The Metallicity Dimension of the Super Earth-cold Jupiter Correlation
Wei Zhu
Abstract
Abstract The correlation between close-in super Earths and distant cold Jupiters in planetary systems has important implications for their formation and evolution. 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>39</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>11</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>12</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>%</mml:mo> </mml:math> , 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.