Table 1. Open in new tab Correlation...

In the observers’ frame	N	log (Y) versus log (ν^obs)	\|$\log (L_{{\rm rad}}^{{\rm obs}})~ {\rm versus}~ \log (\nu ^{{\rm {obs}}})$\|
ALL, historical sample	1594	−0.59	5.5 × 10⁻¹⁵²	−0.31 ± 0.009	−0.48	2.0 × 10⁻⁹¹	−0.35 ± 0.02
ALL, quasi-simultaneous sample	109	−0.18	0.06	−0.34 ± 0.07	−0.05	0.63	−0.38 ± 0.12
FSRQs, historical sample
ALL	750	−0.002	0.95	−0.04 ± 0.04	−0.14	7.8 × 10⁻⁵	−0.29 ± 0.06
Y ≤ 1	288	−0.005	0.93	−0.02 ± 0.03	−0.20	5.0 × 10⁻⁴	−0.35 ± 0.08
Y > 1	462	5.28 × 10⁻⁴	0.98	8.05 × 10⁻⁴ ± 0.04	−0.14	0.002	−0.18 ± 0.07
FSRQs, quasi-simultaneous sample
ALL	81	−0.22	0.05	−0.25 ± 0.13	−0.20	0.08	−0.29 ± 0.20
BL Lacs, historical sample
ALL	844	−0.64	9.6 × 10⁻⁹⁷	−0.28 ± 0.01	−0.04	0.19	−0.02 ± 0.03
Y ≤ 1	726	–0.58	3.3 × 10⁻⁶⁵	−0.22 ± 0.01	0.07	0.07	0.08 ± 0.04
Y > 1	118	−0.19	0.04	−0.06 ± 0.02	−0.17	0.07	−0.21 ± 0.14
BL Lacs, quasi-simultaneous sample
ALL	28	−0.53	0.004	−0.32 ± 0.08	−0.18	0.37	−0.22 ± 0.19
Y ≤ 1	11	−0.54	0.09	−0.20 ± 0.10	0.21	0.54	0.13 ± 0.27
Y > 1	17	−0.03	0.90	−0.14 ± 0.14	0.15	0.56	0.20 ± 0.31
in the comoving frame		log (Y) versus log (ν)	log (L_rad) versus log (ν)
ALL, δ_D-corrected sample	180	−0.10	0.17	−0.03 ± 0.05	0.54	8.8 × 10⁻¹⁵	0.91 ± 0.09
FSRQs, Y > 1	126	−0.23	0.12	−0.24 ± 0.08	0.40	4.4 × 10⁻⁶	0.89 ± 0.17
BL Lacs, Y > 1	51	0.16	0.15	0.06 ± 0.05	0.76	8.8 × 10⁻¹⁵	0.95 ± 0.12

In the observers’ frame

log (Y) versus log (ν^obs)

|$\log (L_{{\rm rad}}^{{\rm obs}})~ {\rm versus}~ \log (\nu ^{{\rm {obs}}})$|

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

ALL, historical sample

1594

−0.59

5.5 × 10⁻¹⁵²

−0.31 ± 0.009

−0.48

2.0 × 10⁻⁹¹

−0.35 ± 0.02

ALL, quasi-simultaneous sample

109

−0.18

0.06

−0.34 ± 0.07

−0.05

0.63

−0.38 ± 0.12

FSRQs, historical sample

ALL

750

−0.002

0.95

−0.04 ± 0.04

−0.14

7.8 × 10⁻⁵

−0.29 ± 0.06

Y ≤ 1

288

−0.005

0.93

−0.02 ± 0.03

−0.20

5.0 × 10⁻⁴

−0.35 ± 0.08

Y > 1

462

5.28 × 10⁻⁴

0.98

8.05 × 10⁻⁴ ± 0.04

−0.14

0.002

−0.18 ± 0.07

FSRQs, quasi-simultaneous sample

ALL

−0.22

0.05

−0.25 ± 0.13

−0.20

0.08

−0.29 ± 0.20

BL Lacs, historical sample

ALL

844

−0.64

9.6 × 10⁻⁹⁷

−0.28 ± 0.01

−0.04

0.19

−0.02 ± 0.03

Y ≤ 1

726

–0.58

3.3 × 10⁻⁶⁵

−0.22 ± 0.01

0.07

0.08 ± 0.04

Y > 1

118

−0.19

0.04

−0.06 ± 0.02

−0.17

0.07

−0.21 ± 0.14

BL Lacs, quasi-simultaneous sample

ALL

−0.53

0.004

−0.32 ± 0.08

−0.18

0.37

−0.22 ± 0.19

Y ≤ 1

−0.54

0.09

−0.20 ± 0.10

0.21

0.54

0.13 ± 0.27

Y > 1

−0.03

0.90

−0.14 ± 0.14

0.15

0.56

0.20 ± 0.31

in the comoving frame

log (Y) versus log (ν)

log (L_rad) versus log (ν)

ALL, δ_D-corrected sample

180

−0.10

0.17

−0.03 ± 0.05

0.54

8.8 × 10⁻¹⁵

0.91 ± 0.09

FSRQs, Y > 1

126

−0.23

0.12

−0.24 ± 0.08

0.40

4.4 × 10⁻⁶

0.89 ± 0.17

BL Lacs, Y > 1

0.16

0.15

0.06 ± 0.05

0.76

8.8 × 10⁻¹⁵

0.95 ± 0.12

In the observers’ frame	N	log (Y) versus log (ν^obs)	\|$\log (L_{{\rm rad}}^{{\rm obs}})~ {\rm versus}~ \log (\nu ^{{\rm {obs}}})$\|
ALL, historical sample	1594	−0.59	5.5 × 10⁻¹⁵²	−0.31 ± 0.009	−0.48	2.0 × 10⁻⁹¹	−0.35 ± 0.02
ALL, quasi-simultaneous sample	109	−0.18	0.06	−0.34 ± 0.07	−0.05	0.63	−0.38 ± 0.12
FSRQs, historical sample
ALL	750	−0.002	0.95	−0.04 ± 0.04	−0.14	7.8 × 10⁻⁵	−0.29 ± 0.06
Y ≤ 1	288	−0.005	0.93	−0.02 ± 0.03	−0.20	5.0 × 10⁻⁴	−0.35 ± 0.08
Y > 1	462	5.28 × 10⁻⁴	0.98	8.05 × 10⁻⁴ ± 0.04	−0.14	0.002	−0.18 ± 0.07
FSRQs, quasi-simultaneous sample
ALL	81	−0.22	0.05	−0.25 ± 0.13	−0.20	0.08	−0.29 ± 0.20
BL Lacs, historical sample
ALL	844	−0.64	9.6 × 10⁻⁹⁷	−0.28 ± 0.01	−0.04	0.19	−0.02 ± 0.03
Y ≤ 1	726	–0.58	3.3 × 10⁻⁶⁵	−0.22 ± 0.01	0.07	0.07	0.08 ± 0.04
Y > 1	118	−0.19	0.04	−0.06 ± 0.02	−0.17	0.07	−0.21 ± 0.14
BL Lacs, quasi-simultaneous sample
ALL	28	−0.53	0.004	−0.32 ± 0.08	−0.18	0.37	−0.22 ± 0.19
Y ≤ 1	11	−0.54	0.09	−0.20 ± 0.10	0.21	0.54	0.13 ± 0.27
Y > 1	17	−0.03	0.90	−0.14 ± 0.14	0.15	0.56	0.20 ± 0.31
in the comoving frame		log (Y) versus log (ν)	log (L_rad) versus log (ν)
ALL, δ_D-corrected sample	180	−0.10	0.17	−0.03 ± 0.05	0.54	8.8 × 10⁻¹⁵	0.91 ± 0.09
FSRQs, Y > 1	126	−0.23	0.12	−0.24 ± 0.08	0.40	4.4 × 10⁻⁶	0.89 ± 0.17
BL Lacs, Y > 1	51	0.16	0.15	0.06 ± 0.05	0.76	8.8 × 10⁻¹⁵	0.95 ± 0.12

Table 1.

Open in new tab

Correlation results of historical, quasi-simultaneous and δ_D-corrected samples. Columns from left to right: (1): the sample studied in correlation analysis; (2): the number of blazars in the sample; (3) and (6) are the Spearman test correlation coefficients; (4) and (7) are the chance probabilities; (5) and (8) are the slopes of the best linear fitting equations.

In the observers’ frame	N	log (Y) versus log (ν^obs)			\|$\log (L_{{\rm rad}}^{{\rm obs}})~ {\rm versus}~ \log (\nu ^{{\rm {obs}}})$\|
		τ	p	s	τ	p	s
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
ALL, historical sample	1594	−0.59	5.5 × 10⁻¹⁵²	−0.31 ± 0.009	−0.48	2.0 × 10⁻⁹¹	−0.35 ± 0.02
ALL, quasi-simultaneous sample	109	−0.18	0.06	−0.34 ± 0.07	−0.05	0.63	−0.38 ± 0.12
FSRQs, historical sample
ALL	750	−0.002	0.95	−0.04 ± 0.04	−0.14	7.8 × 10⁻⁵	−0.29 ± 0.06
Y ≤ 1	288	−0.005	0.93	−0.02 ± 0.03	−0.20	5.0 × 10⁻⁴	−0.35 ± 0.08
Y > 1	462	5.28 × 10⁻⁴	0.98	8.05 × 10⁻⁴ ± 0.04	−0.14	0.002	−0.18 ± 0.07
FSRQs, quasi-simultaneous sample
ALL	81	−0.22	0.05	−0.25 ± 0.13	−0.20	0.08	−0.29 ± 0.20
BL Lacs, historical sample
ALL	844	−0.64	9.6 × 10⁻⁹⁷	−0.28 ± 0.01	−0.04	0.19	−0.02 ± 0.03
Y ≤ 1	726	–0.58	3.3 × 10⁻⁶⁵	−0.22 ± 0.01	0.07	0.07	0.08 ± 0.04
Y > 1	118	−0.19	0.04	−0.06 ± 0.02	−0.17	0.07	−0.21 ± 0.14
BL Lacs, quasi-simultaneous sample
ALL	28	−0.53	0.004	−0.32 ± 0.08	−0.18	0.37	−0.22 ± 0.19
Y ≤ 1	11	−0.54	0.09	−0.20 ± 0.10	0.21	0.54	0.13 ± 0.27
Y > 1	17	−0.03	0.90	−0.14 ± 0.14	0.15	0.56	0.20 ± 0.31
in the comoving frame		log (Y) versus log (ν)			log (L_rad) versus log (ν)
ALL, δ_D-corrected sample	180	−0.10	0.17	−0.03 ± 0.05	0.54	8.8 × 10⁻¹⁵	0.91 ± 0.09
FSRQs, Y > 1	126	−0.23	0.12	−0.24 ± 0.08	0.40	4.4 × 10⁻⁶	0.89 ± 0.17
BL Lacs, Y > 1	51	0.16	0.15	0.06 ± 0.05	0.76	8.8 × 10⁻¹⁵	0.95 ± 0.12

In the observers’ frame	N	log (Y) versus log (ν^obs)			\|$\log (L_{{\rm rad}}^{{\rm obs}})~ {\rm versus}~ \log (\nu ^{{\rm {obs}}})$\|
		τ	p	s	τ	p	s
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
ALL, historical sample	1594	−0.59	5.5 × 10⁻¹⁵²	−0.31 ± 0.009	−0.48	2.0 × 10⁻⁹¹	−0.35 ± 0.02
ALL, quasi-simultaneous sample	109	−0.18	0.06	−0.34 ± 0.07	−0.05	0.63	−0.38 ± 0.12
FSRQs, historical sample
ALL	750	−0.002	0.95	−0.04 ± 0.04	−0.14	7.8 × 10⁻⁵	−0.29 ± 0.06
Y ≤ 1	288	−0.005	0.93	−0.02 ± 0.03	−0.20	5.0 × 10⁻⁴	−0.35 ± 0.08
Y > 1	462	5.28 × 10⁻⁴	0.98	8.05 × 10⁻⁴ ± 0.04	−0.14	0.002	−0.18 ± 0.07
FSRQs, quasi-simultaneous sample
ALL	81	−0.22	0.05	−0.25 ± 0.13	−0.20	0.08	−0.29 ± 0.20
BL Lacs, historical sample
ALL	844	−0.64	9.6 × 10⁻⁹⁷	−0.28 ± 0.01	−0.04	0.19	−0.02 ± 0.03
Y ≤ 1	726	–0.58	3.3 × 10⁻⁶⁵	−0.22 ± 0.01	0.07	0.07	0.08 ± 0.04
Y > 1	118	−0.19	0.04	−0.06 ± 0.02	−0.17	0.07	−0.21 ± 0.14
BL Lacs, quasi-simultaneous sample
ALL	28	−0.53	0.004	−0.32 ± 0.08	−0.18	0.37	−0.22 ± 0.19
Y ≤ 1	11	−0.54	0.09	−0.20 ± 0.10	0.21	0.54	0.13 ± 0.27
Y > 1	17	−0.03	0.90	−0.14 ± 0.14	0.15	0.56	0.20 ± 0.31
in the comoving frame		log (Y) versus log (ν)			log (L_rad) versus log (ν)
ALL, δ_D-corrected sample	180	−0.10	0.17	−0.03 ± 0.05	0.54	8.8 × 10⁻¹⁵	0.91 ± 0.09
FSRQs, Y > 1	126	−0.23	0.12	−0.24 ± 0.08	0.40	4.4 × 10⁻⁶	0.89 ± 0.17
BL Lacs, Y > 1	51	0.16	0.15	0.06 ± 0.05	0.76	8.8 × 10⁻¹⁵	0.95 ± 0.12

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