Constraining Planetary Formation Models Using Conditional Occurrences of Various Planet Types

We report the conditional occurrences between three planetary types: super-Earths (m sin i $<$ 10 M$_\oplus$, P $<$ 100 days), warm Jupiters (m sin i $>$ 95 $M_\oplus$, 10 $<$ P $<$ 100 days), and cold Jupiters (m sin i $>$ 95 M$_\oplus$, P $>$ 400 days) for sun-like stars. We find that while the occurrence of cold Jupiters in systems with super-Earths is $22.2\substack{+8.3\\-5.4}$$\%$, compared to $10$$\%$ for the absolute occurrence rate of cold Jupiters, the occurrence of super-Earths in systems with cold Jupiters is $66.0\substack{+18.0\\-16.0}$$\%$, compared to $30$$\%$ for the absolute occurrence rate of super-Earths for sun-like stars. We find that the enhancement of super-Earths in systems with cold Jupiters is evident for sun-like stars, in agreement with several previous studies. We also conduct occurrence studies between warm Jupiters and super-Earths, and between warm Jupiters and cold Jupiters, to consolidate our methods. We conduct an independent observational test to study the effects of cold Jupiters against the inner multiplicity using the well-established giant planet host star metallicity correlation for all transiting planets found to date. The conditional occurrences we find here can be used to constrain the validity of various planetary formation models. The extremely interesting correlations between the super-Earths, cold Jupiters, and warm Jupiters can also be used to understand the formation histories of these planetary types.