Stability of the Broad-line Region Geometry and Dynamics in Arp 151 Over Seven Years


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A.Pancoast1,21 ,A.J.Barth2 ,K.Horne3 ,T.Treu4 ,B.J.Brewer5,V.N.Bennert6 ,G.Canalizo7,E.L.Gates8, W. Li9,22, M.A. Malkan4 ,D.Sand10,T.Schmidt2,S.Valenti11 ,J.-H.Woo12 ,K. I.Clubb9,M.C.Cooper2 ,S.M.Crawford13 ,

S.F.Hönig14,M.D.Joner15,M.T.Kandrashoff9,M.Lazarova16,A.M.Nierenberg2,E.Romero-Colmenero13,17,D. Son12, E.Tollerud18 ,J.L.Walsh19 ,and H.Winkler20




DepartmentofPhysicsandAstronomy,4129FrederickReinesHall,UniversityofCalifornia,Irvine,CA92697-4575,USA 3

SUPAPhysicsandAstronomy,UniversityofSt.Andrews,Fife,KY169SSScotland,UK 4

DepartmentofPhysicsandAstronomy,UniversityofCalifornia,LosAngeles,CA90095-1547,USA 5

DepartmentofStatistics,TheUniversityofAuckland,PrivateBag92019,Auckland1142,NewZealand 6

PhysicsDepartment,CaliforniaPolytechnicStateUniversity,SanLuisObispo,CA93407,USA 7

DepartmentofPhysicsandAstronomy,UniversityofCalifornia,Riverside,CA92521,USA 8

LickObservatory,P.O.Box85,MountHamilton,CA95140,USA 9

DepartmentofAstronomy,UniversityofCalifornia,Berkeley,CA94720-3411,USA 10

DepartmentofAstronomyandStewardObservatory,UniversityofArizona,933N.CherryAve.,Tucson,AZ85719,USA 11

LasCumbresObservatoryGlobalTelescopeNetwork,6740CortonaDrive,Suite102,Goleta,CA93117,USA 12

AstronomyProgram,DepartmentofPhysicsandAstronomy,SeoulNationalUniversity,Seoul151-742,RepublicofKorea 13

SouthAfricanAstronomicalObservatory,P.O.Box9,Observatory7935,CapeTown,SouthAfrica 14

SchoolofPhysics&Astronomy,UniversityofSouthampton,SouthamptonSO171BJ,UK 15

DepartmentofPhysicsandAstronomy,N283ESC,BrighamYoungUniversity,Provo,UT84602-4360,USA 16

Dept.ofPhysicsandAstronomy,UniversityofNebraskaatKearney,Kearney,NE68849,USA 17

SouthernAfricanLargeTelescopeFoundation,P.O.Box9,Observatory7935,CapeTown,SouthAfrica 18

SpaceTelescopeScienceInstitute,3700SanMartinDr.,Baltimore,MD21218,USA 19

GeorgeP.andCynthiaWoodsMitchellInstituteforFundamentalPhysicsandAstronomy,DepartmentofPhysicsandAstronomy,TexasA&MUniversity, CollegeStation,TX77843-4242,USA


DepartmentofPhysics,UniversityofJohannesburg,P.O.Box524,2006AucklandPark,SouthAfrica Received2017October19;revised2018February27;accepted2018February28;published2018March29


The Seyfert 1 galaxy Arp 151 was monitored as part of three reverberation mapping campaigns spanning 2008–2015.Wepresentmodelingofthesevelocity-resolvedreverberationmappingdatasetsusingageometricand dynamicalmodelforthebroad-lineregion(BLR).Bymodelingeachofthethreedatasetsindependently,weinfer theevolution ofthe BLRstructure inArp151 overatotalof 7 yrand constrain thesystematicuncertainties in nonvaryingparameterssuchastheblackholemass.WefindthattheBLRgeometryofathickdiskviewedcloseto face-onisstableoverthistime,althoughthesizeoftheBLRgrowsbyafactorof∼2.ThedynamicsoftheBLR aredominatedbyinflow,andtheinferredblackholemassisconsistentforthethreedatasets,despitetheincrease inBLRsize.Combiningtheinferenceforthethreedatasetsyieldsablackholemassandstatisticaluncertaintyof log10(MBH/M)=6.82-+0.090.09 withastandard deviationinindividualmeasurements of0.13dex.

Keywords:galaxies: active–galaxies: individual(Arp151)– galaxies:nuclei– methods:statistical

1. Introduction variations seen inthe continuum and later seen inthe broad emission lines that is used as a size estimate of the BLR. Outside the local universe, the most promising method to

CombiningthetimelagwiththevelocityoftheBLRgasv, as measure themasses ofsupermassiveblack holes(BHs)isthe

measuredfromthewidthof thebroademissionlines,we can reverberation mapping technique(Blandford &McKee1982;

measuretheBHmass, Peterson1993;Petersonetal.2004)inaccretingBHsinactive

galactic nuclei(AGNs).UnlikedynamicalBHmassmeasure- M BH= fv2c t G, ( ) 1

ment techniques that require spatially resolving the BH

gravitational sphereof influenceand thusare limitedtolocal where cisthe speed of light,G isthe gravitational constant, and larger BHs within ∼150Mpc (e.g., McConnell & and fisafactorof orderunity thatdependson thegeometry, Ma2013),reverberationmappingresolves themotionsofgas dynamics,andorientationoftheBLR.Whileτandvareoften aroundtheBHtemporallyandisnowbeingappliedtoAGNsat measured to better than 20%, the value of f is generally redshifts of z>2 (Kaspietal. 2007; Kinget al. 2015;Shen unknowninindividualAGNsbecausetheBLRisnotspatially etal.2015).Reverberationmappingreliesonthevariabilityof resolved.The unknown valueof fthus introducesthe largest AGN continuumemissionfromtheBHaccretiondiskas itis sourceofuncertaintyinreverberation-mappedBHmassesand reprocessedbygasinthebroademission-lineregion(BLR). By requires the use of an average value that is calibrated by monitoring anAGN with spectroscopy covering one or more

assuming the same MBH−σ* relation for active and inactive

broad emission lines and photometry of the AGN accretion

galaxies (Onkenetal. 2004; Collinetal. 2006; Greeneetal. diskcontinuumemission,wecanmeasureatimelagτbetween

2010;Wooetal.2010,2013,2015;Grahametal. 2011;Park 21

EinsteinFellow. et al. 2012; Grier et al. 2013; Batiste et al. 2017). While an



massestobemeasuredinover50AGNs(foracompilation,see Bentz&Katz2015),itintroducesanuncertainty inindividual BHmassesthatcouldbeaslargeasthescatterinthe MBH−σ*

relation of ∼0.4dex (a factor of ∼2.5; see, e.g., Park et al. 2012). The only way to reduce this uncertainty is to understand the detailed structure of the BLR and hence measure thevalueoffinindividual AGNs.

The drivetobetter understand theBLRcombined with the small sample size of reverberation-mapped AGNs has motivated two complimentary approaches. The first approach istosubstantiallyincreasethereverberationmappingsamplein terms of both the number of AGNs and of which broad emission lines areused (King etal. 2015; Shen etal. 2015), with Hβ inthe local universe beingreplaced by Mg II λ2799 andC IV λ1549asthebroademissionlinesofchoiceathigher redshifts.Whilereverberationmappingbecomesmore challen-gingathigherredshiftsduetolongertimelagsandlowerAGN variability (e.g., MacLeod et al. 2010), the tight relation between the BLR size and AGN luminosity for Hβ, the

r BLR– L AGN relation(Kaspietal.2000,2005;Bentzetal.2009a, 2013),allowsforthousandsofsingle-epochBHmassestimates

(e.g.,Shenetal.2011)madeusingasinglespectruminplaceof long-term spectroscopic and photometric monitoring (e.g., Vestergaard&Peterson2006;Shen2013;Parketal.2017,and references therein).Oneofthemaingoalsoflarger reverbera-tionmappingcampaignsmonitoringMg II andC IV linesisto reducetheuncertaintyinsingle-epochmassesusingtheselines by measuring their r BLR– L AGN relations directly instead of

calibrating BHmassesrelativetoHβ (e.g., Shenetal. 2016). However,theunknownstructureoftheBLRstillintroducesa large uncertainty inestimatesof the BHmass, sincedifferent broademissionlinesprobedifferentregionsoftheBLRdueto ionizationstratification(Claveletal.1991;Reichertetal.1994) and some lines may be more sensitive to nongravitational forcesfromAGNwinds.

The second approach, of generating a few high-quality reverberation mapping data sets with mainly Hβ inthe local universe,isthereforecriticaltounderstandingsingle-epochBH massesaswell,sinceitprovidesdetailedinformationaboutthe geometry, dynamics, and orientation of the BLR. In the highest-quality data sets, the time lag can be measured in velocity (or wavelength) bins acrossthe broad emissionline, and the structure ofthese velocity-resolved lagsisinterpreted in termsof the general dynamicsof the BLR.Such velocity-resolved reverberation mapping data sets are still in the minority, but the recent application of detailed analysis techniqueshasuncoveredawealthofinformationandthefirst direct measurements of f in individual AGNs (e.g., Pancoast et al. 2014b). Some of the most successfulvelocity-resolved reverberation mapping data sets include the MDM 2007

(Denney et al. 2010), 2010 (Grier et al. 2012), 2012, and 2014 (Fausnaugh et al. 2017) campaigns; the Lick AGN MonitoringProject(LAMP)2008(Bentzetal.2009b;Walsh etal.2009)and2011(Barthetal.2015)campaigns;theLijiang 2012–2013 (Du et al. 2016) and 2015 (Lu et al. 2016) campaigns; and the AGN STORM 2014 campaign(De Rosa et al. 2015; Edelson et al. 2015; Fausnaugh et al. 2016; Pei etal.2017).

The ultimate goalof these campaigns is to understand the velocity-resolved responseof thebroad-lineflux L( vLOS, t ) at

line-of-sight velocity vLOS and observed time t to the AGN

continuumvariability C, ¥ L v , t =



Y ( v ,t) ( -t , ( )2

( LOS ) LOS C t ) d t

where C( t -t) isthecontinuumfluxatearliertime t -t and Ψ is the transferfunction that relates the line and continuum emission as a function of vLOS and time lag τ (Blandford &

McKee1982).Whenchangesinthelineandcontinuumfluxes fromtheirmeanvaluesareusedinEquation(2)insteadoftotal fluxvalues,Ψiscalledthe responsefunctionand isgenerally notthe same as thetransfer function(for adiscussionof this difference, see Section 4 of Goad & Korista 2015).Detailed analysis of velocity-resolved reverberationmapping datasets has focused on either constraining the velocity-resolved responsefunctioninamodel-independentcontextormodeling the reverberation mapping data with a BLR model directly. Both approacheshave theirmerits: constraining the response functionrequiresfewerassumptionsaboutBLRphysics,while modeling the BLR directly requires more assumptions about the physics but yields quantitative constraints on the model parameter values. Response functions have been measured usingtheMEMEchocode(Horneetal.1991;Horne1994)for theLAMP2008datasetforArp151(Bentzetal.2010)andthe 2010 MDM campaign (Grier et al. 2013), while response functions have been measuredusing regularized linear inver-sion(Krolik&Done 1995;Done &Krolik1996) forLAMP 2008(Skielboeetal. 2015).Modelingreverberationmapping datadirectlyusingageometricanddynamicalBLRmodelhas beendone for theLAMP 2008 dataset forArp 151 (Brewer et al. 2011), the LAMP 2011 data set for Mrk 50 (Pancoast et al. 2012), five AGNs from the LAMP 2008 data set

(Pancoastetal.2014b),and fourAGNsfromtheMDM2010 dataset (Grieretal.2017).In addition,ageometry-onlyBLR modelhasbeenappliedtoalarger AGNsamplethatincludes theLAMP2008andMDM2010samples(Lietal.2013).Both approachesofconstrainingtheresponsefunctionandmodeling theBLRshowthattheBLRdynamicscanvarywidelybetween AGNs.Responsefunctionscanshowsymmetryoftheredand blue sides of the line, interpreted as gas orbiting in a disk. Alternatively,responsefunctions canshow responseatlonger timedelaysoneithertheblue(e.g.,Arp151;Bentzetal.2010) orredsideoftheemissionline(e.g.,thevelocity-resolvedlag measurements for Mrk 3227; Denney et al. 2009), usually interpreted as signatures of inflowing or outflowing gas, respectively (although see Bottorff et al. 1997 for prompt red-side response in the context of an outflow model). Modeling the BLR directly shows similar features as MEMEchointheresultingtransferfunctions.

However,therearestillmanyunansweredquestionsaboutthe structureoftheBLRthatcouldsignificantlyimpactourability tomeasureBHmasseswithreverberationmappingtechniques. OneunknownistheextenttowhichBLRstructureevolvesover time. As shown by both the r BLR– L AGN relation for the


Murray&Chiang1997;Elvis2000;Progaetal.2000).While values of the virial product (VP) τv2 measured for the same source overtimehaveshownthattheBHmassisconsistently measured for different broad emission linesand values of the time lag τ (e.g., Peterson & Wandel 1999, 2000; Pei et al.2017),the uncertainties arestill large,and it ispossible that the virial factor f changes with time as well. Another unknownisthefulluncertaintywithwhichBLRpropertiesare currently being measured through the forward-modeling approaches of Pancoast et al. (2014a) and Li et al. (2013). Since BLR modeling is necessary in order to quantify informationdirectlyfromreverberationmappingdataorthrough theinferredresponsefunction,havingacompleteunderstanding ofbothstatisticalandsystematicuncertaintiesisneededinorder tocompletelyruleoutclassesofmodels.Systematic uncertain-ties can be introduced at every stage of the BLR modeling approach, from how the reverberation mapping data are preprocessed to isolatethe emission-lineflux tothe choice of model parameterization and what physics is included for the AGNcontinuumsourceandBLRgas.

Inthispaper,weaimtoaddressthesequestionsbyapplyingthe BLR modelingapproach tothreevelocity-resolvedreverberation mapping datasets forArp151(alsocalledMrk 40)takenover 7 yr, corresponding to the orbital time for gas ∼4 lt-daysfromtheBH.Themaingoals ofthisanalysisare to(1) probe possible evolution in BLR structure, (2) investigate the reproducibilityofBLRmodelingresultsforindependentdatasets of the same source, and (3) constrain possible sources of systematicuncertaintyinBLRmodelinganalysis.Thethreedata setsaredescribedinSection2,andabriefoverviewoftheBLR modelisgiveninSection3.ResultsfromBLRmodelinganalysis ofeachofthedatasetsindividuallyandajointinferenceonBLR structurearedetailedinSection4.PossibleevolutionintheBLR geometryanddynamicsandtheeffectsofsystemicuncertainties aredescribedinSection5,alongwithacomparisonbetweenthe transferfunctionsfromBLRmodelingandtheresponsefunctions from MEMEcho analysis. Finally, a summary of our work is given in Section6. AllfinalvaluesfordistancesandBHmasses frommodelingtheBLRaregivenintherestframeoftheAGN. Toconverttotheobservedframe,multiplydistancesandtheBH massby1+z=1.021091,wherezistheredshift.

2. Data

We now describe the three velocity-resolved reverberation mapping datasets forArp151 withsampling,resolution,and dataqualitycharacteristicslistedinTable1.

2.1. LAMP2008

The LAMP 2008 reverberation mapping campaign was the first totargetArp151 and includesphotometric monitoringof theAGNcontinuumintheBand Vbands(Walshetal.2009) andspectroscopicmonitoringintheopticalfrom4300to7100Å

(Bentzetal.2009b).TheAGNcontinuumlightcurvesforArp 151 were measured with standard aperture photometry techni-quesusingdatafromthe0.80mTenagraIItelescopeinsouthern Arizona that is part of the Tenagra Observatories complex. Optical spectroscopyis from theKast Spectrograph (Miller& Stone1993)onthe3mShaneTelescopeatLickObservatory.

Table1 DataCharacteristics

LAMP2008 LAMP2011 LCO2015

(1)Dates 2008Mar25– 2011Mar27– 2014Dec

Jun1 Jun13 6–2015Jun5

(2)ncont 84 91 119

(3)nline 43 39 55

(4)Dtcont (days) 0.93 0.94 1.03

(5)Dtline(days) 1.02 1.04 1.51

(6)SpectralS/N 80 72 22.5

(7)Dlinstru(Å) 5.06 2.47 3.44

(8)Pixelscale(Å) 2 1 1.74

(9)Slitwidth 4″ 4″ 1 6

(10)Extraction 10 1 10 3 8 8


Note.The tablerows are as follows: (1)range ofdates for spectroscopic monitoring,(2) number ofepochs in the AGN continuumlight curve, (3) number of epochs of spectroscopy, (4) median time between continuum epochs, (5)median time between spectral epochs, (6)median S/Nof the spectraintheopticalcontinuum,(7)instrumentalresolution(linedispersion,σ; seeSection2ofPancoastetal. 2014b),(8)spectralpixelscale,(9)slitwidthof spectroscopy,and(10)extractionregionwidthusedtogeneratespectra.Values foritems(6),(9),and(10)aretakenfromBentzetal. (2009b),Barthetal. (2015),andValentietal.(2015)forLAMP2008,LAMP2011,andLCO2015, respectively.


Arp 151 was monitored again as part of the LAMP 2011 reverberationmapping campaign, withphotometric monitoring in the V band (A. Pancoast et al. 2018, in preparation) and spectroscopic monitoring in the optical from 3440 to 8200Å

(Barthetal.2015).TheAGNcontinuumlightcurveforArp151 was measured with difference-imaging techniques using data frommultipletelescopes,includingthe0.91mtelescopeatWest MountainObservatory, the 2mFaulkes Telescopes Northand SouthintheLasCumbresObservatorynetwork(LCO; Brown etal.2013),the0.76mKatzmanAutomaticImagingTelescope at Lick Observatory (Filippenko et al. 2001), and the 0.6m Super-LOTIS telescope at Steward Observatory, Kitt Peak. Opticalspectroscopy isfrom the KastSpectrograph (Miller & Stone1993)onthe3mShaneTelescopeatLickObservatory.


Arp 151 was also monitored as part of the ongoing LCO AGN KeyProjectreverberationmapping campaign(hereafter LCO 2015) with photometric monitoring of the AGN continuum intheVband and spectroscopicmonitoring inthe opticalfrom∼3200to10000Å(Valentietal.2015).TheAGN continuum light curve for Arp 151 was measured with the automatedaperture photometry scripts describedby Peietal.

(2014)usingdatafromLCOnetworktelescopes,includingthe 1m telescopeatMcDonald Observatory and the 2mFaulkes Telescope North. Optical spectroscopy is from the FLOYDS Spectrographonthe2mFaulkesTelescopeNorth.

2.4. SpectralDecomposition


Figure1.Spectraldecompositionofthemeanspectrum(toppanels)andthermslineprofile forthe Hβcomponent(bottompanels)fortheLAMP2008,LAMP2011, andLCO2015Arp151datasets.TheverticaldashedlinesshowthewavelengthrangesusedformodelingtheBLR.Inadditiontothemeandataspectrum(black line),thespectraldecompositioncomponentsshowninthetoppanelincludethefullmodel(topredline),AGNpower-lawcontinuum(greenline),hostgalaxy starlight(yellowline),narrow[OIII]emissionlines(blueline), HeII(magentaline,mostlytoofaintatthewavelengthsshown), FeII(cyanline),andHβcomponent constructedbysubtractingallcomponentsexceptforbroadandnarrowHβfromthedata(bottomredline).Thewavelengthsshownonthex-axisaretheobserved wavelengths,andthefluxunitsforboththemeanandrmsspectraareinarbitraryunits.

spectra were decomposed into contributions from the power-law AGNcontinuum;thehostgalaxystarlight;emissionlines for Hβ, HeII, and [O III], and a template for Fe II emission blends. While the spectral decomposition scripts allow for additionalcomponentsofHe I at4471,4922,and5016Å,these componentswerenotincludedinthefitbecausetheywerenot consistently differentiated from Fe II and other overlapping features intheredwingof Hβfor individualspectralepochs. ThebluewingofHβislesscontaminated,withnosubstantial overlap with He II.Anexample ofthe spectraldecomposition intheregionaroundHβisshownforeachdatasetinFigure1, alongwiththeroot-mean-square(rms)spectrum.Notethatthe rmsfluxinthecontinuumishigherfortheLCO2015dataset due tothelowersignal-to-noiseratio(S/N)ofthespectra.

The spectral decomposition was done using three different Fe II templates from Boroson & Green (1992), Véron-Cetty et al. (2004), and Kovačević et al. (2010). While the results fromthethreeFe II templatesareoftenverysimilar(e.g.,Barth etal. 2015),sometimes thereare differences inthe integrated emission-linelight-curvescatterorinthermsspectrum.Forour analysis of Arp 151, we use the Kovačević et al. (2010) templatebecauseitisabletobetterfitthedata.Boththeχ2and the reduced χ2, which compensates for the larger number of free parameters, are smallest for the Kovačević et al. (2010) template. The integrated emission-line light-curve scatter and therms spectrumareverysimilarforthedifferenttemplates.

Toreducesystematicuncertaintiesintroducedbyassuminga smoothmodelforHβinthespectraldecomposition,weisolate the Hβ emissiontobeused inouranalysisbysubtractingall spectral decomposition components from the data except for broad and narrowHβ. Examples of theisolated Hβ emission are alsoshowninFigure1.Whilethe spectraldecomposition scriptdoesnotprovidestatisticaluncertaintiesfromthespectral modeling,testsusingaMonteCarloproceduretoestimatethe

original statistical uncertainties of the optical spectra for our analysis.

3. The Geometric and Dynamical Model of the BLR

In this section,we give an overviewand define themodel parametersof ourparameterized phenomenologicalmodelfor theBLR.AfulldescriptionisgivenbyPancoastetal.(2014a). We model the distribution of broad-line emission using many massless point test particles that linearly and instanta-neouslyreprocesstheAGNcontinuumfluxfromtheaccretion diskintoemission-linefluxseenbytheobserver.Theaccretion disk isassumed to be apoint sourceat the origin that emits isotropically. The accretiondisk photonsare reprocessedinto line emission with a time lag that is determined by a point particle’spositionandawavelengthofemittedlinefluxthatis determinedbyapointparticle’svelocity.

In order to calculate the line emission from each point particle at any given time, we need to know the AGN continuumfluxbetweenthedatapointsinthelightcurve.We generateacontinuousmodeloftheAGNcontinuumlightcurve using Gaussian processes. By simultaneously exploring the parameter space of the Gaussian process model parameters, wecanincludetheuncertaintiesfrominterpolationbetweenthe AGNcontinuumlightcurvedatapointsinourinferenceofthe BLRmodelparameters.WecanalsousetheAGNcontinuum light-curvemodeltoextrapolatetoearlierorlatertimesbeyond theextent of the datainorder toevaluate thecontribution of point particles with long time lags at the beginning of the campaignand modelthe responseof theBLRafter theAGN continuummonitoringhasended.

3.1. Geometry

Theradialdistributionofpointparticlesisparameterizedby agammadistribution,

final flux uncertainties for LAMP 2011 suggest that the

additionalstatisticaluncertaintyintroducedbyspectraldecom- p r( ∣ a q, ) µ r a-1exp



⎟ ( )




Parameter LAMP2008 LAMP2011 LCO2015 CombinedDataSets StandardDeviation

tCCF(days) 3.99-+0.680.49 5.61+-0.840.66 7.52-+1.061.43 L L

rmax(lt-days) 44.85 27.39 54.71 L L

rmean(lt-days) 4.07-+0.420.42 6.77-+0.500.52 7.09-+1.171.42 L L

rmedian(lt-days) 2.74-+0.600.65 5.35-+0.540.50 4.32-+0.891.16 L L

rmin(lt-days) 0.57-+0.310.20 0.71-+0.380.40 0.50-+0.370.52 0.65-+0.120.15 0.08

sr (lt-days) 3.89-+0.630.74 5.62+-0.631.03 8.03-+1.592.02 L L

tmean(days) 3.65-+0.380.34 5.99+-0.350.41 6.04-+0.860.80 L L tmedian(days) 2.28-+0.530.60 4.52+-0.360.43 3.37-+0.550.62 L L β 1.14+-0.280.26 0.90-+0.110.14 1.21-+0.130.15 1.01-+0.090.17 0.13 qo (deg) 24.6-+7.85.5 18.0-+6.65.7 22.2-+10.09.4 21.8-+5.42.7 2.72 qi (deg) 23.7-+7.65.1 15.1-+5.03.7 19.7-+9.38.1 15.3-+5.23.9 3.54 κ -0.23-+0.150.28 -0.06-+0.300.32 0.10-+0.310.28 -0.19-+0.150.29 0.13 γ 3.60-+1.381.01 2.80-+1.131.39 3.78-+1.190.89 3.81-+0.970.93 0.42 ξ 0.22-+0.160.33 0.23-+0.130.18 0.28-+0.170.23 0.17-+0.090.16 0.03

( M M )

log10 BH 6.66-+0.170.26 6.93-+0.330.16 6.92-+0.230.50 6.82-+0.090.09 0.13

fellip 0.21-+0.150.26 0.30-+0.170.13 0.18-+0.130.16 0.18-+0.130.14 0.05

fflow 0.25-+0.180.17 0.25-+0.160.18 0.26-+0.170.16 0.27-+0.200.15 0.004

qe (deg) 14.8-+10.216.9 13.6-+9.116.0 20.1-+13.518.1 10.1-+6.28.8 2.83 sturb 0.012+-0.0100.041 0.046-+0.0400.034 0.010-+0.0080.029 0.044-+0.0370.030 0.017

Note.Medianvaluesand68%confidenceintervalsforthemainBLRgeometryanddynamicsmodelparameters.ThevaluesforthecolumnCombinedDataSetsare measuredfromthejointposteriorPDFsforthethreedatasets.Thevaluesforthelastcolumn,StandardDeviation,arethestandarddeviationofthevaluesforthethree individualdatasets.ThefixedvaluesforrmaxusedinBLRmodelingareshown,aswellasthecentroidtimelagtCCFfromcross-correlationfunctionanalysisfrom Bentzetal.(2009b),A.J.Barthetal.(2018,inpreparation),andValentietal.(2015)forLAMP2008,LAMP2011,andLCO2015,respectively.Allvaluesare redshift-correctedtotheAGNrestframe.

that is shifted radially from the origin by the Schwarzschild radius, Rs= 2GM BH c 2,plusaminimumradiusof theBLR, rmin. This shifted gamma distribution is also truncated at an

outer radius rmax (listedinTable2).Weperformachange of

variablesfrom( ,θ,rmin)to(μ,β,F)inordertoworkinunits

of themeanradius,μ,suchthat

m = r min+ aq, ( ) 4

b =

a 1

, ( ) 5

F =


+ r

r ,



( ) 6


standard deviation of the radial distribution is then given by sr = ( 1 -F) mb.Forthe threefreeparameters, (μ,β,F),the prior probability distribution is uniform in the log of the parameterbetween1.02×10−3lt-daysandroutforμ,uniform

between 0and 2forβ,and uniformbetween 0and 1forF. Spherical symmetry is broken by defining a half-opening angle of the point particles, θo, such that values of θo→0°

(90°) correspond to a thin disk (spherical) geometry with a uniformpriorbetween0°and90°.AnobserverviewstheBLR fromaninclinationangle,θi,whereθi→0°(90°)corresponds toaface-on(edge-on)orientation,and thepriorisuniformin cos (θi) between 0° and 90°. The emission from each point particleisgivenarelativeweight,W,between0 and1,

1 f

( )

W ( ) f = + kcos( ) , 7


whereκisafreeparameterwithauniformpriorbetween−0.5 and0.5andfistheanglebetweentheobserver’slineofsight

totheoriginandthepointparticle’slineofsighttotheorigin. When κ→−0.5(0.5),thenthe far(near)side oftheBLR is contributing more line emission. We also allow the point particlestobeclusterednearthefacesofthedisk,suchthatthe angleθofapointparticlefromthediskis


q = arccos( cosqo+ ( 1 -cosqo)U ), ( )8

whereUisarandomnumberdrawnuniformlybetween0and1 andγisafreeparameterwithauniformpriorbetween1and5. When γ→1 (5), point particles are evenly distributed in

(clustered at the faces of) the disk. Finally, we allow for a transparent to opaque disk midplane, where ξ is twice the fraction of point particles below the disk midplane. When

ξ→0(1),themidplaneisopaque(transparent),withauniform priorbetween 0and 1.


The velocities of the point particles depend upon the BH mass, MBH, which has a uniform prior in the log of the

parameterbetween2.78×104and1.67×109Me. We define twotypesofKeplerianorbitsforthepointparticlesintheplane oftheirradialandtangentialvelocities.Thefirsttypeoforbitis drawnfromaGaussiandistributionintheradialandtangential velocityplanecenteredonthecircularorbitvalue,resultingin bound elliptical orbits. A fraction, fellip,of the point particles

have these near-circular elliptical orbits, where fellip has a


no(all)point particleswith velocitiesofthis type.



outflow and fow has a uniform prior between 0 and 1. The

center ofthedistribution ofthis secondtypeoforbitcanalso be rotated onan ellipse towardthe circularorbit valueby an angleθe thathasauniformpriorbetween0°and90°.Finally, for each point particle, we include a contribution from randomlyoriented macroturbulentvelocitieswith magnitude

circ, ( )

v turb= ( 0,sturb)∣v ∣ 9

wherevcircisthecircularvelocityatthepoint particle’sradius

and ( 0,sturb) is a random number drawn from a Gaussian


The prior of σturb is uniform in the log of the parameter

between 0.001and 0.1.


Foraspecificsetof modelparametervalues,the positions, velocities, and weights of each point particle are determined, and, usingaGaussianprocess modelfortheAGN continuum light curve,wecangenerateatimeseries ofmodel emission-lineprofilesinvelocityspace.Toconvertthemodelspectrato wavelengthspace,weincludetheeffectsofrelativisticDoppler shift and gravitational redshift. The model spectra are also blurred by the time-variable instrumental resolution of the spectroscopic monitoringdata,whichismeasuredby compar-ingtheintrinsicwidthofthenarrow[O III]λ5007emissionline measured by Whittle (1992) to the measured width for each observation, with typical values listed in Table 1. We also model the narrow component of the Hβ emission line as a Gaussianwiththesameintrinsicwidthas[O III]λ5007blurred bytheinstrumentalresolution.Finally,duetotheimportanceof defining the center of the broad emission line and thus the region where point particles with zero line-of-sight velocity contributelineflux,thesystematiccentralwavelengthisafree parameter with a narrow Gaussian prior with a standard deviationof1ÅforLAMP2008and4ÅforLAMP2011and LCO 2015. The implications of this choice for the standard deviation of the systematic central wavelength prior are discussedinSection5.1.3.

3.4.Exploring theModelParameter Space

We explore the high-dimensional parameter space of the AGN continuumlight-curvemodel andtheBLR modelusing the diffusive nested sampling code DNest3 (Brewer et al. 2011).Diffusivenestedsamplingprovidesposteriorprobability distribution functions (PDFs) and calculates the “evidence,” allowing for comparison of models that are parameterized differently. Wecompare the broad and narrow emission-line models to the broad and narrow emission-line data using a Gaussian likelihood function. In order to calculate posterior PDFs inpostprocessing,we soften thelikelihood function by dividing the log of the likelihood by atemperature T, where

T…1. Using values of T>1 accounts for effects such as underestimateduncertaintiesinthespectraldataortheinability of asimple modeltofitthefull complexityofthedata. Fora Gaussian likelihood function, setting T>1 is equivalent to increasingtheuncertaintiesonthespectraldataby T .Weuse values of T=65 (45) for LAMP 2008, 60 (45) for LAMP 2011,and30(30)forLCO2015formodelingthefull(partial) line profile. The lower values of temperature needed for the LCO 2015 dataset are due tothe higher uncertainties of the

spectralfluxes.Theselargevaluesoftemperaturemeanthatthe numericalnoisefromspecificplacementof thepoint particles in position and velocity space for a given set of parameter valuesismuchlessthanthespectralfluxerrorstimes T . We check all results for convergence by comparing the inferred parameterdistributionsfromthefirstand secondhalvesofthe modelingrun.

4. Results

Wenowpresenttheresultsfromapplyingourgeometricand dynamical model for the BLR to three velocity-resolved reverberationmappingdatasets forArp151. As discussedin Section5.1,oneofthesourcesofsystematicuncertaintyinour analysisistheisolationofHβfluxintheredwing,wherethe choiceofFe II templateandpossiblecontributionofHe I lines introducedifferences inthe Hβ redwing thatcan exceedthe spectral flux uncertainties. To address this, we present two limitingcasesforallthreedatasetsofmodelingthefullHβred wingor approximately half of the redwing. After describing the results for the individual data sets, we then combine the results to provide a joint inference on the BLR model parameters. The median and 68% confidence intervalsof the inferredBLRmodelparametervaluesaregiveninTable2.


TheLAMP 2008dataset forArp 151has previouslybeen analyzedusing the BLRmodeling approach by Brewer etal.

(2011)and Pancoastetal. (2014b).Our analysisdiffers from thatofPancoastetal.(2014b)inthreeways. First,we usean updatedmodelfortheBLRthatincludesthesystematiccentral wavelengthofthebroademissionlineasafreeparameteranda maximumouterradiusfortheBLR.Second,theHβ emission-line profile has been isolated from the spectrum using a different spectral decomposition code and the Fe II template fromKovačevićetal. (2010)insteadof thatfromBoroson & Green(1992).Third,inadditiontomodelingtheHβ emission-lineprofileover thewavelength rangeof4899–5037Åinthe observedframe,wealsoexcludeapproximatelyhalfofthered wingandmodeltheHβemission-lineprofileovertherangeof 4899–4985Å.Forbothwavelengthrangesofthedata,theBLR model is able to capture the shape of the Hβ emission-line profile and the large-scale changes of the integrated Hβ line flux,asshowninthetoppanelsof Figure2.

TheLAMP 2011dataset for Arp151 isthe secondinthe sampletobeanalyzedusingtheBLRmodelingapproach,after Mrk50(Pancoastetal.2012).ComparedtoLAMP2008,the LAMP2011datasetshowedsimilarlyhighvariabilitybutwith increased instrumental resolution. Again, we model both the full Hβ emission-line profile over the range of 4899–5038Å and a truncated version of the Hβ emission-line profile excludingapproximatelyhalfoftheredwingforawavelength rangeof4899–4986Å.Thesewavelengthrangesareveryclose to those used for the LAMP 2008 data set, although with a different pixelscale. As for LAMP 2008,the BLR model is abletoboth fit the shapeof theHβ emission-line profileand followthechangesintheintegratedHβ linefluxasafunction oftime.Examplesofthemodelfittothedataareshowninthe middlepanelsofFigure2.


Figure2.Modelfitstotheemission-lineprofilefortheLAMP2008(toppanels),LAMP2011(middlepanels),andLCO2015(bottompanels)datasets.Thesetofsix panelsontheleftshowsthemodelfitstothefullemission-lineprofile,andthesetofsixpanelsontherightshowsthemodelfittothepartialemission-lineprofile whenpartoftheredwingisexcluded.Ontheleft,foreachdatasetandforboththefullandpartialfitstothedata,weshowtheAGNcontinuumlightcurveatthetop


bottom(bluepoints)withexamplesofthemodelfitdrawnfromtheposteriorPDF(redandgraylines).Ontheright,weshowtwoexamplesofthemodelfit(redlines) toindividualemission-lineprofiles(blueandgreenerrorbarsandlines).

forArp151,theLCO2015datasethassimilarlyhighlevelsof variabilityandinstrumentalresolutionbetweenthetwoLAMP datasetsbutsignificantlylowerS/Nforthespectroscopy.We both model the full Hβ emission-line profile between 4899.8 and 5037.3Åandexcludeapproximately halfoftheredwing tomodelthelineprofilebetween4899.8and 4985.1Å.Other thantwohighlydiscrepantdatapointsintheHβlightcurve,the BLRmodelisabletofittheHβemission-lineprofileshapeand match theoverallvariabilityof theintegratedHβline flux,as shownbythebottompanelsinFigure2.

We show the inferred posterior PDFs for some of the key BLR model parameters in Figures 3–5 for the LAMP 2008, LAMP 2011,and LCO 2015 datasets, respectively. To ease comparisonbetweentheresultsformodelingthetwodifferent wavelengthranges,weshowtheposteriorPDFsfrommodeling the emission-line profileout to∼5037Åin blueand to only ∼4985Å in orange (areas where the two posterior PDFs overlap appear red). An equal 50/50 mixture of orange and blueposteriorPDFsisshownbythethickblackhistogramand used tomeasure themedianand68% confidenceintervalsfor the BLRmodelparameterslistedinthe firstthreecolumns of Table2 anddescribedbelow.

ForthegeometryoftheHβ-emittingBLR,weinferathick diskviewedclosetoface-onwithadiskopeningangleofθo=

+5.5 5.7 +9.4)°

24.6-7.8 (18.0-+6.6, 22.2-10.0 and an inclination angle with +5.1( 3.7

respecttotheobserver’slineofsightofθi=23.7-7.6 15.1+-5.0, 8.1)°

19.7+ (0=face-on) forLAMP 2008 (LAMP 2011,LCO 2015). The distribution of emission decreases exponentially


0.26( +0.14

orsteeperasafunctionofradius,withβ=1.14+-0.28 0.90-0.11,


for LAMP2008(LAMP2011,LCO2015),and the medianradiusof emissionchangesbyalmost afactor oftwo, 1.21+-0.13


2.74 0.65lt-days forLAMP 2008tormedian=

fromrmedian= -0.60

+0.50 ( +

5.35 4.32 1.16)lt-daysforLAMP2011(LCO2015).The asymmetry of emission is inferred to varying degrees by the threedatasets.TheLAMP2008datapreferBLRmodelswhere theHβemissioncomesmorefromthefarsideoftheBLRwith

-0.54 -0.89


respect to the observer (κ=-0.23+-0.15 although more

emissionfromthe nearside ofthe BLRis notruled out,and the LAMP 2011 and LCO 2015 data sets have no strong preference. All three data sets prefer BLR models where the disk midplane is partially or completely opaque, with

+0.33 +0.18 +

ξ=0.22-0.16 (0.23-0.13, 0.28-0.230.17) for LAMP 2008 (LAMP

2011,LCO2015),andacompletelytransparentdiskmidplane isruledoutforLAMP2011.Finally,theLAMP2008andLCO 2015datahaveaslightpreferenceforBLRmodelswithmore


emission from the faces of the disk (γ=3.60-1.38 and +


3.78 0.89,respectively).

For the dynamics of the Hβ-emitting BLR, we infer a combinationofnear-circularellipticaland inflowingorbitsfor the emitting gas, with the fraction of near-circular elliptical

+0.26 +0.13 +0.16)

orbits given by fellip=0.21-0.15 (0.30-0.17, 0.18-0.13 for

LAMP2008(LAMP2011,LCO2015).Theremaininggasis +0.17 +0.16 +0.16)

, inflowing with fow=0.25-0.18 (0.25-0.18, 0.26-0.17 where


halfgravitationallyboundonradialorbits(θe→0°)tomostly gravitationally bound on both tangential and radial orbits

16.9 ( 16.0 +18.1)for (outtoθe∼50°) with θe=14.8+-10.2 13.6+-9.1 ,20.1-13.5

LAMP 2008 (LAMP 2011, LCO 2015). There is also a negligible contribution from macroturbulent velocities with

+0.04 ( +0.03 +0.03). σturb=0.01-0.01 0.05-0.04,0.01-0.01


0.26 0.33 0.50).

inferred to be log10(MBH)=6.66+ (6.93+0.16, 6.92+

Whilethere isa difference of almost0.3dex between the BH massmeasuredforLAMP2008comparedtotheothertwo,this



-Figure3.InferredposteriorPDFsofthemainBLRmodelingparametersfortheLAMP2008datasetfrommodelingthefullemission-lineprofileoutto5037Å(blue histograms)andexcludingpartoftheredwingafter4987Å (redhistogram).AnequalmixtureoftheblueandorangeposteriorPDFsisgivenbythethickblack histogram.

differenceiswithinthestatisticalmeasurementuncertainties,and theposteriorPDFssignificantlyoverlap,asseeninFigure6. The standard deviation in the three BH mass measurements is significantly smaller, at only 0.13dex.It is also interesting to comparetheseBHmassvaluesfromBLRmodelingwithvalues of the VP calculated in traditional reverberation mapping analysis, as shown in the top panel of Figure 7. The VP is related to the BH mass by MBH=f×VP and log10(VP)=

0.075 +0.061, and 0.077

6.086-+0.091, 5.778 0.071 6.053+0.094 for the LAMP 2008 (Bentz et al. 2009b), LAMP 2011 (Barth et al. 2018, in preparation), and LCO 2015 (Valenti et al. 2015) data sets, respectively. The standard deviation in the VP values is 0.14dex, very similar tothe value for BLR modeling. While the statistical uncertainties from calculating the VP are quite small, generally <0.1dex, calculating aVP BHmass requires theadditionalassumptionofchoosingavalueforthevirialfactor

f.Traditionally,anaveragevalueoffisderivedbymatchingthe reverberation mapping sample to the quiescent galaxy sample

MBH–s* relation(Onkenetal.2004; Collin et al.2006; Greene

etal.2010; Wooetal.2010,2013,2015;Grahametal. 2011; Parketal.2012;Grieretal.2013;Batisteetal.2017). However,

the scatter in the MBH–s* relation is measured to be at least

0.4dex(Parketal.2012),suggestingthatthetotaluncertaintyof VP BH masses could be as large as ∼0.4dex for individual AGNs (as discussed by Peterson 2014). This means that the additionaluncertaintyfromtheunknownvalueoffforindividual AGNsissignificantandmustbeincludedwhencomparingBH mass measurement techniques. These results show that BLR modelingforArp151generallyprovidesgreaterprecisionthan VP BH masses with uncertainties <0.4dex, as well as constraints on BLR structure, and thus f, independent of the

MBH–s* relation.

The inferred structure of the Hβ-emittingBLR inArp 151 forthedatasetsdescribedabovecombinestheresultsforboth modeling the full emission-line profile and excluding half of theredwing.However,someoftheBLRmodelparametersare sensitive to how much of the red wing is modeled. As is evident from Figure 3, the parameters in best agreement for LAMP 2008include rmean,θo,θi,fflow, θe, and MBH,whileβ,



Figure4.SameasFigure 3,butfortheLAMP2011dataset.

through fellipand larger inferred uncertainties for MBH. Since MBHisstronglycorrelatedwithθo andθi,theyalsohavelarger

inferred uncertainties when excluding half of the red wing. Overall, modeling the full red wing is significantly more constraining for LAMP 2008, but the results are generally consistentwithoneanother,withthelargestdiscrepancyinthe inferredvaluesofβ,forwhichtheposteriorPDFsonlyslightly overlap.Ontheotherhand,modelingthefullredwingdoesnot providesignificantlybetterconstraintsonBLRstructureforthe LAMP2011dataset,sincetheposteriorPDFsfrommodeling the full and partial red wing almost completely overlap one another(Figure4).Similarly,modelingthefullredwingforthe LCO 2015 data set does not provide significantly better constraints (Figure5).However,there isaslightoffset inthe posterior PDFs for MBH, rmean, β, θo, θi, and ξ, such that

modeling the full red wing leads to larger values of the BH massand,throughthetightcorrelationswiththeinclinationand openingangles,athinnerand moreface-ondisk.


Wenowcombinetheresults forthethree datasetsforArp 151 toobtainajointinferenceontheBLRmodelparameters.

Some parameters, such as the BH mass, we expect to stay constant. Otherparameters, such as the mean radius or other measurements of the radial size of the BLR, we expect to changeinresponse tovariationsin theAGN luminosity.The evolutionofBLRstructure overthe 7yr timeperiodspanned bythethreedatasetsisdiscussedinSection5.2.

We start by defining the set of posterior samples for each dataset individually.Asdescribedintheprevioussection,we marginalizeoverthechoicetomodelthefullorpartialHβred wingbymakinganequal 50/50mixtureofposterior samples fromtheresults foreach case.Sincethe posterior PDFsfrom modeling the full or partial Hβ red wing never perfectly overlap, this addition of posterior PDFs has a general broadening effect on the final posteriors for each data set. The equal mixtures of posterior samples for each data set


Figure5.SameasFigure 3,butfortheLCOAGNKeyProject2015dataset.

order to multiply likelihood functions made of discrete samples, the posterior samples for each data set are first dividedbytheirpriorprobabilityfunctionforpriorsthatarenot flatintheparameter(e.g.,forparameterssuchasBHmassthat havepriorsthatareflatinthelogoftheparameter).Then,the likelihood samples are placed in 100 bins, and the binned likelihood functions are multiplied before applying the prior probabilityfunctionsagain.ThejointinferenceposteriorPDFs are shown bythe thick blackhistograms inFigure 6 and are used to calculate the median and 68% confidence intervals given inthe fourthcolumn ofTable2.Unlike theadditionof posterior PDFs,which generally widens the distributions and increases the uncertainties in the inferred parameter values, multiplying thelikelihood functionsforthe three independent data sets shrinks the final posterior PDFs and decreases the uncertainties ontheinferredparametervalues.

Overall, constraints on the Hβ-emitting BLRgeometry are consistentbetweenthethreedatasets,withtheexceptionofthe size of the BLR, which grows by a factor of almost two between the LAMP 2008 and LAMP 2011 datasets. Dueto almostnooverlapbetweentheposteriorPDFsofthemeanand median radius and time lag between LAMP 2008 and both LAMP2011andLCO2015,wedonotcalculatethecombined

posteriors for Figure6 or Table 2. Forthe asymmetryof the

+ 3.9°),

closetoface-on,thickdisk(θo=21.8 2.7°andθi=15.3+5.2

we infer a preference for a mostly opaque disk midplane



(ξ=0.17-0.160.09) with a completely transparent midplane ruled +0.93),

out,moreemissionfromthefacesofthe disk(γ=3.81-0.97

and a slight preference for more emission back toward the


. centralionizingsource(κ=-0.19+-0.15

TheconstraintsontheHβ-emitting BLRdynamicsarealso consistent between thethree datasets,with less than50% of the emitting material in near-circular elliptical orbits (fellip=


0.18-0.140.13) and the remaining gas in mostly radial inflowing

+0.15 8.8°).

orbits (fow=0.27-0.20 and θe=10.1+-6.2 Finally, the BH 0.09

mass has a combined inference of log10(MBH)=6.82+-0.09,

moreprecisethananyoftheindividualBHmassmeasurements for Arp 151 for a single dataset by ∼0.1dex and the most preciseBHmassfromBLRmodelingtodate.

5. Discussion

5.1.SystematicUncertainties intheBLR ModelingApproach


Figure6.InferredposteriorPDFsofthemainBLRmodelingparametersfortheLAMP2008(bluehistogram),LAMP2011(redhistogram),andLCO2015(cyan histogram)datasets.TheposteriorPDFsforeachdatasetconsistofanequalmixtureofposteriorsamplesfrommodelingthefullemission-lineprofileandapartial emission-lineprofilethatexcludespartoftheredwing.Wealsoshowthejointinference(thickblackhistogram)frommultiplyingtheinferredlikelihooddistributions forthethreedatasetstogether.

statistical uncertainties intheinferred structure ofthe BLRas provided by either MCMC or diffusive nested sampling algorithms. Diffusive nested sampling, inparticular, provides robust statistical uncertainties for the BLR model parameters even in the case of tight parameter degeneracies and multi-modal posterior PDFs. However, there are additional uncer-tainties notcapturedbysamplingstatistics,includingwhatwe defineasHβlineemissionandwhatmodelweusefortheBLR. Wewilldiscussthesesourcesof systematicuncertaintyinthe followingsections.


One of the most important assumptions we make in the processofmodelingtheBLRisthatwecanrobustlyisolatethe broad-line flux fromthe full spectrum using spectral decom-position. However, thisrequires the choiceof both individual templates forcertainspectralcomponentsandwhichemission lines or components are present in the data. The two most difficultchoicestomakeforthethreeArp151datasetsare(1) whichFe II templatetouseand(2)whetherHe I at4471,4922,

and 5016Å rest wavelength is noticeably present in the spectrum. Both of these spectral components overlap the red wingofHβandcanbedifficulttodisentangle.Toquantifythe uncertainty introduced by our choice of Fe II template and exclusion of He I, we compared the standard deviation of spectral decomposition solutions for all three Fe II templates withandwithoutHe I, Dfdecomp,tothespectralfluxerrors,sflux.

Theratioof Dfdecomp sfluxis4(5,2)timeslargerfortheHβred

wingbetween∼4985and5037Åcompared tothe restofthe line,andthemedianvalueofthisratiofortheredwingis2.4


marginalizingoverthechoiceofFe II templateandpresenceof He I inthedata.


One way to probe the magnitude of the systematic uncertainty introduced from spectral decomposition is to compare the BLR properties inferred for the full line profile tothepropertiesinferredwhentheHβredwingisexcluded,as wedescribeinSection4.Thiscomparisonshowsthatmost,but not all, BLR model parameters are consistently inferred. However, thiscomparisonrequiresexcluding justover athird of the line profile, probing another source of systematic uncertainty:howmuchofthelineprofilewemodel.Inaddition toexcludingtheHβredwing,wealsotriedexcludingeitherthe Hβ blue wing or the center of the emission-line profile. Maskingeachregionresultsinslightlydifferentinferenceson BLR modelparameters thatare generallyconsistent withone another, with the two cases of modeling the full line and excluding theredwingprovidingatypicallevelofdifference. However,giventhegoodagreementinspectraldecomposition inthebluewingandcenteroftheemission-lineprofile,wedo not include posterior samples from these runs in our final inferencefor eachdataset,as this wouldgenerallywiden the inferred posteriors due tomodeling a smaller fraction of the data.Excludingtheredwing(bluewing,center)ofHβresults in larger uncertainties for inferred BLR model parametersby 10%±20% (20%±40%, 50%±130%) for LCO 2015. For LAMP2008and2011,excludingtheredwing(center)ofHβ resultsinlargeruncertaintiesby40%±70%(40%±50%)and 3%±30% (20%±50%), respectively.This has animportant implicationforfuturevelocity-resolved reverberationmapping programs focused on wideHβ emissionlines where the line wings maybe heavilycontaminatedbyother spectralfeatures

(e.g.,variableHe II inthebluewingandHe I andvariableFe II

intheredwing):toobtainthesmalleststatistical uncertainties fromBLRmodeling,robustidentificationofHβfluxiscrucial allacrosstheline profilesothatnoportionof thelineprofile needstobeexcluded.


There are many facets of our simply parameterized phenomenological model for the BLR that could introduce systematicuncertaintiesintheinferredmodelparameters.Here wediscusspossiblesourcesofsystematicuncertaintyfrom(1) recent changes to the BLR model, (2) correlations between model parameters, and (3) basic assumptions about the BLR physics.

There are two main changes to the BLR model that were made in the process of analyzingthe three data sets for Arp 151.First,thecentralwavelengthofHβemissionisnowafree parameter with a Gaussian prior of standard deviation 1Å

(LAMP2008)or4Å(LAMP2011,LCO2015).Whileusinga narrower prior for the centralwavelength sometimes leads to more precise inferences on some BLRmodel parameters, the effects are generally small: comparing results from using Gaussian priors ofwidth 1or 4Åmakes differences between the inferred BLR model parameters that are <40% (<40%,

<20%)oftheinferredstatisticaluncertainties forLAMP2008

(LAMP 2011,LCO 2015),with typical values <20% for all three datasets.The second change tothe BLR modelis that there is now a set maximum outer radius of BLR emission,

withvaluesgiveninTable2 foreachdataset.Totestwhether thechoiceof maximumouter radius affectsthe inferredBLR modelparameters,weanalyzedeachdatasetusingavaluefor the maximum radius that was approximately twice as large. This test showed that the choice of maximum radius has a larger effect than the choice of Gaussian prior width for the centralHβwavelength,butthedifferencesbetweentheinferred BLR model parameters are still less than <60% (<50%,


(LAMP2011,LCO2015).Whileadding themaximumradius asafreeparameterwould bethe bestwaytoincorporatethis source of systematic uncertainty into the inferred statistical uncertainty,itcomeswith acomputationalcostof requiringa longerextrapolatedAGNcontinuumlightcurve.

Another source of systematic uncertainty comes from correlations between model parameters, asdescribed indetail byGrieretal.(2017).Onone hand,theabilityof ourflexible BLRmodeltousemultiple,discretecombinationsofparameter values to generate the same distribution of point particles in positionandvelocityspaceinflatesthestatisticaluncertainties on the inferred model parameters compared to the true uncertaintyinspecificpointparticledistributions.Oneexample ofthisisthedegeneracybetweensolutionswithfellip→1and


cases, the dynamics are dominated by near-circular elliptical orbits. On the other hand, however, degeneracies between modelparameterscanilluminatesystematicuncertainties ona largerscalethroughtheidentificationofparametercorrelations that areunphysical for asampleof AGNs.The bestexample identified so far is a correlation between the inclination and openinganglesfortheLAMP2008(Pancoastetal.2014b)and AGN10(Grieretal.2017)samples. Testswith simulateddata confirm that in order to produce single-peaked emission-line profiles,asobservedforLAMP2008and AGN10,ourmodel fortheBLRrequiresthatθoθi.Thisplacesaneffectiveprior onθo between θi and 90°.ThefactthatBLR modelinginfers valuesofθo∼θi suggests that,inreality,θoθi.Whileit is difficulttoquantifyhowmuchthevaluesofθo∼θi arepulled tothe truevalues of either θo or θi,tests with simulated data suggestthattheshapeofthevelocity-resolvedtransferfunction ismore sensitivetovalues of θi.To obtainfully independent inferencesontheinclinationandopeningangles,wewillneed toincludemethodsforcreatingasingle-peakedlineprofilefor valuesofθo<θi infutureBLRmodels.

Finally,theBLRmodelmakesmanyassumptionsaboutthe physics of gas in the inner regions of AGNs that could add significantsystematicuncertaintytoourresults.Whilemanyof these assumptions are discussed in more detail by Pancoast etal. (2014a),recentanalysisofamultiwavelength reverbera-tion mapping campaign of NGC 5548 has brought into question the validity of our assumption that the AGN continuum can be treated as coming from a point source

(Edelsonetal. 2015;Fausnaughetal.2016).Specifically,the datasetforNGC5548providesarobustlymeasuredtimelag between the UV continuum at1367Åas measured usingthe

HubbleSpaceTelescopeand theV-bandopticalcontinuumof +



leadingtoBHmassesfromBLRmodelingthataretoosmallby afactor oftopt tUV,whereτopt (τUV)isthetimelag between

the optical (UV) continuum and Hβ. However, it should be noted that NGC 5548 deviated from the usual r BLR– L AGN

relationduringthiscampaignwithanHβBLRsizesmallerby afactorof∼4comparedtowhattheAGNluminositypredicted

(Pei et al. 2017). If NGC 5548 had not deviated from the

r BLR– L AGN relation, then the time lag between the UV and

optical continuum would only be ∼10% of the time lag between the optical continuum and Hβ, on the order of the statisticaluncertaintiesinferredforthemeanradiusortimelag fromBLRmodeling.

GiventhechangeinBLRsizebetweenthethreedatasetsfor Arp151andthefactthatweinferalargerBHmassforthedata sets with larger BLR radii, we can estimate what time lag between the AGN continuum UV- and optical-emitting accretion disk regions would be required to explain the difference in inferred BH mass. Using the median BH mass valueslistedinTable2 suggeststhatthe UV–opticaltimelag would need to be 0.85 times the optical–Hβ time lag if the larger BH mass we infer is correct. If this were the case, however, even the data sets with larger inferred BLR radii wouldstillbesignificantlyaffectedbytheUV–opticaltimelag. IfweinsteadsolvefortheUV–opticaltimelagwithunknown true BH mass, we estimate UV–optical lags of 30–50 days, dependingonwhat measurementof theradius orlag isused,


resulting in a true BH mass of M, an order of magnitude greater than what we infer. Given the large difference between the estimated UV–optical lag and the inferred optical–Hβ lag, it is unlikely that the difference in inferred BH mass is primarily due to a violation of our assumptionaboutanAGNcontinuumpointsource.Additional simultaneousUVandopticalreverberationmappingcampaigns focused on other AGNs will be necessary to determine how widely the resultsfor NGC 5548canbeappliedtothe larger reverberationmappingsample.


The threedatasetsforArp151 spanatimeperiodof7 yr, which is the orbital time for BLR gas atradii of ∼4 lt-days from the BH. We now discuss any evidence of evolution in BLRstructureoverthistime,withthetimedependenceofkey BLR model parameters shown in Figure 7. As presented in Section 4.2, the largest difference between inferred BLR parametersforthethree datasetsistheinferenceinthe radial sizeoftheBLR,suchthatthemeanandmedianradiiandtime lags forLAMP 2011and LCO 2015areafactor of almost 2 greaterthanforLAMP2008.Asillustratedinthesecondpanel ofFigure7,thechangeinsizedependsuponthemeasurement used, with CCF timelags and mean valuesof the radius and timelagshowingthelargestdifferencesfortheLCO2015data set. Given the r BLR– L AGN relation (Bentzetal. 2009a, 2013),

wemightexpectArp151tohavebrightenedbyuptoafactor of 4 in the AGN continuum during the 2011 and 2015 campaigns.

To test whetherthe AGNcontinuum fluxchanged between thethreedatasets,weremeasuredtheAGNcontinuumV-band lightcurveswithauniformprocedure.Toensurethatthesame levelofhostgalaxyfluxisincludedinallthreelightcurves,we used a uniformphotometric aperture size of4″ and the same comparisonstarsforallthreecampaigns.Wealsorestrictedour analysis to the highest-quality data from each campaign,

Figure7.EvolutionofkeyBLRmodelparametersoverthetimespannedby thethreeArp151datasets.TheBHmassfromBLRmodelingisshownbythe bluepointsinthefirstpanel.Forcomparison,theVPmassesarealsoshownby black circles, where the small black error bars are from the statistical uncertaintiesfrommeasuring theVPandthelargerederrorbarsof0.4dex representanestimateofthesystematicuncertaintiesfromusingameanvalueof f=5.13measuredbyParketal.(2012).Fourmodelparametersdescribingthe BLRsizeareshowninthesecondpanel,includingthemeanandmedianradius (blue and cyan, respectively)and the mean andmedian time lag (redand orange,respectively).TheBLRsize asmeasured bythemodel-independent CCFtimelagisalsoshownbytheblackpointsforcomparison.

including Tenagra Observatory (2008), WMO (2011), and LCOGT (2015). Photometry measurements were made using theautomatedaperturephotometrycodedescribedbyPeietal.


light curves, respectively. Comparing the V-band light curve meanvaluesprovidesalowerlimittotheAGNvariabilitydue toasignificantcontributionfromthehostgalaxyfluxestimated tobe47%forLAMP2008(Walshetal. 2009).

Before including a host galaxy correction, we can first compare the variations in the meanV-band magnitude tothe variability within each reverberation mapping campaign. Comparing the mean V-band magnitudes, the standard deviation of the three measurements is 0.057 mag, with a spread between the maximum and minimum value of 0.133 mag. Calculating these same values for the variability within each data set, we find a standard deviation (spread between maximum and minimumvalue) for eachlight curveof 0.073

(0.322),0.073(0.236),and0.084(0.339)magforLAMP2008, LAMP2011,andLCO2015,respectively.Thisshowsthatthe smallchangesinthemeanV-bandmagnitudearelessthanthe variability within each reverberation mapping campaign. Clearly, the BLR size is changing significantly more than expected from the global r BLR– L AGN relation for all AGNs (Bentz et al. 2013), given the relatively constant V-band luminosity.

While it is possible that long-term variations in AGN luminosityorphotonsathigherenergymayberesponsiblefor thelarger-than-expectedBLRsizein2011and2015,theremay also be a more complicated r BLR– L AGN relationship for

individual AGNs. This last scenario is illustrated by recent reverberationmappingcampaignsforNGC 5548,whereinthe AGN diverged from its native r BLR– L AGN relation to first

increase inAGNluminositywithout acorrespondingincrease in BLR size and then increase in BLR size while actually decreasing in AGN luminosity (Pei et al. 2017). Even when NGC 5548 is following its native r BLR– L AGN relation, it is

steeper thanthe globalrelation and hasa scatterof ∼0.1dex

(Kilerci Eser et al. 2015). These results suggest that the behaviorseeninArp151maynotbesounusual.Onlyfurther monitoringwillbeabletoclarifywhetheritscurrentbehavior in r BLR– L AGN spaceisanomalousorwhetheritalwayschanges

significantly inBLRsizeatafixed AGNluminosity.

We can also investigate whether properties of the BLR geometrychangewiththeBLRsize.Theminimumradiusstays constanttowithinthestatisticaluncertaintiesof0.2–0.5lt-days. However, theshape ofthe radial profilechangesbetween the datasetsinamannerthatappearsindependentfromthesizeof the BLR, in terms of both the radial distribution shape parameter (β)and the standarddeviation (σr).In comparison, otherparametersoftheBLRgeometry,suchastheinclination and openingangles,areconsistentlyinferredforallthreedata sets, while large uncertainties in the inferred asymmetry parameterspreventus fromconstrainingtheirevolution.

The BLR dynamics donot appear dependent on the radial BLRsize,consistentlypreferringamajorityofinflowingorbits. However,theLAMP2011datasetdoespreferalargerfraction of near-circular elliptical orbits, with the peak of theinferred posterior centered on values of fellip∼0.3 instead of near


with changesin the velocity-resolved time lag measurements forthethreedatasets,whereintheLAMP2008andLCO2015 data sets show clear asymmetry in time lag measurements across the Hβ line (Bentz et al. 2009b; Valenti et al. 2015), while the LAMP 2011 data set shows more symmetric lag measurements (Barthetal.2018,inpreparation).

5.3.Comparisonwith MEMEchoResponseFunctions

Another way to constrain the properties of the BLR is to recover the broad emission-line response function without assumingaspecificBLRmodel,asdiscussedinSection1.The responsefunctions obtained from regularized linear inversion

(Krolik & Done 1995; Done & Krolik 1996; Skielboe et al. 2015) or MEMEcho (Horne et al. 1991; Horne 1994) can then be compared qualitatively to the transfer functions from BLR modeling analysis. This comparison provides anothercriticaltest oftheBLR modelingapproachbecauseit canshowwhethertheBLRmodelisflexibleenoughtoproduce the response functions foundin the data. In this section, we comparetransferfunctionsfromBLRmodelingwithresponse functions from MEMEcho for the three Hβ data sets for Arp151.

Fulldetails ofthe MEMEchocode aredescribedbyHorne et al. (1991) and Horne (1994), with previous MEMEcho resultsformultipleopticalbroademissionlinesfortheLAMP 2008datasetgivenbyBentzetal.(2010).Thedatasetsusedin theMEMEchoanalysiswerethe sameasthose usedforBLR modeling,includingreanalysisoftheLAMP2008datasetwith the improved spectral decomposition described in Section 2. Note that while BLR modeling fits a linear echo model

(Equation (2)), photoionized line emission is in general a nonlinear function of the continuum (e.g., Korista & Goad2004).By adoptingalinearechomodel, valuesofΨ(v,

τ)fromBLRmodeling canbeinterpretedassome mixofthe meanandmarginallineresponse.Incontrast,MEMEchousesa tangentapproximationtothenonlinearresponse,thusfittinga linearizedechomodel,

0( )


l t C t ) -C ] d t. ( )

L ( l, t ) = L l +


Y ( , )[ ( -t 0 10 0


Here, C0 is an arbitrary continuum level, L0( )l is the line

emission corresponding to C0, and Y(l t, ) is the marginal

response,i.e.,thechangeinlineemissionpersmallchangein thecontinuum.TheMEMEchofitthenusesmaximumentropy regularizationtofindthe“smoothestpositivefunctions”C(t),L


Nisthenumberofdata.Athighχ2/N,anoverlysmoothmodel underfitsthe data, whileatlow χ2/N, anoverly noisymodel overfitsthedata.Asuitabletrade-offbetweentheseextremesis chosenbyeyetorepresentthebestcompromise.NotethatBLR modeling uses MCMC methods to fully sample the joint posteriorprobabilitydistributionofitsmodelparameters,while MEMEchoexploresaone-parameterfamilyofbest-fitmodels, withuncertainty estimatesrequiringMonteCarlomethods.


Figure8.ComparisonoftransferfunctionsfromBLRmodelingandresponsefunctionsfromMEMEcho.Thetop,middle,andbottomrowsshowresultsforLAMP 2008,LAMP2011,andLCO2015,respectively.TheleftcolumnshowsarepresentativetransferfunctionfromtheposteriorPDFfromBLRmodelingforeachdata set.ThemiddlecolumnshowstheMEMEchoresponsefunctionforasimulateddatasetgeneratedfromtheBLRmodelingposteriorsampleshownintheleftcolumn foreachdataset.TherightcolumnshowstheMEMEchoresponsefunctionforthedata.Lightyellowindicatesthemostemissioninthetransfer(response)functions, whiledarkblueindicatestheleast,withtheabsolutescalesofemission(response)beingrelative.

features in the transfer function that can be made using the BLRmodel,suchasthesharpemissionfeatureintheredwing. ThissuggeststhatabettercomparisonbetweenBLRmodeling and MEMEcho can be made by comparing the MEMEcho response functions for the simulated data and the real data

(secondand thirdcolumns).

However, there are two points to note when making this comparison.First,since theposterior PDFsoftheBLRmodel parametersmostly overlap for thethree Arp 151datasets, as shown in Figure 6, the three transfer functions shown in Figure 8 can also reasonably be interpreted as showing the rangeintransferfunction shapeforany ofthe individualArp 151 datasets, withthe exceptionof thedifferenceinaverage time lag that could cause the transfer function shape to be shifted vertically and compressed horizontally to follow the virial envelope. This does not mean that all three transfer functions shown are equally likely for all three data sets; instead,theLAMP2008andLCO2015datasetshaveahigher fraction of posterior samples with transfer functions showing strongred-wingasymmetry,whiletheLAMP2011datasethas a higher fraction of posterior samples showing a more

symmetric transfer function. These differences in transfer function asymmetry are due to the larger probability of the BLRhavingahigherfractionofpointparticlesinnear-circular ellipticalorbitsforLAMP2011.Thesecondpointtonotewhen comparingthesecondandthirdcolumnsofFigure8 isthatwe donothaveuncertainty estimatesfor theMEMEchoresponse functions,sowecannotmakeaquantitativecomparison.

From a qualitative perspective, the MEMEcho response functions tendtolook similar forthe simulated and real data sets, with two main regionsof high response: at longertime delays in the middle of the line profile (∼4960Å) and at smaller time delays in the red wing of the line profile


6. Summary

WehaveanalyzedthreeHβreverberationmappingdatasets for Arp151takenover7 yrusingageometricanddynamical model for the BLR.By comparing multiple data sets for the sameAGN,weareabletoprobethesystematicuncertaintiesin the inferred Hβ BLR structure and look for evolution of the geometryordynamicsontheorbitaltime.Ourmainresultsare as follows:

1.The inferred BH mass ranges from log10(MBH)=

6.66+0.26 to 0.33 forLAMP 2008and LAMP2011, respectively, with a standard deviation in the three measurements of 0.13dex. Since the individual BH masses agree to within the statistical uncertainties, we calculatethecombinedinferenceontheBHmassfromall three data sets of log10(MBH)=6.82+0.09, which is the

-0.17 6.93+-0.16


mostpreciseBHmassmeasurementfromBLRmodeling todate.

2.The size of the BLR grows by a factor of ∼2 between 2008 and 2011, although theminimum radius staysthe same over all 7 yr. The shape of the radial profile of emissionand the standarddeviation ofthe radialprofile do show small changes for each data set, although the changesarenotcorrelatedwiththeBLRsize.

3.The inclination and opening angles are consistently +2.7°

21.8 15.3+5.2

inferred (θo= -5.4 and θi= -3.9°),despite the change insizeoftheBLR.

4.Each data set constrains the BLR geometry asymmetry parameters to different degrees. While the direction of emissionbacktowardthecentralionizingsourceisonly constrained by the LAMP 2008 data set, all three data sets prefer an opaque disk midplane, such that a transparent midplane is ruled out in a joint inference. There is also a preference for more emission from the facesofthediskfortheLAMP2008and2011datasets. 5.The BLR dynamics are consistently inferred to be dominated by mostly-radial inflowing orbits, with the LAMP2011datasetshowingahighercontributionfrom near-circular elliptical orbits. These differences are consistent withvelocity-resolvedtime laganalysis. 6.Wetrytoincludethesystematicuncertaintyfromspectral

decomposition in the statistical uncertainties above by marginalizing over results including and excluding the redwingofHβ.SpectraldecompositiontoisolatetheHβ line is sensitive tothe choice of Fe II template and the presenceofHe I intheHβredwingatalevelthatisoften greaterthanthespectralfluxuncertainties.Thechoiceof whether to exclude parts of the Hβ profile due to contamination also affects the results by increasing the inferred statistical uncertainties by 3%–50%, depending on theportionoftheline excludedand thespecificdata set.Thissuggeststhatbyimprovingspectral decomposi-tion techniques to marginalize over the inclusion of differentspectralcomponents and templates self-consis-tently, we can significantly reduce BLR modeling uncertaintiesinthefuture.

7. Comparison between BLR modeling and independent MEMEcho analysis suggests that both methods find similartransfer/responsefunction shapes.

Overall, these results show that parameters expectedto be constantintime,suchastheBHmassandinclinationangleof theBLR,areconsistentlyinferredforArp151fromcompletely

independentdatasetsandanalysis.ThissuggeststhattheBLR modeling approach implemented here is robust to reproduci-bility, although there may still be significant systematic uncertainties introduced byourchoiceof aspecificmodel.A lackoflargechangesinother,potentiallytime-dependentBLR modelparametersfor thethree datasets suggeststhat theHβ BLRstructureinArp151isfairlyconstantontheorbitaltime, withtheexceptionoftheradialsizeoftheBLRthatisexpected to change in response to variability in the AGN continuum luminosity.

We thank the Lick Observatory staff for their exceptional supportduringourLAMP 2008and2011observingcampaigns. AP is supported by NASA through Einstein Postdoctoral Fellowship grant number PF5-160141 awarded by the Chandra

X-rayCenter,whichisoperatedbytheSmithsonianAstrophysical ObservatoryforNASAundercontractNAS8-03060.Researchby A.J.B.has beensupportedbyNSF grantAST-1412693. V.N.B. acknowledgesassistancefromNationalScienceFoundation(NSF) ResearchatUndergraduateInstitutions(RUI)grantAST-1312296. Note that findings and conclusions do not necessarily represent viewsoftheNSF.K.H.acknowledgessupportfromSTFC grant ST/M001296/1. S.F.H. acknowledges support from the EU/ Horizon2020 programmeviaERCStartingGrant677117andthe UK STFC via grant ST/N000870/1. Research by D.J.S. is supportedbyNSF grantAST-1412504 and AST-1517649.T.T. gratefully acknowledges support from the Packard Foundations throughaPackardResearchFellowshipandbyNSFthroughgrant AST-1412315. J.H.W. acknowledges support by the National ResearchFoundationofKorea(NRF)grantfundedbytheKorean government(No.2017R1A5A1070354).


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