The Metallicity Dimension of the Super Earth-Cold Jupiter Correlation

The correlation between close-in super Earths and distant cold Jupiters in planetary systems has important implications for their formation and evolution. In contrary to some earlier findings, a recent study conducted by Bonomo et al.\ suggests that the occurrence of cold Jupiter companions is not excessive in super Earth systems. Here we show that this discrepancy can be seen as a Simpson's paradox and is resolved once the metallicity dependence of the super Earth--cold Jupiter relation is taken into account. A common feature is noticed that almost all the cold Jupiter detections with inner super Earth companions are found around metal-rich stars. Focusing on the Sun-like hosts with super-solar metallicities, we show that the frequency of cold Jupiters conditioned on the presence of inner super Earths is $39_{-11}^{+12}\%$, whereas the frequency of cold Jupiters in the same metallicity range is no more than $20\%$. Therefore, the occurrences of close-in super Earths and distant cold Jupiters appear correlated around metal-rich hosts. The relation between the two types of planets remains unclear for stars with metal-poor hosts due to the limited sample size and the much lower occurrence rate of cold Jupiters, but a correlation between the two cannot be ruled out.