Abstract
Context. Elemental abundances of Sun-like stars have been shown to be crucial for understanding the detailed properties of planets surrounding them. However, accurately measuring elemental abundances of M stars, the most abundant class of stars in the solar neighbourhood, is challenging due to their faintness and pervasive molecular features in optical photospheric spectra. As a result, elemental abundances of Sun-like stars have been proposed to constrain those of M stars, particularly by scaling [X/H] given measured [Fe/H].
Aims. This work aims to test the robustness of this convenient practice based on two selected sets of M- and GK-dwarf stellar abundances and a set of rigorous statistical methods.
Methods. We compiled the elemental abundances of a sample of up to 43 M dwarfs for ten major rock-forming elements (Fe, C, O, Mg, Si, Al, Ca, Na, Ni, and Ti) from high-resolution near-infrared stellar surveys including APOGEE, CARMENES, and Subaru. We carried out bootstrap-based linear regressions on the selected sample of M dwarfs to constrain the statistical trends of [X/H] versus [Fe/H] and then compare them with those of GK dwarfs (sampled from the GALAH database). We then applied a two-sample, multivariate Mahalanobis Distance test to assess the significance of the differences in the [X/H]-[Fe/H] trends for individual elemental pairs between M and GK dwarfs.
Results. We find that the null hypothesis – that is, no significant difference in the chemical trends of [X/H] versus [Fe/H] between M and GK dwarfs – is strongly rejected for all elements except for Si, for which the rejection is marginal (p-value close to 0.05), and Na and Ni, for which the results are inconclusive. This finding suggests that assuming no difference may result in biased results, and thus inaccurate constraints on characterising rocky planets around M dwarfs by scaling the (unmeasured) chemical abundances of planet-hosting M dwarfs from the chemical trends of [X/H]–[Fe/H] determined by GK dwarfs.
Conclusions. It is therefore crucial for both the stellar and exoplanet communities to be aware of these observed differences. To better understand these differences, we advocate for dedicated modelling techniques for M-dwarf atmospheres and an increasing set of benchmark, homogeneous abundance analyses. Intermediately, our statistically constrained trends of [X/H]–[Fe/H] for M dwarfs provide a new constraint on estimating M-dwarf elemental abundances given measured [Fe/H] and further on characterising the detailed properties of M-dwarf-hosted rocky worlds.