TOI-4127 b: Eccentric Warm Jupiter

• TOI-4127 b is a Jupiter-sized warm Jupiter with a 56.4-day period, high eccentricity (~0.75), and well-aligned sky-projected spin–orbit geometry.
• Observations combined TESS photometry with NEID, SOPHIE, and HARPS-N spectroscopy to precisely determine its transit parameters, radial velocities, and Rossiter–McLaughlin effect.
• The system’s orbital dynamics challenge traditional migration models, suggesting formation scenarios such as resonant planet-disc interactions or coplanar high-eccentricity migration.

TOI-4127 b is a transiting, Jupiter-sized exoplanet on a long-period, highly eccentric orbit around the late F-type dwarf star TOI-4127. It is classified as a warm Jupiter with period $56.4$ d and moderate insolation, yet its orbital eccentricity is extreme, its periastron distance is small, and its Rossiter–McLaughlin measurement indicates a well-aligned orbit. The system was first established through TESS photometry and NEID and SOPHIE radial velocities, and was later reanalyzed with HARPS-N transit spectroscopy, yielding a sky-projected obliquity consistent with zero and placing TOI-4127 b among the most eccentric well-aligned warm Jupiters known and among the longest-period systems with a measured obliquity (Gupta et al., 2023, Mireles et al., 26 Sep 2025).

1. Discovery and observational basis

TOI-4127 b was discovered in a search for single-transit signals in TESS Sector 20 data. A single transit was found in Sector 20 at 30-min cadence, with a second transit of matching depth in Sector 26, and a third high-quality transit in Sector 53 at 2-min cadence. Sector 40 showed no transit at the corresponding alias, ruling out all but a 56.4-day solution, while a transit-like feature in Sector 47 was flagged low quality in PDCSAP due to scattered light and excluded from modeling. Pixel-level light curves with eleanor confirmed that the events originate from TOI-4127. Follow-up NESSI speckle imaging at WIYN ruled out bound or background sources to $\Delta \mathrm{mag} < 3.3$ at 532 nm and $< 3.9$ at 832 nm beyond $0.2''$, and Gaia DR3 showed no sources within $25''$ (Gupta et al., 2023).

Radial-velocity confirmation used 12 NEID exposures between 2021-02-06 and 2022-01-18 and 21 SOPHIE exposures between 2021-09-27 and 2022-12-07, of which 19 SOPHIE measurements were used. The NEID data yielded a median single-measurement precision of $6.13\ {\rm m\ s^{-1}}$ with SERVAL and $8.09\ {\rm m\ s^{-1}}$ from the DRP; the SOPHIE data achieved $\simeq 8\ {\rm m\ s^{-1}}$ single-exposure precision, with scattered moonlight corrections applied where needed and bisector-span analyses showing no correlation with radial velocity. A later obliquity campaign added HARPS-N transit spectroscopy: 16 total 1200 s exposures, including 15 during a 15 March 2024 transit plus one pre-transit exposure on 24 November 2023, with coverage of $\approx 4.8$ h, airmass $1.38$–$\Delta \mathrm{mag} < 3.3$0, $\Delta \mathrm{mag} < 3.3$1–$\Delta \mathrm{mag} < 3.3$2, and median radial-velocity uncertainty $\Delta \mathrm{mag} < 3.3$3. The HARPS-N data were reduced via the HARPS-N DRS using a G2 mask and reprocessed with Yabi (Mireles et al., 26 Sep 2025).

The observational sequence is notable because it combines single-transit vetting, multi-sector TESS recovery, high-precision Doppler confirmation, and in-transit spectroscopy for spin–orbit characterization. This combination is uncommon for warm Jupiters at $\Delta \mathrm{mag} < 3.3$4 d because their longer orbital periods and transit durations make obliquity measurements more difficult.

2. Stellar and planetary properties

The host star is characterized as a late F-type dwarf. Its reported stellar parameters are $\Delta \mathrm{mag} < 3.3$5, $\Delta \mathrm{mag} < 3.3$6, $\Delta \mathrm{mag} < 3.3$7, $\Delta \mathrm{mag} < 3.3$8 (cgs), $\Delta \mathrm{mag} < 3.3$9, $< 3.9$0, and age $< 3.9$1 Gyr. The discovery analysis derived these quantities from SED+Gaia and also reported $< 3.9$2 and $< 3.9$3 mag (Gupta et al., 2023).

The planetary parameters were first reported as $< 3.9$4 and $< 3.9$5, with bulk density $< 3.9$6. The later HARPS-N joint analysis yielded $< 3.9$7 and $< 3.9$8, with a derived mean density $< 3.9$9 using $0.2''$0. The transit depth was reported as $0.2''$1 ppt, consistent with $0.2''$2 (Gupta et al., 2023, Mireles et al., 26 Sep 2025).

Thermal characterizations differ because the assumptions differ. The discovery paper reported $0.2''$3 and insolation $0.2''$4 for zero albedo and full redistribution at the mean orbital separation. The later analysis reported $0.2''$5, assuming Bond albedo $0.2''$6 and emissivity $0.2''$7, via

$0.2''$8

The discovery paper also emphasized strong phase dependence, reporting $0.2''$9 near transit and $25''$0 near occultation. This thermal contrast reflects the system’s unusually large eccentricity rather than unusually high mean insolation (Gupta et al., 2023).

Projected stellar rotation was reported differently in the two analyses. The discovery paper gave $25''$1 from SPC on TRES and noted that, assuming $25''$2, the minimum rotation period is $25''$3 days. The RM fit later returned $25''$4, a quantity directly relevant to obliquity modeling (Gupta et al., 2023, Mireles et al., 26 Sep 2025).

3. Orbital architecture and transit geometry

The orbital period is measured very precisely: $25''$5 d in the discovery paper and $25''$6 d in the later joint analysis. The corresponding semi-major axis is $25''$7 AU in the original fit and $25''$8 AU in the HARPS-N reanalysis, consistent with the Keplerian relation

$25''$9

The orbit is highly eccentric, with $6.13\ {\rm m\ s^{-1}}$0 in the discovery solution and $6.13\ {\rm m\ s^{-1}}$1 in the later solution. The argument of periastron is $6.13\ {\rm m\ s^{-1}}$2 deg in the first paper and $6.13\ {\rm m\ s^{-1}}$3 deg in the second (Gupta et al., 2023, Mireles et al., 26 Sep 2025).

Transit geometry indicates a nearly edge-on configuration. The orbital inclination is $6.13\ {\rm m\ s^{-1}}$4 deg in the discovery analysis and $6.13\ {\rm m\ s^{-1}}$5 deg in the later one, with impact parameter $6.13\ {\rm m\ s^{-1}}$6 initially and $6.13\ {\rm m\ s^{-1}}$7 in the reanalysis. The scaled separation is $6.13\ {\rm m\ s^{-1}}$8 in the discovery paper and $6.13\ {\rm m\ s^{-1}}$9 in the later paper, while the stellar density derived from the transit fit in the latter is $8.09\ {\rm m\ s^{-1}}$0. The transit epoch is reported as $8.09\ {\rm m\ s^{-1}}$1 BJD for the original ephemeris and as $8.09\ {\rm m\ s^{-1}}$2 in BJD $8.09\ {\rm m\ s^{-1}}$3, equivalently $8.09\ {\rm m\ s^{-1}}$4, for the later fit (Gupta et al., 2023, Mireles et al., 26 Sep 2025).

The orbit’s extreme eccentricity produces large differences between periastron and apastron. Using the discovery solution, the periastron and apastron distances are

$8.09\ {\rm m\ s^{-1}}$5

In stellar radii, these correspond to $8.09\ {\rm m\ s^{-1}}$6 and $8.09\ {\rm m\ s^{-1}}$7. The same analysis gave an eccentric-orbit transit probability of $8.09\ {\rm m\ s^{-1}}$8. The total transit duration is $8.09\ {\rm m\ s^{-1}}$9 h in the geometric estimate, consistent with the later fitted values $\simeq 8\ {\rm m\ s^{-1}}$0 h and $\simeq 8\ {\rm m\ s^{-1}}$1 h (Gupta et al., 2023, Mireles et al., 26 Sep 2025).

These orbital properties place TOI-4127 b in a sparsely populated part of warm-Jupiter parameter space. The discovery paper noted that fewer than ten transiting warm Jupiters with $\simeq 8\ {\rm m\ s^{-1}}$2 masses had $\simeq 8\ {\rm m\ s^{-1}}$3 in the NASA Exoplanet Archive queried on 2023-01-12 (Gupta et al., 2023).

4. Spin–orbit alignment and Rossiter–McLaughlin measurement

The defining result of the later study is a measurement of the Rossiter–McLaughlin effect showing that the system is well aligned. The sky-projected obliquity is

$\simeq 8\ {\rm m\ s^{-1}}$4

and the host star is therefore described as well aligned with the highly eccentric warm Jupiter TOI-4127 b. This makes TOI-4127 one of the most eccentric well-aligned systems to date and one of the longest-period systems with a measured obliquity (Mireles et al., 26 Sep 2025).

The RM analysis used a modified allesfitter framework to perform a joint fit of TESS photometry, NEID/SOPHIE/HARPS-N out-of-transit radial velocities, and HARPS-N in-transit RM velocities. The light curve was modeled with PyTransit; the out-of-transit radial velocities with RadVel; and the RM signal with the tracit package using the Hirano et al. (2011) formulation, explicitly including microturbulence and macroturbulence. Sampling used nested sampling with 500 live points and mostly uniform priors, except normal priors for micro- and macroturbulence. Limb darkening was fitted separately for the TESS and HARPS-N passbands with broad uniform priors, yielding TESS $\simeq 8\ {\rm m\ s^{-1}}$5, $\simeq 8\ {\rm m\ s^{-1}}$6, and HARPS-N $\simeq 8\ {\rm m\ s^{-1}}$7, $\simeq 8\ {\rm m\ s^{-1}}$8. The fit also returned $\simeq 8\ {\rm m\ s^{-1}}$9 and $\approx 4.8$0 (Mireles et al., 26 Sep 2025).

The later paper emphasized that the stellar inclination $\approx 4.8$1 is not measured. An attempted rotation-period search in TESS via GLS was inconclusive, so there is no constraint on the true three-dimensional obliquity $\approx 4.8$2, even though the conversion formula is known: $\approx 4.8$3 This is a central interpretive limitation: near-zero $\approx 4.8$4 implies a well-aligned sky projection, but not a direct measurement of the full three-dimensional spin–orbit angle (Mireles et al., 26 Sep 2025).

The expected RM signal was already recognized in the discovery paper. Using $\approx 4.8$5 from TRES and the transit parameters, the expected RM semi-amplitude was estimated as

$\approx 4.8$6

The later paper gave the generic scaling

$\approx 4.8$7

and, for TOI-4127 b, with $\approx 4.8$8 and $\approx 4.8$9, suggested a characteristic RM amplitude of order a few$1.38$0, consistent with the HARPS-N detection (Gupta et al., 2023, Mireles et al., 26 Sep 2025).

5. Dynamical interpretation and migration pathways

The current orbit is dynamically unusual because it combines $1.38$1 with $1.38$2. The discovery paper argued that the present periastron separation is too large for high-eccentricity tidal migration to circularize the orbit on astrophysically relevant timescales unless the system is undergoing angular-momentum exchange with an undetected outer companion. Using the Adams & Laughlin (2006) prescription with $1.38$3, the tidal circularization timescale was estimated as

$1.38$4

far exceeding the $1.38$5 Gyr stellar age. A simple constant-$1.38$6, constant-$1.38$7 estimate gave $1.38$8–$1.38$9 yr, and the paper also noted that diffusive tidal evolution via coupling to the planetary $\Delta \mathrm{mag} < 3.3$00-mode is ineffective because $\Delta \mathrm{mag} < 3.3$01, whereas the relevant criterion requires periastron $\Delta \mathrm{mag} < 3.3$02 tidal radii (Gupta et al., 2023).

If the orbit were to circularize while conserving angular momentum, the final semi-major axis would be

$\Delta \mathrm{mag} < 3.3$03

with $\Delta \mathrm{mag} < 3.3$04 d. These values lie well outside the canonical hot-Jupiter pile-up at 3–4 days. The later RM paper summarized the same point qualitatively, citing a tidal migration timescale to a hot-Jupiter orbit of order 780 Gyr and therefore disfavoring ongoing classic high-eccentricity tidal migration unless the system undergoes eccentricity oscillations with intervals of even higher $\Delta \mathrm{mag} < 3.3$05 (Gupta et al., 2023, Mireles et al., 26 Sep 2025).

The alignment result complicates formation scenarios. In-situ formation and disk migration naturally produce aligned orbits but cannot easily generate $\Delta \mathrm{mag} < 3.3$06; eccentricity excitation at a disk cavity typically reaches $\Delta \mathrm{mag} < 3.3$07. The later paper therefore highlighted recent simulations in which resonant planet–disc interactions in cavities can raise eccentricity to high values without misalignment, especially for massive planets, a point consistent with TOI-4127 b’s $\Delta \mathrm{mag} < 3.3$08. Planet–planet scattering generally yields high eccentricity and often misalignment, but aligned outcomes are possible in specific cases. Kozai–Lidov oscillations typically produce high eccentricity and misalignment, yet aligned snapshots can occur if the system is observed during low-obliquity phases of the cycle. Coplanar high-eccentricity migration can also yield high $\Delta \mathrm{mag} < 3.3$09 with low $\Delta \mathrm{mag} < 3.3$10 for coupled near-coplanar perturbers, although it likewise requires an additional undetected massive companion (Mireles et al., 26 Sep 2025).

The observed alignment is therefore not equivalent to a demonstration of smooth disk migration. The later paper explicitly stated that typical in-situ formation and disk migration scenarios cannot explain this system, while specific resonant planet–disc interactions, specific cases of planet–planet scattering or Kozai–Lidov oscillations, and coplanar high-eccentricity migration remain viable. A plausible implication is that TOI-4127 b probes a formation channel that preserves low projected obliquity while still accessing the high-eccentricity tail of the warm-Jupiter population.

6. Companion constraints, uncertainties, and future observational tests

Searches for additional bodies have not yet produced a definitive perturber, but they leave important parameter space open. The discovery analysis included a two-instrument linear trend and found a best-fit RV slope of $\Delta \mathrm{mag} < 3.3$11, or $\Delta \mathrm{mag} < 3.3$12, consistent with no trend; generalized Lomb–Scargle periodograms of the residuals showed no significant periodicities. A synthetic population study of long-period giants concluded that most perturbers with RV semi-amplitudes $\Delta \mathrm{mag} < 3.3$13 would have been detectable via radial velocity and/or Gaia, but a large volume of parameter space with $\Delta \mathrm{mag} < 3.3$14 remains unconstrained, and many potential perturbers with $\Delta \mathrm{mag} < 3.3$15 would require $\Delta \mathrm{mag} < 3.3$16 additional NEID-quality radial velocities for a $\Delta \mathrm{mag} < 3.3$17 detection on this star (Gupta et al., 2023).

The later RM study sharpened the companion discussion. It stated that existing radial velocities should have detected many candidate perturbers proposed to drive Kozai–Lidov oscillations or coplanar high-eccentricity migration, but that long-period ($\Delta \mathrm{mag} < 3.3$18 d) or lower-mass perturbers could evade detection. High-resolution imaging with NESSI and Gaia DR3 astrometry constrain some parameter space, yet Gaia RUWE $\Delta \mathrm{mag} < 3.3$19, described as near or beyond the EDR3 anomaly threshold of $\Delta \mathrm{mag} < 3.3$20, hints at a possible unresolved stellar companion. A MOLUSC analysis generated $\Delta \mathrm{mag} < 3.3$21 synthetic companions and found that $\Delta \mathrm{mag} < 3.3$22 are consistent with current constraints, with a mass distribution favoring low-mass stars and a bimodal semi-major-axis distribution peaking around $\Delta \mathrm{mag} < 3.3$23 AU (Mireles et al., 26 Sep 2025).

Several uncertainties remain intrinsic to the obliquity result. The absence of a measured stellar rotation period prevents determining $\Delta \mathrm{mag} < 3.3$24 and hence $\Delta \mathrm{mag} < 3.3$25. The later paper also identified degeneracies involving limb-darkening coefficients and turbulence parameters in RM modeling, $\Delta \mathrm{mag} < 3.3$26 and $\Delta \mathrm{mag} < 3.3$27 covariances, modest TESS contamination in some sectors, and the limitation that a single RM transit restricts sensitivity to subtle RM shape systematics. Instrument-specific jitter terms were included, but correlated stellar activity noise was not explicitly modeled with Gaussian processes in the RM analysis. By contrast, the original discovery paper had modeled photometric variability with a Matérn-$\Delta \mathrm{mag} < 3.3$28 Gaussian process in the transit fit (Gupta et al., 2023, Mireles et al., 26 Sep 2025).

Future work is correspondingly well defined. The later paper recommended long-term precise radial-velocity monitoring to detect trends or additional planets, repeat RM observations to refine $\Delta \mathrm{mag} < 3.3$29 and $\Delta \mathrm{mag} < 3.3$30 and test consistency across epochs, high-contrast imaging to probe for faint stellar or massive planetary companions, and Gaia DR4/DR5 astrometry for acceleration constraints. The discovery paper further noted that the predicted transit windows remain accurate to better than $\Delta \mathrm{mag} < 3.3$31 minutes for $\Delta \mathrm{mag} < 3.3$32 years, that the secondary impact parameter $\Delta \mathrm{mag} < 3.3$33 implies a likely occultation, and that the large irradiation swings make the planet a compelling target for phase-curve studies of radiative timescales, pseudo-synchronous rotation, and disequilibrium chemistry (Gupta et al., 2023, Mireles et al., 26 Sep 2025).

TOI-4127 b therefore occupies a distinctive position in exoplanet demographics: a massive, highly eccentric warm Jupiter in a system whose sky-projected spin–orbit geometry is consistent with alignment. Its orbital architecture disfavors straightforward high-eccentricity tidal migration on the current orbit, while its low measured $\Delta \mathrm{mag} < 3.3$34 constrains but does not resolve the dynamical history. The system is consequently important both as a benchmark for warm-Jupiter obliquity measurements and as a test case for resonant planet–disc interactions, scattering, Kozai–Lidov evolution, and coplanar high-eccentricity migration.