Jupiter-like planets might be common in a low-density environment

The study addresses how common Solar System-like architectures are, particularly the frequency of giant planets beyond the ice line (≈3 au). Jupiter-like planets are defined here as ≥1 MJupiter at 3–12 au. Core-accretion models predict such planets should be common, with semi-major axes linked to the ice line and modified by migration. However, radial velocity (RV) surveys typically report relatively low occurrence rates for cold giants: integrated estimates suggest ≈2–7% for 3–10 MJupiter at 3–10 au, and ≈6–20% for broader giant ranges, implying Solar System analogs might be uncommon. These RV samples mix ages and environments and often require extrapolations near or beyond their sensitivity limits. The β Pictoris Moving Group (BPMG), a nearby (~20 Myr) young association, provides an ideal laboratory for direct imaging of Jupiter-like planets due to proximity and youth, with multiple directly imaged giant planets already known. This work investigates whether Jupiter-like planets are common in the BPMG and reconciles these findings with RV-based frequencies.

Previous RV and microlensing studies report cold giant occurrence rates that vary by method and parameter space. Cumming et al. (2008) imply ~5.5% for Jupiter-like (as defined here) via extrapolation; Wittenmyer et al. (2016) extend to ~7 au with results consistent within errors; Zhu (2022) up to 10 au finds higher rates, ~6.9% (1–10 MJup, 3–10 au) and ~2.2% (3–10 MJup, 3–10 au) for at least one planet; Fernandes et al. (2019) combining RV and Kepler suggest ~4.2% for 1–10 MJup at 3–10 au with caveats on mass–period independence. Microlensing (Gould et al. 2010) indicates ~16% at wider separations. Systems with inner planets show elevated outer giant occurrence (Bryan et al. 2016), not representative of the field. Overall, RV-based frequencies near 3–10 au and 3–10 MJup cluster around ~2.0 ± 1.0%. These results, derived for older field stars spanning diverse birth environments, motivate targeted studies in young, nearby associations like BPMG.

• Sample selection: From BPMG membership lists, selected stars with M > 0.8 M☉; vetted membership and removed likely non-members or systems incompatible with 20 Myr age; final sample N=30 stars (27 systems when counting wide binaries), parallax range ~12–51 mas. Identified companions using Gaia DR3 (visual companions), literature visual binaries, spectroscopic binaries, HCI datasets (SPHERE/GPI), proper motion anomaly (PMa) from Hipparcos–Gaia comparisons, and RUWE as an astrometric quality indicator.
• Stability analysis: For systems with stellar/brown dwarf (BD) companions, applied Holman–Wiegert-type stability criteria (using an eccentricity–separation relation combining close- and wide-binary statistics) to assess whether a 3–12 au planet could be dynamically stable. Found 10 systems where Jupiter-like orbits are unstable; thus 20 stars remain as potential hosts (including one circumbinary case).
• Orbital sampling completeness (HCI): Quantified the probability that a 3–12 au planet would be projected outside the coronagraph (≥150 mas) at least once across available HCI epochs. Monte Carlo with 100,000 trials per star, uniform semi-major axis (3–12 au), two eccentricity priors (adopted uniform e∈[0,0.5]), random inclinations, and observed epoch counts (assumed yearly spacing). Mean detectability across the 20-star subset is 42.3%.
• Direct imaging detections: Counted four Jupiter-like planets (M > 4 MJup) detected by HCI around three BPMG systems within 3–12 au.
• Astrometric indications (PMa): For stars with Hipparcos entries (17/20), used significant PMa (SNR>3) and RUWE constraints to infer additional likely companions in the Jupiter-like regime. Identified four likely planetary companions (HIP 560, HIP 10679, HIP 84586, HIP 88399) not yet imaged, consistent with low HCI detectability due to orbital sampling.
• Frequency estimation: Two approaches: (1) correct direct HCI detections by orbital sampling to infer occurrence of M>4 MJup, 3–12 au; (2) combine direct HCI and significant PMa cases. Adopted the average of the two estimates.
• Mass-function correction: To infer total Jupiter-like (≥1 MJup) occurrence, assumed a power-law mass distribution dN/dM ∝ M^−1.3 over 1–15 MJup, yielding ~37±7% above 4 MJup, implying a factor ~2–3 correction from the M>4 MJup occurrence to total ≥1 MJup.
• Statistical inference: Simulated detection outcomes for 20 stars, drawing detectability P from N(0.39, 0.12) and varying the intrinsic occurrence x. Requiring ≥7 detections reproduces observations when x≈0.99; x>0.50 at 95% confidence.
• Ancillary analyses: Companion demographics (mass ratios, separations), debris disk frequencies, and environmental context of BPMG as a low-density association.

• Stability filtering leaves 20 of 30 BPMG stars (M > 0.8 M☉) that could stably host a 3–12 au planet.
• HCI orbital sampling completeness: average probability to see a 3–12 au planet outside the coronagraph at least once is 42.3% across the 20-star subset.
• Direct imaging finds four Jupiter-like planets (M > 4 MJup) around three systems within 3–12 au. Correcting for orbital sampling yields an occurrence of 36 ± 19% for M > 4 MJup, 3–12 au.
• PMa analysis identifies four additional likely Jupiter-like companions among 17 stars with PMa data; combining direct and indirect detections gives 7/17 → 41 ± 12% occurrence for M > 4 MJup, 3–12 au.
• Adopted occurrence for M > 4 MJup, 3–12 au around BPMG stars (M > 0.8 M☉): 39 ± 12% (average of the two methods).
• Mass-function correction (dN/dM ∝ M^−1.3, 1–15 MJup) implies only 37 ± 7% of Jupiter-like planets exceed 4 MJup, so the total ≥1 MJup occurrence at 3–12 au is higher by a factor ~2–3, consistent with near-unity intrinsic frequency.
• Statistical modeling of detections favors an intrinsic Jupiter-like occurrence x ≈ 0.99; x > 0.50 at 95% confidence.
• The BPMG occurrence is over an order of magnitude higher than RV-based field-star estimates for 3–10 MJup at 3–10 au (~2.0 ± 1.0%).

The findings indicate that Jupiter-like planets are common around BPMG stars with M > 0.8 M☉, addressing the research question by showing markedly higher occurrence than field-star RV surveys. Several factors may reconcile the discrepancy: (1) Stellar mass: BPMG primaries have slightly higher median mass (~1.15 M☉) than typical RV targets; giant planet occurrence grows with stellar mass, partially explaining the increase. (2) Age: BPMG (~20 Myr) planets are primordial; older field systems may lose planets through long-term dynamical evolution or external perturbations, reducing observed frequencies. (3) Binary handling: This study excludes systems where 3–12 au orbits are unstable due to stellar/BD companions, while RV surveys include some such systems, biasing frequencies downward. (4) Environment: BPMG’s low-density birth environment likely preserves protoplanetary disks longer (fewer close encounters, reduced external photoevaporation), favoring core-accretion formation of giants, versus massive clusters where disk lifetimes may be too short. The high debris-disk incidence in BPMG further supports efficient planetesimal and planet formation. The results imply environment plays a major role in setting giant planet demographics, and that Solar System-like architectures could be more typical in low-density associations. Forthcoming Gaia releases will provide broader tests across environments.

This work shows that, after accounting for observational incompleteness, Jupiter-like planets (≥1 MJup at 3–12 au) are likely very common among BPMG stars with M > 0.8 M☉. The corrected occurrence for massive (>4 MJup) Jupiter-like planets is 39 ± 12%, implying a total ≥1 MJup occurrence near unity when adopting empirically motivated mass functions. This contrasts sharply with lower RV-based field-star frequencies and suggests strong dependence on age, stellar mass, and especially birth environment. Future Gaia data (DR4 and beyond), together with continued direct imaging and astrometric monitoring, will critically test these predictions across varied stellar populations and environments, refine mass and orbital distributions, and assess the universality of Solar System-like architectures.

• Sample size is modest (20–30 stars), leading to Poisson/statistical uncertainties.
• Membership of some stars is uncertain; conservative inclusion of ambiguous members without detections lowers inferred frequencies by <10% but introduces potential bias.
• HCI completeness strongly depends on projection effects and limited epochs; the orbital sampling model assumes uniform semi-major axes (3–12 au) and an eccentricity prior (uniform 0–0.5).
• PMa is available only for 17/20 relevant stars; interpretation of PMa involves degeneracies with separation and mass and may be influenced by multiple companions; RUWE-based mass limits are approximate and model-dependent.
• The Jupiter-like mass function slope and bounds are uncertain; different choices alter the mass correction factor.
• Comparison with RV surveys is complicated by differing stellar masses, ages, binary treatments, and environmental histories.
• Eccentricities for directly imaged planets are few and potentially biased, affecting stability and detectability assumptions.