MARTA: Temperature-temperature relationships and strong-line metallicity calibrations from multiple auroral-line detections at cosmic noon

We present the first results from MARTA (Measuring Abundances at high Redshift with the Tₑ Approach), a programme leveraging ultra-deep, medium-resolution JWST/NIRSpec spectroscopy to probe the interstellar medium (ISM) of star-forming galaxies at z ~ 2 - 3. We report detections of one or more auroral lines, including [O III]λ4363, [O II]λλ7320,7330, [S II] λ4068, and [S III] λ6312 for 16 galaxies in the sample, providing measurements of multiple ionic temperatures. We tested the validity of the T[O II]-T[O III] relation at high redshift considering a total sample of 21 objects including literature data, and obtained a shallower slope than in the low-z literature. However, such a slope is consistent with low-redshift data when ultra-low metallicity objects are considered. We assessed the correlation of the T[O II]-T[O III] relationship and its scatter on different physical parameters, finding a mild correlation with the ionisation parameter and radiation field hardness, while no significant correlation with gas density. The location of high-redshift data is also consistent with the low-z literature in the T[O II]-T[S II], and T[S III]-T[O III] relations, although this conclusion is limited with low-number statistics. Finally, we leveraged our sample together with a comprehensive compilation of galaxies with [O III]λ4363 detections from the literature to recalibrate classical strong-line diagnostics at high redshift. MARTA represents a key addition in this space because it provides direct metallicities at moderately high oxygen abundances (12+log(O/H) ~8.0-8.4).