Cold Jupiters and small planets: Friends, foes, or indifferent?

Determining whether there is any correlation between the presence of short-period small planets (SPs) with P ≲ 100 d (a ≲ 0.4 AU) and 1 < Mp < 20 M⊕ and that of outer cold Jupiters (CJs) with a = 1–10 AU and Mp = 0.5–20 MJup around solar-type stars may provide crucial constraints on models of formation and/or migration of SPs. However, discrepant results regarding the occurrence rates of CJs in SP systems have been reported in the literature, with some recent studies suggesting a strong SP-CJ correlation, but only at super-solar metallicities and/or masses of the host stars. Here, we homogeneously recomputed the occurrence rates of CJs at average, sub-solar ([Fe/H] < –0.1), solar (–0.1 ≤ [Fe/H] ≤ 0.1), and super-solar ([Fe/H] > 0.1) metallicities, as well as at average and subintervals of stellar mass, namely 0.6–0.8, 0.8–1.0, and 1.0–1.2 M⊙, using: (i) a carefully selected sample of 217 SP systems detected through transits or radial velocity, and (ii) a large comparison sample of 1167 solar-type stars, regardless of the possible presence of SPs. We determine the integrated occurrence rate of CJs in SP systems to be ${f_{{\rm{CJ|SP}}}} = 11.1_{ - 1.8}^{ + 2.5}\% $ at average metallicity $\overline {\left[ {{\rm{fe/H}}} \right]} = - 0.011 \pm 0.005$ and mass $\overline {\left[ {{M_ \star }} \right]} = 0.916 \pm 0.012\,{{\rm{M}}_ \odot }$; this is consistent with the estimated frequencies of CJs in both the comparison sample (${f_{{\rm{CJ}}}} = 9.8_{ - 0.8}^{ + 0.9}\% $ at $\overline {\left[ {{\rm{fe/H}}} \right]} = - 0.072 \pm 0.009$ and $\overline {{M_ \star }} = 0.994 \pm 0.004\,{{\rm{M}}_ \odot }$) and the HARPS-N survey of transiting SP systems. We find a possible correlation (fCJ|SP > fCJ) only at super-solar mass and metallicity, namely 1.0 ≤ M★ < 1.2 M⊙ and [Fe/H] > 0.1, although with statistical confidence of less than 3σ. To test some theoretical predictions, we also searched for possible SP-CJ relations as a function of SP and CJ multiplicity, as well as SP composition, albeit with the inevitably limited current sample, and we found none. We show that the architectures of SP systems are not indifferent to the presence of CJs, because the multiplicity of SPs strongly depends on the CJ eccentricity, as expected from planetary dynamics. A more comprehensive understanding of the relation between SPs and CJs requires larger samples of SP systems. The increasing number of well-characterized systems and the anticipated discoveries from both the Gaia and PLATO missions will enable a definitive assessment of the impact of CJs on the formation of SPs.