Early Results from the HUMDRUM Survey: A Small, Earth-mass Planet Orbits TOI-1450A

M dwarf stars provide us with an ideal opportunity to study nearby small planets. The HUMDRUM (HUnting for M Dwarf Rocky planets Using MAROON-X) survey uses the MAROON-X spectrograph, which is ideally suited to studying these stars, to measure precise masses of a volume-limited ($<\,30$ pc) sample of transiting M dwarf planets. TOI-1450 is a nearby (22.5 pc) binary system containing a M3 dwarf with a roughly 3000 K companion. Its primary star, TOI-1450A, was identified by $TESS$ to have a 2.04d transit signal, and is included in the HUMDRUM sample. In this paper, we present MAROON-X radial velocities which confirm the planetary nature of this signal and measure its mass at a nearly 10% precision. The 2.04d planet, TOI-1450Ab, has $R_b\,=\,1.13\,\pm\,0.04\,R_\oplus$ and $M_b\,=\,1.26\,\pm\,0.13\,M_\oplus$. It is the second-lowest-mass transiting planet with a high-precision RV mass measurement. With this mass and radius, the planet's mean density is compatible with an Earth-like composition. Given its short orbital period and slightly sub-Earth density, it may be amenable to $JWST$ follow-up to test whether the planet has retained an atmosphere despite extreme heating from the nearby star. We also discover a non-transiting planet in the system with a period of 5.07 days and a $M\mathrm{sin}i_c\,=\,1.53\,\pm\,0.18\,M_\oplus$. We also find a 2.01d signal present in the systems's $TESS$ photometry that likely corresponds to the rotation period of TOI-1450A's binary companion, TOI-1450B. TOI-1450A, meanwhile, appears to have a rotation period of approximately 40 days, which is in-line with our expectations for a mid-M dwarf.
Comment: 31 pages, 17 figures, accepted in AJ