Tracing Outflows from Stellar Feedback in the Early Universe with Lyman-$\alpha$

Blind spectroscopy of massive lensing galaxy clusters with MUSE has revealed large numbers of gravitationally-lensed Lyman-$\alpha$ emitters exhibiting asymmetric profiles at $2.9 \leq z \leq 6.7$, suggesting abundant outflows from low-mass star-forming galaxies in the early universe. Are these primaeval galaxies experiencing their first bursts of star formation, or established galaxies experiencing rejuvenation? With JWST rest-frame optical/NIR continuum imaging now available for many of these objects, we can search for older stellar populations. Here, we search for spectroscopic confirmation of outflows from these galaxies, finding a few high-signal-to-noise cases in which blueshifted interstellar absorption lines are detected. Next, we analyse the star formation histories with combined HST + JWST photometry. We find most them to be well characterised by very young, low metallicity stellar populations. However, despite the rest-frame optical/NIR coverage of JWST, we cannot place strict upper bounds on the mass in old stars (age $> 100\,\text{Myr}$).