Table A.1.
Equations of the scaling relations discussed in Appendix A.
| Reference | Equation |
|---|---|
| Willott et al. (1999) | log(Lkin) = 0.86 ⋅ log(L1.4 GHz) + 14.08 + 1.5 log(fW) |
| Cavagnolo et al. (2010) | Lkin = (1035 W)×100.75[log(νL1.4 GHz)] − 22.84 |
| Shabala & Godfrey (2013) | Lkin = (1036 W) ⋅ 1.5  ⋅ (1 + z) ⋅  |
| Godfrey & Shabala (2013) (FRI) | Lkin = (5 × 1037 W)  |
| Godfrey & Shabala (2013) (FRII) | Lkin = g (1.5 × 1037 W)  |
| Godfrey & Shabala (2016) | log(Lkin) = 36.56 + 0.27 log + 1.4 log + 0.33 |
Notes. All have been converted into the form in which a monochromatic radio luminosity is an input variable. In all cases, Lkin has units of W and the monochromatic radio luminosities (L1.4 GHz, L151 MHz) have units of W Hz−1. For the Willott et al. (1999) relation (see Heckman & Best 2014), a value of fW = 4 was chosen. For the Cavagnolo et al. (2010) relation, ν = 1.4 × 109 Hz. For the Shabala & Godfrey (2013) and Godfrey & Shabala (2013) relations, L151 MHz was obtained by converting the S1.8 GHz values (the XXL-S flux densities measured at the effective frequency) into S151 MHz assuming the spectral index assigned to each XXL-S radio source (see Appendix A in XXL Paper XXXI), g = 2 is the normalisation factor, and D is the source size in kpc. For the Godfrey & Shabala (2016) relation, dL is the luminosity distance in Mpc.
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