We measure resolved (kiloparsec-scale) outflow properties in a sample of 10starburst galaxies from the DUVET sample, using Keck/KCWI observations ofH$\beta$ and [OIII]~$\lambda$5007. We measure $\sim450$ lines-of-sight thatcontain outflows, and use these to study scaling relationships of outflowvelocity ($v_{\rm out}$), mass-loading factor ($\eta$; mass outflow rate perSFR) and mass flux ($\dot{\Sigma}_{\rm out}$; mass outflow rate per area) withco-located SFR surface density ($\Sigma_{\rm SFR}$) and stellar mass surfacedensity ($\Sigma_{\ast}$). We find strong, positive correlations of$\dot{\Sigma}_{\rm out} \propto \Sigma_{\rm SFR}^{1.2}$ and $\dot{\Sigma}_{\rmout} \propto \Sigma_{\ast}^{1.7}$. We also find shallow correlations between$v_{\rm out}$ and both $\Sigma_{\rm SFR}$ and $\Sigma_{\ast}$. Our resolvedobservations do not suggest a threshold in outflows with $\Sigma_{\rm SFR}$,but rather we find that the local specific SFR ($\Sigma_{\rm SFR}/\Sigma_\ast$)is a better predictor of where outflows are detected. We find that outflows arevery common above $\Sigma_{\rm SFR}/\Sigma_\ast\gtrsim 0.1$~Gyr$^{-1}$ and rarebelow this value. We argue that our results are consistent with a picture inwhich outflows are driven by supernovae, and require more significant injectedenergy in higher mass surface density environments to overcome local gravity.The correlations we present here provide a statistically robust, directcomparison for simulations and higher redshift results from JWST.

We present deep JWST NIRSpec observations in the sightline of MACSJ1149.5+2223, a massive cluster of galaxies at $z=0.54$. We report thespectroscopic redshift of 28 sources at $3<z<9.1$, including 9 sources with thedetection of the [OIII]4363 auroral line. Combining these with 16[OIII]4363-detected sources from publicly available JWST data, our sampleconsists of 25 galaxies with robust gas-phase metallicity measurements via thedirect method. We observe a positive correlation between stellar mass andmetallicity, with a $\sim0.5$\,dex offset down below the local relation.Interestingly, we find a larger than expected scatter of $\sim0.3$\,dex aroundthe relation, which cannot be explained by redshift evolution among our sampleor other third parameter. The scatter increases at higher redshift, and weattribute this to the enrichment process having higher stochasticity due toshallower potential wells, more intense feedback processes, and a higher galaxymerger rate. Despite reaching to a considerably low-mass regime ($\logM_*/M_\odot \sim7.3$), our samples have metallicity of $\log$(O/H)$+12>7$, i.e.comparable to the most metal poor galaxies in the local Universe. The search ofprimordial galaxies may be accomplished by extending toward a lower mass and/orby investigating inhomogeneities at smaller spatial scales. Lastly, weinvestigate potential systematics caused by the limitation of JWST's MSAobservations. Caution is warranted when the target exceeds the slit size, asthis situation could allow an overestimation of ``global" metallicity,especially under the presence of strong negative metallicity gradient.