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LETTER A black-hole mass measurement from molecular gas kinematics in NGC4526 TimothyA.Davis1,MartinBureau2,MicheleCappellari2,MarcSarzi3&LeoBlitz4 3 Themassesofthesupermassiveblack-holesfoundingalaxybulges tailedanalysisofthemoleculargasmorphologywillbeconductedina 1 are correlated with a multitude of galaxy properties1,2, leading futurework. Wenote,however,thatthegasstructureslieintheplane 0 tosuggestionsthatgalaxiesandblack-holesmayevolvetogether3. of the galaxy and appear to be regularly rotating; they are therefore 2 Thenumberofreliablymeasuredblack-holemassesissmall,and likelytobedynamicallycold,andagoodtracerofthepotential18. n the number of methods for measuring them is limited4, holding WecreatedagridofsimulationsofNGC4526spanningarangeof a back attempts to understand this co-evolution. Directly measur- SMBHmasses(noSMBH,M =3×106,andthen5×107 –1.45× J BH ing black-hole masses is currently possible with stellar kinemat- 109 M(cid:12) in linear steps) and I-band mass-to-light ratios (M/LI = 0 ics(inearly-typegalaxies),ionised-gaskinematics(insomespiral 0.55–6.15M /L inlinearsteps). Forfulldetailsofthesesimula- 3 andearly-typegalaxies5–7)andinrareobjectswhichhavecentral tionsseeSectio(cid:12)n1.1(cid:12)intheonlinesupplementaryinformation. Wefix maser emission8. Here we report that by modelling the effect of theinclinationofthegasdisk19 (i = 79◦), anduseanaxisymmetric ] O a black-hole on the kinematics of molecular gas it is possible to massmodelofNGC45269(carefullyfittedtoavoidcontaminationdue fitinterferometricobservationsofCOemissionandtherebyaccu- todust;seeSection1.1.2inthesupplementarymaterial)toderivethe C rately estimate black hole masses. We study the dynamics of the circular-velocitycurveexpectedfromtheluminousmatteralone. The h. gasintheearly-typegalaxyNGC4526,andobtainabestfitwhich presence of a SMBH in NGC 4526 manifests itself as an inner Kep- p requiresthepresenceofacentraldark-objectof4.5+−43..20×108 M(cid:12) lerian rise of the rotation curve (above that expected from luminous - (3σ confidence limit). With next generation mm-interferometers matteronly). Onlargerangularscalessuchfast-risingrotationcurves o (e.g. ALMA) these observations could be reproduced in galaxies havebeenobserved,andusedtoinferthemassesofcentralstarclus- r t outto75megaparsecsinlessthe5hoursofobservingtime. The tersandbulges20. Wefitthesemodelstoourobserveddatainorderto s a useofmoleculargasasakinematictracershouldthusallowone determineifsuchanexcessduetoacentraldarkmassisdetectablein [ toestimateblack-holemassesinhundredsofgalaxiesinthelocal NGC4526. universe,manymorethanaccessiblewithcurrenttechniques. 1 Figure 1 shows three different simulated position-velocity dia- For this study, we targeted the fast-rotating early-type galaxy v grams (PVDs) overlaid on the observed PVD of NGC 4526, with (ETG)NGC4526. Thisobjecthasastellarvelocitydispersionwithin 4 ±1(cid:48).(cid:48)15 insets. The first panelshows the bestmodel with noSMBH, oneeffectiveradius9 σ = 222kms−1 . Thisgalaxyhasnothadits 8 e withaclearexcessofhigh-velocitymoleculargasatthecentre. The black-hole mass measured by any other technique to date but, given 1 middlepanelshowsouroverallbest-fitmodel,clearlyreproducingbet- thatmostgalaxieswithbulgesseemtohaveablackhole2,5,fromthe 7 ter the observed PVD at all radii, with M = 4.5×108 M and 1. sσp−heMreBoHfirnefllautieonnc1e0(wSeOcIa)nweosutilmdathteusMbBeHr≈2=×1G0M8M(cid:12)/.σT2he≈SM20BpHc M/LI = 2.65M(cid:12)/L(cid:12). ThefinalpanelsBhHowsamodelwitha(cid:12)much 0 or0(cid:48).(cid:48)25atthe16.4MpcdistanceofNGCS4O52I6(deriveBdHfromsurface- largerSMBH,clearlyincompatiblewithourdata.Thelowerpanelsof 3 Figure1showthetraceextractedfromtheobservedPVD(asdescribed brightness fluctuations11). NGC 4526 also has a large molecular gas 1 in the supplementary material), and associated errors. The grey line reservoir(totalmolecularhydrogenmassM =3.69×108M 12), : H2 (cid:12) showsthetraceextractedfromthemodelsinthesameway(withpoints v previously mapped at low spatial resolution13 (≈4(cid:48)(cid:48)). The molecular denoting the values at the same radius as the observed points). The Xi gasco-rotateswiththestars14andHubbleSpaceTelescope(HST)im- residuals between the data and the model at each position (∆V=data agesshowthatitiscoincidentwithregulardustlanesextendingupto r minusmodel)areshowninthebottompanel.Clearlythebest-fitmodel a thegalaxycentre,stronglysuggestingthatmoleculargaswithregular producesasignificantlybetterfittothedata. kinematicsexistsaroundtheSMBH7. Figure 2 shows the χ2 contours of our fits (conducted as de- scribed in the supplementary material) as a function of M and NGC4526wasobservedintheCO(2-1)line(230GHz)usingthe BH M/L . Aclearglobalminimumispresentatthebest-fitvalues,with CombinedArrayforResearchinMillimetreAstronomy(CARMA)in I A, B and C configurations15. The data were reduced in the standard a minimum reduced χ2 of 1.27. We define uncertainties for each manner16,17, and more details are presented in Figure 1. The spatial of our fitted parameters from likelihood functions of each parame- ter(marginalisedovertheother),byfindingtheregioncontainingre- resolution achieved along the kinematic major axis of the galaxy is 0(cid:48).(cid:48)25(20pc),equaltothepredictedSMBHSOI.Thegasinthissource spectively 68% and 99% of the probability. Our final best-fit values areM =4.5+1.5×108 M withM/L = 2.65±0.21M /L seemstobedistributedinacentralcomponent,andaninnerringwith BH −1.3 (cid:12) I (cid:12) (cid:12) (68% confidence level), and 4.5+4.2 × 108 M with M/L = spiralspurswhichleadoutwardstoanotherringatlargerradii. Ade- −3.1 (cid:12) I 2.65+0.56 M /L (99% confidence level). These values are fully −0.52 (cid:12) (cid:12) 1European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748, Garching-bei- consistent within the 3σ-uncertainties with the reported σe-MBH Mu¨nchen, DE2Sub-departmentofAstrophysics, DepartmentofPhysics, UniversityofOxford, relation10. Our formal uncertainties (0.14 dex and 0.5 dex at 1σ and DenysWilkinsonBuilding,KebleRoad,Oxford,OX13RH,UK3CentreforAstrophysicsResearch, 3σ,respectively)arealsosimilar(andinmanycasessmaller)totheav- UniversityofHertfordshire,Hatfield,HertsAL19AB,UK4DepartmentofAstronomy,Universityof California,Berkeley,CA94720,USA erageuncertaintiesreportedbyotherauthors.Forinstancethemean1σ 1 Position (pc) Position (pc) Position (pc) -250 0 250 -250 0 250 -250 0 250 4 0 0 4 0 0 4 0 0 M = 0.00 M = 4.50E+08 M = 1.20E+09 M/BLH= 2.65 MB/LH= 2.65 MB/LH= 2.30 -1s)2 0 0 I 2 0 0 I 2 0 0 I m k y ( 0 0 0 ocit el V-2 0 0 -2 0 0 -2 0 0 -44 0 0 0 0 -44 0 0 0 0 -44 0 0 0 0 Data Data Data -1m s) 200 χ2reMd=o2d9e.2l 200 χ2reMd=o1d.2e7l 200 χ2reMd=o2d9e.2l k y ( 0 0 0 cit o Vel -200 -200 -200 -400 -400 -400 75 75 75 ∆V 0 0 0 -75 -75 -75 -4 -2 0 2 4 -4 -2 0 2 4 -4 -2 0 2 4 Position (arcsec) Position (arcsec) Position (arcsec) Figure1 NGC4526kinematicmodelsanddata. Top:ModelPVDs(blackcontours),overlaidontheobservedCO(2-1)PVD(filledorangecontours). ThisPVD wascreate|dfromourCO(2-1)observationsofNGC4526fromCARMA.Thesynthesizedbeamsizeachievedintheseobservationsis0(cid:48).(cid:48)27 0(cid:48).(cid:48)17,andthevelocity channelwidthis10kms−1.ThefinalfullyreducedandcalibrateddatacubehasanRMSnoiseof2.88mJybeam−1.ThePVDwascreated×byrotatingthedatacube toalignthekinematicmajoraxisofthemoleculargaswiththex-axis,andthensummingoveronebeamwidtharoundtheaxisintheydirection.Thespatialresolution achievedinthePVDis0(cid:48).(cid:48)25(20pc),equaltothepredictedSMBHSOI.OurresultsdonotdependonthemethodusedtoextractthePVD.Fromleft-to-right,thebest modelwithnoSMBH,theoverallbest-fitmodel,andamodelwithanoverweightSMBH.ThemodelMBHandM/LI areindicatedinthetop-leftcornerofeach panel,andaninsetofthecentral 1(cid:48).(cid:48)15isshowninthebottom-rightcorner.Middle:BlackpointsshowthetraceextractedfromtheobservedPVD,andassociated ± standarderrors.Thegrey-lineshowsthetraceextractedfromthemodels(andthegreycrossesdenotethevalueofthetraceatthesameradiusastheobservedpoints). Bottom:Residualsbetweenthemodelanddataateachposition(∆V=dataminusmodel;kms−1).Theerrorbarsshowninthemiddleandbottomplotscorrespondto theformaluncertaintiesinfittingthetrace(seeSection1.2inthesupplementaryinformation),addedinquadraturewithtwofactorsof5kms−1(toaccountforthe finitevelocitychannelwidthinboththedataandmodel). errorreportedwhenusingdynamicalstellarandionisedgastechniques andusenear-infraredphotometryasdoneinpreviousstudiesofdusty is≈0.6dex10 (howevertheratherdifferentsystematicerrorsinvolved objects23. makedirectcomparisondifficult). Theuseofmoleculargasasakinematictracerholdsgreatpromise Theχ2contoursshowtheusualdegeneracybetweenSMBHmass to increase the total number of SMBH mass measurements in galax- andmass-to-lightratiofoundinotherstudies. Tofitthedatawithouta ies of all types where CO is detected. Angular resolutions of up to SMBH,anegativeM/Lgradientwouldbenecessary,witholderstellar 0(cid:48).(cid:48)15 can be achieved with current mm-interferometers, allowing for populationsdominatingintheinnerparts(highM/L)andyoungstars instancetoresolvetheSOIofa2×108 M SMBHinagalaxywith (cid:12) atlargeradii(lowM/L).WhiletherealM/Lisunlikelytobeexactly σ =200kms−1onlyouttoaround30Mpc. Thenextgenerationof e constant,thisisoppositetothetrendreportedbyreddeningfreestellar millimetreinterferometerswillhaveoveranorderofmagnitudegreater populationstudies21andthatexpectedfromthepresenceofmolecular angularresolution(forexample,≈6masat690GHzwithALMA),as gasandstar-formationinthecentralregions22. well as greatly increased sensitivity. In less the 5 hours of integra- The ability to determine a black-hole mass accurately using tiontimewithALMAonecouldachievethesamesensitivityandlin- molecular-gas can be affected by many of the same issues that af- earresolutionastheobservationspresentedhere,inagalaxy75Mpc fect measurements of ionised-gas. Turbulent motions are in general away. Galaxies of lower mass (with smaller SMBHs) will also be- smallinmoleculargas,butcouldconceivablyincreasearoundablack- comeaccessible. Forinstance,theSOIofaMilkyWay-likeSMBH24 hole. Similarly, iftheinnergasweretobemisalignedfromthestel- (MBH = 4×106 M(cid:12), σe = 105 km s−1) will be resolved up to larbody,ourmassestimatewouldbesystematicallyaffectedinaway ≈50Mpc. that is degenerate with a change in M/L. In this galaxy, however, Measurementsusingasingletechniquewillthusbepossibleover wefindnoevidencethatthevelocitydispersionincreasesintheinner theentirerangeoftheσ -M relation, leadingtomuchneededre- e BH regions(asdescribedinSection1.1.1inthesupplementarymaterial), duceduncertaintiesintheslopeandnormalisationofblackhole-galaxy andconstraintheinnergastobealignedwiththestellarbodywithin relations. Thiswillallowthestudyofalargenumberofspiralgalax- <3◦. Suchamisalignmentcouldchangevelocitiesbyaninsignificant ies,thatcannotcurrentlybeprobedeasilyusingstellardynamicaltech- amount(<∼3kms−1;seeSection1.1.2inthesupplementarymaterial). niques. Furthermore,itwillalsoprovideaccesstoalargernumberof Thepresenceofdustcouldalsocausemassmodelstounderestimate systems than ionised gas techniques (currently limited by the ≈0(cid:48).(cid:48)05 thecontributionofluminousmattertothepotential. Weagainbelieve resolution of HST). Even considering that only some of the accessi- this should not introduce significant errors in this object, because of ble objects will have suitably relaxed and centrally-peaked distribu- ourcarefultreatmentofdustinthemassmodel(seeSection1.1.2in tions of molecular gas, measuring SMBH masses will be possible in the Supplementary Information). Future studies using this technique many hundreds of spiral (and early-type) galaxies, many times more shouldchoosetheirtargetstominimisetheimpactofsucheffects,but thanpossibleusingconventionalstellarandionised-gastracerstoday. canalsoincludewarpsandturbulentmotionsintheirgasdiskmodels23, Thistechniquecouldalsobeextendedusingotherspectrallines,such 2 5 16. Alatalo et al. 2012, The ATLAS3D project XVIII. CARMA CO imag- ingsurveyofearly-typegalaxies, Mon.Not.R.Astron.Soc., accepted (arXiv:1210.5524) 17. R.Sault, P.Teuben, M.Wright, ARetrospectiveViewofMIRIAD,ASP 4 Conf.Series77,433(1995). 18. T.A.Davisetal.,TheATLAS3DProject-XIV.Theextentandkinematics ofmoleculargasinearly-typegalaxies,Mon.Not.R.Astron.Soc.,429, 1,534-555(2013). LI 19. T.A.Davisetal.,TheATLAS3Dproject-V.TheCOTully-Fisherrelation M/ 3 ofearly-typegalaxies,Mon.Not.R.Astron.Soc.414,2,968-984,(2011) 20. Y. Sofue , J. Koda, , H. Nakanishi, & S. Onodera, The Virgo High- Resolution CO Survey: II. Rotation Curves and Dynamical Mass Dis- tributions,Publ.Astron.Soc.Japan.,55,59-74(2003). 2 21. H.Kuntschneretal.,TheSAURONproject-XVII.Stellarpopulationanal- ysisoftheabsorptionlinestrengthmapsof48early-typegalaxies,Mon. Not.R.Astron.Soc.408,97-132,(2010). 22. A.F.Crocker,M.Bureau,L.M.Young,F.Combes,Moleculargasandstar formationinearly-typegalaxies, Mon.Not.R.Astron.Soc.410, 1197- 0 2 4 6 8 10 12 14 1222,(2011). M (108 M ) 23. N.Neumayer,M.Cappellari,J.Reunanen,etal.,TheCentralParsecsof BH O • CentaurusA:High-excitationGas,aMolecularDisk,andtheMassofthe BlackHoleAstrophys.J.671,2,1329-1344,(2007). Figure2 NGC4526SMBHmassuncertainties. ∆χ2 χ2 χ2 24. A.Ghezetal., MeasuringDistanceandPropertiesoftheMilkyWay’s contourso|fourfitstotheCO(2-1)PVD,asafunctionofth≡etwofr−eepmarianmimetuemrs CentralSupermassiveBlackHolewithStellarOrbits,Astroph.J.689,2, MBHandM/LI.Themodelgridisshownwithblackdotsandtheoverallbest- 1044-1062,(2008). fitmodelbyawhitestar. Thesolidshadedcontourswithblacklinescorrespond tothe1-3σlevelswithonedegree-of-freedom(∆χ2=1,4,9)withgoodmodels Acknowledgements The research leading to these results has received inthedarkestareas. The4&5σlevels(∆χ2=16,25)aredenotedwithdashed funding from the European Community’s Seventh Framework Programme. MBissupportedbytherollinggrants‘AstrophysicsatOxford’andfromthe greylines. UK Research Councils. MC acknowledges support from a Royal Society UniversityResearchFellowship. MSacknowledgessupportfromaScience andTechnologyFacilitiesCouncil(STFC)AdvancedFellowship. Supportfor as the very bright atomic gas cooling lines at higher frequencies (in CARMAconstructionwasderivedfromthestatesofCalifornia, Illinois, and ordertoincreasethespatialresolutionachievedevenfurther),andopti- Maryland,theJamesS.McDonnellFoundation,theGordonandBettyMoore callythintransitionssuchas13CO(whichwouldallowdeterminations Foundation, theKennethT.andEileenL.NorrisFoundation, theUniversity ofblack-holemasseseveninsystemsthatareexactlyedgeon). ofChicago,theAssociatesoftheCaliforniaInstituteofTechnology,andthe NationalScienceFoundation.OngoingCARMAdevelopmentandoperations Received11thSeptember;accepted27thNovember2012 aresupportedbytheNationalScienceFoundationunderacooperativeagree- ment,andbytheCARMApartneruniversities. 1. J.Magorrianetal.,TheDemographyofMassiveDarkObjectsinGalaxy AuthorContributions T.A.Dpreparedandreducedtheobservations,and Centers,Astron.J.115,6,2285-2305(1998). createdthemodellingtool. TADandMBpreparedthemanuscript. MCcre- 2. A.Graham,P.Erwin,N.Caon,I.Trujillo,ACorrelationbetweenGalaxy atedthemassmodel. Allauthorsdiscussedtheresultsandimplicationsand LightConcentrationandSupermassiveBlackHoleMass,Astrophys.J. commentedonthemanuscriptatallstages. 563,L11-L14(2001). 3. J.Silk,M.Rees,Quasarsandgalaxyformation,Astron.Astrophys.331, AuthorInformation Reprints and permissions information is available at L1-L4(1998). www.nature.com/reprints. Theauthorsdeclarenocompetingfinancialinter- 4. L. Ferrarese, H. Ford, Supermassive Black Holes in Galactic Nuclei: ests. Readers are welcome to comment on the online version of this ar- Past, Present and Future Research, Space Sci. Rev. 116, 523-624, ticle. Correspondence and requests for materials should be addressed to (2005). T.A.D(email:[email protected]). 5. M.Sarzietal.,SupermassiveBlackHolesinBulges,Astrophys.J.550, 65-74(2001). 6. A. J. Barth et al., Evidence for a Supermassive Black Hole in the S0 GalaxyNGC3245,Astrophys.J.555,685-708(2001). 7. 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T.A.Davisetal.,TheATLAS3Dproject-X.Ontheoriginofthemolecular andionizedgasinearly-typegalaxies,Mon.Not.R.Astron.Soc.417,2, 882-899,(2011). 15. D.Bocketal.,CARMA:CombinedArrayforResearchinMillimeter-Wave Astronomy,Proc.SPIE,6267,13(2006). 3 Supplementary Information Axisymmetric two-integral Jeans and three-integral Schwarzschild dynamical models of the large-scale 1.1 Model Observations stellar kinematics (within 45 ) suggest M/L = ′′ I 3.35 M /L and i = 79 , but stellar population ◦ In this paper we compare the observed CO position- models ⊙of th⊙e inner parts (<5 ) suggest M/L = ′′ I velocity diagram with one created by modelling the 2.6M /L (derivedassumin∼gaKroupaIMF6, which gasdisk. When creatingthese modelswe includedthe islikel⊙yap⊙propriateforthisgalaxy28), presumablybe- observationaleffectsofbeam-smearing,disk-thickness, cause of young stellar populations associated with the velocitydispersion,binning,etc,byutilisingtheKINe- moleculargas.Anyresidualdustobscurationinthevery matic MolecularSimulation(KinMS)mm-waveobser- centreofthegalaxycouldcauseustounderestimatethe vation simulation tool16,25. The simulations used a M/Linthedynamicalmodel,howeverthestellarpopu- beam,pixelsizeandvelocityresolutionidenticaltoour lationM/L estimate(derivedfromananalysisofline- I observations,andanidealisedsurfacebrightnessprofile strengthindicesclosetogetherinwavelength18)isdust- whichfitsthedata.Weuseanaxisymmetricmassmodel independent. of NGC 4526 to derive the circular-velocity curve ex- Theinclinationestimatedfromthedynamicalmodels pectedfromtheluminousmatteralone. Theseelements isconsistentwith thatderivedforthedustdiskandthe ofthemodelsaredescribedindetailbelow. spreadofmeasuredvaluesisverysmall17( 3 ). ◦ ± Ellipse fitting to the inner dust lanes visible in HST 1.1.1Gasdistribution imaging, and to the inner molecular component show that the inner gas is also aligned with the stellar body The distribution of the molecular gas in this source is within<3 AsNGC 4526isclose toedgeon, suchan a required input for the KinMS tool. As we primarily ◦ uncertainty in inclination produces an insignificant er- aimtoassessthekinematicagreementbetweenthedata ror in the projected velocities ( 3 km s 1), which is and models with different SMBH masses (rather than ≈ − insignificantwhen comparedto the uncertaintiesintro- the details of the gas distribution itself), a simple sur- ducedbyother parameters(see Section 1.2 of the sup- face brightness profile fitting the observed distribution plementarymaterial).Wethereforefixtheinclinationof is sufficient. We thereforeadopted a profile composed thegasdiskatallradiitoi=79 . ofa centralGaussianwith full-width-at-half-maximum ◦ FWHM=0.15 12pc, centredatR=0.6 48pc (nu- ′′ ′′ ≈ ≈ clearring)andaGaussianofFWHM=2 160pccen- ′′ ≈ tredatR=5′′ 400pc(mainring). Thisparameterized 1.2Traceextraction ≈ surfacebrightnessprofilefitswelltheradialdistribution of the observedclean componentswithin the inner 6 , ′′ Foraquantitativecomparisonfocusingonthekinemat- andidenticalresultsareobtainedforallsensibleprofile ics,weextractedthe‘trace’oftheouterenvelopeofthe choices. Weassumedagasvelocitydispersionof8km observed and simulated PVDs, every 0.1 in radius (in s 1here(ourresultsdonotdependonchoosinganyrea- ′′ − ordertoNyquistsampleourbeam),byfittingaGaussian sonablevalueforthisparameter). Modelswithσ < gas (alongthe velocity axis) to each spatial bin and taking 10kms 1arerequiredtomatchtheobservedmolecular − the central velocity of the Gaussian plus one standard gasdistributionatallradii. deviationasthetrace. Theuncertaintieswereestimated from the formal uncertainties in the velocity and stan- 1.1.2MassModel dard deviation of the fitted Gaussian, plus two factors of 5 km s 1(to account for the finite velocity channel − The mass model we use in this work is based on a widthinboththedataandmodel).Thesechannelwidth multi-Gaussianexpansion(MGE26)ofF814WHSTand factorsusuallydominate. MDM 1.3-m telescope I-band images (probing both small and large scales), and is parametrised by the I- bandstellarmass-to-lightratioM/L andinclinationi. I Fromitthecircularvelocityofthegalaxycanbecom- 1.3Fitting procedure putedatanyradius. Themodeliscarefullyfittedtore- move any contamination from dust still visible in the Thebestfitwasfoundusingastandardχ2test,compar- I-band.Thedustdiskinthissystemiswelldefined,and ing the one-dimensional trace of the data and simula- wehavemanyresolutionelementsinsidetheSOIofthe tionsoverthecentral 4.5,theareamostaffectedbya ′′ ± SMBH.Thisallowsustocarefullymasktheaffectedre- putativeSMBH(SeeFigure2).Wedidnotfitinsidethe gionswhen conductingthe MGE fit27. The unaffected innermostbeam,wheretheeffectsofbeamsmearingare sectorswerethenusedtoderivetheMGEmodel. Such strongest,leavinguswith68observeddata-points. The aprocesshasbeenshowntoworkwellatrecoveringthe best-fitprofile hasa χ2=86.36,equivalentto a reduced intrinsiclightdistributioninsuchsystems6. χ2=1.27. 4 References 25. http://www.eso.org/ tdavis ∼ 26. E. Emsellem, G. Monnet, R. Bacon, The multi- gaussianexpansionmethod:atoolforbuildingrealistic photometricandkinematicalmodelsofstellarsystemsI. Theformalism,Astron. 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