tokens: expects stalled bubbles (and consequently, a size distribution with slope ≈−2.7) in the presence of cooling, or if this depends on the ambient pressure. In order to answer the question, we have run our simulations for two different pressures. Fig. 12 shows the scatter plot of bubbles (similar to Figs 6 and 8 for our fiducial ISM pressure) for two different values of ISM pressures, at 30 Myr. Essentially, we have decreased the non-thermal contribution in the ambient pressure, by reducing the equivalent temperature from 4 × 10 4 to 2 × 10 4 K (left-hand panel) and then to 10 4 K (right-hand panel). Comparing with Figs 6 (adiabatic case) and 8 , we find that the bubbles in these two cases are not dominated by stalled bubbles, as was the case for Fig. 8 . For the left-hand panel, we find that bubbles with L ∼ 5 × 10 36 erg s −1 stall after a time-scale of ∼7 Myr, and bubbles bigger than that at latter times. When the pressure is further lowered, in the right-hand panel, all bubbles keep growing until 30 Myr, and the circumstance is similar to Fig. 6 . We recall that, in these cases of domination by growing bubbles, the size distribution is likely to be steeper than 1 − 2β, as we confirm below. Figure 12. Scatter plot for bubbles for ambient pressure p 0 = 1.38 × 10 −12 dyne cm −2 (left), and 6.9 × 10 −13 dyne cm −2 (right), at 30 Myr. We show in Fig. 13 the size distribution of the bubbles for these values of pressure at two different times after the onset of star formation (10 and 30 Myr). In general, we find that lowering pressure steepens the size distribution, by allowing low -luminosity bubbles to grow to larger sizes. This trend is shown in Fig. 14 , for two different epochs, 10 and 30 Myr. At lower pressures, there is an evolution of the slope between these time-scales, since bubbles keep growing in low ambient pressure, compared to high-pressure environments. Figure 13. Size distribution of bubbles for ambient pressure p 0 = 2.76 × 10 −12 dyne cm −2 (blue), 1.38 × 10 −12 dyne cm −2 (red), and 6.9 × 10 −13 dynes cm −2 (green), at 10 and 30 Myr. Figure 14. The slope of size distribution as a function of ISM pressure, for two different epochs, 10 Myr (green) and 30 Myr (red). The distributions at lower (non-thermal) pressures also show a positive part at small sizes, in addition to the falling numbers at large sizes as we have seen earlier. The rising part comes from growing young bubbles whose age is smaller than the stalling time of the bubble with the lowest luminosity. This generates a peak in the distribution. The peak depends upon the radius of the stalled bubble with the lowest luminosity at the time being observed. Fig. 13 shows that at higher pressures the peak radius is independent of time but starts varying with time as soon as we start decreasing the pressure. This occurs due to the fact that at higher pressures (such as, at 2.76 × 10 −12 dyne cm −2 ), the bubbles with low luminosities stall much before 10 Myr hence the peak
ner_tags: O O O O O O O O O B-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 B-Formula I-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 B-Formula I-Formula I-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 B-Formula I-Formula I-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