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

A search for correlations with the largest exoplanet samples

¹ INAF – Osservatorio Astrofisico di Torino, via Osservatorio 20, 10025 Pino Torinese, Italy
² Dipartimento di Fisica, Università degli Studi di Torino, via Pietro Giuria 1, 10125 Torino, Italy
³ University of Southern Queensland, Centre for Astrophysics, West Street, Toowoomba, QLD 4350, Australia

^★ Corresponding author: aldo.bonomo@inaf.it

Received: 7 October 2024
Accepted: 20 May 2025

Abstract

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 < M_p < 20 M_⊕ and that of outer cold Jupiters (CJs) with a = 1–10 AU and M_p = 0.5–20 M_Jup 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_CJ|SP = 11.1_−1.8^+2.5% at average metallicity [Fe/H] = −0.011 ± 0.005 and mass M_* = 0.916 ± 0.012 M_⊙; this is consistent with the estimated frequencies of CJs in both the comparison sample ((f_CJ = 9.8_−0.8^+0.9% at [Fe/H] = −0.072 ± 0.009 and M_* = 0.994 ± 0.004 M_⊙)) and the HARPS-N survey of transiting SP systems. We find a possible correlation (f_CJ|SP > f_CJ) 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.