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

wavelengthvariations.Asareferencetimescale,thesoundcrossingtimeinastandardaccretiondiskbetweentheseradiiareestimatedforFairall9andNGC5548byadoptinga =0.998.Theestimatedresultsarelistedincolumn(6)ofTable3.Theminussignsofvaluesincolumn(6)meanthatthevariationsatouterradiileadthevariationsatinnerradii.Itcanbeseenfromcolumns(4)and(6)ofTable3thatthemeasuredtimelagsaremuchsmallerthanthosepredictedbythestandardaccretiondisksinthecaseofaccretion ow uctuationstravellinginwards.

5.DISCUSSIONSANDCONCLUSIONS

Onewayofattemptingtohelptestingthestandardaccretiondiskmodelsisto ndrelationshipsbetweenvariabilityandfundamentalparametersofAGNs,suchasblackholemass.Thediscoveryofsucharelationship–orlackthereof–mayprovideusefulcluestothephysicalmechanismsbehindthevariability.Di erentsourcesofopticalvariationscanbeassociatedwithdi erentcharacteristictimescales,andmanyofthesetimescalesdependonblackholemass.Woldetal.(2007)investigatethedependenceofquasarvariabilityonblackholemass,and ndthatthemeasuredvariabilityamplitudecorrelateswithblackholemass.Collier&Peterson(2001)attemptedtode nearelationshipbetweenblackholemassandcharacteristicvariabilitytimescale.Theyreportedevidenceofblackholemassescorrelatingwithcharacteristicopticalvariabilitytimescalesforasampleof10well-monitoredAGNs.Inthispaper,alinearcorrelationbetweenthemeasuredtimescalesofopticalvariationsandtheblackholemassesisfoundforasampleof26well-monitoredAGNsbyreverberationmapping.ThislinearcorrelationsupportssuggestionofCollier&Peterson(2001).Theslopeofthiscorrelationinequation(15)is～0.12,andthisslopeisconsistentwiththeoneof～0.15predictedbyequation(3)withtheviscosityparameterα=0.1andtheemittingradiusrd=100rg.Theslopesbetweenthethermaltimescaleandtheblackholemassareestimatedforanothertwoemittingradiiofrd=50rgandrd=200rginequation(3)withα=0.1.ThethreetheoreticallinesbetweentimescalesandblackholemassesarepresentedinFigure6b.ItcanbeseeninFigure6bthatthetheoreticallineofrd=100rgmatchestheobserveddatapointsandthebest tlinebetterthantheothertwolinesdo.Thismeansthatthemeasuredcharacteristictimescalesofopticalvariationsarelikelytobefromtheaccretiondiskthermalinstability.Thenthestandardaccretiondiskmodelsarelikelytobeconditionallyfavoredbyobservations.

Anotherwayofattemptingtohelptestingthestandardaccretiondiskmodelsisconnecttheobservedvariabilitytimescalewithoneofthephysicaltimescalesinequations(1)–(4).Amongthefourphysicaltimescales,thethermaltimescaleismostclosetothemeasured