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

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Volume 702 (October 2025)

A&A, 702 (2025) A206

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Table 2.

Best-fit parameters and uncertainties for the Σ_SFR-Σ_CII relation derived from the different fitting methods described in Sect. 3.2.

Fitting Method	log(C₀)^a	β	σ_i
Likelihood Model + L-BFGS-B integration

Original Fit	0.30	0.87	0.19
Source Bootstrapping	$0 . 30_{- 0.04}^{+ 0.05}$ $0.30^{+0.05}_{-0.04}$	$0 . 86_{- 0.11}^{+ 0.15}$ $0.86^{+0.15}_{-0.11}$	$0 . 19_{- 0.03}^{+ 0.03}$ $0.19^{+0.03}_{-0.03}$
Noise Sampling	$0 . 33_{- 0.02}^{+ 0.02}$ $0.33^{+0.02}_{-0.02}$	$0 . 80_{- 0.06}^{+ 0.05}$ $0.80^{+0.05}_{-0.06}$	$0 . 20_{- 0.02}^{+ 0.02}$ $0.20^{+0.02}_{-0.02}$
Hybrid Resampling	$0 . 34_{- 0.04}^{+ 0.05}$ $0.34^{+0.05}_{-0.04}$	$0 . 80_{- 0.13}^{+ 0.15}$ $0.80^{+0.15}_{-0.13}$	$0 . 19_{- 0.03}^{+ 0.04}$ $0.19^{+0.04}_{-0.03}$

Likelihood Model + MCMC

Original Likelihood	0.30	0.87	0.19
Normalised Likelihood	$0 . 30_{- 0.03}^{+ 0.03}$ $0.30^{+0.03}_{-0.03}$	$0 . 87_{- 0.09}^{+ 0.09}$ $0.87^{+0.09}_{-0.09}$	$0 . 20_{- 0.02}^{+ 0.02}$ $0.20^{+0.02}_{-0.02}$

Linmix

All Pixels	0.37	0.92	0.18
Region Averages (B23)	$0 . 22_{- 0.04}^{+ 0.04}$ $0.22^{+0.04}_{-0.04}$	$1 . 02_{- 0.12}^{+ 0.12}$ $1.02^{+0.12}_{-0.12}$	$0 . 06_{- 0.08}^{+ 0.08}$ $0.06^{+0.08}_{-0.08}$

Notes. Parameter uncertainties, when given, were computed using the 16th, 50th, and 84th percentiles of the associated distributions.

^(a)

We present the log(C₀) using a normalisation factor (g₀ = 10^7.5), since the reported uncertainties have been derived using this g₀ cannot easily be extrapolated back to the un-normalised space. However, a subtraction of 7.5 from log(C₀) allows one to obtain the actual relation intercept.

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