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Fig. 3


Effects of varying the initial seed BH mass M0 on the evolution of the bubble radius following Eqs. (15) and (16) (energy-driven case). All other relevant parameters are the same as assumed in Fig. 2. The three green solid curves are computed for M0 = 102,104,106M as labelled. The BH reaches a final mass of 109M at different times t9 (shown by the dotted lines), but the bubble radius at that time, R(t9), is the same whatever the initial seed mass is. For reference, the magenta line shows the time evolution of a bubble inflated by a constant wind power of Lw = fwLE = 6.3 × 1045 erg s-1, corresponding to a 109M BH radiating at its Eddington limit and with fw = 0.05. Because of the scaling between BH mass and the normalization of the shell radius (; Eq. (15)), this curve has a (109/ 104)1 / 5 = 10 times higher the normalization than the black dotted line shown in Fig. 2.

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