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Our data show that the slope of the relation is in line with the canonical <jats:italic>R<\/jats:italic>\u2004\u221d\u2004<jats:italic>L<\/jats:italic><jats:sup>0.5<\/jats:sup> when using an appropriately non-linear correction for bolometric luminosity. In contrast, using optical luminosity or applying a constant bolometric correction to it results in a significant deviation in the slope, suggesting a potential luminosity dependence on the spectral energy distribution. 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