Tests for Standard Accretion Disk Models by Variability in A(12)

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

opticalvariabilitytimescaleasα=0.1.Theviscosityparameterαhasthetypicalvalueof～0.1forthestandardaccretiondisks(Shakura&Sunyaev1973).Avalueofα 1/2isimpliedbytheconditionthattheturbulenceshouldbesubsonicinthestandarddisks(Merloni2003).Alowervalueofα<0.14issuggestedbynumericalinvestigationsforthinaccretiondiskswithaconstante ectivespeedofsound(Afshordi&Paczynski2003).Merloni&Nayakshin(2006)alsolimitedasimilarrangeofα 0.15onthebasisofstudyingthelimit-cycleinstabilityinmagnetizedaccretiondisks.Khajenabi&Shadmehri(2007)adoptedα～0.03–0.3tostudythedynamicalstructureofaself-gravitatingdisk.Thentheviscosityparamterαinthestandarddiskspossiblyhasawiderangeincludingthetypicalvalueofα～0.1.Iftheviscosityparameterαisallowedtorangefrom～0.03to～0.2,thetimescalesofopticalvariationsareconsistentwiththethermaltimescalespredictedbythestandardaccretiondiskmodels.Thisimpliesthatthemeasuredcharacteristictimescalesofopticalvariationsarelikelytobeproducedbytheaccretiondiskthermalinstability.

Theanalysisshowsthatthewavelengthdi erences λarecorrelatedwiththerelevanttimelagsbetweendi erentbandsforNGC7469,butthereisnocorrelationbetweenthetwoquantitiesforNGC5548.Ifthe uxvariationsarecausedbytheaccretion ow uctuationstravellinginwardsacrosstheemittingregions,itislikelythattheshorterwavelengthvari-ationslagthelongerwavelengthvariations.However,thelongerwavelengthvariationslagtheshorterwavelengthvariationsforNGC4151andNGC7469.TheshorterwavelengthvariationslagthelongerwavelengthvariationsforNGC5548exceptthatthevariationsat2787 Alagthoseat1841 A.Thevariationsat1390 Alagthoseat1880 AforFairall9.Iftheoptical/UV uxesarethereprocessedcontinuumwithharderphotonsfromthecenterofaccretiondiskandsofteronesatradiifartherout,itisexpectedthatthelongerwavelengthvariationslagtheshorterwavelengthvariations.However,thelongerwavelengthvariationsleadtheshorterwavelengthvariationsforNGC5548andFairall9,andthisisinconsistentwiththeexpectationinthecaseofcontinuumreprocessing.ThecalculationsforNGC7469andNGC4151showthatthetimelagsestimatedinthecaseofcontinuumreprocessingaremarginallyconsistentwiththemeasuredtimelags.Inaddition,Fairall9andNGC5548havetheblackholemassMBH>5×107M⊙withthelongerwavelengthvariationsleadingtheshorterwavelengthvariations,butNGC4151andNGC7469haveMBH<5×107M⊙withtheshorterwavelengthvariationsleadingthelongerwavelengthvariations(seeTable

3).Thereseemstobeatrendbetweenblackholemassandtimelag.Asblackholemassisabovesomevalue,thelongerwavelengthvariationsmightleadtheshorterwavelengthvariations,butblackholemassisbelowthisvalue,theshorterwavelengthvariationsmightleadthelongerwavelengthvariations.

Theoriginoftheradiationenergiesemittedinaccretiondiskisakeytotheissuethattheharderphotonsleadorlagthesofterones.Fornon-blazartypeobjects,iftheoptical/UVra-