UNCOVER: A NIRSpec Census of Lensed Galaxies at z=8.50-13.08 Probing a High AGN Fraction and Ionized Bubbles in the Shadow

We present JWST NIRSpec prism spectroscopy of gravitationally lensed galaxies at $z\gtrsim9$ found behind the massive galaxy cluster Abell 2744 in the UNCOVER Cycle 1 Treasury Program. We confirm the source redshift via emission lines and/or the Ly$\alpha$ break feature for ten galaxies at z=8.50-13.08 down to $M_{\rm UV}=-17.3$. We achieve a high confirmation rate of 100\% for $z>9$ candidates reported in Atek et al. (2023). Using six sources with multiple emission line detections, we find that the offset of the redshift estimates between the lines and the Ly$\alpha$ break alone with prism can be as large as $\pm0.2$, raising caution in designing future follow-up spectroscopy for the break-only sources with ALMA. With spec-$z$ confirmed sources in UNCOVER and the literature, we derive lower limits on the rest-frame ultraviolet (UV) luminosity function (LF) at $z\simeq9$-12 and find these lower limits to be consistent with recent photometric measurements. We identify at least two unambiguous and several possible active galactic nucleus (AGN) systems based on X-ray emission, broad line (BL) H$\beta$, high ionization line (e.g., NIV]1487, CIV1549) detections, and excess in UVLF. This requires the AGN LFs at $z\simeq$ 9-10 to be comparable or even higher than the X-ray AGN LF estimated at $z\sim6$ and indicates a plausible cause of the high abundance of $z>9$ galaxies claimed in recent photometric studies may be AGNs. One UV-luminous source is confirmed at the same redshift as a dusty BL AGN at $z=8.50$ with a physical separation of 380 kpc in the source plane. These two sources show blueward Ly$\alpha$ line or continuum emission, suggesting that they reside in the same ionized bubble with a radius of $7.69\pm0.18$ pMpc. Our results imply that AGNs have a non-negligible contribution to cosmic reionization.