Correlation between γ -ray and radio emissions in Fermi blazars

Publ. Astron. Soc. Japan (2014) 66 (6), 117 (1 11) doi: 10.1093/pasj/psu111 Advance Access Publication Date: 2014 December 11 117-1 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 510006, 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 415000, China *E-mail: 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 (0.1 100 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 2014. Published by Oxford University Press on behalf of the Astronomical Society of Japan. All rights reserved. For Permissions, please email: journals.permissions@oup.com

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 454.3 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 1. 2.2 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 3 + 1 M dx, (2) here 0.7, M 0.3, f ν is the flux density, at frequency ν.

Publications of the Astronomical Society of Japan, (2014), Vol. 66, No. 6 117-3 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 0238.7+1637 AO 0235+164 44.35 42.19 44.64 2.17 0.940 LBL (187 ± 5.1) e-10 2.023 47.78 0538.8 4405 PKS 0537 441 44.90 42.60 45.18 2.30 0.892 LBL (371 ± 6.8) e-10 2.012 48.03 0738.0+1742 PKS 0735+17 43.64 40.33 43.79 3.31 0.424 LBL (51.6 ± 2.8) e-10 2.047 46.37 0811.4+0149 OJ 014 43.83 42.14 44.17 1.69 1.148 LBL (12.6 ± 1.6) e-10 2.262 46.78 0831.9+0429 PKS 0829+046 42.33 41.02 42.42 1.31 0.174 LBL (50 ± 2.8) e-10 2.047 45.46 1058.4+0133 4C +01.28 44.42 44.32 44.87 0.10 0.888 LBL (51.2 ± 3) e-10 2.217 47.11 1150.1+2419 B2 1147+24 42.47 40.72 42.56 1.76 0.200 LBL (13 ± 1.6) e-10 2.192 44.95 1420.2+5422 OQ 530 42.43 40.32 42.50 2.12 0.153 LBL (7.7 ± 1.2) e-10 2.366 44.38 1540.4+1438 4C +14.60 43.78 42.59 44.00 1.19 0.605 LBL (5.2 ± 1.3) e-10 2.284 45.67 1719.3+1744 PKS 1717+177 42.13 40.00 42.19 2.13 0.137 LBL (22.3 ± 2.1) e-10 1.842 44.99 1800.5+7829 S5 1803+784 43.98 43.70 44.34 0.28 0.680 LBL (44.5 ± 2.3) e-10 2.231 46.75 1824.0+5650 4C +56.27 43.92 43.20 44.20 0.72 0.664 LBL (26.3 ± 2) e-10 2.434 46.45 2004.5+7754 S5 2007+77 43.21 41.94 43.36 1.27 0.342 LBL (10.8 ± 1.5) e-10 2.217 45.39 2133.8 0154 PKS 2131 021 44.30 42.30 44.66 2.00 1.284 LBL (9.5 ± 1.5) e-10 2.317 46.79 2236.4+2828 B2 2234+28A 44.70 42.30 44.95 2.40 0.795 LBL (50.8 ± 2.8) e-10 2.054 47.03 2243.2 2540 PKS 2240 260 43.62 42.90 43.92 0.72 0.774 LBL (16.2 ± 1.8) e-10 2.3 46.44 0424.7+0034 PKS 0422+00 43.21 40.12 43.33 3.09 0.310 LBL (18.6 ± 2) e-10 2.301 45.50 1209.6+4121 B3 1206+416 42.82 42.40 43.07 0.42 0.377 LBL (4.3 ± 1.1) e-10 1.577 45.41 1751.5+0938 OT 081 42.95 39.82 43.07 3.13 0.322 LBL (45.6 ± 3.1) e-10 2.101 46.00 0050.6 0929 PKS 0048 09 43.64 42.44 43.87 1.20 0.635 IBL (38.5 ± 2.5) e-10 2.14 46.63 0112.1+2245 S2 0109+22 42.42 40.49 42.52 1.93 0.265 IBL (71.3 ± 3.2) e-10 2.066 46.01 0710.8+4733 S4 0707+47 44.00 43.96 44.53 0.04 1.292 IBL (8.3 ± 1.4) e-10 2.486 46.73 0757.1+0957 PKS 0754+100 42.94 41.48 43.06 1.46 0.266 IBL (20.5 ± 2) e-10 2.192 45.43 0854.8+2005 OJ 287 43.38 39.98 43.50 3.40 0.306 IBL (35.5 ± 2.4) e-10 2.232 45.79 0958.6+6533 S4 0954+65 43.00 40.95 43.14 2.05 0.368 IBL (13.6 ± 1.5) e-10 2.415 45.51 1221.4+2814 W Comae 42.35 39.48 42.39 2.86 0.103 IBL (55.4 ± 2.9) e-10 2.019 45.02 1748.8+7006 S4 1749+70 44.11 43.05 44.38 1.06 0.770 IBL (21.4 ± 1.7) e-10 2.04 46.62 1806.7+6948 3C 371 41.61 41.08 41.74 0.53 0.051 IBL (38.3 ± 2.2) e-10 2.189 44.12 2202.8+4216 BL Lacertae 42.20 39.91 42.23 2.29 0.069 IBL (105 ± 3.9) e-10 2.107 44.86 0222.6+4302 3C 66A 43.28 43.12 43.62 0.16 0.444 IBL (256 ± 6.1) e-10 1.847 47.20 0721.9+7120 S5 0716+71 42.86 42.28 43.06 0.58 0.300 IBL (183 ± 4.3) e-10 2.007 46.58 0303.4 2407 PKS 0301 243 42.24 42.08 42.54 0.16 0.260 HBL (67.3 ± 3.2) e-10 1.938 46.03 0416.8+0105 1ES 0414+009 41.40 41.48 41.81 0.08 0.287 HBL (6.9 ± 1.4) e-10 1.981 45.12 0745.0+7436 MS 0737.9+7441 41.45 39.79 41.57 1.66 0.315 HBL (6.3 ± 1.1) e-10 1.799 45.27 1015.1+4925 1H 1013+498 41.61 41.29 41.84 0.32 0.212 HBL (78 ± 3.3) e-10 1.723 46.02 1104.4+3812 Mkn 421 40.71 39.87 40.78 0.84 0.031 HBL (297 ± 6.1) e-10 1.771 44.81 1136.7+7009 Mkn 180 40.45 40.33 40.71 0.12 0.046 HBL (11.5 ± 1.3) e-10 1.74 43.76 1217.8+3006 1ES 1215+303 41.82 41.19 41.96 0.63 0.130 HBL (54.9 ± 3) e-10 2.019 45.24 1224.4+2436 MS 1221.8+2452 41.17 39.62 41.27 1.56 0.218 HBL (6.3 ± 1.2) e-10 2.035 44.79 1405.1+0405 MS 1402.3+0416 41.47 40.92 41.69 0.55 0.344 HBL (5.1 ± 1.3) e-10 1.897 45.22 1501.0+2238 MS 1458.8+2249 41.26 39.95 41.37 1.31 0.235 HBL (18.9 ± 1.9) e-10 1.771 45.48 1653.9+3945 Mkn 501 41.21 39.51 41.23 1.69 0.034 HBL (87.7 ± 3.5) e-10 1.738 44.38 1728.2+5015 I Zw 187 40.75 39.83 40.82 0.92 0.055 HBL (8.1 ± 1.3) e-10 1.833 43.72 2158.8 3013 PKS 2155 304 41.69 41.15 41.84 0.54 0.116 HBL (235 ± 5.7) e-10 1.838 45.85 1312.4 2157 PKS 1309 216 43.58 43.38 44.10 0.20 1.491 HBL (21.7 ± 2.2) e-10 2.024 47.35 0006.1+3821 S4 0003+38 42.48 41.35 42.60 1.13 0.229 FSRQ (9.6 ± 1.4) e-10 2.604 44.81 0108.6+0135 4C +01.02 44.96 44.25 45.49 0.71 2.099 FSRQ (63.5 ± 3) e-10 2.262 48.18 0113.7+4948 S4 0110+49 42.99 42.01 43.17 0.98 0.395 FSRQ (8.6 ± 1.5) e-10 2.261 45.42 0136.9+4751 OC 457 44.03 43.12 44.33 0.91 0.859 FSRQ (72 ± 3.2) e-10 2.148 47.24 0137.6 2430 PKS 0135 247 43.83 43.17 44.15 0.66 0.838 FSRQ (10.5 ± 1.4) e-10 2.423 46.32 0145.1 2732 PKS 0142 278 44.06 43.62 44.47 0.43 1.155 FSRQ (20.6 ± 1.8) e-10 2.584 46.99 0217.7+7353 S5 0212+73 44.98 45.12 45.70 0.15 2.367 FSRQ (7.3 ± 1.5) e-10 2.824 47.48 0217.9+0143 PKS 0215+015 44.27 43.39 44.73 0.88 1.721 FSRQ (56.6 ± 2.9) e-10 2.152 47.91 0230.8+4031 B3 0227+403 43.76 41.42 44.07 2.34 1.019 FSRQ (14 ± 1.6) e-10 2.629 46.67

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 0337.0+3200 NRAO 140 44.61 44.26 45.06 0.36 1.259 FSRQ (10.9 ± 2.1) e-10 2.593 46.82 0423.2 0120 PKS 0420 01 44.21 42.27 44.50 1.94 0.916 FSRQ (66.5 ± 3.2) e-10 2.298 47.24 0501.2 0155 S3 0458 02 45.50 44.80 46.05 0.70 2.291 FSRQ (9.1 ± 1.5) e-10 2.517 47.46 0530.8+1333 PKS 0528+134 44.67 45.32 45.62 0.65 2.070 FSRQ (25.7 ± 2.9) e-10 2.218 47.77 0608.0 0836 PKS 0605 08 44.07 44.00 44.53 0.07 0.872 FSRQ (17.8 ± 2.2) e-10 2.358 46.61 0635.5 7516 PKS 0637 75 44.35 44.16 44.73 0.20 0.653 FSRQ (17.3 ± 1.8) e-10 2.648 46.22 0654.2+4514 B3 0650+453 43.55 43.22 43.94 0.33 0.933 FSRQ (34.5 ± 2.3) e-10 2.278 46.98 0733.9+5023 TXS 0730+504 43.74 42.55 43.99 1.19 0.720 FSRQ (6.5 ± 1.2) e-10 2.355 45.95 0739.2+0138 PKS 0736+01 42.90 40.74 42.98 2.17 0.189 FSRQ (25.4 ± 2.3) e-10 2.229 45.17 0750.6+1230 OI 280 43.91 42.60 44.20 1.31 0.889 FSRQ (14.8 ± 1.7) e-10 2.424 46.54 0805.5+6145 TXS 0800+618 44.92 44.48 45.58 0.44 3.033 FSRQ (9.8 ± 1.2) e-10 2.744 47.91 0824.7+3914 4C +39.23 44.36 43.22 44.72 1.14 1.216 FSRQ (4.1 ± 1.1) e-10 2.639 46.35 0903.4+4651 S4 0859+47 44.61 43.80 45.03 0.81 1.470 FSRQ (4.3 ± 1.1) e-10 2.27 46.60 0909.1+0121 PKS 0906+01 44.60 42.80 44.91 1.80 1.026 FSRQ (32.1 ± 2.5) e-10 2.577 47.03 0920.9+4441 S4 0917+44 44.70 44.19 45.26 0.51 2.189 FSRQ (91 ± 3.4) e-10 2.109 48.39 0956.9+2516 OK 290 44.20 42.10 44.43 2.10 0.708 FSRQ (12.6 ± 1.6) e-10 2.394 46.21 0957.7+5522 4C +55.17 44.27 43.57 44.60 0.70 0.899 FSRQ (112 ± 3.8) e-10 1.831 47.57 1014.1+2306 4C +23.24 43.45 42.87 43.72 0.58 0.566 FSRQ (4.6 ± 1.2) e-10 2.536 45.50 1017.0+3531 B2 1015+35B 44.07 43.60 44.49 0.47 1.228 FSRQ (2.29 ± 0.85) e-10 2.895 46.13 1033.2+4117 S4 1030+41 43.80 43.59 44.27 0.21 1.170 FSRQ (11.3 ± 1.4) e-10 2.444 46.69 1023.6+3947 4C +40.25 44.12 43.84 44.58 0.28 1.254 FSRQ (5.7 ± 1.1) e-10 2.438 46.53 1033.9+6050 S4 1030+61 43.90 44.06 44.52 0.15 1.401 FSRQ (42.3 ± 2.2) e-10 2.242 47.54 1048.3+7144 S5 1044+71 44.11 44.68 44.93 0.56 1.150 FSRQ (24.2 ± 1.8) e-10 2.342 47.06 1057.1+7001 S5 1053+70 44.48 44.08 45.09 0.41 2.492 FSRQ (5.9 ± 1) e-10 2.641 47.41 1059.4+8113 S5 1053+81 43.38 43.32 43.81 0.06 0.706 FSRQ (8.3 ± 1.2) e-10 2.579 46.00 1130.3 1448 PKS 1127 14 45.20 43.50 45.54 1.70 1.184 FSRQ (18 ± 1.7) e-10 2.697 46.96 1159.5+2914 Ton 599 43.93 43.03 44.20 0.90 0.725 FSRQ (60.4 ± 2.9) e-10 2.295 46.94 1219.7+0201 PKS 1217+02 42.37 42.06 42.61 0.31 0.241 FSRQ (3.9 ± 1.1) e-10 2.663 44.46 1224.9+2122 4C +21.35 43.18 42.76 43.44 0.41 0.434 FSRQ (354 ± 6.4) e-10 2.122 47.19 1256.1 0547 3C 279 44.52 43.80 44.76 0.72 0.536 FSRQ (256 ± 5.7) e-10 2.221 47.25 1310.6+3222 OP 313 44.30 42.66 44.61 1.64 0.997 FSRQ (53 ± 2.7) e-10 2.105 47.28 1317.9+3426 S4 1315+34 43.46 42.89 43.83 0.57 1.055 FSRQ (3.33 ± 0.93) e-10 2.379 46.10 1322.6+8313 S5 1322+83 43.64 43.57 44.13 0.07 1.024 FSRQ (3.69 ± 0.93) e-10 2.587 46.09 1405.1+0405 PKS 1402+044 45.30 45.00 45.99 0.30 3.215 FSRQ (5.1 ± 1.3) e-10 1.897 47.55 1419.4+3820 B3 1417+385 44.46 44.12 44.99 0.34 1.831 FSRQ (4.5 ± 1) e-10 2.65 46.90 1433.8+4205 B3 1432+422 43.69 43.53 44.18 0.15 1.240 FSRQ (5.4 ± 1.1) e-10 2.261 46.51 1504.3+1029 PKS 1502+106 44.00 42.20 44.46 1.80 1.839 FSRQ (401 ± 7.3) e-10 2.147 48.83 1510.9 0545 PKS 1508 05 43.58 44.61 44.76 1.03 1.185 FSRQ (22.3 ± 2.4) e-10 2.444 47.06 1512.8 0906 PKS 1510 08 43.80 42.46 43.95 1.35 0.360 FSRQ (406 ± 7.2) e-10 2.288 47.00 1549.5+0237 PKS 1546+027 43.45 42.07 43.61 1.37 0.414 FSRQ (18.2 ± 2) e-10 2.455 45.76 1626.1 2948 PKS 1622 29 43.88 42.79 44.16 1.09 0.815 FSRQ (24 ± 2.6) e-10 2.339 46.66 1635.2+3810 4C +38.41 45.30 43.40 45.75 1.90 1.813 FSRQ (116 ± 3.8) e-10 2.248 48.28 1640.7+3945 NRAO 512 44.40 44.20 44.94 0.19 1.660 FSRQ (38.3 ± 3) e-10 2.364 47.69 1642.9+3949 3C 345 44.52 43.39 44.75 1.14 0.593 FSRQ (33.9 ± 2.9) e-10 2.489 46.42 1700.2+6831 TXS 1700+685 42.44 42.34 42.77 0.09 0.301 FSRQ (38 ± 2.1) e-10 2.396 45.75 1714.8+6836 S4 1716+68 43.57 43.75 44.12 0.18 0.777 FSRQ (12.4 ± 1.6) e-10 1.948 46.42 1724.0+4003 S4 1722+40 43.67 43.65 44.17 0.02 1.049 FSRQ (20.6 ± 1.9) e-10 2.342 46.88 1727.1+4531 S4 1726+45 43.75 43.21 44.06 0.55 0.717 FSRQ (15.5 ± 1.6) e-10 2.575 46.29 1728.2+0429 PKS 1725+044 43.20 41.10 43.31 2.10 0.293 FSRQ (12.7 ± 1.9) e-10 2.535 45.22 1733.1 1307 PKS 1730 13 45.00 43.20 45.28 1.80 0.902 FSRQ (31.3 ± 3.2) e-10 2.239 46.91 1739.5+4955 S4 1738+49 44.14 43.33 44.58 0.81 1.545 FSRQ (12.1 ± 1.5) e-10 2.203 47.11 1740.2+5212 4C +51.37 44.60 42.90 44.98 1.70 1.379 FSRQ (25.3 ± 1.9) e-10 2.502 47.29 1849.4+6706 S4 1849+67 43.54 43.41 43.94 0.14 0.657 FSRQ (73.6 ± 2.9) e-10 2.092 46.97 1852.5+4856 S4 1851+48 43.70 43.50 44.18 0.20 1.250 FSRQ (28.6 ± 2.1) e-10 2.283 47.24

Publications of the Astronomical Society of Japan, (2014), Vol. 66, No. 6 117-5 Table 1. (Continued.) Fermi name Other name log Lc log Le log Lt log R z Class Flux α log Lγ 1924.8 2912 PKS B1921 293 44.40 43.60 44.58 0.80 0.352 FSRQ (30.3 ± 2.5) e-10 2.432 45.81 2035.4+1058 PKS 2032+107 43.53 42.01 43.75 1.53 0.601 FSRQ (15.4 ± 1.9) e-10 2.552 46.08 2146.5 1530 PKS 2143 156 43.80 43.10 44.08 0.70 0.698 FSRQ (4.3 ± 1.2) e-10 2.607 45.70 2203.4+1726 PKS 2201+171 44.30 43.30 44.64 1.00 1.076 FSRQ (65.3 ± 3.2) e-10 2.092 47.46 2225.6 0454 3C 446 45.40 43.90 45.79 1.50 1.404 FSRQ (22.3 ± 2.1) e-10 2.436 47.26 2232.4+1143 CTA 102 45.00 43.60 45.32 1.40 1.037 FSRQ (28.8 ± 2.2) e-10 2.327 47.02 2253.9+1609 3C 454.3 44.89 43.76 45.18 1.13 0.859 FSRQ (965 ± 10) e-10 2.226 48.34 2258.0 2759 PKS 2255 282 44.25 43.00 44.55 1.25 0.927 FSRQ (28.7 ± 2.2) e-10 2.257 46.90 2338.1 0229 PKS 2335 027 43.33 43.61 43.97 0.28 1.072 FSRQ (17.3 ± 1.8) e-10 2.442 46.82 2347.9 1629 PKS 2345 16 44.30 42.90 44.51 1.40 0.576 FSRQ (15.6 ± 1.9) e-10 2.356 46.08 0237.8+2846 4C +28.07 44.90 42.90 45.25 2.00 1.213 FSRQ (37.7 ± 2.5) e-10 2.158 47.34 0339.4 0144 PKS 0336 01 44.70 43.20 44.98 1.50 0.852 FSRQ (13.5 ± 1.7) e-10 2.475 46.44 0830.5+2407 S3 0827+24 44.90 43.40 45.20 1.50 0.942 FSRQ (11.2 ± 1.4) e-10 2.674 46.47 0841.6+7052 4C +71.07 45.27 44.00 45.78 1.27 2.172 FSRQ (7.22 ± 9.9) e-10 2.948 47.40 1229.1+0202 3C 273 43.91 43.26 44.05 0.66 0.158 FSRQ (151 ± 4.5) e-10 2.452 45.69 1613.4+3409 OS 319 45.10 43.70 45.49 1.40 1.400 FSRQ (4.9 ± 1.1) e-10 2.307 46.60 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 43.63 ± 1.12 42.62 ± 1.41 43.95 ± 1.23 1.01 ± 0.85 FSRQ 44.13 ± 0.69 43.31 ± 0.89 44.52 ± 0.76 0.83 ± 0.72 BL 42.75 ± 1.18 41.41 ± 1.35 42.95 ± 1.25 1.34 ± 0.97 LBL 43.53 ± 0.84 41.84 ± 1.33 43.75 ± 0.93 1.69 ± 0.97 IBL 42.98 ± 0.75 41.52 ± 1.44 43.17 ± 0.86 1.46 ± 1.07 HBL 41.49 ± 0.76 40.74 ± 1.11 41.67 ± 0.86 0.74 ± 0.60 2.2.1 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 = 43.63 ± 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. 2.2.2 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).

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 = 46.42 ± 1.02 erg s 1. The averaged values for the subclasses respectively are log L γ = 46.77 ± 0.83 erg s 1 for FSRQs, log L γ = 46.17 ± 0.92 erg s 1 for LBLs, log L γ = 45.88 ± 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 0.69 0.083 16.22 3.64 0.83 124 < 10 4 log L core vs log L γ 0.73 0.09 14.53 4.24 0.803 124 < 10 4 log L ext vs log L γ 0.53 0.088 23.95 3.75 0.73 124 < 10 4 FSRQ log L tot vs log L γ 0.77 0.17 12.45 7.64 0.71 79 < 10 4 log L core vs log L γ 0.77 0.21 12.59 9.16 0.65 79 < 10 4 log L ext vs log L γ 0.51 0.18 24.55 7.68 0.55 79 < 10 4 log R vs log L γ 0.063 0.26 46.83 0.29 0.0553 79 24.314% log(r+1) vs log(l γ /L ext ) 0.914 0.24 2.593 0.21 0.655 79 < 10 4 BL log L tot vs log L γ 0.70 0.13 15.73 5.58 0.856 45 < 10 4 log L core vs log L γ 0.73 0.15 14.72 6.26 0.837 45 < 10 4 log L ext vs log L γ 0.55 0.16 22.91 6.55 0.732 45 < 10 4 LBL log L tot vs log L γ 0.97 0.22 3.95 9.48 0.91 19 < 10 4 log L core vs log L γ 1.073 0.25 0.54 10.66 0.91 19 < 10 4 log L ext vs log L γ 0.44 0.30 27.57 12.74 0.6 19 < 10 3 log R vs log L γ 0.032 0.586 46.23 1.01 0.0318 19 27.067% log(r+1) vs log(l γ /L ext ) 1.101 0.227 2.427 0.442 0.928 19 < 10 4 IBL log L tot vs log L γ 0.89 0.41 7.63 18.21 0.83 12 < 10 3 log L core vs log L γ 0.99 0.50 3.38 21.71 0.83 12 < 10 3 log L ext vs log L γ 0.48 0.30 26.12 12.36 0.75 12 < 10 3 log R vs log L γ 0.38 0.544 46.43 0.97 0.442 12 11.432% log(r+1) vs log(l γ /L ext ) 0.847 0.346 3.06 0.625 0.865 12 < 10 3 HBL log L tot vs log L γ 1.01 0.29 3.89 12.84 0.9 14 < 10 4 log L core vs log L γ 1.13 0.32 1.645 13.64 0.91 14 < 10 4 log L ext vs log L γ 0.68 0.32 17.51 13.24 0.8 14 < 10 3 log R vs log L γ 0.503 0.938 45.59 0.89 0.32 14 15.891% log(r+1) vs log(l γ /L ext ) 1.05 0.515 3.572 0.505 0.788 14 < 10 3 F+L logl tot vs log L γ 0.81 0.13 10.51 5.86 0.781 98 < 10 4 log L core vs log L γ 0.86 0.16 8.59 7.1 0.736 98 < 10 4 log L ext vs log L γ 0.47 0.12 26.5 5.43 0.601 98 < 10 4 log R vs log L γ 0.161 0.211 46.82 0.27 0.153 98 8.958% log(r+1) vs log(l γ /L ext ) 0.605 0.098 1.094 0.269 0.78 98 < 10 4

Publications of the Astronomical Society of Japan, (2014), Vol. 66, No. 6 117-7 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 = 3.9 10 10, and p LBLs HBLs = 3.7 10 6 respectively, see the left-hand panel of figure 2. For γ -ray luminosity, we have the averaged values, log L γ = 46.77 ± 0.83 erg s 1 for FSRQs, log L γ = 46.17 ± 0.92 erg s 1 for LBLs, log L γ = 45.88 ± 0.92 erg s 1 for IBLs, and log L γ = 45.22 ± 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

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 = 5.4 10 7, 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 = 3.0 10 4, 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 = 0.756 for log L core and log L γ and r Rγ, z = 0.719 for log L tot and log L γ. The correlation between γ and radio bands perhaps suggests that there

Publications of the Astronomical Society of Japan, (2014), Vol. 66, No. 6 117-9 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 0.83 0.90 0.85 0.283 124 0.18% log L core vs log L γ 0.803 0.86 0.85 0.268 124 0.31% log L ext vs log L γ 0.73 0.82 0.85 0.109 124 13.23% FSRQ log L tot vs log L γ 0.71 0.79 0.76 0.275 79 1.43% log L core vs log L γ 0.65 0.68 0.76 0.280 79 1.29% log L ext vs log L γ 0.55 0.69 0.76 0.054 79 24.40% BL log L tot vs log L γ 0.856 0.872 0.85 0.445 45 0.29% log L core vs log L γ 0.837 0.847 0.85 0.418 45 0.53% log L ext vs log L γ 0.732 0.745 0.85 0.281 45 5.05% LBL log L tot vs log L γ 0.91 0.93 0.86 0.588 19 1.14% log L core vs log L γ 0.91 0.92 0.86 0.594 19 1.04% log L ext vs log L γ 0.60 0.73 0.86-0.080 19 26.00% IBL log L tot vs log L γ 0.83 0.95 0.87 0.023 12 27.22% log L core vs log L γ 0.83 0.94 0.87 0.073 12 26.70% log L ext vs log L γ 0.75 0.76 0.87 0.277 12 19.81% HBL log L tot vs log L γ 0.90 0.82 0.79 0.719 14 0.72% log L core vs log L γ 0.91 0.80 0.79 0.756 14 0.40% log L ext vs log L γ 0.80 0.68 0.79 0.585 14 3.37% F+L logl tot vs log L γ 0.781 0.85 0.80 0.320 98 0.17% log L core vs log L γ 0.736 0.768 0.80 0.316 98 0.19% log L ext vs log L γ 0.601 0.751 0.80 0.001 98 27.27% 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 = 0.153 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 = 0.055 and p = 24.3% for FSRQs; log L γ = (0.032 ± 0.586) log R + (46.23 ± 1.01) with r = 0.0318 and p = 27.1% for LBLs; log L γ = (0.38 ± 0.544) log R + (46.43 ± 0.97) with r = 0.442 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 = 0.732 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 = 0.655 and p < 10 4 for FSRQs; log (L γ /L ext ) = (1.101 ± 0.227) log (1 + R) + (2.427 ± 0.442) with r = 0.928 and p < 10 4 for LBLs; log (L γ /L ext ) = (0.847 ± 0.346) log (1 + R) + (3.06 ± 0.625) with r = 0.865 and p = 0.11% for IBLs;

117-10 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 = 0.788 and p = 0.21% for HBLs; log (L γ /L ext ) = (0.605 ± 0.098) log (1 + R) (1.09 ± 0.269) with r = 0.788 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 10633010, NSFC 11173009, U1431112), 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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