The ALPINE-CRISTAL-JWST survey: spatially resolved star formation relations at $z\sim5$

TL;DR

This study tests the validity of the local KS and [CII]–SFR relations at $z\sim5$ by analysing 13 main-sequence galaxies from the ALPINE and CRISTAL surveys with multi-wavelength data at $\sim$2 kpc resolution. It develops a covariance-aware, pixel-by-pixel SED fitting framework using CIGALE and a tailored likelihood to quantify the $\Sigma_{\rm SFR}$–$\Sigma_{[\rm CII]}$ relation, then explores two [CII]-to-gas conversions. The authors find a resolved [CII]–SFR relation with $\beta = 0.87 \pm 0.15$ and $\sigma_i = 0.19 \pm 0.03$ dex, but demonstrate that the inferred KS relation is highly sensitive to the chosen $[\rm CII]-to-gas$ calibration: a constant $\alpha_{[\rm CII]}$ gives $t_{dep} \sim 0.5$–1 Gyr, while a $\Sigma_{[\rm CII]}$-dependent $W_{[\rm CII]}$ can yield $t_{dep} < 0.1$ Gyr and a slope $\beta \approx 1.75$. These results underscore the need for physically motivated, environment-aware conversions to break the degeneracy and robustly characterize star formation laws in the early Universe. The work demonstrates the power of combining JWST, HST, and ALMA with forward-modeling and simulations to constrain ISM conditions at high redshift.

Abstract

Star formation governs galaxy evolution, shaping stellar mass assembly and gas consumption across cosmic time. The Kennicutt-Schmidt (KS) relation, linking 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] $158 {\rm μm}$ line has recently emerged as a key probe of the cold ISM and star formation in the early Universe. 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 $\sim2$ kpc resolution. We perform pixel-by-pixel spectral energy distribution (SED) modelling with CIGALE on resolution-homogenised images. We develop a statistical framework to fit the [CII]-SFR relation that accounts for pixel covariance and compare our results to classical fitting methods. We test two [CII]-to-gas conversion prescriptions to assess their impact on inferred gas surface densities and depletion times. We find a resolved [CII]-SFR relation with a slope of $0.87 \pm 0.15$ and intrinsic scatter of $0.19 \pm 0.03$ dex, which is shallower and tighter than previous studies at $z\sim5$. The resolved KS relation is highly sensitive to the [CII]-to-gas conversion factor: using a fixed global $α_{\rm [CII]}$ yields depletion times of $0.5$-$1$ Gyr, while a surface brightness-dependent $W_{\rm [CII]}$, places some galaxies with high gas density in the starburst regime ($<0.1$ Gyr). 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 $z\gtrsim4$.

Figures (13)

• Figure 1: Multi-wavelength data for the galaxy VC875, shown at their native resolutions. From left to right : The first row presents HST/ACS F814W (rest-frame 145 nm), JWST/NIRCam F115W (207 nm), F150W (270 nm), and F277W (499 nm). The second row shows JWST/F444W (800 nm), ALMA dust continuum emission around 157 µm, and ALMA [CII] $158\,{\rm \mu m}$ emission. The contours are those of the ALMA [CII] line emission maps starting from $3\sigma$ increasing by steps of $2\sigma$. Ellipses in the bottom-left corners represent the central lobe of the PSF for HST and JWST images, and the synthesised beam for ALMA images.
• Figure 2: Native resolution image of VC875 (left panel) and the homogenised version matching the ALMA resolution (right panel) for the JWST/NIRCam F150W filter. The contours and ellipses are the same as in Fig. \ref{['fig:VC875_native']}.
• Figure 3: Example of physical parameters maps obtained with the CIGALE SED modelling for VC875. From left to right : stellar mass surface density ($\mathrm{M}_\odot\,\mathrm{kpc}^{-2}$), star formation rate surface density averaged over 10 Myrs ($\mathrm{M}_\odot\,\mathrm{yr}^{-1}\,\mathrm{kpc}^{-2}$), mass-weighted age (Myr) and attenuation in FUV rest-frame (mag). The contours are those of the [CII] luminosity map, starting at $3\sigma$ and increasing by steps of $2\sigma$. The ellipse in the bottom left of each panel represent the synthesised ALMA beam. The maps are shown for the pixels having $L_{\rm [CII]}\geq5\sigma_\mathrm{[CII]}$ and S/N$\geq2$ in at least three bands.
• Figure 4: Resolved $[\text{CII}]$-SFR relation for galaxies at $z \sim 5$. The grey contours show the individual pixel distribution for the whole sample. Each pair of coloured points represents a high/low $[\text{CII}]$ density average region for each galaxy of the sample following BetAccGui23KS methodology. The orange line and shaded region shows our best-fit power-law model from the tailored likelihood-based approach with the parameters in the top-left corner (where $\mathrm{log}_{10}(\mathrm{C}_0)$ is the value at $g_0=10^{7.5}\,\mathrm{L}_\odot\,\mathrm{kpc}^{-2}$). The black dashed line presents the extrapolation of the relation derived from a spatially resolved sample of 46 nearby galaxies by Herrera-Camus_2015. We represented the typical errors bars for the individual pixels across the sample with three black squares.
• Figure 5: Kennicutt-Schmidt relation using the $\alpha_\mathrm{[CII]}$ conversion factor (left) and the $W_{\mathrm{[CII]}}$ version (right). The grey contours show the distribution of individual pixel measurements across the entire sample; the pair of points are the BetAccGui23KS region-averages for individual galaxies, colour-coded by redshift. The grey dashed-lines are showing constant gas depletion time. The black dashed line represent the Wang2022 KS relation for local Universe and high redshift main sequence galaxies. We show CO measurements of the global KS relation from the low-z COLD GASS sample (Saintonge2012, crosses) and at redshifts up to $z\sim2.5$ from the PHIBBS (Tacconi2013, plus signs) and PHIBBS2 (Freundlich2019, three-branch stars) programs, together with a resolved $z=2.6$ lensed starburst (Sharon_2013, red points).