Strong rest-UV emission lines in a "little red dot" AGN at $z=7$: Early SMBH growth alongside compact massive star formation?

JWST has now revealed a population of broad-line AGN at $z>4$ characterized by a distinctive SED shape, with very red rest-frame optical and very blue rest-frame UV continuum. While the optical continuum is thought to originate from the accretion disk, the origin of the UV continuum has been largely unclear. We report the detection of the strong rest-frame UV emission lines of CIII]$\lambda\lambda$1907,1909 and CIV$\lambda\lambda$1549,1551 in a "little red dot" AGN, COS-66964. Spectroscopically confirmed at $z=7.0371$, COS-66964 exhibits broad H$\alpha$ emission (FWHM $\sim 2000$ km s$^{-1}$), and weak broad H$\beta$, implying significant dust attenuation to the BLR ($A_V = 3.9^{+1.7}_{-0.9}$). The H$\alpha$ line width implies a central SMBH mass of $M_{\rm BH} = \left(1.9^{+1.6}_{-0.7}\right)\times10^{7}$ M$_\odot$, and an Eddington ratio $\lambda\sim0.3$-$0.5$. While marginal HeII$\lambda4687$ and [FeX]$\lambda6376$ detections further indicate that the AGN dominates in the rest-frame optical, the non-detection of HeII$\lambda1640$ in the UV despite high EW CIII] and CIV ($\sim 35$ {\AA}) is more consistent with photoionization by massive stars. The non-detection of MgII$\lambda\lambda$2800 is similarly inconsistent with an AGN scattered light interpretation. Assuming the rest-frame UV is dominated by stellar light, we derive a stellar mass of $\log M_\star/M_\odot\sim8.5$, implying an elevated $M_{\rm BH}/M_\star$ ratio $\sim2$ orders of magnitude above the local relation, but consistent with other high-$z$ AGN discovered by JWST. The source is unresolved in all bands, implying a very compact size $\lesssim200$ pc in the UV. This suggests that the simultaneous buildup of compact stellar populations (i.e., galaxy bulges) and the central SMBH is ongoing even at $z>7$.