The ALMA-CRISTAL survey: weak evidence for star-formation driven outflows in $z\sim5$ main-sequence galaxies

There is a broad consensus from theory that stellar feedback in galaxies at high redshifts is essential to their evolution, alongside conflicting evidence in the observational literature about its prevalence and efficacy. To this end, we utilize deep, high-resolution [CII] emission line data taken as part of the [CII] resolved ISM in star-forming galaxies with ALMA (CRISTAL) survey. Excluding sources with kinematic evidence for gravitational interactions, we perform a rigorous stacking analysis of the remaining 15 galaxies to search for broad emission features that are too weak to detect in the individual spectra, finding only weak evidence that a broad component is needed to explain the composite spectrum. Additionally, such evidence is mostly driven by CRISTAL-02, which is already known to exhibit strong outflows in multiple ISM phases. Interpreting modest residuals in the stack at $v\sim300$kms$^{-1}$ as an outflow, we derive a mass outflow rate of $\dot{M}_{\rm out}=26\pm11$M$_\odot$yr$^{-1}$ and a cold outflow mass-loading factor of $\eta_m=0.49\pm0.20$. This result holds for the subsample with the highest star-formation rate surface density $(\Sigma_{\rm{SFR}}>1.93$M$_\odot$yr$^{-1}$kpc$^{-2}$) but no such broad component is present in the composite of the lower-star-formation rate density subsample. Our results imply that the process of star-formation-driven feedback may already be in place in typical galaxies at $z=5$, but on average not strong enough to completely quench ongoing star formation.