexplainthelowlevel
central 1 kpc consists of two nuclear spiral arms that can be ofnuclearactivityinthesegalaxies.
1018 S.García-Burilloetal.:MoleculargasinNUcleiofGAlaxies(NUGA).IV.
Fig.4. a) The 12CO(2–1) integrated intensity map obtained with the PdBI (contour levels from 0.15, 0.25, 0.40, 0.70 to 6.2 in steps of
0.5 Jy km s−1 beam−1) is overlaid on the J − H color image from HST (grey scale) observed in the nucleus of NGC6951. The filled el-
lipseatthetoprightcornerrepresentstheCObeamsize.(∆α,∆δ)-offsetsarewithrespecttothelocationoftheAGN(markedbythestar):
(RA ,Dec )=(20h37m14.12s,66d06m20.0s).ThepositionoftheAGNisgivenbythepoint-likeradiocontinuumsourcemeasuredat6cm
2000 2000
and 20 cm by Ho & Ulvestad (2001). The molecular gas distribution in the central 1kpc shows two highly contrasted nuclear spiral arms
containing3×108 M(cid:4)whicharepresentlyfeedingacircumnuclearstarburst.Acompactmolecularcomplex(denotedasG)of∼afew106 M(cid:4)
isdetectedontheAGN.Furthermore,wehavetentativelydetectedanorthernmoleculargascomponentlinkingGwiththeNspiralarm(i.e.,
thespiralrunningNorthfromWest)whichcouldberelatedtothefilamentarydustyspiralseenintheJ−HcolorHSTimage(seealsob)).b)
Thekinematicsalongthemajoraxis(thicklineina))arecompatiblewithcircularmotionsforthegasneartheAGN.Levelsgofrom0.008,
0.0012, 0.016 to 0.076 insteps of 0.006 Jy beam−1. Velocitiesare relativetothe systemic velocity(vLSR = 1441 km s−1; determined from
sys
COkinematicsbySchinnereretal.2005,inprep.)and∆xoffsetsarerelativetotheAGN.
Wefirstexplainthegeneralmethodologyemployedandthe independent of the present gas distribution in the plane. The
basicassumptionsinSect.4.1.Thedifferentstepsaredescribed crucialstepconsistsofusingthetorquefieldtoderivetheangu-
in detail in Sects. 4.1.1and 4.1.2.We discuss in Sect. 4.2 the lar momentumvariationsand the associated flow time-scales.
results obtained from the application of this procedure to the Asexplainedbelow,thelinkismadethroughtheobserveddis-
fourNUGAtargetsexaminedinthiswork. tributionofthegas.
With this aim, we assume that the measured gas column
4.1.Generalmethodology density(N(x,y))derivedfromaCOintensitymapateachoffset
inthegalaxyplaneisafairestimateoftheprobabilityoffind-
Gravitationalforcesarecomputedateachlocationintheplane ing gas at this location at present. In this statistical approach,
ofthegalaxy,usingnear-infraredimagestoderivetheunderly- we implicitly average over all possible orbits of gaseous par-
inggravitationalpotential.Weassumethatthetotalmassbud- ticles and take into account the time spent by the gas clouds
getisdominatedbythestellarcontributionandthusneglectthe along the orbit paths. We assume that CO is a good tracer of
effect of gas self-gravity. We also assume a constant M/L ra- the total gas column density, since HI mass in the nuclei of
tio, and determine its best value by fitting the rotation curve galaxiesistypicallyaverysmallfractionofthetotalgasmass.
constrained by the CO observations. From the 2D force field The torque field is then weighted by N(x,y) at each location
(Fx, Fy) we derive the torques per unit mass at each loca- to derive the time derivative of the local angular momentum
tion(t(x,y) = x Fy−y Fx).Thistorquefield,bydefinition,is surfacedensitydLs(x,y)/dt= N(x,y)×t(x,y).
S.García-Burilloetal.:MoleculargasinNUcleiofGAlaxies(NUGA).IV. 1019
In order to estimate the gas flows induced by these angu-
lar momentum variations we produce azimuthal averages of
dL (x,y)/dt at each radius. The azimuthalaverageat each ra-
s
dius,usingN(x,y)astheactualweightingfunction,represents
theglobalvariationofthespecificgasangularmomentumoc-
curringatthisradius(dL/dt|θ).Finally,thetime-scalesforgas
inflow/outflowcan be derived by estimating the average frac-
tionofangularmomentumtransferredinonerotation.
Thevalidityofourestimateoftheefficiencyofstellargrav-
ity torques to drive angular momentum transfer in the gas is
basedonthefollowingsimplehypothesis:weassumethatthe
gasresponseto the stellar potentialis roughlystationarywith
respect to the potential reference frame during a few rotation
periods.Wewouldliketostressthatevenintheparticularcase
of nuclear bars, which might decouple from the outer stellar
barsundercertaincircumstances,ourassumptionisstillvalid.
When there are severalstellar pattern speedsat differentradii
in a galaxy disk, numerical simulations show that the gas re-
sponse tends to be coupled with the stellar potential pattern
(Friedli & Benz 1995; García-Burillo et al. 1998; Bournaud
&Combes2002, 2005,in prep.).Thegasresponseadjustsits
patternspeedto thatofthe dominantstellar patternata given
radius.
A different case is represented by non-axisymmetric per-
turbationswhichcanbedrivenbygasself-gravityandthatare
partly independent of or possibly decoupled from the stellar
perturbationsofthedisk.Nucleargalaxydiskswithahighgas
surfacedensityandamostlyaxisymmetricstellarpotentialcan
be prone to develop this kind of gas self-gravitating pertur-
bation. In this limiting case (not contemplated here), and al-
thoughourcalculationisstillformallycorrect,theinclusionof
gasself-gravityisrequiredtoderivethecorrecttorquebudget.
Inparticular,ifthegasdiskdecouplesfromthestellarpattern,
theazimuthallyaveragedgravitytorquesexertedbythestellar
pattern on the gas will very likely be close to zero. The main
sourceforthetorquesifanyshouldcomefromthegasinstabil-
ityitself.
Note also that any radial variation of the CO-to-H con-
2
version factor (X ) is not expected to affect the estimated
CO
time-scales as these are independentof the global normaliza-
tion factoras a functionof radius. If X variesas a function
CO
of azimuth at a fixed radius, there could be a potential bias.
However, observational evidence indicates that the dominant
variation of X in the central regions of galaxies is radial
CO
(Solomon&Barrett1991;Reganetal.2001).
Fig.5. a) (Upper panel) We overlaid the 12CO(1–0) PdBI intensity Intheapproachfollowedtoderivethegravitationalpoten-
map (contours) on the K-band image of Knapen et al. (1995) (grey tialwehaveassumedthatthebulgeisasflattenedasthedisk,
scale)obtainedforthenucleusofNGC4321;bothimageshavebeen
andthusnoattempthasbeenmadetoseparatethebulgefrom
deprojectedontothegalaxyplane.UnitsonX/Yaxes(∆X /∆Y )cor-
G G thepurediskcontribution.Theimplicitassumptionofahighly
respond toarcsecoffsetsalongthemajor/minor axeswithrespectto
flattenedbulgeisprobablynotwrongforsomebarredgalaxies
the AGN. The nuclear bar - BAR(n) - is parallel to the large-scale
bar-BAR.b)(Lowerpanels) Strengths(Q,i = 1,2) andphases(φ, butforothersit willoverestimatethe radialforcesby atmost
i i
i = 1,2) ofthem = 1andm = 2-Fouriercomponents ofthestellar afactorof2(e.g.,Buta&Block2001).Ontheotherhand,the
potentialinsidetheimagefield-of-view(r =1100pc).Theφ-angles effectof bulgestretchingdueto deprojectioncan enhancethe
i
are measured from the +X axis in the counter-clockwise direction. strength of bars, especially if they are aligned with the minor
ThetotalstrengthofthepotentialisrepresentedbyQ .Q-valuesfor axisandtheinclinationanglesarelarge.Asthisisnotthecase
T
r < 50pc(notshown) areblankedduetoinsufficientgridsampling forthegalaxiesanalyzedhere,weinsteadexpectthatthevalue
closetothenucleus. derivedforthegravitytorqueswillbetypicallyunderestimated
1020 S.García-Burilloetal.:MoleculargasinNUcleiofGAlaxies(NUGA).IV.
in our case by a factor 1.5–2 althoughthey will still have the NGC4321,whereweusedthe1–0line).Toestimatetheradial
samesign. gas flow induced by the torques, we have first computed the
torqueperunitmassaveragedovertheazimuth,using N(x,y)
astheactualweightingfunction,i.e.:
4.1.1. Evaluationofstellar potentials (cid:4)
The first step is to derive the stellar potential in the nuclear t(R)= θN(x,y(cid:4))×(xFy−yFx)· (5)
disks of these galaxies, using the high-resolutionNIR images θN(x,y)
describedinSect.2.2.OurworkinghypothesisisthatNIRim-
Results obtained for t(R) based on the CO(1–0) and
ages are less affected than optical ones by dust extinction or
CO(2–1) maps were seen to be virtually identical within the
by stellar populationbiases (Quillen et al. 1994). The images
errors.Figures9bto12bshowtheresultsderivedfromthe1–
arefirstdeprojectedaccordingtotheanglesPAandigivenin
0 line maps. By definition, t(R) represents the time derivative
Table1.Theimagesarethencompletedintheverticaldimen-
ofthespecificangularmomentum-L-ofthegasaveragedaz-
sion by assuming an isothermal plane model with a constant imuthally,i.e., t(R) = dL/dt |θ. To derive azimuthalaverages,
scale height,equalto∼1/12thoftheradialscale-lengthofthe weassumearadialbinning(∆R)whichcorrespondstotheorig-
image. The potential is then derived by a Fourier transform
inalresolutionoftheNIRimages.Similarlytothetorquemaps,
method. We also assumed a constant mass-to-light (M/L) ra- thesignoft(R),either+or–,defineswhetherthegasmaygain
tio, obtainedby fitting the observedCO rotationcurve - v -
rot or lose angular momentum, respectively. More precisely, we
for each galaxy.The potential- Φ(R,θ) - is then decomposed evaluate the AGN feeding efficiency by deriving the average
inthedifferentm-modes:
fraction of the gas specific angular momentum transferred in
(cid:1)
onerotation (T ) by the stellar potential,as a functionof ra-
Φ(R,θ)=Φ (R)+ Φ (R)cos(mθ−φ (R)) (1) rot
0 m m dius,i.e.,bythenon-dimensionalfunction∆L/Ldefinedas:
m ∆L dL (cid:5)(cid:5)(cid:5) 1 (cid:5)(cid:5)(cid:5) t(R)
where Φm(R)and φm(R) representthe amplitudeand phaseof L = dt (cid:5)(cid:5)θ× L (cid:5)(cid:5)θ×Trot = Lθ ×Trot (6)
them-mode,respectively.
Following Combes & Sanders (1981), we define the whereLθisassumedtobewellrepresentedbyitsaxisymmetric
strengthofthem-Fouriercomponent,Q (R)as average,i.e., Lθ = R×vrot.Theabsolutevalueof L/∆Ldeter-
m
mineshowlongwillittakeforthestellar potentialtotransfer
Q (R)=mΦ /R|F (R)|. (2) the equivalentof the total gas angular momentum. Assuming
m m 0
thatthe gas responseto the stellar potentialis stationary with
Thecorrespondingstrengthofthetotalnon-axisymmetricper-
respect to the potential reference frame during a few rotation
turbationisdefinedby: periods,asmallvalueof∆L/Limpliesthatthestellarpotential
(cid:2) (cid:3)
Q (R)= FTmax(R) = R1 ∂Φ∂(Rθ,θ) max (3) itshein1e–ffi0cmieanptsaotfprtheseeannt.aTlyhzeedt(Rga)laanxdie∆sLar/eLdciusprvlaeyseddeirnivFedigfsr.o9mb
T F0(R) dΦ0(R) to12b.
dR
To calculate how much gas mass is involved in the trans-
where Fmax(R) representsthe maximumamplitudeofthe tan-
T ferdrivenbythestellarpotentialwehaveestimatedtheradial
gential force over all θ and F0(R) is the mean axisymmetric trend for the mass inflow (– sign)/outflow(+sign) rate of gas
radialforce. perunitlengthasafunctionofradius(inunitsofM(cid:4)yr−1pc−1
Figures5a,bto8a,billustratethequantitativedescriptionof
inFigs.13ato16a)asfollows:
gravitationalpotentialsgivenby[Qi=1,2,QT,φi=1,2]forthefour (cid:5)(cid:5) (cid:5)(cid:5)
galaxiesexaminedinthiswork. d2M = dL (cid:5)(cid:5)(cid:5) × 1 (cid:5)(cid:5)(cid:5) ×2πR× N(x,y)|θ (7)
dRdt dt θ L θ
where N(x,y)| is the radial profile of N(x,y) averaged over
4.1.2. Efficiencyofgravitationaltorques θ
theazimuthforaradialbinning∆R.
After having calculated the forces per unit mass (Fx and Fy) Theinflow/outflowratesintegratedouttoacertainradiusR
from the derivatives of Φ(R,θ) at each pixel, the torques per canbederivedas:
unitmass-t(x,y)-canbecomputedby: dM (cid:1) d2M
= ×∆R. (8)
t(x,y)= xFy−yFx. (4) dt dRdt
Figures 13b to 16b display these integrated rates in units
Thesenseofthecirculationofthegasinthegalaxyplanede- ofM(cid:4) yr−1.
terminesthesignoft(x,y):positive(negative)ifthetorqueac-
celerates(decelerates)thegasat(x,y).Wehavenextobtained
4.2.TrackingdowngravitationaltorquesinNUGA
thegravitationaltorquemapsweightedbythegascolumnden-
sitiesderivedfromtheCO1–0and2–1lines, N(x,y),i.e.,we targets
derivet(x,y)×N(x,y).Theserepresenttheeffectivevariations
4.2.1. NGC4321
of angular momentum density in the galaxy plane. We show
in Figs. 9a to 12a the normalized version of these maps, i.e., Figure 5a shows the K-band image of the nucleus of
divided by [| N(x,y)×t(x,y)|] for the 2–1 line (exceptfor NGC4321,obtainedbyKnapenetal.(1995),deprojectedonto
max