Tests for Standard Accretion Disk Models by Variability in A(9)

In this paper, standard accretion disk models of AGNs are tested using light curves of 26 objects well observed for reverberation mapping. Time scales of variations are estimated by the most common definition of the variability time scale and the zero-cros

binwidth τasintheDCF.IthasbeenshowninpracticethatthecalculationoftheZDCFismorerobustthantheICCFandtheDCFwhenappliedtosparselyandunequallysampledlightcurves(e.g.,Edelsonetal.1996;Giveon1999;Royetal.2000).TheZDCFiscalculatedinthispaper.

Ingeneral,itseemstobetruethatthetimelagisbettercharacterizedbythecentroidτcentoftheDCFandtheICCFratherthanbythepeakτpeak,namely,thetimelagwherethelinearcorrelationcoe cienthasitsmaximumvaluermax(e.g.,Petersonetal.2004,2005).τpeakismuchlessstablethanτcentinboththeDCFandtheICCF,andτpeakismuchlessstableintheDCFthanintheICCF(Petersonetal.2005).ThenwepreferthatthetimelagestimatedfromtheZDCFmethodischaracterizedbythecentroidτcentoftheZDCF,fortheZDCFisanimprovementoftheDCFmethod.Thecentroidtimelagsτcentarecomputedusingallpointswithcorrelationcoe cientsr≥0.8rmax,andtheuncertaintiesfortimelagsofdatapointsintheZDCFarecomputedwithalargenumber(1,000)ofMonteCarlorealizations.TheZDCFsoffourobjectsarepresentedinFigures2–5,andthemeasuredtimelagsarelistedincolumn(4)ofTable3.

parisontoModels

ThereisacorrelationbetweentheblackholemassM8andthemeasuredcharacteristicvariabilitytimescaleτwithPearsoncorrelationcoe cientr=0.760atthechanceprob-abilityP=6.6×10 6(seeFig.6).Theregressionlines ttedbythebisectorregressionanalysisare

τ/(1+z)=0.27(±0.04)+0.12(±0.02)M8yrs.(15)

Ifrd～100rginequation(3)withviscosityparameterα=0.1,thereisarelationofτth～0.15M8.Thoughtheinterceptinequation(15)di ersfromtheinterceptpredictedbyequation(3),thispredictedslopeof～0.15isconsistentwiththeoneinequation(15).Thisindicatesthatthelinearcorrelationbetweenblackholemassandcharacteristicvariabilitytimesaleisqualitativelyconsistentwiththeexpectationofequation(3)thatthethermaltimescaleisessentiallylinearlyrelatedwiththeblackholemass.Thus,equation(15)isqualitativelyconsistentwithexpectationsofthestandardaccretiondiskmodels.

Accordingtothestandardaccretiondiskmodels,theoptical/UVemissionsareproducedthermallyinaccretiondisks.Thestandardaccretiondiskmodelsareusedtoestimatetheradiiofmaximumoptical/UVemissions.Weconsideraccretiondisktobecomposedofringswithapproximatelyuniformtemperatureradiatinglocallyasblackbody,andestimatetheradiiofmaximum uxemissionatdi erentwavelengthsusingadiskradialtemperaturepro legivenbyequation(5).Thenthelightcrossing,dynamical,thermal,andsoundcrossing