Angular clustering and bias of photometric quasars in the Kilo-Degree Survey Data Release 4

We investigate the angular clustering and effective bias of photometrically selected quasars in the Kilo-Degree Survey Data Release 4 (KiDS DR4). We update the previous photometric redshifts (photo-$z$s) of the KiDS quasars using Hybrid-z, a deep learning framework combining four-band KiDS images and nine-band KiDS+VIKING magnitudes. Hybrid-z is trained on the latest Dark Energy Spectroscopic Instrument (DESI) DR1 and Sloan Digital Sky Survey (SDSS) DR17 quasars matching with KiDS, and achieves average bias $\langle \delta z \rangle < 0.01$ and scatter $\sim 0.04(1 + z)$ on a test sample. The updated catalog of $\sim 157k$ quasars over $777~\mathrm{deg}^2$ is divided into four tomographic bins spanning $0.1 \leq z_{\mathrm{phot}} \leq 2.7$. In each bin, we measure the angular two-point correlation function and compare it with theoretical predictions for dark matter clustering. We estimate the best-fit scale-independent quasar bias, which increases from $b \approx 1.6$ at $z \approx 0.6$ to $b \approx 4.0$ at $z \approx 2.2$, and is well matched by a quadratic relation in redshift. Our clustering analysis indicates that KiDS quasars reside in dark matter halos of mass $\log_{10}(M_{\mathrm{eff}}/h^{-1}M_\odot)$ in the range $\sim 12.7$--$12.9$ and effective peak heights $\nu_{\mathrm{eff}}$ rising from $\sim 1.5$ to $2.9$ over our redshift span. We study two systematics that could affect the bias derivation: stellar contamination and the redshift distribution assumed in the theoretical modeling. The former has a negligible effect, whereas the latter significantly impacts the derived $b(z)$, emphasizing the importance of redshift calibration. Our work is the first cosmological application of quasars selected from KiDS and paves the way for future extensions in the final KiDS DR5, the Legacy Survey of Space and Time, or the 4-metre Multi-Object Spectroscopic Telescope.