TOI-1438 Multi-Planet System Overview

• TOI-1438 is a multi-planet system featuring two transiting sub-Neptunes with short orbital periods and one candidate non-transiting giant detected via radial velocities.
• Transit and RV measurements provide precise values for radii (2.75–3.04 R⊕) and masses (≈9–11 M⊕) of the inner planets, indicating significant volatile envelopes.
• The system’s distinct architecture with a large period gap between inner and outer companions offers insights into diverse planet formation, migration, and atmospheric evolution processes.

The TOI-1438 system is a multi-planetary system centered on a K0V-type star, characterized by two closely packed, low-mass, transiting sub-Neptunes and a candidate long-period, massive, non-transiting planet detected via radial velocities. Discovered by the Transiting Exoplanet Survey Satellite (TESS) and subjected to five years of precise HARPS-N spectroscopic follow-up, this system exhibits a striking architecture—featuring an inner pair of volatile-rich sub-Neptunes with short orbital periods and an outermost massive companion at a separation associated with an orbital period ratio of several hundred relative to the inner system.

1. Observational Summary and Planetary Properties

The TESS transit data, combined with extensive ground-based radial velocity (RV) measurements, enable robust characterization of the two inner planets, labeled b and c. Both are sub-Neptunes, with measured radii and masses:

• Planet b: $R_b = 3.04 \pm 0.19\,R_\oplus$, $M_b = 9.4 \pm 1.8\,M_\oplus$
• Planet c: $R_c = 2.75 \pm 0.14\,R_\oplus$, $M_c = 10.6 \pm 2.1\,M_\oplus$

Their orbital periods are precisely determined as 5.1 days (b) and 9.4 days (c), derived from the transit ephemerides. Incident stellar fluxes (“instellations”) are $145 \pm 10$ and $65 \pm 4\,F_\oplus$ for b and c, respectively. These correspond to physical separations in the compact, close-in regime.

The derived bulk densities—$1.8 \pm 0.5$ g cm$^{-3}$ for b and $2.9 \pm 0.7$ g cm$^{-3}$ for c—unambiguously indicate compositions enriched in volatiles relative to purely rocky interiors. These parameters, together with the low densities, necessitate the presence of significant volatile envelopes (e.g., H/He and/or H$_2$O layers).

Key formulae involved in the structural and orbital analysis include:

• Transit impact parameter: $b = \cos i \times \left(a / R_\mathrm{s}\right)$
• Jeans escape parameter (atmospheric retention criterion):

$$\Lambda = \frac{G M_\mathrm{p} m_\mathrm{H}}{k_\mathrm{B} T_\mathrm{eq} R_\mathrm{p}}$$

2. Interior Structure and Composition Inference

Planetary interiors are modeled by coupling measured mass and radius to multi-layer compositional models, under assumptions of an iron-rich core, a silicate mantle, and a volatile-rich envelope. Modeling utilizes both the mass-radius tabulation of Agui et al. (for icy worlds with water-rich envelopes over rocky cores) and forward models based on GASTLI (GAS gianT modeL for Interiors), which admit mixed deep layers and a high-metallicity (including H/He) outer envelope.

The interior retrievals establish that both planets exhibit significant volatile content, but the envelope mass fractions differ markedly:

• Planet b supports up to 2.5% hydrogen/helium by mass in its high-metallicity envelope.
• Planet c is constrained to at most 0.2% hydrogen/helium mass fraction.

This compositional dichotomy is maintained across core assumptions (Fe-rock or ice-rock). A volatile-rich (e.g., water or water-like) envelope is a prerequisite for matching the observed low densities. The compositional models rely on standard equations of state such as the Vinet EOS for Fe and silicates, as well as boundary condition procedures for mass–radius relationships.

Atmospheric retention and susceptibility to hydrodynamic escape are assessed using the Jeans parameter, crucial for evaluating whether low-mass, close-in planets can retain primordial envelopes:

$$\Lambda = \frac{G\,M_\mathrm{p}\,m_\mathrm{H}} {k_\mathrm{B}\,T_\mathrm{eq}\,R_\mathrm{p}}$$

where $T_\mathrm{eq}$ is the planet’s equilibrium temperature, $m_\mathrm{H}$ the hydrogen atom mass, and constants as usual.

3. Radial Velocity Evidence for a Third Companion

Beyond the two transiting sub-Neptunes, the five-year HARPS-N and HIRES RV time series reveal a prominent long-period signal (“signal d”). After subtracting b and c’s signatures, periodograms identify a significant peak corresponding to a period of $7.6^{+1.6}_{-2.4}$ years.

A Keplerian fit for signal d yields:

• RV semi-amplitude: $35^{+3}_{-5}$ m s$^{-1}$
• Inferred minimum mass: $2.1 \pm 0.3\,M_\mathrm{Jup}$
• Orbital eccentricity: $0.25^{+0.08}_{-0.11}$ (with a Beta-distributed prior favoring modest values)

Diagnostic tests with additional RV activity indicators (e.g., Ca II H & K emission, differential line width, Na D lines) exhibit long-period power at comparable periods. While Keplerian-like signal persistence across wavelength sub-bands supports a planetary origin, stellar activity (e.g., magnetic cycles) remains a viable, non-exclusive explanation. The authors caution that disentangling planetary from stellar origins for signal d requires an extended RV monitoring baseline to fully characterize the low-frequency component.

4. System Architecture and Dynamical Context

TOI-1438 presents a pronounced architectural dichotomy:

• Inner system: compact sub-Neptunes, near-circular orbits, negligible TTVs, indicating a “dynamically cold” configuration.
• Outer candidate: massive ($\sim$ 2$M_\mathrm{Jup}$), long-period ($\sim$ 7.6 years) planet, yielding an orbital period gap of $\sim$ 300 between the inner and outer planets.

This architecture is rare compared to the majority of known multiplanet systems. Only a handful—e.g., Kepler-48, TOI-4010—feature closely packed low-mass planets and a distant giant separated by large period ratios. Such architectures may emerge from planetary formation and migration pathways that preserve the inner system’s compactness while allowing an outer giant planet to form or migrate outward.

The large dynamical gap, with no planets yet detected in intermediate orbits, may indicate undetected smaller planets or a genuinely bifurcated system architecture. The absence of strong TTVs suggests a lack of mean-motion resonance or significant mutual perturbation in the current epoch.

5. Implications for Planet Formation and Evolution

The contrasting envelope retention capabilities of planets b and c, despite similar masses and radii, carry implications for atmospheric loss mechanisms, disk evolution, and initial composition variations. The upper limit on H/He mass fraction for planet c, compared to the more permissive envelope on planet b, may reflect divergent accretion histories or more efficient atmospheric escape post-formation.

The existence of a massive, distant planet cospatial with compact inner sub-Neptunes prompts considerations of disk-driven migration, in situ assembly, and the role of external perturbers. A plausible implication is that late-stage dynamical stability or migration barriers enabled the preservation of the inner system while allowing for the formation or retention of a wide-orbit giant.

6. Prospects for Future Observations

Outstanding questions center on confirming the planetary nature of signal d and further constraining the atmospheric and interior compositions of b and c. Recommendations include:

• Continued RV monitoring to extend the time baseline, crucial for resolving the orbital period and nature of signal d.
• Complementary techniques such as photometric monitoring for activity-induced variability or high-resolution imaging to detect possible additional companions.
• Target-of-opportunity transit and transmission spectroscopy (e.g., JWST), though the sub-Neptunes’ Transmission Spectroscopy Metric (TSM) is on the lower end; such studies would further inform compositional diversity.

Confirmation of a triple-planet configuration would position TOI-1438 as a benchmark for understanding the interplay between low-mass, compact inner systems and massive, distant companions.

7. Comparative Context and Rarity

The TOI-1438 system, if the outer companion is confirmed planetary, is among the rare few with a distinctly separated dichotomy: innermost sub-Neptunes with short periods and a lone outer Jupiter-mass planet with a period ratio of $\mathcal{O}(10^{2}$–$10^{3})$. This configuration contrasts with the more common architectures of closely packed, similar-mass planets and offers a valuable laboratory for testing theories of planet formation, migration, and long-term dynamical stability. Further monitoring and paper will clarify whether TOI-1438 represents an evolutionary endpoint or a transitional state in multiplanetary system development (Persson et al., 29 Aug 2025).