TESS planets in known radial velocity cold Jupiter systems: Hot super Earth occurrence is enhanced by cold Jupiters

Abstract: The correlation between inner super-Earths (SEs) and outer cold Jupiters (CJs) provides an important constraint on the formation and dynamical evolution of planetary systems. Previous studies have suggested a positive connection between these two populations, particularly around metal-rich stars, and proposed that nearly all CJ-hosting stars may also harbor inner SEs. In this work, we use TESS transits to investigate the occurrence of hot SEs in systems with known CJs detected by radial velocity (RV). Out of a statistical sample of 132 CJ systems, we identify five transiting hot super-Earths ($1$-$4R_\oplus$, $P<10\mathrm{d}$) around four stars, including one new candidate (TOI-6965.01) around HD 50554. To enable statistical analysis, we first validate the two candidates around HD 50554 using TESS photometry, archival RV measurements, and Gaia astrometry. After accounting for detection sensitivity and geometric transit probability, we find that the presence of CJs enhances the occurrence rate of hot super-Earths by a factor of $8.1^{+4.3}_{-3.2}$ relative to field stars, with the case of no enhancement ruled out at the 99.9% confidence level. Taking into account the average multiplicity of hot SEs, we find that about 87% of CJ systems host at least one hot SE. Our results provide strong supporting evidence for a positive SE-CJ correlation. We also briefly explore the correlation around metal-poor hosts and for specific sub-populations (e.g., warm super-Earths or cold super-Jupiters).

• The paper directly measures the inverse super-Earth–cold Jupiter relationship using TESS transits around 132 radial-velocity cold-Jupiter systems and finds an 8.1^{+4.3}_{-3.2}-fold enhancement in hot super-Earth occurrence over field stars.
• A uniform BLS search with injection–recovery completeness tests identified five 1–4 Earth-radius planets on periods shorter than 10 days, including two validated likely rocky planets around HD 50554.
• The results imply that roughly 87% of cold-Jupiter systems host at least one hot super-Earth, support a positive correlation across metallicities, and challenge claims that super-Jupiters suppress inner small planets.

The super Earth–cold Jupiter (SE–CJ) connection is one of the central empirical constraints on planet formation theory, yet most observational work has measured only one direction of the conditional probability, $P(\rm CJ|SE)$. The paper by Liu, Zhu, Gan, and Dai (2602.11017) attacks the inverse quantity—$P({\rm SE|CJ})$—directly, using TESS transit photometry to search for hot super-Earths (HSEs; $1$–$4\,R_\oplus$, $P<10$ d) around stars with known radial-velocity cold Jupiters. The headline result is that CJs enhance HSE occurrence by a factor of $8.1^{+4.3}_{-3.2}$ relative to field stars, with no enhancement ruled out at 99.9% confidence.

Sample construction and transit search

The authors assemble a statistically clean sample from the NASA Exoplanet Archive: single, Sun-like main-sequence hosts ($0.6<M_\star/M_\odot<1.4$, $R_\star<2\,R_\odot$) with at least one RV-discovered CJ ($0.3<M_p\sin i/M_{\rm J}<20$, $P>300$ d, $P({\rm SE|CJ})$0 au). Systems containing hot or warm Jupiters are excluded to avoid follow-up selection biases, as are systems whose CJs were found via targeted follow-up of transiting planets. The final sample comprises 132 systems hosting 149 CJs. Notably excluded are well-known mixed systems such as 55 Cancri and HD 191939 for these same bias reasons.

A custom BLS-based pipeline searches SPOC PDCSAP light curves over periods of 1–10 days, adopting TESS-style detection thresholds (BLS significance >9 and S/N$P({\rm SE|CJ})$1 >9). Five transiting HSEs around four stars survive: $P({\rm SE|CJ})$2 Men c, HD 86226 c, HD 219134 b and c, and a new candidate TOI-6965.01 around HD 50554. Two additional TOI candidates (TOI-6965.02 at 28 days, outside the search range, and TOI-6709.01 below the S/N threshold) are not counted in the statistics. Three targets showing short-period sinusoidal variability are retained after injection–recovery tests showed injected transits remain detectable.

Detection completeness is quantified through injection–recovery experiments (200 injections per star), yielding an average sensitivity of roughly 50% for 1–4 $P({\rm SE|CJ})$3 planets at 1–10 day periods across the sample. Geometric transit probability assumes isotropic inclinations—an assumption the authors flag as imperfect given that RV CJ orbits may be inclination-biased and mutual inclinations can be large in low-multiplicity systems (e.g., $P({\rm SE|CJ})$4 Mensae).

Validation of two planets around HD 50554

HD 50554, host of a $P({\rm SE|CJ})$5 ($P({\rm SE|CJ})$6 true mass from Gaia/Hipparcos astrometry) eccentric CJ at $P({\rm SE|CJ})$7 au, yields two validated transiting candidates. MCMC modeling of four TESS sectors gives radii of $P({\rm SE|CJ})$8 (TOI-6965.01, $P({\rm SE|CJ})$9 d) and $1$0 (TOI-6965.02, $1$1 d)—both below the radius valley and therefore likely rocky. Archival CLS and ELODIE RVs place 95% mass upper limits of $1$2 and $1$3. Validation combines odd–even checks, secondary-eclipse non-detection, absence of stellar companions within ~30 au (RV trend plus Gaia DR3), and exclusion of background eclipsing binaries: the required faint background stars would produce deep V-shaped eclipses inconsistent with the observed ingress durations, and unresolved background scenarios have a probability of order $1$4. Both planets are confirmed, though only the inner one enters the statistical sample.

Occurrence enhancement

Under a null-correlation hypothesis, scaling the Kepler-derived HSE occurrence map of Zhu & Dong (2021) by transit probability and detection efficiency predicts only $1$5 detections among 132 stars, versus five observed. With a Poisson likelihood and flat prior on the enhancement factor $1$6, the posterior is Gamma-shaped and gives:

Assumption	Enhancement factor
Zhu & Dong (2021) occurrence map	$1$7
Petigura et al. (2018) occurrence map	$1$8

The result is robust to alternative CJ/WJ definitions (e.g., $1$9 for $4\,R_\oplus$0). Converting to absolute rates, $4\,R_\oplus$1, implying essentially every CJ system hosts at least one HSE on average. Correcting for multiplicity (using the observed sample multiplicity of 1.25, conservative relative to the $4\,R_\oplus$2 typical of SE systems), the authors estimate $4\,R_\oplus$3—consistent with the near-unity value inferred indirectly by Zhu & Wu (2018) and Bryan et al. (2019) via Bayes' theorem, but now measured directly without error-propagation uncertainty.

One systematic deserves note: the RV CJ sample is more metal-rich than the Kepler field, which would raise the field HSE rate by a factor of ~1.3 given the weak metallicity dependence ($4\,R_\oplus$4); this is small compared to the statistical uncertainty but would modestly reduce $4\,R_\oplus$5 if corrected.

Metallicity dependence and sub-populations

Because $4\,R_\oplus$6 is largely insensitive to metallicity (HSE occurrence correlates weakly with [Fe/H], unlike CJ occurrence), this approach probes the correlation where $4\,R_\oplus$7 measurements fail. Splitting the sample at solar metallicity gives 1/43 versus 3/88 HSE detections in the metal-poor and metal-rich subsamples—both far above the null-correlation expectation (~0.006) and mutually consistent, suggesting the correlation persists at sub-solar metallicity. A stricter split at [Fe/H]=0.05 yields 0/34 versus 2/80, still consistent with a positive correlation though not conclusive.

Regarding giant-planet mass, the four CJ hosts span nearly the full allowed mass range ($4\,R_\oplus$8 for HD 219134 h to $4\,R_\oplus$9 for $P<10$0 Men b), including two super-Jupiters. This directly contradicts the claim of Lefèvre & Mulders (2025) that inner low-mass planets correlate preferentially with Saturn-mass rather than super-Jupiter companions, although the small numbers make any statistical division highly sensitive to classification choices. Intriguingly, the two super-Jupiter systems ($P<10$1 Men, HD 50554) are dynamically hot—eccentricities ~0.5–0.6 and mutual inclinations $P<10$2–$P<10$3—while the two Saturn-mass systems are dynamically cold ($P<10$4). Whether this reflects a genuine dichotomy or a smooth architectural distribution remains open.

Limitations and open questions

Several caveats bear directly on the results. The isotropic-inclination assumption underlying the completeness correction is uncertain for systems with dynamically excited giants like $P<10$5 Men and HD 50554, where large mutual inclinations reduce effective transit probabilities. The multiplicity correction for $P<10$6 uses the observed sample multiplicity (1.25) rather than a measured intrinsic HSE multiplicity. The metallicity dependence of the correlation at the metal-poor end remains unconstrained beyond consistency arguments, and the warm super-Earth question—whether WSE systems correlate positively or negatively with CJs, given theoretical expectations of perturbation by eccentric giants—cannot be answered with current data. Finally, whether the dynamical temperature dichotomy between super-Jupiter and Saturn-mass hosts is real requires larger samples, potentially leveraging Gaia astrometric giant-planet detections.

Conclusion

By combining a uniformly selected RV cold Jupiter census with a uniform TESS transit search and full completeness treatment, this work provides the first direct, high-significance measurement of the inverted conditional rate linking outer giants and inner small planets. The enhancement factor of $P<10$7 and the implied $P<10$8 fraction of CJ systems hosting hot super-Earths strongly support a positive SE–CJ correlation, extend it to the metal-poor regime, and challenge claims that super-Jupiters lack inner super-Earth companions.