Chaotic quadruple secular evolution and the production of misaligned exomoons and Warm Jupiters in stellar multiples

We study the chaotic and secular evolution of hierarchical quadruple systems in the $3+1$ configuration, focusing on the evolution of mutual inclination of the inner binaries as the system undergoes coupled Lidov-Kozai (LK) oscillations. We include short-range forces (SRF; such as those due to tidal and rotational distortions) that control the eccentricity excitation of the inner binary. The evolution of mutual inclination is described, a priori, by two dimensionless parameters, $\pazocal{R}_0$, the ratio between the inner and outer LK time-scales and $\epsilon_{SRF}$, the ratio between the SRF precession and the inner LK precession rates. We find that the chaotic zones for the mutual inclination depend mainly on $\pazocal{R}_0$, while $\epsilon_{SRF}$ controls mainly the range of eccentricity excitation. The mutual inclination evolves chaotically for $1\lesssim \pazocal{R}_0\lesssim 10$, leading to large misalignments. For $0.4 \lesssim \pazocal{R}_0 \lesssim 0.8$, the system could be weakly excited and produce bimodal distribution of mutual inclination angles. Our results can be applied to exomoons-planets in stellar binaries and Warm/Hot Jupiters in stellar triples. Such systems could develop large mutual inclination angles if the inner binary is tight enough, and also high eccentricities, depending of the strength of the short-range forces. Future detections of tilted Warm/Hot Jupiters and exomoons could put our mechanism under observational tests.