Searching for Emission Lines at $z>11$: The Role of Damped Lyman-$\alpha$ and Hints About the Escape of Ionizing Photons

We describe new ultra-deep James Webb Space Telescope (JWST) NIRSpec PRISM and grating spectra for the galaxies JADES-GS-z11-0 ($z_{\mathrm{spec}} = 11.122^{+0.005}_{-0.003}$) and JADES-GS-z13-0 ($z_{\mathrm{spec}} = 13.20^{+0.03}_{-0.04}$), the most distant spectroscopically-confirmed galaxy discovered in the first year of JWST observations. The extraordinary depth of these observations (75 hours and 56 hours, respectively) provides a unique opportunity to explore the redshifts, stellar properties, UV magnitudes, and slopes for these two sources. For JADES-GS-z11-0, we find evidence for multiple emission lines, including [\ion{O}{2}]$\lambda\lambda3726,3729$\AA and [\ion{Ne}{3}$]\lambda3869$\AA, resulting in a spectroscopic redshift we determine with 94\% confidence. We present stringent upper limits on the emission line fluxes and line equivalent widths for JADES-GS-z13-0. At this spectroscopic redshift, the Lyman-$\alpha$ break in JADES-GS-z11-0 can be fit with a damped Lyman-$\alpha$ absorber with $\log{(N_\mathrm{HI}/\mathrm{cm}^{-2})} = 22.42^{+0.093}_{-0.120}$. These results demonstrate how neutral hydrogen fraction and Lyman-damping wings may impact the recovery of spectroscopic redshifts for sources like these, providing insight into the overprediction of the photometric redshifts seen for distant galaxies observed with JWST. In addition, we analyze updated NIRCam photometry to calculate the morphological properties of these resolved sources, and find a secondary source $0.3^{\prime\prime}$ south of JADES-GS-z11-0 at a similar photometric redshift, hinting at how galaxies grow through interactions in the early Universe.