The ALPINE-CRISTAL-JWST survey: Spatially resolved star formation relations at z ∼ 5

¹ Université de Strasbourg, CNRS, Observatoire Astronomique de Strasbourg, UMR 7550, 67000 Strasbourg, France
² Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, 06000 Nice, France
³ Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France
⁴ INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Gobetti 93/3, 40129 Bologna, Italy
⁵ Instituto de Estudios Astrofísicos, Facultad de Ingeniería y Ciencias, Universidad Diego Portales, Av. Ejército 441, Santiago, Chile
⁶ Millenium Nucleus for Galaxies (MINGAL), Concepción, Chile
⁷ Departamento de Astronomía, Universidad de Concepción, Barrio, Universitario, Concepción, Chile
⁸ Dipartimento di Fisica e Astronomia, Universitè di Padova, Vicolo dell’Osservatorio 3, Padova, Italy
⁹ INAF – Osservatorio Astronomico di Padova, Vicolo dell’ Osservatorio 5, 35122 Padova, Italy
¹⁰ International Centre for Radio Astronomy Research (ICRAR), The University of Western Australia, M468, 35 Stirling Highway, Crawley, WA 6009, Australia
¹¹ ARC Center of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Canberra, Australia
¹² Sterrenkundig Observatorium, Ghent University, Krijgslaan 281 - S9, B9000 Ghent, Belgium
¹³ Department of Astronomy, University of Geneva, Chemin Pegasi 51, 1290 Versoix, Switzerland
¹⁴ Institut d’Astrophysique de Paris, Sorbonne Université, CNRS, UMR 7095, 98 bis bd Arago, 75014 Paris, France
¹⁵ IPAC, California Institute of Technology, 1200 E California Boulevard, Pasadena, CA 91125, USA
¹⁶ Center for Frontier Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
¹⁷ Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Firenze, Italy
¹⁸ INAF – Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
¹⁹ Hiroshima Astrophysical Science Center, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan
²⁰ Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
²¹ Gemini Observatory, NSF NOIRLab, 670 N. A’ohoku Place, Hilo, Hawai’i 96720, USA
²² Department of Physics and Astronomy, University of California, Davis, One Shields Ave., Davis, CA 95616, USA
²³ Department of Physics and Astronomy and George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, 4242 TAMU, College Station, TX 77843-4242, USA
²⁴ Department of Physics and Astronomy, University of California, Riverside, 900 University Avenue, Riverside, CA 92521, USA
²⁵ Instituto de Física y Astronomía, Universidad de Valparaíso, Avda. Gran Bretaña 1111, Valparaíso, Chile
²⁶ INAF – Osservatorio astronomico d’Abruzzo, Via Maggini SNC, 64100 Teramo, Italy
²⁷ National Centre for Nuclear Research, ul. Pasteura 7, 02-093 Warsaw, Poland
²⁸ Dipartimento di Fisica e Astronomia “Augusto Righi”, Alma Mater Studiorum, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
²⁹ Dept. Fisica Teorica y del Cosmos, Universidad de Granada, Granada, Spain
³⁰ Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
³¹ Scuola Internazionale Superiore Studi Avanzati (SISSA), Physics Area, Via Bonomea 265, 34136 Trieste, Italy
³² Departamento de Astronomía, Universidad de Concepción, Barrio Universitario, Concepción, Chile
³³ Department of Astronomy and Yonsei University Observatory, Yonsei University, Seoul 03722, Republic of Korea
³⁴ Institute of Astronomy, Graduate School of Science, The University of Tokyo, 2-21-1 Osawa, Mitaka, Tokyo 181-0015, Japan

^⋆ Corresponding author: cedric.accard@astro.unistra.fr

Received: 27 June 2025
Accepted: 15 August 2025

Abstract

Context. Star formation governs galaxy evolution, shaping stellar mass assembly and gas consumption across cosmic time. The Kennicutt-Schmidt (KS) relation, linking the star formation rate (SFR) and gas surface densities, is fundamental to understand star formation regulation, yet remains poorly constrained at z > 2 due to observational limitations and uncertainties in locally calibrated gas tracers. The [CII] 158 μm line has recently emerged as a key probe of the cold ISM and star formation in the early Universe.

Aims. We investigate whether the resolved [CII]–SFR and KS relations established at low redshift remain valid at 4 < z < 6 by analysing 13 main-sequence galaxies from the ALPINE and CRISTAL surveys, using multi-wavelength data (HST, JWST, ALMA) at ∼2 kpc resolution.

Methods. We performed pixel-by-pixel spectral energy distribution (SED) modelling with CIGALE on resolution-homogenised images. We developed a statistical framework to fit the [CII]–SFR relation that accounts for pixel covariance and compare our results to classical fitting methods. We tested two [CII]-to-gas conversion prescriptions to assess their impact on inferred gas surface densities and depletion times.

Results. We find a resolved [CII]–SFR relation with a slope of 0.87 ± 0.15 and intrinsic scatter of 0.19 ± 0.03 dex, which is shallower and tighter than previous studies at z ∼ 5. The resolved KS relation is highly sensitive to the [CII]-to-gas conversion factor: using a fixed global α_[CII] yields depletion times of 0.5–1 Gyr, while a surface brightness-dependent W_[CII], accounting for local ISM conditions, places some galaxies with high gas density in the starburst regime (< 0.1 Gyr).

Conclusions. Future inputs from both simulations and observations are required to better understand how the [CII]-to-gas conversion factor depends on local ISM properties. We need to break this fundamental limit to properly study the KS relation at z ≳ 4.