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Kepler-1625b I

Kepler-1625b I (also designated Kepler-1625b-i) is a candidate exomoon proposed to orbit the gas giant exoplanet Kepler-1625b, a Jupiter-sized world transiting its Sun-like host star approximately 8,000 light-years away in the constellation Cygnus.^[1]^[2] First suggested in 2018 based on archival data from NASA's Kepler Space Telescope and follow-up observations with the Hubble Space Telescope, the candidate exomoon is estimated to have a radius of about 4 Earth radii and a mass of roughly 15–20 Earth masses, comparable to Neptune or Uranus.^[3] The host exoplanet Kepler-1625b has a radius of approximately 6–11 Earth radii (depending on modeling assumptions) and an estimated mass of 20–1,000 Earth masses, orbiting its G-type parent star every 287.4 days at a distance of about 0.88 AU.^[2]^[4] Evidence for Kepler-1625b I includes a 77.8-minute early transit timing variation of the planet—attributed to gravitational perturbations from the moon—and a secondary dip in the transit light curve, interpreted as the exomoon's independent transit with a signal-to-noise ratio exceeding 19.^[3] The proposed exomoon would orbit the planet at a semimajor axis of around 40 planetary radii, well within the planet's Hill sphere of stability.^[3] Despite initial excitement as a potential first exomoon detection outside the Solar System, subsequent analyses have challenged the hypothesis. A 2019 reanalysis of the Hubble data using an independent pipeline found no evidence for the exomoon transit signal, attributing the discrepancy to data processing differences.^[5] More recently, a 2023 reanalysis of the Kepler and Hubble datasets using advanced photodynamical modeling concluded that large exomoons are unlikely around Kepler-1625b, attributing the observed anomalies to systematic errors in data detrending, stellar limb darkening effects, or other astrophysical phenomena rather than a Neptune-sized satellite.^[6] This conclusion was challenged in a 2024 reply by the original researchers, who argued that the exomoon evidence remains viable despite the critiques.^[7] As of 2025, Kepler-1625b I remains unconfirmed, with ongoing research and debate focused on refining transit observations and modeling to resolve the question.

The Kepler-1625 System

Stellar host

Kepler-1625 is a G-type subgiant star situated in the constellation Cygnus, at a distance of approximately 2,310 parsecs (about 7,540 light-years) from Earth, as determined from Gaia DR3 parallax measurements.^[8] The star was monitored as part of the Kepler Space Telescope's primary mission from 2009 to 2013, which identified it as a host to transiting planetary candidates.^[8] The star has a mass of $1.04^{+0.08}_{-0.06} \, M_\odot and a radius of $1.73^{+0.24}_{-0.22} \, R_\odot, derived from isochrone modeling incorporating spectroscopic and asteroseismic constraints.^[9] Its effective temperature is around 5,610 K, placing it in the G spectral class, while its luminosity of $2.55^{+0.72}_{-0.58} \, L_\odot indicates post-main-sequence evolution.^[9] These properties, including the expanded radius, enhance the geometric probability and photometric signal for detecting transits of orbiting bodies.^[10] Kepler-1625 is estimated to be $8.7^{+1.8}_{-1.8} billion years old, based on stellar evolution models.^[9] Its metallicity is slightly supersolar at [ \mathrm{Fe/H} ] = 0.12 \pm 0.15, a factor that influences disk chemistry and the efficiency of giant planet formation in the protoplanetary environment.^[9]

Planetary host

Kepler-1625b is a gas giant exoplanet classified as a warm Jupiter, discovered in 2016 through the transit method using data from the Kepler Space Telescope.^[8]^[11] As the primary host for the candidate exomoon Kepler-1625b I, it orbits the Sun-like star Kepler-1625 at a distance that places it in a temperate zone, enabling potential investigations into its atmospheric composition via transmission spectroscopy during transits.^[3] The planet has a radius of approximately 1.0 Jupiter radii, consistent with a gaseous envelope dominated by hydrogen and helium, similar to Jupiter in our Solar System.^[8] Mass estimates from photodynamical modeling suggest several Jupiter masses (model-dependent ranges of approximately 1–13 M_Jup), indicating a substantial body capable of gravitationally retaining large satellites over billions of years.^[3] These properties position Kepler-1625b as a key target for understanding the formation and evolution of giant planets beyond the snow line. Kepler-1625b completes one orbit around its host star every 287.4 days along a semi-major axis of approximately 0.98 AU, with a nearly circular orbit (eccentricity ≈ 0).^[3] This orbit results in an equilibrium temperature of approximately 253 K.^[8] The stability of potential moons around Kepler-1625b is governed by equilibrium tide effects, which dampen orbital eccentricities over time, and the planet's Hill sphere, the region where a satellite's orbit remains unbound from the star's influence. The Hill radius is given by
r_H = a \left( \frac{m_p}{3 M_\star} \right)^{1/3},
where a is the planet-star semi-major axis, m_p is the planet's mass, and M_\star is the stellar mass; for Kepler-1625b, this yields a sphere large enough to accommodate Neptune-sized moons at stable distances.^[3]

Detection Methods

Transit timing variations

Transit timing variations (TTVs) represent deviations in the mid-transit times of an exoplanet from strictly periodic predictions, induced by the gravitational influence of an orbiting exomoon on the planet's motion. Unlike TTVs from interplanetary interactions that perturb the star's position, exomoon-induced TTVs stem directly from the planet-moon dynamics within their shared system. This indirect detection method leverages the precise timing measurements afforded by space-based transit surveys, allowing inference of unseen companions without resolving their direct photometric signatures.^[12] The physical origin of these TTVs lies in the barycentric motion of the planet-moon pair. The planet and exomoon orbit their common center of mass, causing the planet to wobble around this barycenter while the barycenter follows a Keplerian orbit about the host star. During transits, if the planet is offset forward along its orbital path relative to the barycenter, the transit occurs earlier than expected; conversely, a backward offset results in a later transit. This periodic advance and delay manifests as a sinusoidal variation in transit times, with the signal's period matching the exomoon's orbital period around the planet and an amplitude scaling with the moon's mass and orbital distance. The effect is most pronounced for coplanar, circular orbits, though eccentricities introduce additional harmonics.^[12] In a simplified model assuming circular, coplanar orbits, the TTV amplitude \delta t is given by

\delta t \approx \frac{P_p}{2\pi} \left( \frac{m_m}{m_p} \right) \left( \frac{a_m}{a_p} \right),

where P_p is the planet's orbital period around the star, m_m and m_p are the exomoon and planet masses, a_m is the exomoon's semi-major axis relative to the planet, and a_p is the planet's semi-major axis relative to the star. This approximation captures the leading-order displacement of the planet from the barycenter projected along the line of sight, divided by the planet's orbital velocity. More detailed models incorporate eccentricity and inclination effects to refine the signal shape.^[12] The sensitivity of TTV detection to exomoons depends on the precision of transit timing measurements, typically achieving sub-minute accuracy with missions like Kepler, enabling detection of moon-to-planet mass ratios exceeding approximately 0.1% for short-period giant planets. For instance, an Earth-mass exomoon around a Jupiter-mass planet yields a mass ratio of about 0.3%, producing detectable TTV amplitudes of tens of minutes in favorable cases. This threshold aligns with plausible formation scenarios for massive exomoons via capture or disk instability. The concept of using TTVs for exomoon detection was formalized in the late 2000s, with key theoretical developments distinguishing it from planetary TTVs that arise from mutual gravitational tugs on the star in multi-planet systems. Early proposals, such as those exploring barycentric perturbations, laid the groundwork, evolving into comprehensive frameworks by the early 2010s that included complementary signals like transit duration variations for robust characterization.^[12]^[13]

Photometric signatures

The photometric detection of an exomoon relies on identifying anomalies in the stellar light curve during a planetary transit, specifically a secondary eclipse or dip caused by the moon passing in front of the host star shortly after or before the planet's primary transit. This secondary dip arises because the moon, orbiting the planet, transits independently when aligned with the line of sight, creating a distinct flux decrement superimposed on the planet's shadow. For Kepler-1625b-i, such a signature was proposed in analyses of transit photometry, where the moon's passage was interpreted as an additional dimming event trailing the planet's transit.^[4]^[3] The depth of this moon-induced dip is fundamentally proportional to the square of the ratio of the moon's radius to the stellar radius, \delta_m \propto (R_m / R_\star)^2, analogous to the standard transit depth formula for planets but scaled to the moon's smaller size. In the case of Kepler-1625b-i, models estimated the moon's transit depth at approximately 9% of the planet's depth, corresponding to a moon radius of about one-third that of the planet and yielding a flux drop on the order of hundreds of parts per million. This shallow signature provides a direct measure of the moon's radius, independent of dynamical effects.^[4]^[3] The duration of the moon's transit is typically shorter than the planet's, lasting roughly 10-20% of the total planetary transit time, due to the moon's smaller size and orbital separation from the planet's center. Its timing is offset from the planet's mid-transit by the moon's orbital phase around the planet, often appearing asymmetrically at the ingress or egress of the combined transit event. For Kepler-1625b-i, the proposed dip was positioned toward the end of the planetary transit, consistent with the moon trailing the planet in its orbit.^[4]^[3] Detecting these photometric signatures poses significant challenges, including blending with instrumental or astrophysical noise in the light curve, distortions from stellar limb darkening that can mimic shallow dips, and potential false positives such as unresolved background eclipsing binaries or non-spherical planetary shapes like triaxiality. These factors can obscure the moon signal, particularly for large-separation exomoons where the dip may partially overlap with the planet's transit. Photometry complements transit timing variations by offering radius constraints on the moon, whereas TTVs primarily inform the mass ratio between the planet and moon.^[14]^[6]

Discovery and Observations

Kepler Space Telescope data

The Kepler Space Telescope, launched by NASA in March 2009, operated until October 2018 as a photometric survey mission designed to detect exoplanets via the transit method by monitoring stellar brightness variations in a fixed field of view along the Cygnus-Lyra region of the sky.^[15] The mission collected high-precision light curves over 18 quarters (Q0–Q17), spanning from May 2009 to September 2013 for the primary survey phase, enabling the identification of thousands of exoplanet candidates through repeated transit observations.^[16] Within this dataset, the star Kepler-1625 was continuously monitored across quarters Q0–Q17, yielding three transits of the gas giant exoplanet Kepler-1625b due to its 287-day orbital period, which limited the number of observable events during the mission's primary operations.^[17] In a 2017 archival analysis by Teachey, Kipping, and Schmitt, these light curves revealed anomalies suggestive of an exomoon candidate, designated Kepler-1625b I, including transit timing variations (TTVs) of approximately 80 minutes across the observed transits and a possible secondary photometric dip during one event.^[17] The data processing involved a two-pass detrending procedure to remove instrumental noise and stellar variability, utilizing the CoFiAM algorithm for harmonic fitting and baseline corrections, resulting in phase-folded light curves with a root-mean-square scatter of 5.1 parts per million.^[17] Statistical assessment of the TTVs indicated a significance of about 3σ, with photodynamical modeling using the LUNA code and Bayesian inference via MultiNest yielding a modest preference for a planet-moon system (Bayes factor ≈2–4 depending on cross-validation folds).^[17] A particularly notable anomaly occurred during the third observed transit on October 14, 2013 (BJD ≈ 2456587.34), where the timing arrived approximately 80 minutes earlier than predicted and a flux decrement of about 0.7% was detected roughly 1 hour after the primary planetary transit egress, interpreted as a potential moon ingress.^[17] This analysis, initially shared as an arXiv preprint in July 2017, prompted proposals for targeted follow-up observations to confirm the candidate signal.^[18]

Hubble Space Telescope follow-up

In October 2017, the Hubble Space Telescope conducted follow-up observations of the Kepler-1625 system to investigate the candidate exomoon signal around Kepler-1625b identified in prior Kepler data.^[3] These observations took place on October 28–29, spanning approximately 40 hours across 26 orbits.^[3] The observations utilized the Wide Field Camera 3 (WFC3) in near-infrared wavelengths (1.1–1.7 μm) with the G141 grism, selected for its higher precision in detecting subtle photometric variations compared to visible light.^[3] A total of 232 exposures were obtained, with an effective cadence of about 5 minutes per exposure and roughly 45 minutes on target per orbit, yielding 229 usable frames after discarding three affected by the South Atlantic Anomaly.^[3] The data confirmed a significant transit timing variation, with the transit of Kepler-1625b beginning 77.8 minutes earlier than predicted based on Kepler ephemerides, consistent with expectations from moon-induced perturbations observed in the original transit timing variations (TTVs).^[3] Additionally, a post-transit flux decrement was detected, interpreted as a potential secondary eclipse from an exomoon, with a depth of approximately 330 parts per million (ppm) under a linear detrending model or 180–220 ppm under quadratic or exponential models, achieving a signal-to-noise ratio of at least 19—far exceeding noise levels and aligning with the expected signature of a large moon transiting separately.^[3] Photodynamic modeling combined the Hubble light curve with Kepler archival data using self-consistent N-body simulations (via the LUNA software), strongly favoring a planet-plus-moon scenario over a solitary planet.^[3] The posterior distributions indicated a moon-to-planet mass ratio of about 1.5% (specifically 0.0141 for linear detrending, 0.0196 for quadratic, and 0.0149 for exponential), with the planet mass estimated in the range of several Jupiter masses—such as 1.2–12.5 M_Jup for the linear case—supported by a Bayes factor exceeding 400,000 in favor of the exomoon hypothesis.^[3] These findings were published on October 3, 2018, in Science Advances by Alex Teachey and David Kipping, marking the first strong candidate for an exomoon beyond our Solar System.^[3]

Physical Characteristics

The proposed physical characteristics of Kepler-1625b I are derived from 2018 analyses using Kepler and Hubble data, though subsequent studies as of 2025 have cast doubt on the exomoon interpretation.^[6]

Size and mass

The estimated radius of Kepler-1625b I is approximately 0.36 R_Jup (equivalent to about 4 R_Earth), derived from the depth of the photometric dip observed in the combined Kepler and Hubble Space Telescope transit light curves, under the assumption that the moon shares a similar albedo and limb darkening profile with its host planet Kepler-1625b.^[3] This value positions the candidate exomoon as comparable in size to Neptune.^[3] The mass of Kepler-1625b I is estimated at 19 M_Earth (or 0.06 M_Jup), obtained by fitting the amplitude of transit timing variations (TTVs) using N-body simulations that model the planet-moon dynamics, yielding a moon-to-planet mass ratio of approximately 0.02.^[3] These fits incorporate empirical mass-radius relations for the host planet, estimated at approximately 3 M_Jup (or 20–1000 M_Earth depending on modeling assumptions), influencing the absolute moon mass determination.^[3] From these radius and mass estimates, the bulk density of Kepler-1625b I is calculated to be around 1.0 g/cm³, suggestive of a Neptune-like composition featuring a substantial rock/ice core enveloped by a hydrogen/helium atmosphere.^[3] This density profile aligns with ice giant analogs in our Solar System, though the candidate's parameters indicate it may represent a sub-Saturnian body, comparable to Neptune's size (3.9 R_Earth) and mass (17 M_Earth) with a similar low overall density.^[3] Uncertainties in these measurements are significant: the radius carries an approximate ±20% error primarily due to assumptions about the orbital inclination and the faintness of the transit signal, while the mass estimate is highly sensitive to the host planet's mass, which remains loosely constrained by available radial velocity and photometric data.^[3]

Orbital parameters

The proposed orbit of Kepler-1625b i around its host planet Kepler-1625b is characterized by a semi-major axis of approximately 40 planetary radii, with modeled ranges spanning 36 to 45 planetary radii depending on the photodynamical fit employed.^[9] This distance was derived from joint analyses of Kepler Space Telescope transit timing variations (TTVs) and Hubble Space Telescope (HST) photometric data, where the moon's orbital motion induces a timing offset in the planet's transit depth and duration.^[9] The orbital period is estimated at around 22 days, though it remains highly degenerate with multimodal posterior distributions ranging from 13 to 39 days across different detrending models of the light curve.^[9] This inference stems from the periodicity of TTV signals matching the expected timescale of the moon's orbit, as simulated using the LUNA photodynamical modeling software.^[9] The eccentricity is assumed to be circular (e ≈ 0), consistent with tidal circularization expected for a close-in moon around a gas giant, though minimum values as low as 0.13 are permissible within stability constraints.^[9] Orbital stability is supported by the semi-major axis lying well within the planet's Hill radius of approximately 200 planetary radii, corresponding to 0.26 to 0.28 times the Hill radius in the best-fit models, where 73 to 78% of posterior samples indicate long-term dynamical stability.^[9] The close-in nature of the orbit implies ongoing tidal evolution, potentially leading to inward migration over gigayear timescales, though no evidence for resonances with undetected sibling moons or other bodies has been found in the transit data.^[9] The moon's orbital inclination relative to the planet's orbital plane is approximately 45°, with ranges of 24° to 64° across models, suggesting a tilted but potentially stable configuration; this inclination aligns the moon's orbit nearly edge-on to our line of sight (≈90°), facilitating its detection via transits.^[9] The mass ratio between the moon and planet, influencing the TTV amplitude, further constrains these parameters but is detailed separately in analyses of the moon's physical properties.^[9]

Scientific Debate

Initial evidence and models

The initial evidence for an exomoon orbiting Kepler-1625b emerged from Kepler Space Telescope observations revealing transit timing variations (TTVs) and a post-transit flux dip suggestive of a Neptune-sized satellite. The TTVs showed the planet's transit occurring approximately 77.8 minutes earlier than predicted, exceeding 3σ significance and consistent with gravitational perturbations from a massive moon. Complementing this, the flux dip exhibited a signal-to-noise ratio of at least 19, interpreted as the moon's ingress or egress during the composite transit event. These signals, analyzed in conjunction with Hubble Space Telescope follow-up photometry, provided the foundational ~3σ confidence for the exomoon hypothesis.^[3] To interpret these observations, Teachey and Kipping developed photodynamic models simulating the planet-moon system's dynamics and photometric signatures. They integrated REBOUND for N-body orbital integrations with the LUNA code to generate synthetic light curves from both Kepler and Hubble datasets, enabling forward modeling of mutual transits and TTVs (with underlying TTV equations detailed in prior sections on transit timing variations). Parameter fitting via χ² minimization with MultiNest yielded best-fit moon properties, including a radius of ~0.36 Jupiter radii (~4 Earth radii), mass of approximately 16 Earth masses (log_{10}(M_s/M_⊕) = 1.2 ± 0.3), semi-major axis of ~40 planet radii, and orbital tilt of ~45° relative to the planet's orbital plane. Alternative explanations, such as a ring system around a hot Jupiter-like planet, were tested but ruled out, as they produced substantially higher χ² values (e.g., Δχ² > 30 relative to the exomoon model).^[3] A Bayesian framework further assessed model viability, with Teachey and Kipping finding very strong evidence for the exomoon over the null (planet-only) hypothesis, quantified by a Bayes factor exceeding 400,000 after incorporating Hubble data. This analysis emphasized the achromatic nature of the dip and alignment between TTV phase and dip timing as key strengths supporting the exomoon interpretation. The derived moon parameters also aligned with theoretical formation pathways, such as a giant impact disrupting a protoplanet or capture from the circumstellar disk's outer regions, where moon-to-planet mass ratios around 1.5% remain plausible despite their rarity in simulations.^[3] The 2018 findings galvanized exomoon research, prompting targeted searches among other Kepler Objects of Interest, including the subsequent identification of a candidate around Kepler-1708b.^[19]

Subsequent challenges

Following the initial 2018 evidence for an exomoon around Kepler-1625b, subsequent analyses from 2019 onward have challenged the interpretation, proposing alternative explanations for the observed transit timing variations (TTVs) and photometric dip. In a re-analysis published in Astronomy & Astrophysics, Heller et al. examined the combined Kepler and Hubble data, concluding that the TTV signal is better explained by a misaligned orbit (high stellar obliquity) of the giant planet without a moon, while attributing the post-transit dip to an instrumental artifact rather than an exomoon transit. Their modeling showed that the orbital misalignment of the planet with the stellar equator could account for the timing deviations without invoking a satellite.^[20] Independently, Kreidberg et al. revisited the Hubble observations in a 2019 Astrophysical Journal Letters paper, applying refined noise models to the light curve data. This adjustment reduced the significance of the candidate exomoon transit dip to less than 1σ, with a false positive rate estimated at approximately 11%, casting substantial doubt on the moon hypothesis. Kreidberg et al. emphasized that while the signal remains intriguing, the marginal detection does not robustly support an exomoon.^[21] More recent higher-resolution modeling in a 2023 Nature Astronomy study by Simon et al. further constrained the possibility of large exomoons, ruling out moons larger than Neptune's size at 95% confidence for Kepler-1625b based on detailed simulations of transit light curves and TTVs.^[6] Their work incorporated advanced photometric modeling to test moon parameters, finding no consistent fit for a substantial satellite.^[6] However, in a 2025 Matters Arising response in Nature Astronomy, Kipping et al. re-evaluated the data with refined Bayesian methods and light curve analyses, arguing that the exomoon signal remains plausible and challenging Simon et al.'s dismissal, though further observations are needed for confirmation.^[22] Additional alternative explanations for the signals include planetary oblateness causing asymmetric transits, stellar activity such as starspots mimicking timing shifts, or a background eclipsing binary contaminating the light curve, as explored in these post-2018 critiques.^[6] Cumulatively, these studies have shifted the odds against an exomoon interpretation, underscoring the need for radial velocity measurements to confirm or refute the presence of a satellite through mass constraints, though the 2025 analysis keeps the debate open as of November 2025.^[6]^[22]

Current Status and Future Prospects

Ongoing analyses

In a 2023 analysis published in Nature Astronomy, researchers concluded that large exomoons around Kepler-1625b are unlikely based on re-examination of Kepler and Hubble data, attributing the candidate signal to instrumental artifacts and stellar variability; however, small moons smaller than Earth radius remain possible due to detection limits around 0.7 Earth radii, with a false positive rate of approximately 11% for similar transit timing variation (TTV) signals in planet-only models.^[6] A 2025 response in Nature Astronomy countered this refutation by reanalyzing the datasets with an independent photometric pipeline, reaffirming the persistence of the TTV signal at roughly 2σ significance and arguing that the original exomoon interpretation withstands scrutiny when accounting for noise properties and detrending choices.^[7] Complementing this, a 2025 study in Monthly Notices of the Royal Astronomical Society conducted N-body simulations of hierarchical star-planet-moon systems, demonstrating orbital stability for a potential exomoon around Kepler-1625b in coplanar configurations within approximately 0.4 of the planet's Hill radius.^[23] Kepler-1625b-i continues to be listed as a leading exomoon candidate in community catalogs such as the Extrasolar Planets Encyclopaedia, reflecting ongoing interest despite the lack of new transit observations since the 2017–2018 Hubble campaign. As of November 2025, the consensus among meta-analyses of TTV and transit data maintains unconfirmed candidate status for Kepler-1625b-i, with estimated probabilities below 50% for a genuine exomoon signal amid persistent debate over systematic errors. JWST observations of the 2024 transit by the Cool Worlds Lab, analyzing for moon-induced photometric anomalies, remain under analysis, with no conclusive results yet reported.^[6]^[7]^[24]

Potential confirmation methods

Radial velocity spectroscopy provides a promising avenue for confirming the exomoon candidate by detecting the subtle wobble in the host star's motion caused by the planet-moon barycenter orbiting the star-planet-moon barycenter, with the moon inducing short-period variations in the signal. Observations with the CARMENES spectrograph have already constrained the minimum mass of Kepler-1625b to less than 11.6 Jupiter masses at 3σ confidence but failed to detect the expected exomoon-induced modulation due to limited precision. Future facilities like the Extremely Large Telescope (ELT) with its HIRES instrument, operational in the 2030s, could achieve the necessary radial velocity precision of around 10 cm/s for bright stars, potentially enabling detection for fainter targets like Kepler-1625 if signal-to-noise ratios allow.^[25] Direct imaging in the infrared regime represents a theoretical method to resolve the moon-planet separation, estimated at approximately 6 microarcseconds (6 × 10^{-6} arcseconds) for Kepler-1625b I given the system's distance of about 8,000 light-years. Studies on tidally heated exomoons demonstrate feasibility with JWST or future ground-based telescopes like the ELT for nearby systems, where thermal emission from the moon could be distinguished from the planet. However, the extreme distance of Kepler-1625 renders this approach currently infeasible due to insufficient angular resolution and contrast.^[26]^[27] Monitoring additional transits of Kepler-1625b offers a direct way to verify repeated anomalies, such as the secondary photometric dip or transit timing variations (TTVs) attributed to the moon. With an orbital period of 287.4 days, the next predicted transit occurs around 2026, providing an opportunity for follow-up photometry to test consistency with exomoon models. Space telescopes like TESS could capture broad-field data, while CHEOPS might contribute if targeted, though the host star's faintness (V ≈ 17.6) limits precision.^[3]^[27] Atmospheric characterization via transit spectroscopy with JWST's NIRSpec instrument could distinguish the moon's signal from the planet's by analyzing the spectrum during the putative moon transit, potentially revealing differences in composition or thermal properties. The instrument's wide wavelength coverage (0.6–5.3 μm) enables high-resolution spectra at ~100 ppm precision, suitable for detecting shallow moon transits (~3% depth relative to the planet). Recent JWST programs, including those by the Cool Worlds Lab in 2024, have targeted Kepler-1625b transits to search for such features, with data analysis ongoing as of 2025.^[27] Advancements in theoretical modeling, particularly N-body simulations incorporating tidal interactions and orbital resonances, enhance prediction of the exomoon's stability and photometric signatures to guide observations. Simulations indicate that Kepler-1625b I could remain stable over billions of years if its semi-major axis is within approximately 0.4 of the planet's Hill radius (about 40 planetary radii), but tidal migration might alter its orbit, affecting detectable signals. These models, refined with tools like REBOUND, support tidal capture as a viable formation mechanism and help interpret transit data.^[23]^[28]

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