The GAPS Programme with HARPS-N at TNG LXXVII. Occurrence rates of small close-in planets in the presence of cold Jupiters

Abstract: Context. The architecture of our Solar System, with inner small planets (ISPs) and outer giants, may or may not be common. Understanding whether a correlation exists between ISPs and outer cold giants is key to evaluating how common systems with a similar architecture to our own are. Aims. This study aims to build a large, homogeneous sample of systems hosting cold Jupiters (CJs, a > 1 au, msini > 0.1 M$_J$) detected via radial velocities (RVs), and to assess the presence of additional ISPs (P < 400 d, 3 < msini < 31.7 M$_{\oplus}$), studying the correlation between these two types of objects. Methods. We selected 137 stars known to host a CJ, including 23 which also harbor a hot Jupiter and were treated separately. Data from various instruments were compiled, including unpublished data gathered with HARPS-N within the GAPS program, and consistently fitted using PyORBIT. We derived RV detection maps and calculated occurrence rates for ISPs, cross-validating results with two independent codes. The sample was divided into subgroups to evaluate how system parameters influence planet occurrence. Results. We confirmed the 213 already known planets in the 137 systems and also identified six new candidates. We divided them, based on mass and period, into Neptunes (10 < m sin i < 31.7 M$_{\oplus}$) and Super-Earths (3 < m sin i < 10 M$_{\oplus}$), and into hot (1 < P < 10 d), warm (10 < P < 100 d), and cool (100 < P < 400 d). We found occurrences of 5%, 13%, and 12% for hot, warm, and cool Neptunes, respectively, and 11% and 16% for hot and warm Super-Earths, respectively. Systems with dynamically stable inner regions show higher rates of small planets. These findings are consistent with previous studies showing no strong correlation between ISPs and CJs at average stellar metallicity and mass, and suggest that HJs may be more commonly associated with external giants.

• The paper quantifies occurrence rates of inner small planets in systems hosting cold Jupiters using extensive, high-precision RV data.
• The methodology employs a multi-step target selection and Bayesian model selection with Gaussian Process regression to mitigate stellar activity.
• The findings reveal that dynamically stable inner regions significantly enhance the occurrence of warm Neptunes and Super-Earths.

Occurrence Rates of Small Close-in Planets in the Presence of Cold Jupiters

Abstract and Context

The study systematically investigates the conditional occurrence rates of inner small planets (ISPs) in planetary systems with cold Jupiters (CJs) as probed by high-precision radial velocity (RV) observations. Drawing on an extensive and homogeneous target selection from the NASA Exoplanet Archive, complemented by new data from the GAPS programme with HARPS-N at TNG, the analysis emphasizes the dynamic and demographic linkage between ISPs (3–31.7 $\,M_{\oplus}$, $P < 400$ d) and CJs ($m_{\mathrm{sini}} > 0.1\,M_{\mathrm{J}}$, $a_{\mathrm{peri}} > 1$ au). The fundamental question addressed is whether architectures similar to our Solar System—with tightly packed inner small planets and outer giants—are commonplace, and which physical parameters modulate this correlation.

Sample Selection and Methodology

A unique feature of this investigation is the rigorous, multi-step selection pipeline yielding a sample of 137 FGK stars hosting empirically confirmed CJs, excluding systems with inner ($a < 1$ au) gas giants, M dwarfs, and close binaries. This curated list ensures stratified sensitivity to low-mass inner planets, leveraging datasets from legacy HIRES, HARPS(-N), SOPHIE, and other RV instruments, as well as unpublished HARPS-N GAPS monitoring.

The RV analysis is conducted using the PyORBIT framework, augmented by Gaussian Process regression for stellar activity mitigation and sophisticated injection-recovery completeness tests. Two independent codes are cross-validated for occurrence rate estimation, utilizing logarithmic grids in period and mass, with detection thresholds established via Bayesian model selection ($\Delta$BIC $>$ 10) and GLS/FAP statistics. RV detection maps are generated for each target and aggregated to compute sample-averaged completeness as a function of mass and period, essential for robust frequency inference.

Results: Occurrence Rates and New Candidates

The final sample yields 161 planets in systems without inner gas giants and 58 in systems with inner giants. Six new planetary candidates are reported, subjected to thorough vetting of activity-induced RV anomalies. Occurrence rates for ISPs across specified period and mass bins are:

• Hot Neptunes (1–10 d, 10–31.7 $\,M_{\oplus}$): $\sim 5\%$
• Warm Neptunes (10–100 d, 10–31.7 $\,M_{\oplus}$): $P < 400$0
• Cool Neptunes (100–400 d, 10–31.7 $P < 400$1): $P < 400$2
• Hot Super-Earths (1–10 d, 3–10 $P < 400$3): $P < 400$4
• Warm Super-Earths (10–100 d, 3–10 $P < 400$5): $P < 400$6

Notably, warm (10–100 d) planets are strongly associated with dynamically stable inner regions—systems where the Hill radius analysis indicates $P < 400$7 au. This stability criterion correlates with higher ISP occurrence, particularly for warm Neptunes and Super-Earths.

Theoretical Implications: Planet Formation and Dynamical Stability

The derived rates reveal that the canonical Solar System architecture is not statistically dominant among CJ hosts, but such arrangements are not rare. The absence of a statistically significant excess of ISPs in CJ systems at average stellar metallicity and mass aligns with findings from Bonomo et al. (2023, 2025) and contrasts with claims of strong positive correlation in previous statistical works (Zhu & Wu 2018, Bryan et al. 2019).

Dynamically stable architectures—CJ with low eccentricity, moderate mass, and sufficiently large semi-major axis—are preferentially correlated with the presence of ISPs. This supports the theoretical paradigm where outer giants regulate accretion and migration of inner small planets, consistent with N-body simulations and population synthesis models (Agnew et al. 2017, Schlecker et al. 2021, Bitsch et al. 2020). Systems with dynamically hot CJs (high $P < 400$8), Super-Jupiters, or those with small Hill radii exhibit suppressed ISP occurrence due to increased dynamical perturbations.

Comparison with Literature and Contradictory Claims

Direct comparisons with occurrence rates from HIRES/CLS (Rosenthal et al. 2022), Barbato et al. (2018), and complementary studies (Bonomo et al. 2023, 2025) show agreement within $P < 400$9. The conditional probability of hosting ISPs given a CJ, as derived in this work ($m_{\mathrm{sini}} > 0.1\,M_{\mathrm{J}}$0), closely matches blind survey results ($m_{\mathrm{sini}} > 0.1\,M_{\mathrm{J}}$1 from Rosenthal et al.). There is no evidence here for an overabundance of CJs in ISP-hosting systems—a conclusion reinforced by formal application of Bayes’ theorem and in tension with earlier claims of strong positive correlation.

For hot and warm Jupiters, the occurrence rate ($m_{\mathrm{sini}} > 0.1\,M_{\mathrm{J}}$2–$m_{\mathrm{sini}} > 0.1\,M_{\mathrm{J}}$3) in CJ-host systems is slightly elevated ($m_{\mathrm{sini}} > 0.1\,M_{\mathrm{J}}$4) relative to field star surveys but within the uncertainties reported by Howard et al. (2010), Wittenmyer et al. (2020), and Su et al. (2024). This suggests that HJs may be more frequently accompanied by exterior giants, a result with implications for migration and dynamical history.

Practical Implications and Future Prospects

Practically, this quantification of architecture frequencies informs target prioritization for next-generation RV and transit surveys, direct imaging campaigns, and mission planning for habitable planet searches. The results stress the necessity of accounting for dynamical stability and completeness effects in occurrence rate statistics.

Theoretically, the findings constrain planetary formation and migration models, emphasizing the non-trivial dependence of ISP–CJ linkage on stellar type, metallicity, and giant planet dynamical properties. Future research will profit from expanded RV time baselines, improved stellar activity mitigation, and integration of astrometric constraints (e.g., Gaia PMa), particularly for long-period trends and eccentric giants.

Conclusion

This comprehensive statistical analysis demonstrates that while Solar System-like architectures are not universal among CJ systems, they are sufficiently abundant to warrant focused study. Warm inner small planets are preferentially found in dynamically stable environments orchestrated by their outer giants. The absence of strong average positive correlation between ISPs and CJs challenges earlier population-level claims and underscores the multifactorial nature of planetary system formation. These results fortify the empirical foundation for theoretical inference and practical strategy in exoplanetary science.