Dust per Unit Gas Against Metallicity: A Power-Law Test on Five Published Systems

Whether the dust-to-gas ratio falls linearly with metallicity or faster decides how much solid material low-metallicity galaxies can form and hide. This paper fits a power law to representative published dust-to-gas ratios for the Milky Way, the Magellanic Clouds, and two metal-poor dwarfs, and compares the fit with strict linear scaling. The fitted slope is 1.605 with a normalisation at solar metallicity of 0.01181, the root-mean-square residual is 0.075 dex for the power law against 0.44 dex for linear scaling, and at one tenth solar metallicity the two prescriptions differ by an order of magnitude in implication: the power law predicts 0.000293 against the linear value 0.001. The representative midpoints favour steeper-than-linear decline, consistent with grain growth in the interstellar medium, rather than stellar production alone, setting the dust content at high metallicity. The input values are published midpoints, stated as such, and the fit is computed, not measured.