NEXUS: A Spectroscopic Census of Broad-line AGNs and Little Red Dots at $3\lesssim z\lesssim 6$

We present a spectroscopic sample of 23 broad-line AGNs (BLAGNs) at $3\lesssim z\lesssim 6$ selected using F322W2+F444W NIRCam/WFSS grism spectroscopy of the central 100 ${\rm arcmin^2}$ area of the NEXUS survey. Among these BLAGNs, 15 are classified as Little Red Dots (LRDs) based on their rest-frame UV-optical spectral slopes and compact morphology. The number density of LRDs is $\sim 10^{-5}\,{\rm cMpc^{-3}}$, with a hint of declining towards the lower end of the probed redshift range. These BLAGNs and LRDs span broad H$\alpha$ luminosities of $\sim 10^{42.2}-10^{43.7}\,{\rm erg\,s^{-1}}$, black hole masses of $\sim 10^{6.3}-10^{8.4}\,M_\odot$, and Eddington ratios of $\sim 0.1-1$ (median value 0.4), though the black hole mass and Eddington ratio estimates carry large systematic uncertainties. Half of the LRDs show strong Balmer absorption, suggesting high-density gas surrounding the line-emitting region. We detect extended (hundreds of parsec) rest-frame UV-optical emission from the host galaxy in the majority of these LRDs, which contributes significantly or even dominantly to their total UV emission. This host emission largely accounts for the peculiar UV upturn of the LRD spectral energy distribution. We also measure the small-scale ($\lesssim 1\,{\rm cMpc}$) clustering of these BLAGNs and LRDs by cross-correlating with a photometric galaxy sample. Extrapolating the power-law two-point correlation function model to large linear scales, we infer a linear bias of $3.30_{-2.04}^{+2.88}$ and typical halo masses of a few $\times 10^{11}\,h^{-1}M_\odot$ for BLAGNs at the sample median redshift of $z\sim 4.5$. However, the inferred linear bias and halo masses of LRDs, while formally consistent with those for BLAGNs at $\sim 1.5\sigma$, appear too large to be compatible with their space density, suggesting LRDs may have strong excess clustering on small scales.