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

¹ Università di Firenze, Dipartimento di Fisica e Astronomia, Via G. Sansone 1, 50019 Sesto Fiorentino, Florence, Italy
² INAF – Arcetri Astrophysical Observatory, Largo E. Fermi 5, I-50125 Florence, Italy
³ European Southern Observatory, Karl-Schwarzschild Straße 2, D-85748 Garching bei, München, Germany
⁴ Department of Physics, University of Arkansas, 226 Physics Building, 825 West Dickson Street, Fayetteville, AR 72701, USA
⁵ Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy
⁶ Institute for Astronomy, University of Edinburgh, Royal Observatory, Edinburgh EH9 3HJ, UK
⁷ Centre for Astrophysics Research, Department of Physics, Astronomy and Mathematics, University of Hertfordshire, Hatfield AL10 9AB, UK
⁸ AURA for European Space Agency, Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21210, USA
⁹ Cavendish Laboratory, University of Cambridge, 19 JJ Thomson Avenue, Cambridge CB3 0HE, UK
¹⁰ Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge CB30HA, UK
¹¹ University of Trento, Via Sommarive 14, I-38123 Trento, Italy

^⋆ Corresponding author.

Received: 28 March 2025
Accepted: 20 September 2025

Abstract

We present the first results from MARTA (Measuring Abundances at high Redshift with the T_e 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 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 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 II]–T[O III] 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 II]–T[S II] and T[S III]–T[O III] 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 III] 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).