tokens: and smaller p -values. Figure 4. The slope of the power-law fit to the d N /d m p mass distributions over time. The power-law index p is calculated according to equation ( 16 ). Top panel: the data for the L02 simulations. Bottom panel: the data for all seven simulations. As in Fig. 3 , when computing the power-law index, every data point in all of the L02 simulations is included in the calculation for p , and the same goes for the L04 data. Both panels: The shaded region represents σ , the error in p , calculated according to equation ( 17 ). In the bottom panel, when the larger domains are considered and the planetesimal populations from the multiple L02 and L04 runs are combined, there is much less variance in the value for p . The steady, decreasing trend with time is readily apparent. At t = 50Ω −1 , when enough planetesimals have formed to compute a reliable value for p , the values range between 1.6 and 2.0 across the different sized simulations, and well after planetesimals have formed, at t = 150Ω −1 , the values are between 1.4 and 1.6. A decrease in p represents a shift towards fewer and more massive planetesimals at late times. A trend toward larger masses with time is somewhat expected. However, a clear demonstration of this trend has not been demonstrated in previous studies. In fig. 3 from Simon et al. ( 2017 ), the authors show data for p over time in their simulations, but only over a relatively narrow range of time. 4 Similarly, Schäfer et al. ( 2017 ) show how the values of their fit parameters change over time, but also only for a narrow window. This decrease in distribution fit parameters emphasizes that care is needed when attempting to extract a single value for the power-law index or a single set of parameters that describes the mass distribution of planetesimals formed by the SI. The mass distribution is transient and should be expected to evolve indefinitely, albeit as a slowing rate, particularly when a larger simulation domain provides for more material as shown in the next section. 3.3 Total mass of dust in planetesimals and the onset of planetesimal formation Fig. 5 shows the total mass of the planetesimals in the simulations over time. As in Fig. 2 , the larger domain simulations are divided into smaller subdomains with the same area as the L02 runs. The L08 run shows the largest variance in these data. After t = 40Ω −1 , the spread in the total dust mass in planetesimals in any of the subdomains from the L08 run spans 5– of the total mass of dust in a single subdomain. The data from the L02 and L04 runs generally fit within the maximum-minimum bounds of the L08 run. Once again we note that simply re-running these simulations with a different random seed leads to significantly different consequences for planetesimals formation, shown here directly by the wide spread denoted by the red shaded region that is quite similar to the region-to-region variation in the larger domains. Figure 5. The total mass of the
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