Time variability of the core-shift effect in the blazar 3C 454.3

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Volume 672 (April 2023)

A&A, 672 (2023) A130

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Table 5.

Spearman’s rank and Pearson correlation coefficients.

Relations	Spearman		Pearson	Fitting function

	Correlation coefficient (ρ)	p-value	Correlation coefficient (r)	Power-law
Δr_CX – S_core at 5 GHz	0.37	0.14
Δr_CX – S_core at 8 GHz	0.19	0.46
Δr_XU – S_core at 8 GHz	−0.48	0.05	-0.46	(0.24 ± 0.06)
Δr_XU – S_core at 15 GHz	−0.12	0.66
Δr_UK – S_core at 15 GHz	0.59	0.01	0.37	(0.05 ± 0.01)
Δr_UK – S_core at 22−24 GHz	0.60	0.01	0.40	(0.05 ± 0.01)
Δr_KQ – S_core at 22−24 GHz	0.77	0.0003	0.60	(0.02 ± 0.01)
Δr_KQ – S_core at 43 GHz	0.64	0.006	0.71	(0.010 ± 0.004)
Δr_CQ – S_MRO at 37 GHz	0.63	0.008	0.22	(0.3 ± 0.1)
Δr_CQ – S_core at 43 GHz	0.52	0.03	0.23	(0.35 ± 0.09)

r_core – S_core at 5 GHz	0.40	0.12
r_core – S_core at 8 GHz	0.61	0.02^(*)	0.75	(58.3 ± 9.3)
r_core – S_core at 15 GHz	0.84	0.0003	0.71	(19.3 ± 2.8)
r_core – S_core at 22−24 GHz	0.74	0.001	0.77	(7.9 ± 1.7)
r_core – S_core at 43 GHz	0.49	0.05	0.77	(2.1 ± 2.0)

k_r – S_core at 5 GHz	0.28	0.30
k_r – S_core at 8 GHz	0.67	0.006	0.80	(0.55 ± 0.05)
				(0.5 ± 0.1)+(0.15 ± 0.03) S_core
k_r – S_core at 15 GHz	0.44	0.12	0.74
k_r – S_core at 22−24 GHz	0.56	0.03	0.81	(0.48 ± 0.06)
				(0.6 ± 0.1)+(0.04 ± 0.01) S_core
k_r – S_MRO at 37 GHz	0.50	0.05	0.77	(0.39 ± 0.08) ^(†)
				(0.5 ± 0.1)+(0.03 ± 0.01) S_core
k_r – S_core at 43 GHz	0.52	0.04	0.76	(0.52 ± 0.09) ^(†)
				(0.5 ± 0.1)+(0.04 ± 0.01) S_core

PA – k_r	−0.42	0.11

Correlations with B_1pc values assuming k_r = 1

B_CQ, 1pc – S_core at 5 GHz	0.54	0.03	0.47
B_CQ, 1pc – S_core at 8 GHz	0.29	0.26
B_CQ, 1pc– S_core at 15 GHz	0.56	0.02	0.05
B_CQ, 1pc – S_core at 22−24 GHz	0.61	0.01	0.12
B_CQ, 1pc – S_core at 43 GHz	0.52	0.03	0.23
B_CQ, 1pc – S_MRO at 37 GHz	0.63	0.008	0.24

Notes. Power-law fits are given only for the relations with p-values < 0.05. Additional linear fits are provided for the k_r − S_core relationship.

^(*)

Excluding the data point of 37 pc.

^(†)

The fits do not include the data at k_r = 0.45 and k_r = 0.52. These are taken as outliers in the scatter plots. By including these points, the power-law fits become much less steep with indices: 0.05 ± 0.18 at 37 GHz and 0.04 ± 0.14 at 43 GHz.

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