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the blazar is the class of the active galactic nuclei ( agn ) which has the most number of extragalactic source in the very - high - energy gamma - ray regime ( @xmath4 gev)@xcite .
they are characterized by double - peaked nonthermal emission with spectral energy distribution ( sed ) in radio to gamma - ray regime .
blazars include bl lacertae objects ( bl lacs ) and flat spectrum radio quasars ( fsrqs ) .
in addition bl lacs include high - frequency peaked bl lac objects ( hbls ) , intermediate - frequency peaked bl lac objects ( ibls ) and low - frequency peaked bl lac objects ( lbls ) . in the leptonic model ,
the low and high bump of sed is explained by the synchrotron and the synchrotron self compton ( ssc ) and/or external compton ( ec ) radiations .
the estimation of ec in the second hump is a matter of great importance in estimating external photons .
one of the characteristic of the blazar spectra is blazar sequence . in 1998 , fossati et al . combined three complete blazar samples@xcite ; the 2 jy samples of fsrqs@xcite , the radio selected 1 jy samples of bl lacs@xcite and the x - ray selected sample(einstein slew survey ) of bl lacs @xcite .
the thirty - third sources of selected sample were detected in high - energy gamma - ray regime ( @xmath4 mev ) by the egret instrument on - board the compton gamma ray observatory ( cgro ) .
these sources were devided 5 bins based on the 5 ghz radio luminosity and averaged the sed of the each type of the blazars .
the made sed suggested some relationship ; first , the synchrotron peak frequency and the bolometric luminosity have the anti - correlation .
second , the synchrotron peak frequency and the compton peak frequency have the positive - correlation . finally , the compton dominance ( the ratio of the inverse compton to synchrotron luminosity ) and the bolometric luminosity have positive - correlation .
these correlations are known as `` the blazar sequence '' in considering the blazar physics .
we aim to reveal the relation between the evolution process of agns and the blazar sequence based on the systematical study for many blazars .    in this study , we calculated @xmath5 agns ( blazars ) to find the difference of the variability amplitude in blazar types and evolution of the variability amplitude ( activity ) .
we applied the fractional variability amplitude ( @xmath6 ) to calculate the variability amplitude considering the error .
the @xmath6 is defined as eq.([eq : fvar ] ) which was given by vaughan et al .
( 2003 ) .
@xmath7    note that @xmath8 is the total variance of the light curve , @xmath9 is the mean square of flux error and @xmath10 is the square of mean flux .
fvar error ( uncertainty ) is defined as eq.([eq : fvarerr ] ) by poutanen et al .
( 2008 ) .    @xmath11    where @xmath12 is defined as eq.([eq : fvarerr2 ] ) by vaughan et al .
( 2003 ) @xmath13    @xmath6 is often used in computation variability amplitude for each spectral band@xcite .    in this study
, we studied the flux variation of agns with the @xmath6 on the high - energy gamma - ray regime to get the variation charactor of each class ( type ) .
[ cols="^,^,^,^,^,^,^,^,^ " , ]     [ tab : blazarlist ]    we selected agns from the second lat agn catalog ( 2lac)@xcite and tevcat@xcite .
selection criteria were as follows ,    1 .
: it was decided which subclass was belonged to ( hbl or ibl or lbl or fsrq ) .
: it had known redshift .
flux @xmath14 @xmath2 s@xmath3 in 2lac.[enu : flux ]    table [ tab : blazarlist ] shows the analyzed agn list which 102 sources are included in . source name , redshift , and class(type ) are cited from 2lac and tevcat .
the redshift of pks 1424 + 240 was referred to furniss(2013)@xcite . according to the tevcat@xcite ,
the blazar class of s3 0218 + 357 ( z=0.944 ) was not determined but we used it as high redshift vhe gamma - ray emitter .
we analysed the fermi reprocessed pass 7 data between 2008 august 04 and 2014 june 09 , using the unbinned likelihood analysis with the fermi science tools package version v9r33p0 available from the fermi science support center ( fssc)@xcite .
the likelihood analysis was selected that the events with photon energies in the range of 0.1 - 300 gev and a region of interest ( roi ) of 10 degrees centered at the position of table [ tab : blazarlist ] sources .
we used `` source '' class ( `` evclass = 2 '' ) including both front and back events , because the `` source '' class is recommended for off - plane point source analysis by the likelihood analysis @xcite .
we excluded events with zenith angles larger than 100 degrees and time intervals when the rocking angle was larger than 52 degrees .
the set of the instrument response functions of `` p7rep_source_v15 '' was applied .
models which were used in this study include the isotropic diffuse background ( iso_source_v05.txt@xcite ) , galactic diffuse background ( gll_iem_v05_rev1.fit@xcite ) and the second fermi lat catalog ( 2fgl ) sources in roi of 10 degrees centered at the position of table [ tab : blazarlist ] sources .
the spectrum model was according to the 2fgl . target blazars ( table [ tab : blazarlist ] ) were fitted with a log - parabola ( lp ) : @xmath15 because lp is typically used for modeling blazar spectra@xcite .
s@xmath3 mev@xmath3 ] is normalization parameter , e@xmath18 [ mev ] is scale parameter , @xmath19 is spectrum index . if the parameter @xmath20 is zero , lp is equal to powar - law spectrum .
in this paper we fixed e@xmath18 parameter of targets to e@xmath18 = 100 mev .
we judged the flux variation of target sources by some steps .
+ step i : gamma - ray light curves , which width of the time bins was fixed on 30 days ( shortest bin in this study ) , was made .
+ step ii : if calculated @xmath6 was not required `` selection criteria '' , we adopted more large bin size ( 60 days , 90 days , 150 days , and 300 days ) .
+ `` selection criteria '' were as follows , _
i. _ more than 40 % of the calculated integral flux of each bin were detected . _
_ significant ( over 2@xmath21 ) variation was detected by the @xmath22 test in the analyzed period .
if the selection criteria _ i. _ and _ ii . _
cleared , @xmath6 of the target could be calculated .
figure [ eq : lc ] shows the light curves of mrk 421 and pks 0454 - 234 as the light curve samples , which are the typical hbl and fsrq sources , respectively .
the green dashed lines represent the average flux of whole period .
each @xmath6 and averaged flux were culculated as mrk421 : @xmath6 = 39.3 @xmath23 1.3 % averaged flux = @xmath24 cm@xmath3 s@xmath3 , pks0454 : @xmath6 = 58.7 @xmath23 1.3 % averaged flux = @xmath26 cm@xmath3 s@xmath3 .
note , the @xmath6 calculation was performed only over the 9 ts bins .
another @xmath6s were obtained in the same method and the @xmath6 as a function of the redshift is shown in fig.[fig : fvardist ] .
square and circle marks indicate tevcat and not tevcat sources , respectively .
each subclass of blazars are plotted in different colors ( blue : fsrq , red : hbl , magenta : ibl , green : lbl , yellow : fri , black : uncertain type . ) . in figure
[ fig : fvardist ] , fvar indicates the variability amplitude of the gev gamma - ray light curve .
gev gamma ray from fsrqs could be detected at high redshift(z @xmath27 0.5 ) and have the large fvar .
in addition , hbl and ibl assemble in z @xmath28 0.5 . from these features
, blazar subclass seems to change along the increasing redshift .
+ peculiar features were as follows ; + ao 0235 + 164 ( z = 0.94 , lbl ) has particularly high @xmath6 ( 117 @xmath23 2.8 ) in lbls .
this source was discussed that it might be fsrq type blazar @xcite ; therefore , high @xmath6 value of this source might be caused by the fsrq like characters .
s3 0218 + 357 ( z = 0.944 , uncertain type ) which has the highest @xmath6 ( 190 @xmath23 2.8 ) in this analyzed sources is a gravitationally lensed blazar@xcite , hence the very high @xmath6 value might be enhanced by the gravitationally lensed effect .    from fig .
[ fig : fvardist ] , the @xmath6 as a function of the redshift seems connection with fsrqs @xmath29 lbls @xmath29 hbls ( ibls ) .
this trend shows possibility of the activity evolution and blazar class evolution .
figure [ fig : fvarhist ] shows the @xmath6 histogram which is projected in the vertical axis of fig .
[ fig : fvardist ] .
the different colors show each subclass of blazars ( blue : fsrq , red : hbl , magenta : ibl , green : lbl , yellow : fri , black : uncertain type ) . however , there are some problems in this study . first , the middle - high redshift ( z @xmath27 0.2 ) low @xmath6 sources were not sufficient for discussions without selection effects .
second , this study could not considered the short time scale variability ( @xmath28 30days ) .
thus , it is necessary to analyze the low @xmath6 sources and short time scale .
we selected 102 agns ( blazars ) to reveal the relation between the evolution process of agns and the blazar sequence .
we applied the fractional variability amplitude ( @xmath6 ) to calculate the variability amplitude considering the error .
+ the analyzed agns were selected from the second lat agn catalog ( 2lac)@xcite and tevcat@xcite .
the analyzed data was fermi reprocessed pass 7 data between 2008 august 04 and 2014 june 09 , using the unbinned likelihood analysis with the fermi science tools .
+ from these features , blazar subclass seems to change along the increasing redshift ( connection with fsrqs @xmath29 lbls @xmath29 hbls ( ibls ) ) .
this trend shows possibility of the activity evolution and blazar class evolution .
peculiar features were as follows ; ao 0235 + 164 ( z = 0.94 , lbl ) has particularly high @xmath6 ( 117 @xmath23 2.8 ) in lbls .
this source was discussed that it might be fsrq type blazar @xcite ; therefore , high @xmath6 value of this source might be caused by the fsrq like characters .
s3 0218 + 357 ( z = 0.944 , uncertain type ) which has the highest @xmath6 ( 190 @xmath23 2.8 ) in this analyzed sources is a gravitationally lensed blazar@xcite , hence the very high @xmath6 value might be enhanced by the gravitationally lensed effect .
+ however , there are some problems in this study .
first , the middle - high redshift ( z @xmath27 0.2 ) low @xmath6 sources were not sufficient for discussions without selection effects .
second , this study could not considered the short time scale variability ( @xmath28 30days ) .
thus , it is necessary to analyze the low @xmath6 sources and short time scale .
one of the most important problem of the blazar astrophysics is to understand the physical origin of the blazar sequence . in this study , we focus on the gev gamma - ray variability of blazars and evolution perspective we search the relation between the redshift and the variability amplitude of blazars for each blazar subclass . 
 we analyzed the fermi - lat data of the tev blazars and the bright agns ( flux @xmath0 4@xmath1 @xmath2s@xmath3 ) selected from the 2lac ( the 2nd lat agn catalog ) data base . as a result , we found a hint of the correlation between the redshift and the variability amplitude in the fsrqs . 
 furthermore the bl lacs which have relatively lower peak frequency of the synchrotron radiation and relatively lower redshift , have a tendency to have a smaller variability amplitude .