tokens: shorter than the radiative length-scale, over which substantial radiative energy losses would occur. These results are independent of black hole mass. Figure 5. Figures (a–f) show the distance travelled by the jet before reaching equipartition for a range of values of the reconnection parameters A rec and d , from ( 97 ) and fractional Eddington jet power f Edd . We stop integration of the jet evolution equations at a distance of 10 8 r s if the jet plasma has not yet reached equipartition, since radiative energy losses at larger distances than this are insignificant. The jet parameters used to obtain these results are shown under Model C in Table 2 and the radiative losses corresponding to these models are shown in Fig. 4 . We find that the dimensionless distance to equipartition, X equi = z equi / r s , depends weakly on the fractional Eddington accretion rate, f Edd . The distance to equipartition decreases slowly with increasing f Edd . These results are independent of black hole mass, M . Figure 6. The desirable region of parameter space for jets with different fractional Eddington luminosities and reconnection parameters from Figs 4 and 5 . Here, ‘desirable’ means that the jet reaches equipartition at a distance, z equi , between 100 and 10 8 r s , whilst not radiating more than 95 per cent of its initial energy in reaching this point. The unfavoured regions of parameter space which do not fulfill these criteria are coloured in black. The jet parameters used to obtain these results are shown under Model C in Table 2 . Due to more severe radiative losses at higher fractional Eddington jet powers ( f Edd ), the desirable region becomes more restrictive for higher values of f Edd . This means that lower power jets are able to reach equipartition at smaller distances whilst retaining at least 5 per cent of their initial energy. For jet powers close to the Eddington luminosity ( f Edd > 0.1), the strong radiative losses essentially prohibit the jet from coming into equipartition at a distance smaller than ∼10 4 r s , since otherwise, the jet radiates away more than 95 per cent of its initial power in the compact base region with high magnetic field strengths. This is consistent with our earlier results in Fig. 3 , in which we found that the base of the jet must be highly magnetized in order not to suffer from devastating radiative energy losses. We also see that large negative values of the reconnection power-law d are effectively prohibited, since reconnection occurring predominantly at the base of the jet will result in heavy radiative losses in the strong magnetic fields. These results are independent of black hole mass. In terms of the equipartition fraction or magnetization, which we define as σ = U B / U e ± , the equation becomes It can be more convenient to use this expression when solving the evolution equations numerically, if U B / U e ± becomes very large. 8.1 Constraining the rate of reconnection in the jet Finally, we try to
ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O