AMICO galaxy clusters in KiDS-DR3: Cosmological constraints from angular power spectrum and correlation function

We study the tomographic clustering properties of the photometric cluster catalogue derived from the Third Data Release of the Kilo Degree Survey, focusing on the angular correlation function and its spherical harmonic counterpart, the angular power spectrum. We measure the angular correlation function and power spectrum from a sample of 5162 clusters, with an intrinsic richness $\lambda^*\geq 15$, in the photometric redshift range $z\in [0.1, 0.6]$, comparing our measurements with theoretical models, in the framework of the $\Lambda$-Cold Dark Matter cosmology. We perform a Monte Carlo Markov Chain analysis to constrain the cosmological parameters $\Omega_{\mathrm{m}}$, $\sigma_8$ and the structure growth parameter $S_8\equiv\sigma_8 \sqrt{\Omega_{\mathrm{m}}/0.3}$. We adopt Gaussian priors on the parameters of the mass-richness relation, based on the posterior distributions derived from a previous joint analysis of cluster counts and weak lensing mass measurements carried out with the same catalogue. From the angular correlation function, we obtain $\Omega_{\mathrm{m}}=0.32^{+0.05}_{-0.04}$, $\sigma_8=0.77^{+0.13}_{-0.09}$ and $S_8=0.80^{+0.08}_{-0.06}$, in agreement, within $1\sigma$, with 3D clustering result based on the same cluster sample and with existing complementary studies on other datasets. For the angular power spectrum, we derive statistically consistent results, in particular $\Omega_{\mathrm{m}}=0.24^{+0.05}_{-0.04}$ and $S_8=0.93^{+0.11}_{-0.12}$, while the constraint on $\sigma_8$ alone is weaker with respect to the one provided by the angular correlation function, $\sigma_8=1.01^{+0.25}_{-0.17}$. Our results show that the 2D clustering from photometric cluster surveys can provide competitive cosmological constraints with respect to the full 3D clustering statistics, and can be successfully applied to ongoing and forthcoming spectro/photometric surveys.