The ALPINE-CRISTAL-JWST Survey: Gas-phase abundance gradients of main sequence star-forming galaxies and their kinematics at $4 < z < 6$

We present gas-phase radial metallicity profiles for 20 main-sequence galaxies at $4<z<6$, primarily based on JWST NIRSpec IFU observations obtained as part of the JWST-ALPINE-CRISTAL programme. Our study aims to connect the metallicity gradients of these galaxies with their kinematic properties from [CII]158$\mu$m ALMA observations. We mapped the radial profiles of oxygen abundance using the strong-line method leveraging the rich set of rest-frame optical emission lines. Linear fits to the annular-binned radial profiles show that, on average, the metallicity gradients are slightly positive with a median of $+0.039 \pm 0.010{\rm dexkpc^{-1}}$. There are no substantial systematic offsets in gradients when using different line diagnostics. However, only three galaxies show a gradient $>0.05{\rm dexkpc^{-1}}$ at $1\sigma$, and none have a significant negative gradient. We investigated the correlation between the metallicity gradients and the intrinsic gas velocity dispersion $\sigma_0$ as well as the $V_{\rm rot}/\sigma_0$ ratio of the disks. Combining our sample with mass-matched literature samples at $3<z<7$, we found a negative shallow correlation between $V_{\rm rot}/\sigma_0$ and the metallicity gradients, but no strong relationships with $\sigma_0$. As $V_{\rm rot}/\sigma_0$ increases towards later cosmic times, the observed negative trend with $V_{\rm rot}/\sigma_0$ is consistent with the overall cosmic evolution of metallicity gradients from high to low redshifts. This suggests that disk maturity plays a crucial role in shaping the radial metallicity gradients. [Abridged abstract]