Abstract
Elemental abundances of Sun-like stars are crucial for understanding the detailed properties of their planets. However, measuring elemental abundances in M stars is challenging due to their faintness and pervasive molecular features in optical spectra. To address this, elemental abundances of Sun-like stars have been proposed to constrain those of M stars by scaling [X/H] with measured [Fe/H]. This study tests the robustness of this practice using M- and GK-dwarf stellar abundances and rigorous statistical methods. We compile elemental abundances for 43 M dwarfs for 10 major rock-forming elements (Fe, C, O, Mg, Si, Al, Ca, Na, Ni, and Ti) from high-resolution near-infrared stellar surveys. We perform bootstrap-based linear regressions on the M dwarfs to determine the trends of [X/H] vs. [Fe/H] and compare them with GK dwarfs. A 2-sample, multivariate Mahalanobis Distance test is applied to assess the significance of differences in [X/H]--[Fe/H] trends for individual elemental pairs between M and GK dwarfs. The null hypothesis of no significant difference in chemical trends between M and GK dwarfs is strongly rejected for all elements except Si, for which rejection is marginal, and Na and Ni, for which results are inconclusive. This suggests that assuming no difference may lead to biased results and inaccurate constraints on rocky planets around M dwarfs. Therefore, it is crucial for both the stellar and exoplanet communities to recognise these differences. To better understand these differences, we advocate for dedicated modelling techniques for M dwarf atmospheres and more homogeneous abundance analyses. Our statistically constrained trends of [X/H]--[Fe/H] for M dwarfs offer a new constraint on estimating M-dwarf elemental abundances given measured [Fe/H], aiding in characterising the properties of M dwarf-hosted rocky worlds.