Tests for Standard Accretion Disk Models by Variability in A(10)

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

timescalesareestimatedbyequations(1)–(4),respectively,assumingviscosityparameterα=0.1.Thecalculatedresultsarepresentedincolumns(4)–(7)ofTable2,respectively.Itcanbeseenfromcolumns(2)–(7)ofTable2thatthethermaltimescalesaremostclosetotheopticalvariabilitytimescalesamongthefourphysicaltimescales,butthelightcrossinganddynamicaltimescalesaremuchsmallerthanthemeasuredtimescalesofopticalvariations,andthesoundcrossingtimescalesaremuchlargerthanthemeasuredtimescales.Thismightindicatethattheopticalvariationsresultfromthethermalinstabilityinaccretiondisksoronemechanismrelatedtoit.Though,itcannotbea rmedthattheopticalvariationsresultfromtheaccretiondiskthermalinstability,thelinearrelationpresentedinequation

(15)isqualitativelyconsistentwithexpectationofequation(3)thatthethermaltimescaleisessentiallylinearlyrelatedwiththeblackholemass.Theseaboveresultsareobtainedbyadoptingtheviscosityparameterα=0.1foreachsourceinoursample.Inpractice,variousvaluesofαaresuggestedandusedininvestigations(e.g.,Afshordi&Paczynski2003;Khajenabi&Shadmehri2007;Merloni2003;Merloni&Nayakshin2006;Parievetal.2003).Iftheviscosityparameterαisallowedtorangefromα～0.03toα～0.2(e.g.,Afshordi&Paczynski2003),calculationsshowthatthecombinationsofα～0.03–0.2anda =0.5–0.998canresultinthethermaltimescalesthatareinwellagreementwiththeopticalvariabilitytimescalespresentedinTable2.Thenitislikelythattheopticalvariationsresultfromtheaccretiondiskthermalinstability.

Theradiationenergiesemittedinaccretiondisksareprobablyfromthecontinuumthermalreprocessingand/orthelocalviscositydissipation(e.g.,Ulrichetal.1997).IftheX-raysilluminatingopticallythickmaterialinthindiskproducetheoptical–UVemissionsthroughthermalreprocessing,theopticalandUVvariationsfollowingtheX-rayvariationsareprobablycorrelatedwiththeUVvariationsleadingtheopticalones.Thetimelagsinthecaseofcontinuumthermalreprocessingareestimatedforthestandardaccretiondiskswithblackholespinparametera =0.5,0.8,0.9,and0.998.Therelevanttimelagsarelistedincolumn(5)ofTable3.Theplussignsofvaluesincolumn(5)meanthatthevariationsatlongerwavelengthslagthevariationsatshorterwavelengths.Itcanbeseenfromcolumns

(4)and(5)ofTable3thatthemeasuredtimelagsaremarginallyconsistentwiththosepredictedbythestandardaccretiondisksforNGC4151andNGC7469.ThisimpliesthattheopticalandUVemissionsarelikelytobethereprocessedX-raysforNGC4151andNGC7469.Inaddition,thetimelagsdecreaseslightlyasspinparametera increases.ForFairall9andNGC5548,thesignsofthecontinuumthermalreprocessingtimelagsarecontrarytothoseofthemeasuredtimelags.Thisindicatesthattheoptical/UVemissionsareunlikelytobethereprocessedX-raysforFairall9andNGC5548.Ifvariationsintheaccretion owa ect rstthe uxatouterradii,andthenintheinnerregion,thismayberesultincorrelatedoptical/UVlightcurveswithlongerwavelengthvariationsleadingshorter