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 that leverages ultra-deep, medium-resolution JWST/NIRSpec spectroscopy to probe the interstellar medium of star-forming galaxies at z ∼ 2 − 3. We report detections of one or more auroral lines, including [O <ns0:sc>III</ns0:sc>] λ4363, [O <ns0:sc>II</ns0:sc>] λλ7320, 7330, [S <ns0:sc>II</ns0:sc>] λ4068, and [S <ns0:sc>III</ns0:sc>] λ6312, for 16 galaxies in the sample, providing measurements of multiple ionic temperatures. We tested the validity of the T[O <ns0:sc>II</ns0:sc>]–T[O <ns0:sc>III</ns0:sc>] relation at high redshifts 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 <ns0:sc>II</ns0:sc>]–T[O <ns0:sc>III</ns0:sc>] relationship and its scatter on different physical parameters, finding a mild correlation with the ionisation parameter and radiation field hardness, and no significant correlation with gas density. The location of high-redshift data is also consistent with the low-z literature in the T[O <ns0:sc>II</ns0:sc>]–T[S <ns0:sc>II</ns0:sc>] and T[S <ns0:sc>III</ns0:sc>]–T[O <ns0:sc>III</ns0:sc>] relations, although this conclusion is limited due to low-number statistics. Finally, we leveraged our sample together with a comprehensive compilation of galaxies with [O <ns0:sc>III</ns0:sc>] λ4363 detections from the literature to recalibrate classical strong-line diagnostics at high redshifts. 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).