The evolutionary sequence of Fermi blazars

Astrophys Space Sci (2014) 349:895–908DOI 10.1007/s10509-013-1667-z

O R I G I NA L A RT I C L E

The evolutionary sequence of Fermi blazars

Yongjuan Cha · Haojing Zhang · Xiong Zhang ·Dingrong Xiong · Bijun Li · Xia Dong · Jin Li

Received: 18 May 2013 / Accepted: 7 October 2013 / Published online: 5 November 2013© Springer Science+Business Media Dordrecht 2013

Abstract Using γ -ray data (αγ , Fγ ) detected by FermiLarge Area Telescope (LAT) and black hole mass whichhas been compiled from literatures for 116 Fermi blazars,we calculated intrinsic γ -ray luminosity, intrinsic bolomet-ric luminosity, intrinsic Eddington ratio and studied the re-lationships between all above parameters and redshift, be-tween αγ and Lγ . Furthermore, we obtained the histogramsof key parameters. Our results are the following: (1) Themain reason for the evolutionary sequence of three sub-classes (HBLs, LBLs, FSRQs) may be Eddington ratiorather than black hole mass; (2) FSRQs occupy in the ear-lier, high-luminosity, high Eddington ratio, violent phase ofthe galactic evolution sequence, while BL Lac objects oc-cur in the low luminosity, low Eddington ratio, late phase ofthe galactic evolution sequence; (3) These results imply thatthe evolutionary track of Fermi blazars is FSRQs −→ LBLs−→ HBLs.

Keywords Galaxies evolution · Black hole physic ·Fundamental parameters · Fermi blazars

1 Introduction

Blazars are the brightest and the most variable high-energysources among active galactic nuclei and have continuousspectral energy distributions (SEDs). They exhibit a non-thermal continuum from radio to optical/UV, X-ray, andeven γ -ray wavelengths. Blazars are often divided into

Y. Cha · H. Zhang (B) · X. Zhang · D. Xiong · B. Li · X. Dong ·J. LiDepartment of Physics, Yunnan Normal University, 650500,Kunming, Chinae-mail: [email protected]

subcategories of BL Lacs objects and flat spectrum radioquasars (FSRQs). The classes are characterized by rapid op-tical variability, high and variable optical polarization, andflat radio spectra. All of these extreme properties can in-dicate that blazars are the most active objects in the uni-verse. The main difference between the two blazars classeslies in their distributions of redshift and their emission linesstrength: BL Lacs are characterized by the lack of strongemission lines (equivalent width EW ≤ 5 Å) and mostlyfound at low redshift (z < 0.1) on the basis of the absorp-tion lines of underlying elliptical galaxies (Xie et al. 2004b),while FSRQs have strong broad emission lines of similarstrength to normal quasars (Scarpa and Falomo 1997).

Traditionally, BL Lac objects discovered in radio skysurveys are called radio-selected BL Lac objects (RBLs),and those discovered in X-ray sky surveys are called X-ray-selected BL Lacs (XBLs). Recently, a new classification hasbeen introduced, based on the fact that the peak wavelengthof the synchrotron luminosity in blazars is anti-correlatedwith the ratio of X-ray to radio flux. On this basis, BL Lacscan be divided into “High-energy peaked BL Lacs” (HBLs)and “Low-energy peaked BL Lacs” (LBLs; Padovani andGiommi 1995). The relationship between HBLs and LBLshas been studied by many authors (Bao et al. 2008; Giommiet al. 1990, 1995; Padovani and Giommi 1995). Giommiet al. (1995) found the observed peak of emitted power oftwo subclasses located at different wavelengths. The SEDsof HBLs and LBLs are significantly different. Padovani andGiommi (1995) and Giommi et al. (1990) found two sub-classes that occupy different regions in the αr.o–αo.x plane.There exist the correlations between minimum soft X-rayflux and radio flux, and also between radio and opticalfluxes for the subsample of HBLs, but not for that of LBLs(Padovani and Giommi 1995). In a word, the classificationof HBLs and LBLs is based on a physical difference but

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896 Astrophys Space Sci (2014) 349:895–908

not on the observing band: in the HBLs the X-ray emis-sion is produced by synchrotron emission, whereas in theLBLs, the X-ray is dominated by the inverse Compton com-ponent (Bondi et al. 2001), the classification of HBLs andLBLs is better and has more physical significance than theclassification of XBLs and RBLs. BL Lacs and FSRQs aregrouped together under the denomination of blazars, whicheliminates the somewhat ambiguous issue about the strengthof the emission lines as a classification criterion. However,it is also an open problem for blazars whether the differentphenomenologies can be understood within a single class ofmodels or require different astrophysical scenarios. There-fore, a detailed research about the cosmological evolutionof the blazars is very significant. Searching the connec-tion of different types of blazars would substantially pro-mote our understanding about the fundamental nature ofblazars. Therefore, the relationship among different typesof blazars is very interesting. The FSRQs behavior, whichexhibits strong cosmological evolution (Goldschmidt et al.1999), might include a strong component of luminosity evo-lution (see Boyle et al. 2000 for the optical band, DellaCeca et al. 1994 for the X-ray band, Ghisellini et al. 2009and Ackermann et al. 2011 for the γ -ray band); the BLLac objects in contrast show no signs of similar behavior(e.g., Giommi et al. 1999). The two subclasses of blazarsappear to be a continuous sequence from FSRQs to BLLac objects (Xie et al. 2001). This trend is characterizedby decreasing bolometric luminosity, increasing peak fre-quencies, and a decreasing fraction of power in γ -ray com-pared with lower frequency radiation (Sambruna et al. 1996;Fossati et al. 1998).

The connection between the subclasses of blazars hasbeen studied by many authors (e.g., Sambruna et al. 1996;Ghisellini et al. 1998; Xie et al. 2001; Georganopouloset al. 2001; D’Elia and Cavaliere 2001; Böttcher and Der-mer 2002; Li et al. 2010). Based on a radio-optical analysisof the evolution of radio quasars and based on a very smallnumber of BL Lac objects, Vagnetti et al. (1991) suggestedthat there might be no need for two separate unified schemesfor the FSRQs and BL Lac objects. They are connected inan evolutionary sequence with strong-lined objects changingwith time into weak-lined objects where the optical contin-uum is dominated by a beamed component that swamps theemissions lines. Ghisellini et al. (1998) used a large sam-ple of blazars broadband spectra to study these differencesand found an increase of peak frequency in a sequence ofFSRQs to BL Lac objects. D’Elia and Cavaliere (2001) ar-gued that the BL Lac objects are mainly powered by therotational energy extraction of central supermassive blackholes (SMBHs) via the Blandford-Znajek (BZ) mechanism,while FSRQs require a dominant contribution from the ac-cretion of the central SMBHs. They suggested that as thegas and dust around an FSRQ is gradually exhausted, the

Eddington ratio decreases. Based on the first Fermi sample,Li et al. (2010) complied the optical, X-ray, and γ -ray datafor 54 Fermi blazars and studied the relationship betweenthe broadband spectral index αox and αxγ , as well as the re-lationship between the intrinsic composite spectral indicesαxox and αγ xγ for this sample. The relationship betweenαox and αxγ reveals that FSRQs and LBLs almost occupythe same region, i.e., they have similar spectral propertiesand suggest that the distribution of αxγ of HBLs is differ-ent from that of FSRQs and LBLs, which hints that theremay be different spectral properties between HBLs, FSRQs,and LBLs. The relationship between αxox and αγ xγ revealsthat flat spectrum radio quasars and low-energy peaked BLLacertae follow a continuous trend, whereas high-energypeaked BL Lacertae follow a separate distinct trend.

Based on the isotropic luminosity and spectral index ofthe first Fermi sources, Ghisellini et al. (2009) proposed thatFSRQs accrete at or above a critical mass accretion rate(Mcric), whereas BL Lacs at a rate below Mcric, which re-sults in their observed large luminosity differences, more-over, they found that the spectral shape/γ -ray luminosity(αγ –Lγ ) plane revealed a clear separation between FSRQsand BL Lacs and found that blazars obey a spectral se-quence. However, it is still uncertain whether the differentsubclasses of blazars are connected through an evolutionarysequence, or whether they are in limited periods of AGNactivity on parallel evolutionary paths, the actual cause ofthe FSRQs/BL Lacs division is still not confirmed. Spectralenergy distribution (SED) modeling suggests that jet emis-sions of FSRQs are dominated by external Compton (EC)processes. In this case, the relativistic particles in the jet up-scatter external low-energy photons leading to the genera-tion of γ -ray photons. The source of low-energy photonscould be the underlying accretion disk, the broad-line re-gion, the dusty torus etc. On the other hand, SEDs of BL Lacsources are better fitted by synchrotron self-Compton (SSC)emissions, when the synchrotron photons of the jet are up-scattered via inverse Compton processes by relativistic par-ticles in the jet. Therefore, observed data suggest that the rel-ativistic beaming effects in the two classes are not same andhence the intrinsic luminosity (which is the luminosity cor-rected for relativistic beaming), which is the property of theunderlying accretion disk, should be treated as a more fun-damental quantity than the observed luminosity in order tounderstand the origin of difference between the two sourceclasses (Mukhopadhyay et al. 2012).

In this work we collected 116 blazars detected by FermiLAT and restudy the relationship between FSRQs and BLLac objects and the evolutionary law of blazar sequence bycomparing key parameters of blazars: the mass of centralSMBHs, the intrinsic γ -ray luminosity, the intrinsic bolo-metric luminosity, and the intrinsic Eddington ratio. The pa-per is structured as follows: in Sect. 2, we present the en-tire set of data and the association procedures; Sect. 3 is

Astrophys Space Sci (2014) 349:895–908 897

devoted to the analysis of the relationship between funda-mental parameters and redshift, between αγ and intrinsic Lγ

and showing the histograms of key parameters, conclusionsand discussions are in Sect. 4. The cosmological parame-ters H0 = 70 km s−1 Mpc−1, Ωm = 0.3, and ΩΛ = 0.7 havebeen adopted in this work.

2 Sample and data description

The Fermi satellite is detecting γ -ray emission from a largenumber of blazars (flat-spectrum radio quasars and BL Lac-ertae objects). The second catalog of active galactic nuclei(2LAC) detected by the Fermi Large Area Telescope (LAT)includes 1017 γ -ray sources located at high Galactic lat-itudes (|b| > 10◦) (Ackermann et al. 2011). These γ -raysources are detected with a test statistic (TS) which is greaterthan 25. And they associate statistically with AGNs. How-ever, some of these are affected by analysis issues and someare associated with multiple AGNs. Consequently, the cleansample includes 886 AGNs, comprising 395 BL Lacertaeobjects (BL Lacs), 310 flat spectrum radio quasar (FSRQs),157 candidate blazars of unknown type, 8 misaligned AGNs,4 narrow-line Seyfert 1 (NLS1s), 10 AGNs of other typesand 2 starburst galaxies. Source detection is based on theaverage flux over the 24-month period and flux measure-ments are included in 5 energy bands (Abdo et al. 2012;Xiong et al. 2013).

Ackermann et al. (2011) get the redshift distributions ofFSRQs and BL Lac objects which are very similar to thoseobtained with 1LAC (Abdo et al. 2010a). The distributionpeaks around z = 1 for FSRQs and extends to z = 3.10.The distribution peaks at a lower redshift for BL Lac objectsand 56 % of the BL Lac objects have no measured redshifts.These distributions gradually extend to lower redshifts as thelocation of the synchrotron peak shifts to higher frequency,i.e., from LSPs to HSPs. Comparisons between the proper-ties of BL Lac objects and FSRQs must carefully take intoaccount the redshift incompleteness, given that more thanhalf of the BL Lac objects in the 2LAC lack redshifts. Thesample of blazars lacking redshifts therefore does not repre-sent a uniform subsample of any one class of objects withmeasured redshift. This incompleteness influences any con-clusions concerning luminosity or other properties that de-pend on knowledge of redshift (Abdo et al. 2010b). In thesecond LAT AGN Catalog only ∼200 BL Lac have a red-shift measurement, so our sample is a representative set ofFermi-detected BL Lacs.

We tried to select the largest group of blazars detectedby Fermi LAT with reliable redshift and black hole mass.At first, we considered the sample of blazars studied by Xieet al. (1991, 2004a, 2004b), Wu et al. (2002), Woo and Urry

(2002), Chai et al. (2012), Sbarrato et al. (2012) which con-structed a relatively large sample of blazars with informa-tion about the measured redshift and black hole mass. Thenwe cross-correlated the blazars sample with the clean 2LACsample (Abdo et al. 2012; Ackermann et al. 2011). At last,by combining these catalogues, we found 116 sources.

The SMBH masses of AGNs are important for under-standing the nature of AGN activities, however, there areonly very limited methods which can be used to derive themass of them. Krolik (2001) assumed that broad-line cloudsare virialized, and the black hole mass can be estimated:

MBH = RBLRν2G−1 (1)

The virial assumption may not be correct, radiation pres-sure and/or magnetic fields may contribute significantly tothe dynamics (Krolik 2001), and outflows or winds couldcause the observed line widths to exceed those induced bythe black hole potential alone (Woo and Urry 2002). In thesecases the black hole mass calculated from Eq. (1) would beoverestimated.

In nearby galaxies there is apparently a close connec-tion between the central black hole and the bulge kine-matics. Specifically, black hole mass (determined from spa-tially resolved kinematics) correlates well with stellar ve-locity dispersion, as MBH ∝ σ 3.75 (Gebhardt et al. 2000) orMBH ∝ σ 4.8 (Ferrarese and Merritt 2000). From the collec-tive analysis by Tremaine et al. (2002):

MBH = 1.349 × 108M�(σ/200 km s−1)4.02 (2)

However, for most AGNs it is difficult to measure the cen-tral velocity dispersions of their host galaxies directly withthe spectroscopic studies. Wu et al. (2002) adopt the funda-mental plane for ellipticals to estimate the central velocitydispersion and black hole mass for a number of AGNs withmorphology parameters of their elliptical host galaxies ob-tained by the Hubble Space Telescope imaging observations.

Xie et al. (2004a) searched for shortest time scale of vari-ation reported and assumed that the SMBH is a Kerr blackhole with the maximum possible speed of rotation for theblack hole accretion mode, the black hole mass also can beestimated:

MBH = 1.62 × 104(σ/1 + z)�tmin,obM� (3)

where σ is the Doppler factor and

σ ≥((

5 × 10−43 �Lob/�tmin,ob

0.057

)1/(4+a))(4)

In a world, black hole mass can be estimated via differentapproaches. We collect and compare all Fermi blazars blackhole mass estimates from many literatures. When more thanone value of black hole mass was found in the literature, wetake the average value of them.


The γ -ray energy flux and photon spectral index at 0.1–100 GeV come from clean Fermi LAT Second Source Cat-alog (2FGL, Abdo et al. 2012). All flux densities of thissample are K-corrected according to Sν = Sobs

ν (1 + z)α−1,where α is the spectral index and αγ = αPh − 1 (Chenget al. 2000). The luminosity is calculated from the relationLν = 4πd2

LSν , and dL is the luminosity distance,

dL(z) = c

H0(1 + z)

∫ z

0

[ΩΛ + Ωm

(1 + z′)3]−1/2

dz′ (5)

Eq. (5) obtained from Venters et al. (2009).Mukhopadhyay et al. (2012) assumed that the blazars lu-

minosity mostly comes from the jet which is believed to bemade up of relativistic particles, either in a continuous flowor as discrete blobs. The γ -ray emission of jet arises dueto either SSC and/or EC processes. They consider that theobserved beamed luminosity (Lobs) and the intrinsic lumi-nosity (Lint) are related by (Dermer 1995)

Lobs = Lintδm+n (6)

where m = 2 for a continuous jet and m = 3 for a discretejet, n = αγ for SSC process and n = 2αγ + 1 for EC pro-cess, when αγ is the energy spectral index. One can obtainthe intrinsic luminosity Lint of the source from Eq. (6) byknowing Lobs and δ. Mukhopadhyay et al. (2012) use an av-erage value of δ for blazars and individual spectral indiceswhile calculating unbeamed/intrinsic luminosities of FSRQsand BL Lacs. In order to obtain Lint, they consider a contin-uous jet for the BL Lac group having SSC emission and con-sider a combination of SSC and EC emission models in theframework of continuous jet for the FSRQ group. Since thefraction of SSC and EC combination is not well constrained,they consider different scenarios: (a) 50 % SSC and 50 %EC contributions, (b) 25 % SSC and 75 % EC contributions,(c) 10 % SSC and 90 % EC contributions, and (d) 100 % ECcontribution.

A very important factor to determine the intrinsic lumi-nosity of a blazar is δ. There are mainly two approaches todetermine δ (Mukhopadhyay et al. 2012):

(i) SED modelingConsidering the opacity arguments, it is generally be-

lieved that the γ -ray emitting region is located closer tothe central black hole. Hence, SED modeling beyond radiomay be more appropriate, since it more accurately repre-sents the region of γ -ray emission. Unfortunately, in mostcases SED data gathered across wavelengths are not simul-taneous. Further, SED modeling involves a large number ofmodel parameters and, hence, typically results in large un-certainties. Another important parameter, jet to line-of-sightangle (θjet), is not measured, rather a nominal value of θjet istypically considered for this modeling. Moreover, for mostof the cases, the goodness of fit is not examined and, hence,

the parameter values are not optimized. Based on SED mod-eling of 85 blazars from the first 3 months’ Fermi observa-tion, Ghisellini et al. (2010) found that the values of Γ forblazars are within the range of 10–15.

(ii) radio Very Large Baseline Interferometry (VLBI) mea-surement

The values of Γ and δ can also be determined from VLBIobservations based on direct observation of the brightnesstemperature of the source (Tb,obs). Comparing Tb,obs withthe intrinsic brightness temperature of the source (Tb,int),Hovatta et al. (2009) determine δ

δvar =(

1.47 × 1013 �Smaxd2L

ν2�t2(1 + z)Tb,int

)(7)

where �Smax is the flare amplitude in Janskys, ν is the ob-serving frequency in GHz, �t is the timescale of the fastestflare in the source in days, dL is the luminosity distancein Mpc, and z is the redshift. This method of estimatingδvar relies on the assumption that every source occasionallyreaches Tb,int = 5 × 1010 K (this technique Tb,int is often as-sumed to be the equipartition temperature), that the Dopplerfactor is constant with time, and that the flux density curve atmm-wavelengths is a superposition of flares with mixed du-ration and amplitude (Hovatta et al. 2009). Thus, identifyingthe sharpest, fastest flare over a long period of time gives thebest estimate of the true Doppler factor, but This assumptionmakes the estimated values of Γ and δ less accurate.

Jorstad et al. (2005) suggest that the values of Γ and δ

could also be determined from VLBI observations adopt-ing yet another technique. In this technique, δ is derived bycomparing the timescale of decline in flux density with thelight travel time across the emitting region. The variabilityDoppler factors are derived as

δvar = sD

c�tvar(1 + z)(8)

where D is the luminosity distance, s is the angular sizeof the component, z is the redshift, and they define thetimescale of the variability for each superluminal compo-nent as δvar = dt/ ln(Smax/Smin) (Burbidge et al. 1974),Smax and Smin are the measured maximum and minimumflux densities, respectively, and dt is the time in years be-tween Smax and Smin. This approach yields more appropri-ate values in comparison to other alternate methods. Ac-cording to this approach and considering the large errors,Mukhopadhyay et al. (2012) assume that the intrinsic δ

(also Γ ) distribution and the corresponding errors are Gaus-sian and get that the average values of δ = 20.6 ± 8.4 andΓ = 15.1 ± 4.6 for both FSRQs and BL Lacs.

Based on all above point, with the average value of δ =20.6 and using Eq. (6) we estimate the intrinsic γ -ray lu-minosity and intrinsic bolometric luminosity. We consider acontinuous jet for the BL Lac group having SSC emission


and consider a combination of SSC and EC emission mod-els in the framework of continuous jet for the FSRQ group.Since the fraction of SSC and EC combination is not wellconstrained, we randomly select 60 % FSRQ having SSCemission and the rest (40 %) having EC emission for ourFSRQ sample.

The data for our sample are listed in Table 1 with fol-lowing headings: column (1) other name; column (2) nameof the second Fermi LAT catalog; column (3) is right as-cension from NED; column (4) is declination from NED;column (5) classification of the sources (RQ = flat spectrumradio quasar, L = LBLs, H = HBLs); column (6) z: redshiftfrom NED; column (7) log M

M� : the black hole mass; column

(8) references of the black hole mass data; column (9) αph:Photon spectral index of γ -ray photon; column (10) logLγ :log of the intrinsic γ -ray luminosity at 0.1–100 GeV inunits of erg s−1; column (11) references for γ -ray data (aph,Lγ ); column (12) logLbol: log of the intrinsic bolometricluminosity in units of erg s−1 (Lbol ≈ 2Lγ ); column (13)Lbol/LEdd: the intrinsic Eddington ratio (m = Lbol/LEdd).

3 Statistical analysis and evolution simulation

3.1 Redshift distributions

The redshift distributions of the various classes (HBLs,LBLs, FSRQs) are shown in Fig. 1 which are the histogramsof the redshift. It is clear that most of HBLs have redshift inthe range of 0.031 to 0.163; the redshift of LBLs range from0.163 to 1.329; and most redshift of FSRQs are in the rangeof 1.329 to 2.978. A few of LBLs and FSRQs are cross-overin the range of 0.336 to 1.320. Moreover, we can find that thedistribution peaks around z = 1.000 for FSRQs and extendsto z = 3.000, most of BL Lac objects found at low redshift(z < 1).

3.2 Black hole mass distributions

Black hole mass is a fundamental property of Fermi blazars.Figure 2 shows the histograms of the black hole mass forthree kinds of blazars. From Fig. 2, we can find that the blackhole mass of the three subclasses (HBLs, LBLs, FSRQs)are cross-over in the range of 6.683 to 10.39, and most ofFSRQs have black hole masses in the range of 8.821 to9.505. Although the average mass of FSRQs is larger thanHBLs and LBLs, there is no significant difference in theblack hole masses between three subclasses.

3.3 γ -ray energy spectral index and γ -ray luminositydistributions

The γ -ray energy spectral index distributions are given inFig. 3 for the different classes of blazars. We can find the en-

ergy spectral index distributions of three kinds of blazars aresimilar. The distribution peaks for each of the blazar classesis around αγ = 0.64 (HBLs), αγ = 1.09 (LBLs), αγ = 1.37(FSRQs) respectively.

The γ -ray luminosity is plotted as a function of redshiftin Fig. 4. A Malmquist bias is readily apparent in this fig-ure as only high γ -ray luminosity sources (mostly FSRQs)are detected at large distances. Given their γ -ray luminositydistribution, most BL Lac objects could not be detected ifthey were located at redshifts greater than 1.

Figure 5 gives the γ -ray spectral index versus γ -ray lu-minosity plane. From Fig. 5 we can find that the spectralindex vs γ -ray luminosity plane revealed a clear separa-tion between FSRQs, LBLs and HBLs (This correlation hasbeen discussed in detail in the context of the “blazar divide”(Ghisellini et al. 2009)) and the evolutionary sequence iscontinuous. At the same time, there is a few of LBLs andFSRQs are cross-over. FSRQs and HBLs occupy separatedregions, while LBLs bridge the gap between FSRQs andHBLs, which implies that three kinds of blazars have dif-ferent spectral properties and LBLs may be the intermediatestate.

3.4 Bolometric luminosity distributions

The bolometric luminosity is another important parameterfor understanding the nature of blazars. Based on the rela-tivistic beaming model of blazars, the observed flux densityis enhanced by a factor δm+n (Eq. (6)), i.e., the observedbolometric luminosity must be corrected for the Doppler ef-fect. Ghisellini et al. (2009) strongly confirmed the idea thatblazars obey a spectral sequence, controlled by the bolomet-ric luminosity, of which the γ -ray one is good proxy. So inthis paper we took the γ -ray luminosity to stand for approx-imately half of the bolometric luminosity (Fan et al. 1999),i.e., Lbol ≈ 2Lγ , The results are listed in column (12) ofTable 1. Figure 6 shows the histograms of the bolometricluminosity for three kinds of blazars and Fig. 7 gives thedistribution of redshift vs bolometric luminosity of our sam-ple. From Fig. 6, we can find that the bolometric luminos-ity of the three subclasses are in the range of 1038 to 1044

erg s−1 and the average bolometric luminosity of FSRQs islarger than HBLs and LBLs in the intermediate state. FromFig. 7, we also can get the evolutionary sequence of threesubclasses of blazars. FSRQs mainly distributed in the upperright region of the evolutionary diagram, i.e., FSRQs havemore high bolometric luminosity and redshift than those ofHBLs and LBLs, and bolometric luminosity and redshift de-crease slowly along with the evolution, after that, FSRQsevolves into LBLs, and LBLs occur in a transition phase be-tween FSRQs and HBLs. A large proportion of high bolo-metric luminosity objects are at high redshift.


Tabl

e1

The

sam

ple

ofFe

rmib

laza

rsw

ithob

serv

atio

nald

ata

and

resu

lts

Oth

erna

me

2FG

Lna

me

RA

DE

CC

lass

Red

shif

log

M M�

Ref

αph

logL

γR

eflo

gL

bol

Lbo

l/L

Edd

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

0317

+183

2FG

LJ0

319.

6+18

4949

.909

418

.826

6H

0.19

8.21

51

1.55

094

40.5

2174

518

840

.822

7751

73.

1176

8E−0

6

0323

+022

2FG

LJ0

326.

1+02

2451

.545

12.

4125

H0.

147

9.21

22.

0563

39.5

7404

418

839

.875

0741

73.

5573

8E−0

8

0414

+009

2FG

LJ0

416.

8+01

0564

.208

81.

0922

H0.

287

8.38

61.

9808

640

.053

8921

68

40.3

5492

216

7.26

071E

−07

0502

+675

2FG

LJ0

508.

0+67

3777

.013

167

.625

2H

0.41

69.

095

61.

4891

41.7

3599

165

842

.037

0216

46.

7309

8E−0

6

0706

+591

32F

GL

J071

0.5+

5908

107.

629

59.1

394

H0.

125

8.77

56

1.53

373

40.0

4877

669

840

.349

8066

82.

8897

7E−0

7

0737

+746

2FG

LJ0

745.

0+74

3611

6.27

4574

.601

5H

0.31

58.

425

61.

7992

140

.361

0281

58

40.6

6205

814

1.32

775E

−06

0806

+524

2FG

LJ0

809.

8+52

1812

2.45

9852

.307

9H

0.13

78.

86

1.93

785

39.9

4514

728

40.2

4617

722.

1489

9E−0

7

0912

+297

2FG

LJ0

915.

8+29

3213

8.96

2929

.544

H0.

195

1.87

473

40.3

0904

733

840

.610

0773

3

1011

+496

2FG

LJ1

015.

1+49

2515

3.78

8549

.432

4H

0.21

28.

285

61.

7225

141

.042

8254

88

41.3

4385

548

8.80

871E

−06

1028

+511

2FG

LJ1

031.

0+50

5315

7.76

1550

.894

7H

0.36

18.

126

1.81

457

40.7

3749

989

841

.038

5298

96.

3765

6E−0

6

1101

+384

2FG

LJ1

104.

4+38

1216

6.11

9938

.213

4H

0.03

18.

034

1,6

1.77

058

39.9

4019

658

40.2

4122

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462

41.7

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728

842

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7744

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5

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J120

9.7+

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182.

4429

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217

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0.85

8.94

52.

4636

540

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6315

98

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4766

158

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897E

−07

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4.42

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1318

5.61

574.

2225

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0.96

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245

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0.43

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875

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225

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2766

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4524

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669

8.56

52.

5396

140

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6509

840

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6809

5.44

174E

−07


Tabl

e1

(Con

tinu

ed)

Oth

erna

me

2FG

Lna

me

RA

DE

CC

lass

Red

shif

log

M M�

Ref

αph

logL

γR

eflo

gL

bol

Lbo

l/L

Edd

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

B2

1348

+30B

2FG

LJ1

350.

8+30

3520

7.71

2930

.588

6R

Q0.

712

8.69

52.

4491

840

.538

4157

58

40.8

3944

575

1.08

518E

−06

PKS1

434+

235

2FG

LJ1

436.

9+23

1921

9.23

2823

.329

1R

Q1.

547

8.44

52.

4093

741

.307

6428

58

41.6

0867

284

1.13

43E−0

5

PKS1

502+

106

2FG

LJ1

504.

3+10

2922

6.09

5110

.488

3R

Q1.

839

9.64

52.

1471

443

.550

3723

28

43.8

5140

232

0.00

0125

158

PKS1

509+

022

2FG

LJ1

512.

2+02

0122

8.06

992.

0228

RQ

0.21

98.

845

2.17

384

39.9

6696

906

840

.267

9990

62.

0608

9E−0

7

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1510

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2FG

LJ1

512.

8-09

0622

8.20

71−9

.103

4R

Q0.

368.

65

2.28

839

41.7

3495

433

842

.035

9843

22.

0991

4E−0

5

PKS1

546+

027

2FG

LJ1

549.

5+02

3723

7.38

822.

6274

RQ

0.41

48.

611,

62.

4551

440

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6332

48

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8866

324

9.21

977E

−07

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5.64

2FG

LJ1

550.

7+05

2623

7.68

725.

4343

RQ

1.41

79.

385

2.32

035

41.6

1867

682

841

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7068

12.

6654

1E−0

6

PKS1

551+

130

2FG

LJ1

553.

5+12

5523

8.38

7612

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2R

Q1.

308

9.1

52.

0267

642

.328

8403

28

42.6

2987

031

2.60

572E

−05

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0.45

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LJ1

608.

5+10

2924

2.14

8310

.494

4R

Q1.

231

8.64

52.

3309

641

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7928

18

42.0

6282

281

2.03

648E

−05

B2

1611

+34

2FG

LJ1

613.

4+34

0924

3.37

1634

.159

4R

Q1.

399

9.12

52.

3070

141

.295

0804

78

41.5

9611

047

2.30

233E

−06

1622

-297

2FG

LJ1

626.

1-29

4824

6.52

86−2

9.80

93R

Q0.

815

95

2.33

855

41.3

4189

595

841

.642

9259

43.

3805

1E−0

6

4C+3

8.41

2FG

LJ1

635.

2+38

1024

8.80

9138

.171

2R

Q1.

813

9.53

12.

2479

443

.024

5837

48

43.3

2561

374

4.80

475E

−05

OX

169

2FG

LJ2

143.

5+17

4332

5.87

9217

.719

8R

Q0.

213

8.6

1,6

2.57

9639

.993

5381

38

40.2

9456

812

3.80

737E

−07

2223

-052

2FG

LJ2

225.

6-04

5433

6.42

4−4

.901

1R

Q1.

404

8.2

12.

4357

341

.884

2751

18

42.1

8530

517.

4363

8E−0

5

PKS

2227

-08

2FG

LJ2

229.

7-08

3233

7.44

12−8

.545

9R

Q1.

599

8.95

52.

4061

842

.413

3160

88

42.7

1434

608

4.47

098E

−05

CTA

102

2FG

LJ2

232.

4+11

4333

8.12

1411

.724

3R

Q1.

037

8.7

12.

3265

341

.776

6613

18

42.0

7769

131

1.83

547E

−05

3C45

4.3

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253.

9+16

0934

3.49

7416

.152

6R

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859

8.7

1,6

2.22

639

43.1

2159

916

843

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6291

50.

0004

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9

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Fig. 1 Histogram of the redshift distribution of our Fermi blazars sam-ple. H stands for HBLs, L stands for LBLs, RQ stands for flat spectrumradio quasars (FSRQs)

Fig. 2 Histogram of the black hole masses distribution of our Fermiblazars sample. H stands for HBLs, L stands for LBLs, RQ stands forflat spectrum radio quasars (FSRQs)

3.5 Eddington ratio distributions

The Eddington ratio is an important parameter for under-standing the nature of blazars. Based on accretion disk the-ory and the relativistic beaming model of blazars, we knowthat radiation efficiency is associated with Eddington accre-tion. Using the total intrinsic bolometric luminosity and Ed-dington luminosity, we estimated the intrinsic Eddington ra-tio, where m = Lbol/LEdd

LEdd = −4πGMmpc

σT= 1.25 × 1038

(M

M�

)erg s−1 (9)

The results are listed in column (13) of Table 1. Figure 8shows the histograms of the intrinsic Eddington accretionfor three kinds of blazars and Fig. 9 gives the distributionof redshift vs intrinsic Eddington ratio of our sample. FromTable 1 and Figs. 8, 9, one finds that the intrinsic Edding-ton ratio of three subclasses are quite different. FSRQs withhigh redshift have more high intrinsic Eddington ratio than

Fig. 3 Histogram of the αγ distribution of our Fermi blazars sample.H stands for HBLs, L stands for LBLs, RQ stands for flat spectrumradio quasars (FSRQs)

Fig. 4 γ -ray luminosity vs redshift for our Fermi blazars sample. Hstands for HBLs, L stands for LBLs, RQ stands for flat spectrum radioquasars (FSRQs)

the low redshift objects (LBLs, HBLs). For HBLs and LBLs,their intrinsic Eddington ratio are very smaller, in the range3.721 × 10−7–6.460 × 10−6 (HBLs) and 6.460 × 10−6–3.305 × 10−5 (LBLs). However, the intrinsic Eddington ra-tio of FSRQs are larger in the range 1.309 × 10−5–1.401 ×10−4.

4 Conclusions and discussions

The Fermi second AGN catalog paper is mentioned thatgiven the luminosity distribution of BL Lacs, most of themwould not have been detected if they have a redshift z > 1.Clearly, there is a observation bias in the redshift distribu-tion. Also, major fraction of BL Lacs do not have redshiftinformation. The observed deficit of BL Lac objects at neg-ative Galactic latitudes compared to positive latitudes (Ack-ermann et al. 2011, Fig. 10) is not fully accounted for by


Fig. 5 γ -ray luminosity vs Energy spectral index αγ for our Fermiblazars sample. H stands for HBLs, L stands for LBLs, RQ stands forflat spectrum radio quasars (FSRQs)

Fig. 6 Histogram of the bolometric luminosity distribution of ourFermi blazars sample. H stands for HBLs, L stands for LBLs, RQstands for flat spectrum radio quasars (FSRQs)

blazars of unknown type, suggesting that a significant num-ber of blazars (at least 60) is present in the unassociated sam-ple of 2FGL sources. This deficit results primarily from thegreater incompleteness of the current counterpart catalogsat southern declinations, in particular, the BZCAT (Massaroet al. 2009), which is biased by the greater number of north-ern hemisphere arrays that have better exposure to positiveGalactic latitudes. There is furthermore a modest anisotropyin LAT exposure favoring positive Galactic latitudes. Thelack of extensive archival multiwavelength data also leadsto an incomplete characterization of the 2LAC Clean Sam-ple. Consequently they find that Two hundred twenty of the395 BL Lac objects (∼55 %) lack measured redshifts, andthis fraction is roughly the same for LSP, ISP, and HSP BLLac objects.

We considered only the sources of known redshift in thispaper. As discussed in Ghisellini et al. (2011), if the BLLac objects in the 2LAC Catalog with unknown redshift willturn out to be at z ∼< 0.5–1, the unknown redshift BL Lacs

Fig. 7 Bolometric luminosity versus redshift for our Fermi blazarssample. H stands for HBLs, L stands for LBLs, RQ stands for flat spec-trum radio quasars (FSRQs)

Fig. 8 Histogram of Eddington ratio distribution for our Fermi blazarssample. H stands for HBLs, L stands for LBLs, RQ stands for flat spec-trum radio quasars (FSRQs)

would lie in the region already occupied by the other BLLacs which have measured redshifts (see Fig. 1 and Fig. 2of Ghisellini et al. (2011)), i.e., the unknown redshift BLLacs will fit in the phenomenological blazar sequence, theywould be with low and moderate luminosity, with the ma-jority having a flat γ -ray slope, the fact that their spectrumis featureless implies that their emission lines are intrinsi-cally weak. Instead, if z ∼ 2, these unknown redshift sourceswould be “outliers” and would have a γ -ray luminosity aslarge as the powerful FSRQs, there have two possibility:(i) They have powerful lines and an even more powerfulcontinuum, swamping the emission lines. In this case, andfor average black hole masses, their LBLR/LEdd is large, asit is Lγ /LEdd. They together with the other FSRQs (theseobjects in the “FSRQs quadrant”); (ii) They have intrinsi-cally weak lines, and average black hole masses. In this caseLBLR/LEdd would be small, but Lγ /LEdd is large, i.e., therewould be no correlation between LBLR/LEdd and Lγ /LEdd,now devoid of sources. These sources would have a power-


Fig. 9 Eddington ratio versus redshift for our Fermi blazars sample. Hstands for HBLs, L stands for LBLs, RQ stands for flat spectrum radioquasars (FSRQs)

ful non-thermal emission, possibly extremely beamed, evenif their accretion disk is weak. Based on the point, Ghis-ellini et al. (2011) suggest a new classification criterion dis-tinguishing BL Lac objects from FSRQs, based on the lu-minosity of the broad emission lines measured in Eddingtonunits. The physically-based scheme is not affected by thepossible redshift values of the BL Lacs with unknown z andcan strengthen possible problems concerning the blazar se-quence. So, the relationship among three kinds of blazarsdeserves further investigation on a large sample in our fol-lowing research.

All our results about redshift, γ -ray energy spectral indexand γ -ray luminosity are in very good agreement with Ack-ermann et al. (2011) presented in the Fermi second AGNcatalog paper. In our study, our results are the following:(i) The distribution peaks around z = 1 for FSRQs and ex-tends to z = 3.000. The distribution peaks at a lower redshiftfor BL Lac objects, most of BL Lac objects found at lowredshift (z < 1); (ii) A Malmquist bias is readily apparentin Fig. 4 as only high-luminosity sources (mostly FSRQs)are detected at large distances. Given their γ -ray luminos-ity distribution, most BL Lac objects could not be detectedif they were located at redshifts greater than 1; (iii) Fig. 5shows energy spectral index versus γ -ray luminosity. Thiscorrelation has been discussed in detail in the context ofthe “blazar divide” (Ghisellini et al. 2009). From these con-sequences, we can declare that although our sample is in-complete, it has certain representativeness. The propertiesof FSRQs and BL Lacs (see Figs. 1, 3, 4, 5) we obtain fromour sample that can reflect the properties of the 2nd FermiAGN complete and clean sample which have measured red-shifts. Savolainen et al. (2010) find that the LAT-detectedblazars have on average higher Doppler factors than non-LAT-detected blazars. Moreover, they find statistically sig-nificant differences in the viewing angle distributions be-tween FSRQs and BL Lacs and the γ -ray emission is en-

hanced by Doppler boosting. So, With the δ, using Eq. (6),we get the unbeamed/intrinsic luminosity of FSRQs and BLLacs before conducting the comparative study. We find thatthe intrinsic luminosity decrease significantly in comparisonto the observed values, that is the most significant differencewith Ackermann et al. (2011).

Unlike stellar evolution, astronomers are still far frompiecing together a scenario of galactic evolution in whichall the different types of galaxy would find a natural place(Kembhavi and Narlika 1999; Xie et al. 2004a). Do threekinds of blazars (FSRQs, HBLs, LBLs) come in sequencealong a unique evolutionary track? Or are they in two dif-ferent stages and alternative tracks? Are quasars expectedto occur in the beginning, or toward the end of galacticevolution—or do they occur randomly at any time? In thiswork we tried to find out the relationship between threesubclasses and the evolutionary law of blazars sequence bycomparing five key parameters of blazars: the mass of cen-tral SMBHs, γ -ray energy spectral index, the intrinsic γ -rayluminosity, the intrinsic bolometric luminosity, and the in-trinsic Eddington ratio. The principal results are as follows:

(1) The masses of our blazars sample range from 107.45 to1010.39 M�. No significant difference in black hole massis found for three kinds of blazars, the results are inagreement with previous investigators (Wu et al. 2002;Urry et al. 2000; Sbarrato et al. 2012). Urry et al. (2000)mentioned that there are no systematic differences in thehost galaxies of HBLs and LBLs. This suggests that thedifferent observational features of three subclasses maybe mainly dominated by different Eddington ratio ratherthan by the black hole mass, i.e., the key parameter ofevolutionary sequence is Eddington ratio rather than theSMBH mass.

(2) In this work we present a possible interpretation of theseparation of FSRQs, LBLs and HBLs in the αγ –Lγ

plane (Fig. 5) which revealed a clear separation betweenthree kinds of blazars. Moreover, there is a well de-fined trend, with BL Lac objects being harder and lessluminous than FSRQs. A possible interpretation couldsimply be to assume two independent populations withdifferent physical conditions as to the origin, propaga-tion and radiative properties of their jets. This howeverwould not account for the contiguity which should becoincidental. The jets of BL Lac objects thus propagatein a medium starved of external radiation (weak disk,weak lines), and this makes the emitting electrons ac-celerated in the jet to cool less, and to reach very highenergies. Their emitted high energy spectrum, producedmainly by the synchrotron self-Compton mechanism,is less luminous and harder than in FSRQs. The lattersources in fact have a radiatively efficient accretion diskand a corresponding standard broad line region. If thejet dissipates most of its power within the broad line


region, then the emitting electrons will efficiently cool(mostly by external Compton), will reach only moder-ate energies, and will produce a high energy peak below100 MeV. According to this idea the power of the jetsin all blazars is proportional to the Eddington ratio, thatcan change in a continuous way from one objects to theother (Ghisellini et al. 2009).

(3) Using published γ -ray fluxes, we calculate bolomet-ric luminosities of our sample and investigate the dis-tribution of redshift and bolometric luminosity. FSRQsand BL Lac objects are in a continuum: FSRQs occupythe region of high luminosity and high redshift, HBLsoccupy the region of low luminosity and low redshift,while LBLs occupy the region of intermediate luminos-ity and redshift.

(4) The key parameter of the evolutionary sequence of threesubclasses (HBLs, LBLs, FSRQs) is Eddington ratiorather than the SMBH mass. The depletion of accretionpower can lead to the decrease of the Eddington ratio,which may result in the transition of different accretionmodes (Wu et al. 2002).

(5) According to our study, the Eddington ratio are quitedifferent between FSRQs, LBLs and HBLs, for LBLsand HBLs the Eddington ratio are much smaller, how-ever, for FSRQs the rates are larger, this result is con-sistent with the results of D’Elia and Cavaliere (2001).A possible interpretation of this phenomenon is the ex-haustion of the gas stockpile available for accretion inthe host galaxy (Cattaneo et al. 1999; Haehnelt andKauffmann 2000). Cattaneo et al. (1999) and Haehneltand Kauffmann (2000) argued that with the gradual de-pletion of the gas, FSRQs (mainly fueled by accretion)will switch to BL Lac objects (mostly fed by Kerr blackhole rotational energy extraction via the BZ mecha-nism). The evolution of FSRQs occur in the earlier, vio-lent phase of the elliptical galaxy evolutionary sequenceto supply a dense environment around the FSRQs and aperiod of rapid black hole growth, which contain a sig-nificant amount of gases in their central regions. Thesegases, as well as producing the observed emission lines,are used to produce the violent radio and optical activ-ity. When these gases are used up or expelled, the emis-sion lines will become very weak or disappear and theoperation of the central engine become more variable,that is, the FSRQs evolves into LBLS. LBLS occur ina transition phase between FSRQs and HBLs. The re-sults mentioned above show that Eddington ratio is themost strongly evolving parameter in a unified schemefor blazars.

Acknowledgements We thank the anonymous referee for valuablecomments and suggestions. We are very grateful to the Science Foun-dation of Yunnan Province of China. This work is supported by theNational Nature Science Foundation of China (11163007, U1231203).

This research has made use of the NASA/IPAC Extragalactic Database(NED), that is operated by Jet Propulsion Laboratory, California Insti-tute of Technology, under contract with the National Aeronautics andSpace Administration.

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The evolutionary sequence of Fermi blazars

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