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Results of our simulations assessing the accuracy of our PNLF modelling, while holding to the standard form of the PNLF with a fixed c2 = 0.307 value and optimising the distance modulus μPNLF. Each blue dot shows the difference ΔμPNLF = μPNLF best − fit − μPNLF in between the returned best-fit μPNLF value and the input value when fitting synthetic PNLFs drawn from a parent incompleteness-corrected PNLF model with a varying NPNe sim number of PNe. In this case, the parent distribution assumes a distance modulus μPNLF in = 31.45 and the same completeness function as observed in FCC 193 (top panel) and FCC 147 (bottom panel), which reaches about 2.5 and 1.5 mag below the apparent magnitude of the PNLF cutoff, respectively (see FCC147 FCC193 PNLF in Fig. C.2). As NPNe sim increases, the scatter in the ΔμPNLF values decreases while overall returning an unbiased answer, even at low NPNe sim, as traced also by the binned median red line. The red shaded region traces the 1σ confidence limit.
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