Quantization of Planetary Systems and its Dependency on Stellar Rotation

With the discovery of now more than 500 exoplanets, we present a statistical analysis of the planetary orbital periods and their relationship to the rotation periods of their parent stars. We test whether the structural variables of planetary orbits, i.e. planetary angular momentum and orbital period, are `quantized' in integer or half-integer multiples of the parent star's rotation period. The Solar System is first shown to exhibit quantized planetary orbits that correlate with the Sun's rotation period. The analysis is then expanded over 443 exoplanets to statistically validate this quantization and its association with stellar rotation. The results imply that the exoplanetary orbital periods are highly correlated with the parent star's rotation periods and follow a discrete half-integer relationship with orbital ranks n=0.5, 1.0, 1.5, 2.0, 2.5, etc. The probability of obtaining these results by pure chance is p<0.024. We discuss various mechanisms that could justify this planetary quantization, such as the hybrid gravitational instability models of planet formation, along with possible physical mechanisms such as the inner disc's magnetospheric truncation, tidal dissipation, and resonance trapping. In conclusion, we statistically demonstrate that a quantized orbital structure should emerge from the formation processes of planetary systems and that this orbital quantization is highly dependent on the parent star's rotation period.