Exploring Cosmic Dawn with PANORAMIC II: Cosmic Variance and Galaxy Clustering at $z\sim10$

Observational campaigns with JWST have revealed a higher-than-expected abundance of UV-bright galaxies at $z\gtrsim10$, with various proposed theoretical explanations. A powerful complementary constraint to break degeneracies between different models is galaxy clustering. In this paper, we combine PANORAMIC pure parallel and legacy imaging along 34 independent sightlines to measure the cosmic variance ($\sigma_{\rm CV}$) in the number count of Lyman break galaxies at $z\sim10$ which is directly related to their clustering strength. We find $\sigma_{\rm CV}=0.96^{+0.20}_{-0.18}$, $1.46^{+0.54}_{-0.44}$, and $1.71^{+0.72}_{-0.59}$ per NIRCam pointing ($\sim9.7\,{\rm arcmin}^2$, $\lesssim1.5\,{\rm pMpc}$ at $z\sim10$) for galaxies with M$_{\rm UV}<-19.5$, $-20$, and $-20.5$. Comparing to galaxies in the UniverseMachine, we find that $\sigma_{\rm CV}$ is consistent with our measurements, but that the number densities are a factor $\gtrsim5$ lower. We implement simple models in the UniverseMachine that represent different physical mechanisms to enhance the number density of UV-bright galaxies. All models decrease $\sigma_{\rm CV}$ by placing galaxies at fixed M$_{\rm UV}$ in lower mass halos, but they do so to varying degrees. Combined constraints on $\sigma_{\rm CV}$ and the UVLF tentatively disfavor models that globally increase the star formation efficiency (SFE) or the scatter in the M$_{\rm UV}$-$M_{\rm halo}$ relation, while models that decrease the mass-to-light ratio, or assume a power-law scaling of the SFE with $M_{\rm halo}$ agree better with the data. We show that with sufficient additional independent sightlines, robust discrimination between models is possible, paving the way for powerful constraints on the physics of early galaxy evolution through NIRCam pure parallel imaging.