Table A.1: Slope of the envelope of the log  $L_{{\rm H}\alpha} - \log~\sigma_{\rm nt}$ relation for the H  II regions of NGC 3359 from H  II region catalogues obtained using different criteria to estimate the H  II region cut-off isophote (Col. 1). The slopes (Cols. 2 and 4) have been obtained with the procedure described in Sect. 6.2, and each value represents the median value of the slopes obtained by stepping the starting luminosity in the luminosity bins by 0.01 dex. Columns 2 and 4 show the median value when taking into account only H  II regions with luminosities greater than log  $L_{\scriptsize\mbox{H$\alpha$ }}>$ 38.4 and 38.8 (in erg s-1) respectively. The standard deviation of each set of slopes is given in Cols. 3 and 5. Column 6 shows the completeness limit of the H  II region catalogue obtained for each cut-off isophote criterion. The symbol "-'' means that there are not enough points to fit an envelope in that case.
Cut-off for log  $L_{{\rm H}\alpha}>38.4$ for log  $L_{{\rm H}\alpha}>38.8$ Complet.
isophote slope stdev slope stdev limit
$I_{\rm peak}/e$ 1.18 0.08 1.2 0.2 37.4
0.5 $I_{\rm peak}$ 1.2 0.2 - - 37.4
3 rms 1.4 0.3 1.4 0.3 37.1
5 rms 1.5 0.2 1.4 0.3 37.2
7 rms 1.5 0.2 1.4 0.3 37.4


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