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Fig. 12

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Goodness-of-fit parameter χ2 as a function of the exponent β and characteristic mass of the exponential tapering Mexp (top panels) as well as of the exponent of the power-law part α and the characteristic tapering mass (bottom panels). The different panels depict the parameters of exponentially tapered power laws fit to the cumulative mass distributions of the sink particles in different models or of the clump mass distribution identified by the clump finder, respectively. The goodness-of-fit parameter is defined in Eq. (11) and normalised to the lowest value for the respective model. Tapering exponents between 1 and 1.5 are preferred for the sink particle mass distributions in models without sink particle mergers (first and second panel), a value close to 1 for the clump mass distribution (third panel), and values between 1 and 2.5 or even higher for our model including mergers (fourth panel). Furthermore, power-law exponents ranging from 0.4 to 0.6 yield low goodness-of-fit parameter values for all models, with the values for exponents down to 0 being comparably low for the model with the fiducial sink particle creation criteria and excluding mergers (first panel). Lastly, characteristic tapering masses of the order of 103G1H3PK2${10^{ - 3}}{G^{ - 1}}{H^3}P_{\rm{K}}^{ - 2}$ provide the best fits for the model with mergers, and of the order of 104G1H3PK2${10^{ - 4}}{G^{ - 1}}{H^3}P_{\rm{K}}^{ - 2}$ for the other three models.

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