Correlation between γ -ray and radio emissions in Fermi blazars

Transcription

1 Publ. Astron. Soc. Japan (2014) 66 (6), 117 (1 11) doi: /pasj/psu111 Advance Access Publication Date: 2014 December Correlation between γ -ray and radio emissions in Fermi blazars De-Xiang WU, 1,2, Jun-Hui FAN, 1,2, Yi LIU, 1,2 Jiang-He YANG, 1,3 Jing-Meng HAO, 1,2 Zhi-Yuan PEI, 1 and Chao LIN 1 1 Center for Astrophysics, Guangzhou University, Guangzhou , China 2 Astron. Sci. and Tech. Research Lab. of Dept. of Edu. of Guangdong Province, China 3 Department of Physics and Electronics Science, Hunan University of Arts and Science, Changde , China * dxwuhl@gmail.com (DW);fjh@gzhu.edu.cn (JF, corresponding author) Received 2014 April 14; Accepted 2014 September 3 Abstract Blazars as a special subclass of Active Galactic Nuclei (AGNs) consist of two classes, namely Flat Spectrum Radio Quasars (FSRQs) and BL Lacertae objects (BL Lacs). We compiled information about core and extended radio emissions of 124 γ -ray ( GeV) loud blazars (79 FSRQs and 45 BL Lacs). Correlation is found between γ -ray and 5 GHz radio luminosities when the dependence of these two parameters on redshift is taken into account. The correlation suggests that, as well as the radio emission, the γ -ray emission may be strongly beamed. We find no correlation between the γ -ray luminosity (L γ ) and the core-dominance parameter R = L core /L ext,wherel core is the VLBI core emission at 5 GHz, L ext is the extended (lobe) radio emissions at 5 GHz, but there is a strong correlation between log(l γ /L ext ) and log(1 + R). Key words: BL Lacertae objects: general galaxies: jets telescopes: Fermi (LAT) 1 Introduction Blazars as a special subclass of AGNs are subdivided in two classes, namely Flat Spectrum Radio Quasars (FSRQs) and BL Lacertae objects (BL Lacs), while BL Lacs can also be classified further as low-peaked BL Lacertae objects (LBLs) and intermediate-peaked BL Lacertae objects (IBLs), and high-peaked BL Lacertae objects (HBLs) from spectral energy distribution (SEDs: Urry & Padovani 1995). FSRQs and BLs have many similar observational properties, such as strong γ -ray emissions, superluminal motion, high and variable polarization, and rapid variability (Fan et al. 2012). γ -ray emissions are a common property of Blazars (Fan et al. 2013a). EGRET detected 66 high confidence γ -ray bright blazars (Hartman et al. 1999).Basedonthe EGRET data, correlations between the γ -ray emissions and lower energetic bands were investigated (Dondi & Ghisellini 1995; Valtaoja & Teraesanta 1995; Comastri et al. 1997; Fan et al. 1998; Cheng et al. 1999; Fan 2000; Zhang et al. 2001). After the launch of Fermi/LAT, more than 1000 blazars have been detected (Abdo et al. 2010; Ackermann et al. 2011; Nolan et al. 2012), so many Fermi blazars provide us with a good opportunity to study the nature of γ -ray emissions. Pushkarev et al. (2010) found that the γ -rays are correlated with core-radio emissions. The correlations between γ -ray emissions and radio emissions at different frequencies are discussed (Fan et al. 2010; Kovalev et al. 2009; Hovatta et al. 2010; Savolainen et al. 2010; Giroletti et al. 2010; Ackermann et al. 2011; Giroletti et al. 2012; Giovannini et al. 2014). C The Author Published by Oxford University Press on behalf of the Astronomical Society of Japan. All rights reserved. For Permissions, please journals.permissions@oup.com

2 117-2 Publications of the Astronomical Society of Japan, (2014), Vol. 66, No. 6 Kovalev et al. (2009) compared the radio jet emissions of AGNs measured by the VLBA at 15 GHz with their associated γ -ray properties detected by Fermi/LAT, found the γ -ray photon flux to correlate with the quasisimultaneously measured compact radio flux density, and proposed that the jets of bright γ -ray AGNs have preferentially higher Doppler-boosting factors. They identified the parsec-scale radio core as a likely location for both the γ -ray and radio flares, which appear within typical timescales of up to a few months of each other. The multi-frequency behavior in the blazar 3C shows that the lower frequency events are co-spatial with the γ -ray outburst and that the lower frequency activities are correlated with the variabilities in the γ -ray regions (Jorstad et al. 2013). It is known that the Doppler-boosting factor, δ = 1/[Ɣ(1 βcos θ)] (here Ɣ is the Lorentz factor, β is the speed of jet in units of the speed of light, and θ is the viewing angle), is not easy to determine. Some methods were proposed for Dopper factor determination (Ghisellini et al. 1993; Lähteenimäki & Valtaoja et al. 1999; Fan et al. 2009, 2014; Hovatta et al. 2009; Lister et al. 2009; Savolainen et al. 2010). Savolainen et al. (2010) combined the estimated jet Doppler factors from the flux density monitoring data from Metsähovi Radio Observatory with the apparent jet speeds obtained from high-resolution VLBA images from the MOJAVE program, and derived Lorentz factors, and viewing angles for a sample of 62 blazars. Based on the 62 blazars, they compared the Doppler factors, Lorentz factors, and viewing angles of Fermi/LAT detected blazars and the non-fermi/lat detected sources, and found that Fermi/LAT blazars have higher Doppler factors than do non-fermi/lat blazars and γ -bright blazars have narrower co-moving viewing angles than γ -ray weak blazars. Fuhrmann et al. (2014) claimed that the bulk γ -ray emission/variability is likely connected to the same shocked radio features. Radio emissions in blazars are strongly beamed, the close correlation between the averaged γ -ray luminosity (or flux density) and radio luminosity (or flux density) suggests that the γ -ray may be strongly beamed, or the region of γ -ray emission and that of radio emission are related, they may be far away from each other (like different parts of a relativistic jet with the γ -ray emission originating upstream of the radio emission) (Max-Moerbeck et al. 2014). In 2011, we calculated the core-dominance parameter, R = S core /S ext (or L core /L ext ) for a sample of 1223 radio sources. In the sample, we compiled their VLBI core and extended (lobe) emissions from the literature and transferred those emissions into those at 5 GHz if their radio observations were not made at 5 GHz by adopting α core = 0, and α ext = 0.75 (S ν α ). Combining our previous sample (Fan et al. 2011) and the blazar sample (Massaro et al. 2011), we can get a blazar sample with core-dominance parameters (or extended and core radio emissions). In the present work we will combine the blazar sample with core-dominance parameters and the 2FGL sample to get Fermi blazars with core-dominance parameters, and discuss the correlations between γ -ray emissions and the core, the extended, and the total radio luminosity, and the relationship between the γ -ray luminosity and the core-dominance parameter. The paper is arranged as follows: in section 2 we will describe the sample and give some relationship analysis. In section 3 we will give some discussions and conclusions. We adopt H 0 = 73 km s 1 Mpc 1 throughout this paper. 2 Sample and results 2.1 Sample Using the second catalog of Fermi γ -ray large area telescope (LAT)-2FGL, the largest Blazar catalogue (Massaro et al. 2011), and the radio source sample with core-dominance parameters (Fan et al. 2011), we compiled a sample of 124 γ -ray loud blazars [79 FSRQs and 45 BL Lacs (including 19 LBLs, 12 IBLs, 14 HBLs)], the corresponding data are shown in table 1. In table 1, column (1) gives the name of the Fermi source, column (2) other name, column (3) core radio luminosity, log L core in units of erg s 1, column (4) extended luminosity, log L ext in units of erg s 1, column (5) total radio luminosity log L tot in units of erg s 1, column (6) core-dominance parameter, log R = log (L core /L ext ), column (7) redshift, column (8) type of the sources, column (9) γ -ray photon flux in units of photons cm 2 s 1, column (10) photon spectral index, column (11) γ -ray luminosity in units of erg s Calculation and results Luminosity can be calculated by νl ν = 4πd 2 L ν f ν, (1) here d L is the luminosity distance, which, when the -CDM model is adopted, can be expressed, d L = c H 0 1+z 1 1 M x M dx, (2) here 0.7, M 0.3, f ν is the flux density, at frequency ν.

3 Publications of the Astronomical Society of Japan, (2014), Vol. 66, No Table 1. The radio and γ -ray data for the whole sample. Fermi name Other name log Lc log Le log Lt log R z Class Flux α log Lγ AO LBL (187 ± 5.1) e PKS LBL (371 ± 6.8) e PKS LBL (51.6 ± 2.8) e OJ LBL (12.6 ± 1.6) e PKS LBL (50 ± 2.8) e C LBL (51.2 ± 3) e B LBL (13 ± 1.6) e OQ LBL (7.7 ± 1.2) e C LBL (5.2 ± 1.3) e PKS LBL (22.3 ± 2.1) e S LBL (44.5 ± 2.3) e C LBL (26.3 ± 2) e S LBL (10.8 ± 1.5) e PKS LBL (9.5 ± 1.5) e B A LBL (50.8 ± 2.8) e PKS LBL (16.2 ± 1.8) e PKS LBL (18.6 ± 2) e B LBL (4.3 ± 1.1) e OT LBL (45.6 ± 3.1) e PKS IBL (38.5 ± 2.5) e S IBL (71.3 ± 3.2) e S IBL (8.3 ± 1.4) e PKS IBL (20.5 ± 2) e OJ IBL (35.5 ± 2.4) e S IBL (13.6 ± 1.5) e W Comae IBL (55.4 ± 2.9) e S IBL (21.4 ± 1.7) e C IBL (38.3 ± 2.2) e BL Lacertae IBL (105 ± 3.9) e C 66A IBL (256 ± 6.1) e S IBL (183 ± 4.3) e PKS HBL (67.3 ± 3.2) e ES HBL (6.9 ± 1.4) e MS HBL (6.3 ± 1.1) e H HBL (78 ± 3.3) e Mkn HBL (297 ± 6.1) e Mkn HBL (11.5 ± 1.3) e ES HBL (54.9 ± 3) e MS HBL (6.3 ± 1.2) e MS HBL (5.1 ± 1.3) e MS HBL (18.9 ± 1.9) e Mkn HBL (87.7 ± 3.5) e I Zw HBL (8.1 ± 1.3) e PKS HBL (235 ± 5.7) e PKS HBL (21.7 ± 2.2) e S FSRQ (9.6 ± 1.4) e C FSRQ (63.5 ± 3) e S FSRQ (8.6 ± 1.5) e OC FSRQ (72 ± 3.2) e PKS FSRQ (10.5 ± 1.4) e PKS FSRQ (20.6 ± 1.8) e S FSRQ (7.3 ± 1.5) e PKS FSRQ (56.6 ± 2.9) e B FSRQ (14 ± 1.6) e

4 117-4 Publications of the Astronomical Society of Japan, (2014), Vol. 66, No. 6 Table 1. (Continued.) Fermi name Other name log Lc log Le loglt log R z Class Flux α log Lγ NRAO FSRQ (10.9 ± 2.1) e PKS FSRQ (66.5 ± 3.2) e S FSRQ (9.1 ± 1.5) e PKS FSRQ (25.7 ± 2.9) e PKS FSRQ (17.8 ± 2.2) e PKS FSRQ (17.3 ± 1.8) e B FSRQ (34.5 ± 2.3) e TXS FSRQ (6.5 ± 1.2) e PKS FSRQ (25.4 ± 2.3) e OI FSRQ (14.8 ± 1.7) e TXS FSRQ (9.8 ± 1.2) e C FSRQ (4.1 ± 1.1) e S FSRQ (4.3 ± 1.1) e PKS FSRQ (32.1 ± 2.5) e S FSRQ (91 ± 3.4) e OK FSRQ (12.6 ± 1.6) e C FSRQ (112 ± 3.8) e C FSRQ (4.6 ± 1.2) e B B FSRQ (2.29 ± 0.85) e S FSRQ (11.3 ± 1.4) e C FSRQ (5.7 ± 1.1) e S FSRQ (42.3 ± 2.2) e S FSRQ (24.2 ± 1.8) e S FSRQ (5.9 ± 1) e S FSRQ (8.3 ± 1.2) e PKS FSRQ (18 ± 1.7) e Ton FSRQ (60.4 ± 2.9) e PKS FSRQ (3.9 ± 1.1) e C FSRQ (354 ± 6.4) e C FSRQ (256 ± 5.7) e OP FSRQ (53 ± 2.7) e S FSRQ (3.33 ± 0.93) e S FSRQ (3.69 ± 0.93) e PKS FSRQ (5.1 ± 1.3) e B FSRQ (4.5 ± 1) e B FSRQ (5.4 ± 1.1) e PKS FSRQ (401 ± 7.3) e PKS FSRQ (22.3 ± 2.4) e PKS FSRQ (406 ± 7.2) e PKS FSRQ (18.2 ± 2) e PKS FSRQ (24 ± 2.6) e C FSRQ (116 ± 3.8) e NRAO FSRQ (38.3 ± 3) e C FSRQ (33.9 ± 2.9) e TXS FSRQ (38 ± 2.1) e S FSRQ (12.4 ± 1.6) e S FSRQ (20.6 ± 1.9) e S FSRQ (15.5 ± 1.6) e PKS FSRQ (12.7 ± 1.9) e PKS FSRQ (31.3 ± 3.2) e S FSRQ (12.1 ± 1.5) e C FSRQ (25.3 ± 1.9) e S FSRQ (73.6 ± 2.9) e S FSRQ (28.6 ± 2.1) e

5 Publications of the Astronomical Society of Japan, (2014), Vol. 66, No Table 1. (Continued.) Fermi name Other name log Lc log Le log Lt log R z Class Flux α log Lγ PKS B FSRQ (30.3 ± 2.5) e PKS FSRQ (15.4 ± 1.9) e PKS FSRQ (4.3 ± 1.2) e PKS FSRQ (65.3 ± 3.2) e C FSRQ (22.3 ± 2.1) e CTA FSRQ (28.8 ± 2.2) e C FSRQ (965 ± 10) e PKS FSRQ (28.7 ± 2.2) e PKS FSRQ (17.3 ± 1.8) e PKS FSRQ (15.6 ± 1.9) e C FSRQ (37.7 ± 2.5) e PKS FSRQ (13.5 ± 1.7) e S FSRQ (11.2 ± 1.4) e C FSRQ (7.22 ± 9.9) e C FSRQ (151 ± 4.5) e OS FSRQ (4.9 ± 1.1) e Table 2. Averaged radio luminosity and core-dominance parameter values for the whole sample and subclasses. Type L core (erg s 1 ) L ext (erg s 1 ) L tot (erg s 1 ) logr ALL ± ± ± ± 0.85 FSRQ ± ± ± ± 0.72 BL ± ± ± ± 0.97 LBL ± ± ± ± 0.97 IBL ± ± ± ± 1.07 HBL ± ± ± ± Radio luminosity For the radio data, as done in our previous work (Fan et al. 2011), we converted the radio emissions to 5 GHz (6 cm) if the data in the literature are not at 5 GHz. In the transforming process, we adopted α core = 0, and α ext = 0.75, then we K-corrected the radio flux densities at 5 GHz, finally we calculated the corresponding luminosity (L core, L ext,andl tot ) and core-dominance parameter, R, which can be expressed as R = S core /S ext (= L core /L ext ). The corresponding calculations are listed in table 1. For the radio luminosity, we could get averaged values, log L tot =43.95 ± 1.23 erg s 1, log L core = ± 1.12 erg s 1, and log L ext =42.62 ± 1.41 erg s 1 for the whole sample. Considering the subclasses separately, we can also get their averaged values and show them in table 2, inwhich, column (1) stands for the type, column (2) for core radio luminosity log L core, column (3) for extended radio luminosity log L ext, column (4) for total radio luminosity log L tot, and column (5) for core-dominance parameter log R γ -ray luminosity For the γ -rays, we can calculate their luminosities from γ -ray photons as done in Fan et al. (2013b). The γ -ray luminosity can be expressed as L γ = 4πd 2 L (1 + z)(α ph 2) f, (3) here α ph is the photon spectral index, f is the flux expressed as E U E L f = N (EL E U) ln E U if α ph = 2, (4) E U E L E L otherwise f = N (EL E U) 1 α ph ( E 2 α ph U 2 α ph ( E 1 α ph U ) E 2 α ph L E 1 α ph L ). (5) The flux is in units of GeV cm 2 s 1,andN EL E U stands for the integral photons with units of photons, cm 2 s 1,inthe energy range from E L to E U (in this paper, E L stands for 1 GeV and E U for 100 GeV).

6 117-6 Publications of the Astronomical Society of Japan, (2014), Vol. 66, No. 6 The γ -ray luminosity, L γ, is calculated for the whole sample and shown in Column (12) of table 1. For the whole sample, we have log L γ = ± 1.02 erg s 1. The averaged values for the subclasses respectively are log L γ = ± 0.83 erg s 1 for FSRQs, log L γ = ± 0.92 erg s 1 for LBLs, log L γ = ± 0.92 erg s 1 for IBLs, and log L γ =45.22 ± 0.95 erg s 1 HBLs. In order to study the correlation between γ -ray luminosity and radio luminosity, we can use the Pearsons correlation, y = ax + b (Press 2007; Pavlidou et al. 2012): r = (xi x)(y i y) (xi x) 2 (yi y) 2 (6) Here, x is the mean value of x i, y is the mean value of y i. The results are shown in table 3, in which column (1) gives the considered sample, column (2) the correlation, column (3) the parameter a, column (4) 1 σ uncertainty of a, column (5) the parameters b, column (6) 1 σ uncertainty of b, column (7) the correlation coefficient, column (8) the number of sources, and column (9) the chance probability. We applied the linear correlation regression to the whole sample and subclasses, we found that the γ -ray luminosity is correlated with the total, core, and extended radio luminosity, the corresponding results are shown in figure 1 and table 3. Table 3. Linear fitting results y = (a ± a)x + b ± b and correlation coefficient. Type Correlation a a b b r r γ N p ALL log L tot vs log L γ < 10 4 log L core vs log L γ < 10 4 log L ext vs log L γ < 10 4 FSRQ log L tot vs log L γ < 10 4 log L core vs log L γ < 10 4 log L ext vs log L γ < 10 4 log R vs log L γ % log(r+1) vs log(l γ /L ext ) < 10 4 BL log L tot vs log L γ < 10 4 log L core vs log L γ < 10 4 log L ext vs log L γ < 10 4 LBL log L tot vs log L γ < 10 4 log L core vs log L γ < 10 4 log L ext vs log L γ < 10 3 log R vs log L γ % log(r+1) vs log(l γ /L ext ) < 10 4 IBL log L tot vs log L γ < 10 3 log L core vs log L γ < 10 3 log L ext vs log L γ < 10 3 log R vs log L γ % log(r+1) vs log(l γ /L ext ) < 10 3 HBL log L tot vs log L γ < 10 4 log L core vs log L γ < 10 4 log L ext vs log L γ < 10 3 log R vs log L γ % log(r+1) vs log(l γ /L ext ) < 10 3 F+L logl tot vs log L γ < 10 4 log L core vs log L γ < 10 4 log L ext vs log L γ < 10 4 log R vs log L γ % log(r+1) vs log(l γ /L ext ) < 10 4

7 Publications of the Astronomical Society of Japan, (2014), Vol. 66, No Fig. 1. Plots for γ -ray luminosity, log L γ vs radio luminosity log L radio. Left-hand panel: γ luminosity, log L γ vs core radio luminosity, log L core, center panel: γ luminosity, log L γ vs extended radio luminosity, log L ext, right-hand panel: γ luminosity, log L γ vs total radio luminosity, log L tot. Filled triangles stand for LBLs, open triangles for IBLs, filled points for HBLs, and circles for FSRQs. The straight lines stand for best linear fitting results. Fig. 2. Histogram (upper) and cumulative distribution (lower) of the luminosity. The left-hand panel is for the radio luminosity, solid line stands for FSRQs, dashed line for HBLs, dotted line for IBLs, and dash-dot line for LBLs. The right-hand panel is for the γ -ray luminosity, the lines stand for the same subclasses as in the left panel. 3 Discussion and conclusion For the calculated radio and γ -ray luminosities, we used a Kolmogorov Smirnov (K S) test to study the differences in radio and γ -ray luminosities between different subclasses, the histograms and cumulative distributions being shown in figure 2. We found that the averaged value of one subclass is different from that of others. For radio luminosity, there is a tendency for the averaged values, log L FSRQs > log L LBLs > log L IBLs > log L HBLs for total, core, and extended radio luminosities. The probabilities for the total radio luminosity distributions of any two subclasses (FSRQs and LBLs, FSRQS and HBLs, and LBLS and HBLs) to be from the same distribution are p FSRQs LBLs = 1.9%, p FSRQs HBLs = , and p LBLs HBLs = respectively, see the left-hand panel of figure 2. For γ -ray luminosity, we have the averaged values, log L γ = ± 0.83 erg s 1 for FSRQs, log L γ = ± 0.92 erg s 1 for LBLs, log L γ = ± 0.92 erg s 1 for IBLs, and log L γ = ± 0.95 erg s 1 for HBLs, which suggests a tendency for the averaged values being similar to radio luminosity: log L γ FSRQs > log L γ LBLs > log L γ IBLs > log L γ HBLs. The probabilities for the γ -ray luminosity distributions of any two subclasses (FSRQs and LBLs, FSRQS and HBLs, and LBLS and HBLs) to be from the

8 117-8 Publications of the Astronomical Society of Japan, (2014), Vol. 66, No. 6 Fig. 3. Histogram (left-hand panel) and cumulative distribution (right-hand panel) of the core-dominance parameter, log R. Solid line stands for FSRQs, dashed line for HBLs, dotted line for IBLs, and dash-dot line for LBLs. same distribution are p FSRQs LBLs = 3.9%, p FSRQs HBLs = , and p LBLs HBLs = 2.9% respectively, see the right-hand panel of figure 2. For the core-dominance parameter, we have log R LBLs > log R IBLs > log R HBLs log R FSRQs. K S tests show that the probability for any two to be from the same distributions are p FSRQs LBLs = , p FSRQs HBLs = 91.9%, and p LBLs HBLs 10 3 respectively, see figure 3. We can see that there is no difference in core-dominance parameter distributions between FSRQs and HBLs. In addition, the tendency for log R is different from those in luminosities. From our analysis, there is correlation between γ -ray luminosity and radio luminosity (core, extended, and total luminosity) for the whole sample, subclasses (FSRQs and BLs), and the subclasses of BLs. From figure 1, we can also find that the HBLs deviate from other subclasses, it shows that for the same core or total radio luminosity, the γ -ray luminosities in HBLs are higher than those in FSRQs and LBLs, but for the same extended radio luminosity, the γ -ray luminosities in HBLs are lower than those in FSRQs and LBLs. Does that mean that the γ -ray emission mechanism in HBLs is different from those in the FSRQs and LBLs? 3.1 Correlation between γ and radio luminosities The luminosity calculation suggests that there is an apparent mutual-band luminosity correlation since the luminosity depends on the luminosity distance (or redshift). To investigate a real correlation, one has to exclude the effect of luminosity distance (redshift) on the luminosity. To exclude the redshift effect from γ -ray and radio luminosities, we can use the method of Padovani (1992), r Rγ,z = r Rγ r Rz r γ z (1 r 2Rz )(1 r 2γ z ) (7) where r Rγ stands for the correlation coefficient between variables L R and L γ, r Rz for the correlation coefficient between variables L R and redshift, z, r γ z for the correlation coefficient between variables L γ and z, r Rγ, z stands for the correlation coefficient between variables L R and L γ with the redshift effect excluded. When the expression (7) was applied to the correlations between the γ -ray and radio luminosities, the correlation between luminosity and redshift, we obtained the correlation coefficients after removing the effect of redshift and listed them in table 4, in which, column (1) gives the considered sample, column (2) correlations, column (3) correlation coefficient between L radio and L γ without removing the redshift effect, column (4) correlation coefficient between L radio and redshift z, column (5) correlation coefficient between L γ and redshift z, column (6) correlation coefficient after removing the redshift effect, column (7) number of considered sample, and column (8) chance probability for the two distribution to come from the same distribution. We can say that after the redshift effect is excluded, there is still a correlation between γ -ray and radio luminosities for the whole sample and BLs subclasses, there is a marginal correlation for FSRQs. For the subclasses of BL Lacertae objects, we found that the correlation is very strong for HBLs with r Rγ, z = for log L core and log L γ and r Rγ, z = for log L tot and log L γ. The correlation between γ and radio bands perhaps suggests that there

9 Publications of the Astronomical Society of Japan, (2014), Vol. 66, No Table 4. Correlation coefficients. Type Correlation r r γ r r z r γ z r core N p ALL log L tot vs log L γ % log L core vs log L γ % log L ext vs log L γ % FSRQ log L tot vs log L γ % log L core vs log L γ % log L ext vs log L γ % BL log L tot vs log L γ % log L core vs log L γ % log L ext vs log L γ % LBL log L tot vs log L γ % log L core vs log L γ % log L ext vs log L γ % IBL log L tot vs log L γ % log L core vs log L γ % log L ext vs log L γ % HBL log L tot vs log L γ % log L core vs log L γ % log L ext vs log L γ % F+L logl tot vs log L γ % log L core vs log L γ % log L ext vs log L γ % is some association between the two bands, for instance the two bands are strongly beamed and an SSC emission mechanism is responsible for the emissions from radio to γ -rays. log L γ = (0.503 ± 0.938) log R + (45.59 ± 0.89) with r = 0.32 and p = 15.9% for HBLs; log L γ = (0.161 ± 0.211) log R + (46.82 ± 0.27) with r = and p = 8.96% for LBLs + FSRQs. 3.2 Luminosity and core-dominance parameter von Montigny et al. (1995) found that most EGRET γ -ray sources show superluminal motion. Radio emissions in blazars are strongly beamed, the correlated γ -ray and radio emissions reveal that γ -ray emissions are strongly beamed. The core-dominance parameter, R = L core /L ext, to some extend, is a proxy for the beaming effect. Therefore, one can expect that there should be a positive correlation between the γ -ray and the coredominance parameter, log R. However, when the relevant data in table 1 are taken into account for the 124 sources, we obtain: log L γ = (0.633 ± 0.26) log R + (46.83 ± 0.29) with r = and p = 24.3% for FSRQs; log L γ = (0.032 ± 0.586) log R + (46.23 ± 1.01) with r = and p = 27.1% for LBLs; log L γ = (0.38 ± 0.544) log R + (46.43 ± 0.97) with r = and p = 11.4% for IBLs; It is clear that there is no expected positive correlation between γ -ray luminosity and core-dominance parameter. The results are shown in the left-hand panel in figure 4 and in table 3. However, when we used the ratio of γ -ray luminosity to the extended radio luminosity to investigate the correlation with the core-dominance parameter, we found that there are clear correlations for the whole sample and the subclasses: log (L γ /L ext ) = (0.946 ± 0.158) log (1 + R) + (2.74 ± 0.212) with r = and p < 10 4 for the whole sample; log (L γ /L ext ) = (0.914 ± 0.24) log (1 + R) + (2.59 ± 0.21) with r = and p < 10 4 for FSRQs; log (L γ /L ext ) = (1.101 ± 0.227) log (1 + R) + (2.427 ± 0.442) with r = and p < 10 4 for LBLs; log (L γ /L ext ) = (0.847 ± 0.346) log (1 + R) + (3.06 ± 0.625) with r = and p = 0.11% for IBLs;

10 Publications of the Astronomical Society of Japan, (2014), Vol. 66, No. 6 Fig. 4. Left-hand graph for γ -ray luminosity, log L γ against core dominate parameters, log R. Right-hand graph for the ratio of γ -ray luminosity, log L γ to the extended radio luminosity, log(l γ /L ext ) against log (1+R). Filled triangles stand for LBLs, open triangles for IBLs, filled points for HBLs, and circles for FSRQs. The straight lines stand for best linear fitting results. log (L γ /L ext ) = (1.05 ± 0.515) log (1 + R) + (3.572 ± 0.505) with r = and p = 0.21% for HBLs; log (L γ /L ext ) = (0.605 ± 0.098) log (1 + R) (1.09 ± 0.269) with r = and p < 10 4 for LBLs + FSRQs. The results are also shown in the right-hand panel in figure 4 and in table 3. In the radio bands, the emissions are composed of two components, L = L core + L ext = (1 + R)L ext. Our statistical results give L γ /L ext (1 + R). Does that mean that γ -ray luminosity consists of two components as do the radio bands? From the right-hand panel in figure 4, we can also see that HBLs deviate from the rest subclasses. 3.3 Conclusions In this work, we compiled a sample of 124 Fermi blazars with available core and extended radio emissions. From the analysis on the sample, we can come to the following conclusions: (1) There is a correlation between the γ -ray luminosity and radio luminosity; it suggests that the γ -ray emissions in Fermi blazars may be strongly beamed or that the SSC model is responsible for γ -ray emissions. (2) There is a close correlation between the ratio of γ -ray to the extended radio luminosity and the core-dominance parameter. (3) There is a sequence FSRQSs LBLs IBLs HBLs for radio and γ -ray luminosities. Acknowledgments This work is partially supported by the National Natural Science Foundation of China (NSFC , NSFC , U ), Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (GDUPS)(2009), Yangcheng Scholar Funded Scheme (10A027S), and supports for Astrophysics Key Subject of both Guangdong province and Guangzhou City. Thanks are given to the anonymous referee for their useful comments and suggestions. References Abdo, A. A., et al. 2010, ApJS, 188, 405 Ackermann, M., et al. 2011, ApJ, 743, 171 Cheng, K. S., Fan, J. H., & Zhang, L. 1999, A&A, 352, 32 Comastri, A., Fossati, G., Ghisellini, G., & Molendi, S. 1997, ApJ, 480, 534 Dondi, L., & Ghisellini, G. 1995, MNRAS, 273, 583 Fan, J. H. 2000, A&A, 358, 841 Fan, J. H., Adam, G., Xie, G. Z., Cao, S. L., Lin, R. G., & Copin, Y. 1998, A&A, 338, 27 Fan, J. H., Bastieri, D., Yang, J. H., Liu, Y., Hua, T.-X., Yuan, Y.-H., & Wu, D.-X. 2014, Res. Astron. Astrophys., 14, 1135 Fan,J.H.,Huang,Y.,He,T.M.,Yang,J.H.,Hua,T.X.,Liu,Y., & Wang, Y. X. 2009, PASJ, 61, 639 Fan, J. H., Liu, Y., Li, Y., Zhang, Q. F., Tao, J., & Kurtanidze, O. 2011, J. Astrophys. Astron., 32, 67 Fan, J. H., Yang, J. H., Liu, Y., & Zhang, J. Y. 2013a, Res. Astron. Astrophys., 13, 259 Fan, J. H., Yang, J. H., Tao, J., Huang, Y., & Liu, Y. 2010, PASJ, 62, 211 Fan, J. H., Yang, J. H., Yuan, Y. H., Wang, J., & Gao, Y. 2012, ApJ, 761, 125 Fan, J. H., Yang, J. H., Zhang, J. Y., Hua, T. X., Liu, Y., Qin, Y.-P., & Huang, Y. 2013b, PASJ, 65, 25

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