Physical properties of very powerful FRII radio galaxies

Table 6:

Fits to the data (b = 1).
Relationship	Slope	Y intercept	$\chi^2$	Corr.?
T vs. 1 + z	$-3.20 \pm 0.4$	$9.5 \pm 0.8$	113.9	Y
Log T vs. Log (1 + z)	$-1.90 \pm 0.3$	$1.12 \pm 0.07$	131.5	Y
T vs. r	$-3.40 \pm 2.5 \times 10^{-3}$	$3.1 \pm 0.5$	255	N
Log T vs. Log r	$-0.15 \pm 0.12$	$1 \pm 0.3$	253.1	N
$E_{\rm T}$ vs. 1 + z	$3.50 \pm 0.6$	$-2.7 \pm 1$	113.7	Y
Log $E_{\rm T}$ vs. Log (1 + z)	$1.90 \pm 0.3$	$0.11 \pm 0.07$	131.5	Y
$E_{\rm T}$ vs. r	$1.00 \pm 3 \times 10^{-3}$	$2.7 \pm 0.4$	171.3	N
Log $E_{\rm T}$ vs. Log r	$0.15 \pm 0.12$	$0.3 \pm 0.3$	253.1	N
$n_{\rm a}$ vs. r	$-5.00 \pm 1 \times 10^{-6}$	$0.002 \pm 0.003$	300.9	N
Log $n_{\rm a}$ vs. Log r	$-1.38 \pm 0.14$	$0.3 \pm 0.3$	328.3	Y
Log $n_{\rm a}$ vs. Log (1 + z)	$-1.60 \pm 0.6$	$-2.27 \pm 0.17$	760.3	N
v/c vs. r	$7.10 \pm 1.1 \times 10^{-4}$	$0.02 \pm 0.01$	572.8	N
Log v/c vs. Log r	$0.54 \pm 0.12$	$-1.9 \pm 0.3$	827.6	N
v/c vs. 1 + z	$0.10 \pm 0.03$	$-0.07 \pm 0.05$	823.7	N
Log v/c vs. Log (1 + z)	$1.80 \pm 0.3$	$-1.24 \pm 0.09$	771.5	N
L_j vs. r	$0.04 \pm 0.03$	$15 \pm 5$	873.8	N
Log L_j vs. Log r	$0.50 \pm 0.2$	$0.4 \pm 0.5$	2072	N
L_j vs. 1 + z	$44.00 \pm 10$	$-50 \pm 17$	690.5	N
Log L_j vs. Log (1 + z)	$4.70 \pm 0.5$	$0.44 \pm 0.13$	933.1	N

The best fits to the radio source relationships for b = 1. Column 1: the relationship. v/c is the lobe expansion velocity, r is the core-hotspot separation, L_j ( $\times 10^{44}$ erg s^-1) is the beam power, $n_{\rm a}$ ( $\times 10^{-3}$ cm ^-3) is the ambient density, T is the source lifetime, and $E_{\rm T}$ is the total energy. Column 2: the best fit slope. Column 3: the best fit Y intercept. Column 4: the $\chi^2$ for 60 points and 58 degrees of freedom. Column 5: is there a correlation? The uncertainty of the best fit parameter is multiplied by $\sqrt{(\chi^2/58)}$ to obtain the normalized uncertainty in the best fit parameter, and this is compared with the value of the best fit parameter to determine whether the correlation is significant.

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