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Spot-Crossing Variations Confirm a Misaligned Orbit for a Planet Transiting an M Dwarf

T0 review · 2 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read TOI-3884 b travels on a misaligned orbit and crosses a large polar starspot on its M-dwarf host.

desk verdict A well-observed confirmation of a misaligned orbit over a polar spot on TOI-3884, but the headline obliquity is prior-dominated and should be treated as conditional on stellar parameters. read the letter →

arxiv 2506.11998 v2 pith:C33JJQDN submitted 2025-06-13 astro-ph.EP astro-ph.SR

Patrick Tamburo , Samuel W. Yee , Juliana García-Mejía , David Charbonneau , Allyson Bieryla , Karen A. Collins , Avi Shporer This is my paper · ORCID
classification astro-ph.EPastro-ph.SR
keywords exoplanetsstarspotsstellarobliquityMdwarfstransitphotometryspot-crossingeventsrotationpolar
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper establishes that the transiting planet TOI-3884 b is not orbiting in its host star's equatorial plane. The authors combine long-term photometric monitoring from the Tierras Observatory with six resolved transit light curves to measure a stellar rotation period of $P_\mathrm{rot} = 11.020 \pm 0.015$ days and to show that the persistent bump inside every transit is the planet passing over a single large spot sitting at $80.5^\circ$ latitude, very close to the star's pole. The best-fit geometry has the star's spin axis tilted so that one pole points nearly at the observer ($i_\star = 22.3^\circ$) and the planet's orbit misaligned from the stellar spin by $\psi_\star = 77.4^\circ$. If correct, TOI-3884 becomes the first M-dwarf benchmark in which spot-crossing variations confirm a misaligned orbit and expose a long-lived polar spot to repeated observation.

What carries the argument

The load-bearing element is a simultaneous model of a rotating spotted stellar surface and the planet's transits, computed with the starry package's spherical-harmonic expansion of surface brightness. A single top-hat spot with radius, contrast, latitude, longitude, and smoothing is placed on the star; as the star rotates with period $P_\mathrm{rot}$, the spot moves in and out of the transit chord, changing the shape and timing of the spot-crossing bump between epochs, while the same spot produces the out-of-transit sinusoidal modulation. Fitting both data sets together breaks the degeneracy that a static spot model cannot resolve and directly constrains the angle between the stellar spin axis and the planetary orbit normal, $\psi_\star$.

What would settle it

Measure the star's projected rotation velocity $v \sin i_\star$ from a high-resolution spectrum: the model predicts $0.57 \pm 0.04$ km/s, so a value well outside that range would falsify the derived spin geometry, and an independent stellar-density determination from Gaia parallax and stellar models would settle whether the impact parameter is near $0.03$ or near $0.40$, which changes the headline obliquity.

Watch

Extended reading notes

Core claim

The central claim is that TOI-3884 b has a strongly misaligned orbit and that the spot-crossing events seen in every transit occur because the planet passes over a large spot located very close to the visible rotational pole of its M4 host. The authors fit the star's sinusoidal 1% rotational modulation and the epoch-to-epoch changes in transit shape simultaneously, yielding $P_\mathrm{rot} = 11.020 \pm 0.015$ days, a spot radius of $31.2^\circ$, a spot latitude of $80.5^\circ \pm 1.2^\circ$, and a true stellar obliquity of $\psi_\star = 77.4^{+2.3}_{-2.5}$ degrees with a stellar inclination of $i_\star = 22.3^{+1.8}_{-1.6}$ degrees. This rules out the alternative that the planet's orbital period is synchronized with stellar rotation so the same spot is always under the transit chord. The model also explains why some earlier TESS transits showed no obvious spot crossing: at certain rotation phases the spot rotates out of the transit chord. Archival Zwicky Transient Facility photometry shows an approximately 11-day signal across roughly seven years, suggesting the polar spot is long-lived.

Load-bearing premise

The headline obliquity value assumes the star's mass and radius (and therefore its density) follow the Gaussian priors from the earlier Libby-Roberts analysis; if the true density is lower, the transit chord would sit farther from the star's center and the derived tilt would shift from about $77^\circ$ to about $118^\circ$, so the precise number is only as trustworthy as those priors.

Editorial extensions

If this is right

  • The aligned-scenario alternative is ruled out because the stellar rotation period is not an integer fraction of the orbital period: $P_\mathrm{rot}/P_\mathrm{orb} = 2.4249 \pm 0.0033$.
  • TOI-3884 becomes a benchmark for studying polar starspot evolution on an M dwarf, with photometric evidence that the spot has persisted for at least seven years.
  • The model's predicted spot longitudes (Table 3) give observers a direct handle on how starspot contamination will affect the JWST Cycle 3 transmission spectra of TOI-3884 b.
  • The planet joins the small population of misaligned hot Neptunes around cool stars that favor nearly polar orbits, which may point toward disk torquing or secular perturbations by an unseen companion.
  • If the spot remains stable, future transits will cross it at different angles, allowing a map of the stellar pole and direct constraints on spot latitude drift and spot lifetime.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A test the authors do not run: compare the spot longitudes predicted for the two JWST programs against the actual transit shapes; a systematic offset would reveal spot migration or differential rotation, while agreement would extend the spot's stability baseline.
  • If the polar spot really survives for years on a star rotating as slowly as 11 days, it would weaken the usual link between polar spots and rapid rotation and motivate dynamo models for slowly rotating convective stars.
  • The same spot-crossing technique could be applied to other M-dwarf planets with persistent transit bumps, giving an obliquity measurement path for cool stars where Rossiter–McLaughlin spectroscopy is difficult.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. This paper presents Tierras Observatory photometry of TOI-3884 spanning 2024 November 13 to 2025 May 30, including six transits of TOI-3884 b and sparse out-of-transit monitoring. A Lomb-Scargle analysis finds a stellar rotation period of 11.020 +/- 0.015 days, with supporting but weaker archival ZTF detections. The authors simultaneously fit the rotational modulation and the transit shapes with a starry model containing one starspot, stellar rotation, and a Keplerian orbit, obtaining a near-pole-on star (i_star = 22.3 deg) with a large polar spot (r_spot = 31.2 deg, latitude 80.5 deg) and a strongly misaligned orbit (lambda_star = 305.1 deg, psi_star = 77.4 deg). They discuss a positive/negative pole degeneracy, apply the model to archival TESS transits, provide JWST spot-phase predictions, and compare with the independent analysis of Mori et al. (2025). The qualitative picture of a misaligned orbit crossing a persistent polar spot is well supported by the data, but the numerical obliquity depends on the adopted stellar mass and radius priors.

Significance. If the result holds, TOI-3884 b would be a benchmark system: a hot Neptune around an M dwarf on a strongly misaligned orbit crossing a long-lived polar spot, with JWST observations already scheduled. The paper has several concrete strengths: an independent 11-day rotation detection from Tierras and ZTF, a global simultaneous model with 37 parameters over 2019 points (reduced chi-squared = 0.94), an explicit treatment of the positive/negative pole degeneracy, and falsifiable JWST spot-longitude predictions. The central quantitative claim is not yet robust, however. The quoted psi_star = 77.4 deg arises from Gaussian priors on the stellar mass and radius that fix the impact parameter, and the transit duration alone cannot break the b-rho_star degeneracy because the duration scales as rho_star^-1/3 sqrt(1-b^2). The paper therefore needs a robustness demonstration before the specific obliquity value can be adopted as a benchmark.

major comments (2)
  1. [Section 3.2, Table 2, and Section 4.5] The headline value psi_star = 77.4 deg +2.3/-2.5 is prior-dominated rather than data-dominated. The Gaussian priors on M_star and R_star from Libby-Roberts et al. (2023) fix rho_star ~ 14.4 g cm^-3 and hence a/R_star ~ 25.06, which drives b = 0.029 and ip = 89.93 deg. The argument in Section 4.5 that Mori et al.'s b = 0.40 is disfavored because it requires rho_star = 11.85 g cm^-3 below the LR23 value is not decisive: for a fixed orbital period, the transit duration scales as rho_star^-1/3 sqrt(1-b^2), so (rho_star=14.4, b=0.03) and (rho_star=11.85, b=0.40) produce nearly identical durations, and the fitted eccentricity (0.042 +/- 0.044) weakens the duration constraint further. The authors should demonstrate directly that the Tierras light curves select b~0 in the absence of the LR23 rho_star prior, or marginalize psi_star over the full allowed stellar-density range, before quoting the obliquity with +/-2.5 deg errors. As written, the abstract's numerical claim is not robust to the b-rho_star degeneracy.
  2. [Section 3.2 and Figure 5] The single-spot model is explicitly a poor fit to Transit 258 in both the Tierras and FLWO g'-band data, and the two-spot test in Section 3.2 locks all stellar and planetary parameters to the one-spot best-fit values rather than treating the second spot as part of the full global model. Because the spot-crossing morphology is the diagnostic that constrains i_star, lambda_spot, and psi_star, an epoch containing an additional spot crossing implies that the one-spot parameter uncertainties may be underestimated. I recommend either including a second spot in the global fit (or marginalizing over its presence) or explicitly checking that the psi_star posterior is unchanged when Transit 258 is removed from the fit.
minor comments (5)
  1. [Section 4.5] The comparison with Mori et al. reports two mutually inconsistent values of the true obliquity in consecutive paragraphs: psi = 118.1 deg +5.6/-2.3 in the first paragraph and psi = 61.9 deg +2.3/-5.6 in the second. Please correct the typo and reconcile the text, because the current wording makes it difficult to assess the claimed 4.6-sigma discrepancy.
  2. [Figure 2 caption] The caption contains a duplicated phrase, 'with i_star = 22.3 deg, lambda_star = 305.1 deg, ip = 89.934 deg, and and lambda_spot = 80.5 deg'; the extra 'and' should be removed.
  3. [Section 3.2] The text refers to 'LSO SSO 1-m' in the description of the fitted data sets; this should read 'LCO SSO 1-m' for consistency with Section 2.2 and Table 1.
  4. [Section 4.2 and Abstract] The archival ZTF support for a seven-year spot lifetime is weak: the i-band periodogram peak has FAP = 19% and the g-band peak has FAP = 4.7%, with only the r-band peak significant at FAP = 0.046%. The abstract's statement that the spot 'has persisted for at least seven years' is stronger than the evidence; the body text's 'suggests the possibility' is appropriately hedged.
  5. [Section 3.3] The MCMC description reports 62 walkers and 100,000 steps but does not provide a convergence diagnostic (e.g., autocorrelation time or Gelman-Rubin statistic). Adding one would strengthen the reported uncertainties.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the true stellar obliquity is a fitted outcome from a joint model with broad priors, not an input or a repackaged fit.

full rationale

The paper's central claim, ψ⋆ = 77.4° +2.3/−2.5, is derived from fitted parameters (i⋆ = 22.3°, λ⋆ = 305.1°, ip = 89.934°) that are free parameters with uniform or weakly informative priors, not quantities defined in terms of the headline obliquity. The rotation period Prot = 11.020 ± 0.015 d is also a fitted parameter, constrained jointly by the Tierras photometric modulation and the transit spot-crossing shapes; this is a simultaneous, self-consistent model rather than a prediction circularly tied to its inputs. The ZTF archival period check is an independent dataset, and the paper honestly reports that TESS data do not independently show the 11-day spot modulation. The stellar mass and radius priors from Libby-Roberts et al. (2023) do influence the impact parameter and hence the exact obliquity value, but this is a statistical sensitivity, not a definitional circularity; the paper explicitly compares with the alternative Mori et al. (2025) solution and discusses the discrepancy. No load-bearing self-citation chain, no imported uniqueness theorem, and no ansatz smuggled in solely by citation are present. The mild concern that the same Tierras dataset provides both the rotation period and the spot-crossing phases is not circularity: the model must fit all data simultaneously and does so with reduced χ² = 0.94, and the derived obliquity is not an input to any fit. Therefore the derivation chain is self-contained, and any residual concerns about prior dependence belong to robustness, not circularity.

Assumptions & free parameters 16 free parameters · 8 assumptions · 0 invented entities

The central result rests on a 37-parameter MCMC fit to Tierras, FLWO, and LCO photometry. The derived obliquity and spot geometry are functions of fitted parameters (i_star, i_p, lambda_star, and the spot parameters). The most consequential inputs pulled from prior work are the Libby-Roberts et al. (2023) stellar mass and radius priors, the Claret and Bloemen limb-darkening tables, the SPHINX spectral models, and the starry surface formalism; none of these are independently derived in this paper. No new physical entities are introduced; the polar starspot is an inferred surface feature previously proposed by Libby-Roberts et al. (2023), not a new theoretical construct.

free parameters (16)
  • Prot = 11.020 ± 0.015 days
    Stellar rotation period; fitted in the joint model and supported by Lomb-Scargle and ZTF periodograms. Drives the rotating spot geometry.
  • i_star = 22.3° +1.8/−1.6
    Stellar inclination; uniform prior 0-90°; key input to the derived true obliquity.
  • r_spot = 31.2° +2.4/−1.9
    Spot radius in degrees; uniform prior 22.5-100; a principal output of the spot model.
  • lambda_spot = 80.5° ± 1.2°
    Spot latitude; near-polar; central to the polar spot interpretation.
  • phi_spot = 117.4° +4.9/−4.8
    Spot longitude at t=0; determines the spot's rotational phase at each transit.
  • s_spot = 0.169 +0.038/−0.043
    Gaussian smoothing of the top-hat spot; controls spot edge sharpness.
  • Teff_spot = 2791 K +61/−72
    Spot temperature; combined with Teff_star and SPHINX models to set the spot contrast in each filter.
  • Teff_star = 2985 ± 65 K
    Stellar effective temperature in the fit; the paper cautions the posterior is not a reliable photospheric temperature.
  • Rp/Rstar = 0.1906 ± 0.0022
    Planet-to-star radius ratio; affects the transit depth and shape.
  • i_p = 89.934° +0.048/−0.094
    Orbital inclination; nearly edge-on; with i_star and lambda_star determines the true obliquity.
  • lambda_star = 305.1° +5.4/−5.3
    Sky-projected stellar obliquity; converted to the conventional definition; a direct input to the true obliquity.
  • e = 0.042 +0.044/−0.029
    Orbital eccentricity; prior from Libby-Roberts et al. (2023); affects transit shape.
  • M_star = 0.295 +0.017/−0.018 M_sun
    Stellar mass; Gaussian prior from Libby-Roberts et al. (2023); sets the stellar density that fixes the transit impact parameter.
  • R_star = 0.306 ± 0.010 R_sun
    Stellar radius; Gaussian prior from Libby-Roberts et al. (2023); together with M_star sets the density and hence the transit duration and impact parameter.
  • Limb darkening coefficients (six values) = u1, u2 per filter; see Table 2
    Quadratic limb-darkening coefficients with Gaussian priors; affect transit and spot-crossing shape.
  • Nuisance parameters (nightly offsets, global slope, airmass corrections) = Various; see Table 2
    Fitted to absorb systematics and not physically interpreted; they do not affect the central geometry.
assumptions (8)
  • domain assumption A single top-hat spot with Gaussian smoothing, represented by a starry l=10 spherical harmonic expansion, adequately describes the stellar surface over the whole observing baseline.
    Section 3.2; the paper itself shows this fails for Transit 258, where a second spot is added ad hoc.
  • domain assumption The star rotates rigidly with a single rotation period, and the spot does not migrate or change size over the six-month baseline, nor negligibly until the last JWST epochs.
    Section 4.4 explicitly assumes negligible spot evolution for the JWST predictions.
  • domain assumption The spot contrast is computed from SPHINX M-dwarf spectral models with sampled Teff_star and Teff_spot, assuming log g = 5.0 and Z = 0.0, and using accurate filter transmission curves.
    Section 3.2, Equation 1; the computed contrast drives the amplitude of rotational modulation and spot-crossing bumps.
  • domain assumption The stellar mass and radius priors from Libby-Roberts et al. (2023) isochrone analysis are correct, fixing the stellar density and thus the transit impact parameter.
    Table 2; Section 4.5 relies on the implied stellar density to prefer b = 0.03 over Mori et al.'s b = 0.40.
  • domain assumption The photometric 11-day periodicity is the stellar rotation period, not an alias or instrumental effect; the window-function alias handling is correct.
    Section 3.1; supported by the ZTF r-band detection, but the g- and i-band detections are not individually significant.
  • domain assumption The limb-darkening central values from TESS analysis for the Tierras filter and from Claret and Bloemen (2011) for g' and i' are reasonable, with the wide Gaussian priors being adequate.
    Section 3.2; the broad priors of σ = 0.2 mitigate but do not eliminate model dependence.
  • standard math The positive- and negative-pole solutions are exactly symmetric, so restricting i_star to the range 0-90 degrees does not bias the derived true obliquity.
    Section 3.2 and Figure 2 show the two families produce identical light curves, with the true obliquity unchanged under the transformation.
  • domain assumption The SPHINX spectral grid interpolations at log g = 5.0 and Z = 0.0 provide accurate continuum ratios across the Tierras, g', and i' filter bands.
    Section 3.2; the spot contrast used in the model depends directly on these interpolated spectra.

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Cite this review

Pith. "Pith review of Spot-Crossing Variations Confirm a Misaligned Orbit for a Planet Transiting an M Dwarf." pith.science (2026). https://pith.science/paper/C33JJQDN

@misc{pith2026250611998,
  author       = {Pith},
  title        = {Pith review of: Spot-Crossing Variations Confirm a Misaligned Orbit for a Planet Transiting an M Dwarf},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/C33JJQDN}},
  note         = {Machine review of arXiv:2506.11998}
}
abstract

TOI-3884~b is an unusual 6.4~R$_\oplus$ planet orbiting an M4 host, whose transits display large and persistent spot-crossing events. We used the \textit{Tierras} Observatory to monitor both the long-term photometric variability of TOI-3884 and changes in the spot-crossing events across multiple transits of the planet. We show that the star rotates with a period of $11.020 \pm 0.015$~days. We simultaneously model the rotational modulation of the star and variations in transit shapes that arise due to rotation of the spot, allowing us to determine the true stellar obliquity, $\psi_\star$. The data are best described by a planet on a misaligned orbit around a highly inclined star ($\psi_\star = {77.4^\circ} ^{+2.3^\circ}_{-2.5^\circ}$; $i_\star = {22.3^\circ}^{+1.8^\circ}_{-1.6^\circ}$) that hosts a large polar starspot ($r_\mathrm{spot} = {31.2^\circ}^{+2.4^\circ}_{-1.9^\circ}$; $\lambda_\mathrm{spot} = {80.5^\circ}\pm1.2^\circ$). Archival photometry from the Zwicky Transient Facility suggests that this polar spot has persisted on TOI-3884 for at least seven years. The TOI-3884 system provides a benchmark for studying the evolution of a polar spot on an M dwarf.

Figures

Figures reproduced from arXiv: 2506.11998 by the authors.

Figure 1
Figure 1. First panel: The Tierras light curve of TOI-3884. Individual 60-s exposures are shown as points color-coded by time, while the medians fluxes measured on each night are shown as white points with error bars. Dashed lines indicate the epochs of the transit observations summarized in [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. An illustration of the degeneracy between “positive” pole solutions and “negative” pole solutions during two different transit events: one with the spot located at longitude ϕspot = 0◦ , the other at ϕspot = 218◦ . For each event, a positive surface configuration is shown (blue) with i⋆ = 22.3 ◦ , λ⋆ = 305.1 ◦ , ip = 89.934◦ , and and λspot = 80.5 ◦ , along with the conjugate negative solution (orange): i ′ ⋆ = 180◦… view at source ↗
Figure 3
Figure 3. Top left: The full Tierras light curve at native cadence (gray points) and binned over each night (white points with black outlines) along with the best-fit MCMC model (black). Colored regions indicate the nights during which transit observations occurred. Bottom left: The residuals from the best-fit model. Top right: The best-fit starry map at the first Tierras time stamp. By construction, our models includes solut… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Tierras transit observations of TOI-3884. The left column indicates the rotational phase of the star at mid-transit. The middle column shows the data and the best-fit transit model in black. The magenta lines show 100 models generated from random samples from the MCMC.…
Figure 5
Figure 5. Figure 5: Simultaneous observations of Transit 258 with Tierras (top panel) and FLWO 1.2-m in g ′ -band (bottom panel). The best-fit model is shown as a solid black line and 100 models generated from random samples from the MCMC are shown in magenta. We have applied a linear air…
Figure 7
Figure 7. Figure 7: The first frame of an animation showing how the stellar surface changes as the star rotates (top panel), and how the transit would look if it were observed with the corresponding surface configuration (bottom panel). The full animation, computed at 4◦ intervals for one…
Figure 8
Figure 8. Figure 8: First row: Archival ZTF g-band (left column), r-band (middle column), and i-band (right column) photometry. Points are colored by time, which is calculated with respect to the first Tierras exposure. Second row: The LS periodograms of the three light curves from 5–17 d…
Figure 9
Figure 9. Figure 9: TESS transit observations of TOI-3884 from Sec￾tors 46 and 49. The gray points are the two-minute cadence PDCSAP data from the SPOC analysis, while black points with error bars show the data binned over 16-minute inter￾vals. The numbers in the lower right of each panel…

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