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Simulations of starspot anomalies within TESS exoplanetary transit light curves -- I. The detection limits of starspot anomalies in TESS light curves

T0 review · 2 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

Pith's one-line read Starspot anomalies will be observable in TESS 2-minute transit light curves, with detection limits of 4,900 ± 1,700 km for M4V, 13,800 ± 6,000 km for M1V, and 15,900 ± 6,800 km for K5V host stars.

desk verdict Solid TESS starspot detectability grid with a real factor-of-two flux normalization error in Eq. 7 and an overstated abstract; radius limits survive. read the letter →

arxiv 1908.05747 v1 pith:JNCTBBEB submitted 2019-08-15 astro-ph.EP

classification astro-ph.EP
keywords starspotanomaliesTESStransitlightcurvesPRISMdetectionlimitsMdwarfstarscontrastphotometricprecision
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 aims to establish whether the brief brightness 'blips' produced when a transiting planet eclipses a starspot will be visible in TESS 2-minute cadence data, and to quantify the smallest spot that can be detected around the K and M dwarf stars TESS targets. Using 20,573 simulated transits with the PRISM transit-starspot model across 3,888 scenarios, the authors find that spot anomalies will indeed be observable. The smallest spot seen under optimal conditions has radius about 1,900 km, while the mean detection limits are 4,900 ± 1,700 km (M4V), 13,800 ± 6,000 km (M1V), and 15,900 ± 6,800 km (K5V). The work also characterises how the smallest detectable spot-induced flux change depends on the planet-to-star radius ratio, reaching a minimum $\Delta F_\mathrm{spot} = 0.00015 \pm 0.00001$ at $k = 0.082 \pm 0.004$. If right, TESS light curves of active K and M dwarfs will routinely contain measurable spot anomalies, which is both a modelling complication and an opportunity for starspot tracking.

What carries the argument

The central object is PRISM, a pixellation-based transit-starspot model that tiles the stellar disc into two-dimensional elements, assigns each element an intensity (with quadratic limb darkening and a blackbody-based spot contrast $\rho_\mathrm{spot}$), and integrates the received flux as the planet crosses. The load-bearing detection procedure compares the mean amplitude of the simulated spot anomaly, averaged over the in-transit data points that describe it, with the rms scatter of the light curve; a spot is counted as detected only when that mean exceeds $2.0\sigma$. This statistic, not the spot physics alone, sets every numerical limit, and it is the reason the paper finds a planet-size-dependent detection bias.

What would settle it

Inject starspot anomalies of the predicted threshold sizes into real TESS 2-minute light curves of active M4V, M1V, and K5V dwarfs, add the same Gaussian noise levels, and measure the recovery rate under the $2.0\sigma$ mean-amplitude rule; if recovery falls well below expectation, the claimed detection limits are optimistic. Conversely, a systematic search of TESS archival single transits that never finds blips at the predicted scales would falsify the observability conclusion.

Watch

Extended reading notes

Core claim

The central claim is that a starspot occulted by a transiting planet will produce a detectable brightening 'blip' in TESS 2-minute data for realistic M4V, M1V, and K5V hosts, with specific size limits. The authors define detection by the mean amplitude of the anomaly exceeding $2.0\sigma$ of the photometric noise within a single transit, and use this to derive $r_\mathrm{spot} = 0.045 \pm 0.016\,R_*$ for M4V, $0.040 \pm 0.017\,R_*$ for M1V, and $0.038 \pm 0.016\,R_*$ for K5V, corresponding to $4{,}900 \pm 1{,}700$ km, $13{,}800 \pm 6{,}000$ km, and $15{,}900 \pm 6{,}800$ km. Under the most favourable combinations (cool spots, 600 nm, 60 ppm noise), the smallest detected spot is $r_\mathrm{spot} = 0.017\,R_*$, or about 1,900 km on an M4V star. They also find a universal relation between the spot flux change $\Delta F_\mathrm{spot}$ and the planetary transit flux change $\Delta F_p$, with the minimum detectable $\Delta F_\mathrm{spot} = 0.00015 \pm 0.00001$ at $k = 0.082 \pm 0.004$. An additional result is the unexpected trend that small, hot spots are only detected by larger planets, which the authors attribute to the fixed 2-minute cadence and the mean-amplitude detection statistic.

Load-bearing premise

The results stand on the choice that a spot is 'detected' only when the mean amplitude of its in-transit blip exceeds $2.0\sigma$ of the photometric noise in a single transit; a different detection statistic or the use of phase-folded transits would move every reported limit.

Editorial extensions

If this is right

  • Many TESS transit light curves of active K and M dwarfs will contain measurable starspot blips, so analyses of those systems should include transit-starspot modelling rather than treating the transit shape as spot-free.
  • The quoted radius limits give a concrete target scale: spots larger than roughly 4,900 km on an M4V dwarf should generally be recoverable in single 2-minute transits, with the best-case floor near 1,900 km.
  • The quadratic $\Delta F_\mathrm{spot}$–$\Delta F_p$ relation lets observers predict, for a given transit depth, the smallest spot flux deficit and lowest contrast that TESS can reveal, which can guide target selection for spot studies.
  • Unmodelled spot anomalies can bias measured planetary radii, limb-darkening coefficients, and transit timings; the paper's detection limits therefore bracket the severity of this bias for TESS systems.
  • Detectable single-transit spot anomalies enable the starspot-tracking technique for measuring stellar rotation and sky-projected spin-orbit obliquity in systems where the Rossiter-McLaughlin effect is impractical.

Reading between the lines

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

  • An obvious extension the authors leave implicit is that a full likelihood-ratio or joint multi-transit analysis, rather than a single-transit mean-amplitude threshold, would likely push the effective detection limits somewhat smaller; their numbers should be read as conservative for dedicated analyses.
  • The predicted abundance of detectable blips implies that archival TESS light curves can be mined for single-transit spot occultations; counting their occurrence as a function of stellar activity would test the underlying spot-coverage assumptions.
  • The same simulation pipeline could be rerun for the 20-second cadence TESS mode, which should substantially improve the small-planet/small-hot-spot cases that the 2-minute cadence punishes.
  • The $\Delta F_\mathrm{spot}$–$\Delta F_p$ relation could be turned into an estimator for spot contrast from a measured blip and known transit depth, effectively giving a spot-temperature diagnostic in the TESS band.
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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 / 4 minor

Summary. The manuscript presents a large grid of forward-model simulations, using the PRISM transit-starspot code, of starspot anomalies in TESS 2-minute-cadence transit light curves of M4V, M1V, and K5V host stars. A starspot is deemed detected when the mean amplitude of the anomaly, averaged over the in-transit points describing the blip, exceeds 2.0 sigma of the injected Gaussian photometric noise. The authors report per-scenario minimum detectable spot radii, global detection limits of 4900 +/- 1700 km (M4V), 13800 +/- 6000 km (M1V), and 15900 +/- 6800 km (K5V), and a fitted quadratic relation between the spot flux deficit and the planet transit depth (Eq. 9), from which they quote a minimum detectable DeltaF_spot = 0.00015 +/- 0.00001 at k = 0.082 +/- 0.004. The central qualitative conclusion is that starspot anomalies will be observable in many TESS 2-minute transit light curves of K and M dwarfs.

Significance. If the quantitative calibration is corrected, the paper is a useful, transparent reference point for the TESS community: it gives a concrete expectation that starspot 'blips' will appear in 2-minute-cadence transits, and it quantifies how the detectability depends on spot temperature, wavelength, noise, orbital period, and planet size. The strengths include a large and clearly described simulation grid, a forward model benchmarked against JKTEBOP to about 10 ppm, explicit model-recovery tests motivating the detection threshold, and the promise to release the simulated light curves. However, the flux-deficit normalization in Eq. (7) is incorrect by approximately a factor of two, which propagates into Eq. (9), Figs. 11-12, and the abstract's DeltaF_spot value; this is a load-bearing quantitative error, although the radius-based detection limits from the PRISM simulations themselves are not affected. The numeric limits also depend on the chosen 2-sigma mean-amplitude detection statistic. With those caveats, the broad conclusion that starspot anomalies will be observable in TESS transit light curves is defensible.

major comments (2)
  1. [Section 3.6, Table 4 and Eq. (9)] The definition of DeltaF_spot is normalized incorrectly. For a spot at the centre of the stellar disc occulted by a planet, the flux deficit relative to the unspotted disc is set by the spot's projected area on the sky, pi R*^2 sin^2(rspot), divided by the full stellar disc area pi R*^2, i.e. DeltaF_spot = sin^2(rspot)(1 - rho_spot). Equation (7) instead uses the spherical-cap area normalized by the hemisphere area, (1 - cos rspot)(1 - rho_spot). For the small angular radii used throughout the paper (rspot <= 0.35 rad), sin^2(rspot) ~ 2(1 - cos rspot), so every DeltaF_spot value, the fitted coefficients in Eq. (9), the abstract's headline DeltaF_spot = 0.00015 +/- 0.00001, and the Section 3.6 contrast-extrapolation examples are too low by roughly this factor. In particular, the example claiming that a rspot = 1 degree spot cannot be detected for a 1 R_Jup planet around a 1 R_sun star would likely be reversed under the correct normalization. The optimum location k = 0.082 is nearly unaffected because the factor is approximately constant across the fitted range, and the radius detection limits computed directly from PRISM are unaffected. The authors should recompute all flux-deficit results with the projected-area normalization.
  2. [Section 3, detection criterion] Section 3.6, Table 4 and Eq. (9): The conversion from per-scenario rspot limits to DeltaF_spot uses a single mean contrast, rho_bar_spot, per spectral class (Table 4) rather than the actual rho_spot for each of the 1296 scenarios. Because rspot and rho_spot are correlated in the simulations, the product of the means is not the mean of the products, which introduces a systematic bias in the DeltaF_spot points used to fit Eq. (9). When correcting Eq. (7), the authors should recompute Fig. 12 and Eq. (9) using the per-scenario rho_spot values, or demonstrate quantitatively that the averaging is unbiased.
minor comments (4)
  1. [Section 2.3] The number of M4V simulations is given as 6870 in Section 3.1 but 6718 in the Table A.1 caption; analogous discrepancies appear for M1V (7769 in the text vs. 7812 in Table A.2) and for K5V (5934 in the text vs. 6737 in Table A.3). These should be made consistent.
  2. [Section 2.3] The injected noise levels are described as the 'photometric sensitivity' of TESS; please clarify whether the 60-200 ppm values are point-to-point rms per 2-minute cadence sample, and how the cited 60 ppm hr^-1/2 noise floor is converted to the 2-minute cadence used in the simulations.
  3. [Section 3.6] Both DeltaF_p = k^2 and DeltaF_spot ignore limb darkening, even though PRISM applies quadratic limb darkening and the spot is placed at disc centre. For the limb-darkening coefficients used here, the centre-to-mean intensity ratio is about 1.15, which would alter the absolute flux-deficit values beyond the factor-of-two issue in Eq. (7); the approximations should be stated explicitly and ideally corrected.
  4. [Section 2.1] The use of three monochromatic wavelengths (600, 785, 1000 nm) to represent the TESS passband is a simplification, since rho_spot is wavelength-dependent and the TESS band is broad; a sentence quantifying the expected systematic uncertainty from not integrating over the full passband would be helpful.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; simulations are forward models with independent benchmarking, and the one self-citation (PRISM) is not load-bearing.

full rationale

The paper's derivation chain is a forward simulation study: PRISM generates synthetic TESS transit light curves with known starspot parameters, noise is added, and the detection limit is the smallest input rspot whose mean anomaly amplitude exceeds the adopted 2.0-sigma threshold. The 2.0-sigma criterion is not a hidden fit to the conclusions; it is an explicit detection statistic justified by parameter-recovery tests described in Section 3. The only self-citation of consequence is PRISM itself (Tregloan-Reed et al. 2013, 2015, 2018), but PRISM is benchmarked against the independent JKTEBOP code (Section 2, average difference ~10 ppm) and has been used by other groups, so it qualifies as independent support under the rules rather than a load-bearing self-citation. The quadratic relation in Eq. 9 is an empirical fit to simulation outputs, not a derivation that assumes Eq. 9 or the abstract's minimum DeltaF_spot. The reviewer's hemisphere-area normalization concern about Eq. 7 is a quantitative correctness issue, not circularity, because it does not make any derived quantity identical to an input by construction. The stated unexpected trend is explicitly attributed to the cadence and mean-amplitude detection method, and is not presented as an independent prediction from an assumed conclusion. Overall, the central claims are self-contained conditional on the adopted detection metric.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The central claim depends mainly on PRISM's forward model, the chosen noise model, and the detection statistic. No new physical entities are introduced; the only fitted quantities are the coefficients of the empirical DeltaF_spot relation and the 2-sigma detection threshold.

free parameters (4)
  • Detection threshold for anomaly amplitude = 2.0 sigma (rms)
    Chosen by hand after tests showing that 1.5-2 sigma fits give non-physical parameter uncertainties; this threshold directly sets all reported detection limits. Section 3.
  • Quadratic coefficient a in Eq. 9 = 0.00028 +/- 0.00001
    Fitted to the 27 simulated (t, DeltaF_spot) points for the three host stars; used to locate the minimum detectable DeltaF_spot.
  • Quadratic coefficient b in Eq. 9 = -0.00121 +/- 0.00001
    Fitted simultaneously with a and c; part of the empirical DeltaF_spot versus log10(1/DeltaF_p) relation.
  • Quadratic coefficient c in Eq. 9 = 0.00147 +/- 0.00002
    Fitted constant term; the resulting minimum DeltaF_spot is 0.00015 at k = 0.082.
assumptions (7)
  • domain assumption Starspot and photosphere radiate as blackbodies, so spot contrast rho_spot follows Eq. 2 (Silva 2003).
    Used in Section 2.1 to set the 36 rho_spot values from Teff, Tspot, and wavelength; ignores real stellar spectra and magnetic effects.
  • domain assumption The transit and starspot signals are accurately modeled by PRISM's pixellation scheme with quadratic limb darkening.
    PRISM is benchmarked against JKTEBOP to about 10 ppm (Section 2), but the simulations assume no unocculted spot variability, faculae, or granulation signals.
  • domain assumption Noise is white and Gaussian at 60, 100, 150, or 200 ppm rms with no red noise or systematics.
    Section 2.3 adds Gaussian noise; real TESS light curves contain correlated systematics despite pipeline processing, so the quoted limits may be optimistic.
  • domain assumption A starspot anomaly can generally be detected only in a single transit because stellar rotation moves the spot between transits.
    Stated in Section 2.3; if a long-lived spot is visible in multiple transits with the same geometry, phase folding would improve detectability and lower the limits.
  • domain assumption The starspot is placed at the centre of the stellar disc to minimize foreshortening, giving the smallest detectable rspot.
    Section 2.3 states that spots closer to the limb need larger rspot for the same projected area; real spots usually are not at disc centre, so the absolute 'smallest spot' numbers are optimistic for typical geometries.
  • domain assumption The mean amplitude of the starspot anomaly, not the maximum, is the correct detection statistic.
    Section 3 and Section 3.5; this choice creates the reported planet-size trend. If the maximum or a full likelihood ratio were used, the quantitative limits would change.
  • standard math Standard physics: Kepler's third law, solid angle formula, and Planck function.
    Used to set orbital distances (Table 1), DeltaF conversions (Eqs. 4-7), and spot contrasts (Eq. 2).

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Cite this review

Pith. "Pith review of Simulations of starspot anomalies within TESS exoplanetary transit light curves -- I. The detection limits of starspot anomalies in TESS light curves." pith.science (2026). https://pith.science/paper/JNCTBBEB

@misc{pith2026190805747,
  author       = {Pith},
  title        = {Pith review of: Simulations of starspot anomalies within TESS exoplanetary transit light curves -- I. The detection limits of starspot anomalies in TESS light curves},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JNCTBBEB}},
  note         = {Machine review of arXiv:1908.05747}
}
abstract

20573 simulations of planetary transits around spotted stars were conducted using the transit-starspot model, \texttt{PRISM}. In total 3888 different scenarios were considered using three different host star spectral types, M4V, M1V and K5V. The mean amplitude of the starspot anomaly was measured and compared to the photometric precision of the light curve, to determine if the starspot anomaly's characteristic "blip" was noticeable in the light curve. The simulations show that, starspot anomalies will be observable in TESS 2\,min cadence data. The smallest starspot detectable in TESS transit light curves has a radius of $\approx1900$\,km. The starspot detection limits for the three host stars are: $4900\pm1700$\,km (M4V), $13800\pm6000$\,km (M1V) and $15900\pm6800$\,km (K5V). The smallest change in flux of the starspot ($\Delta F_\mathrm{spot} = 0.00015\pm0.00001$) can be detected when the ratio between the planetary and stellar radii, $k = 0.082\pm0.004$. The results confirm known dependencies between the amplitude of the starspot anomaly and the photometric parameters of the light curve. The results allowed the characterisation of the relationship between the change in flux of the starspot anomaly and the change in flux of the planetary transit for TESS transit light curves.

Figures

Figures reproduced from arXiv: 1908.05747 by the authors.

Figure 1
Figure 1. Simulated two minute cadence TESS light curve, of a 1R⊕ planet orbiting an M4V dwarf star with P = 12 d and an rms scatter of 104 ppm (generated by PRISM). The transit duration is approximately eight minutes and only three data points lie within the transit. rspot needs to increase, so to maintain the same two dimensional projected surface area of the starspot. Because we want to detect the smallest starspot for a g… view at source ↗
Figure 2
Figure 2. Example light curve (left) and stellar disc (right) generated by PRISM. Light curve: The solid line represents the noise-free synthetic light curve containing the starspot anomaly, while, the filled circles rep￾resent the “spot-free” synthetic light curve (see Section 3) with added Gaussian noise. Stellar disc: The central solid line represents the stellar equator (assuming orbital alignment) and the upper and lower… view at source ↗
Figure 3
Figure 3. Two simulated transit light curves generated by PRISM. These were both generated using a 1.0R⊕ Earth-sized planet transiting a 3200 K, 0.155R⊙ M4V dwarf star with i = 90.0 ◦ and P = 1 d. The starspot properties are: θ = 0 ◦ , φ = 90◦ , rspot = 0.009R∗ (left), rspot = 0.017R∗ (right) and Tspot = 3000 K. The observational wavelength and the rms scatter for the simulated transits were set at 600 nm and 60 ppm respectiv… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Three simulated transit light curves (top panels) and stellar disc outputs (bottom panels), generated by PRISM. Light curves: The solid lines represents the noise-free synthetic light curves containing the starspot anomaly, while, the filled circles represent the “spot…
Figure 5
Figure 5. Figure 5: Two simulated transit light curves generated by PRISM. These were both generated using a 2.75R⊕ sub-Neptune planet transiting a 3700 K, 0.493R⊙ M1V dwarf star with i = 90.0 ◦ and P = 3 d. The starspot properties are: θ = 0 ◦ , φ = 90◦ , rspot = 0.009R∗ (left), rspot = …
Figure 6
Figure 6. Figure 6: Two simulated transit light curves generated by PRISM. These were both generated using a 4.5R⊕ Neptune-sized planet transiting a 4100 K, 0.623R⊙ K5V dwarf star with i = 90.0 ◦ and P = 4 d. The starspot properties are: θ = 0 ◦ , φ = 90◦ , rspot = 0.009R∗ (red), rspot = …
Figure 7
Figure 7. Figure 7: Four simulated transit light curves, generated by PRISM. The observational wavelength of the simulated transits was 785 nm. These were generated using a 3.0R⊕ sub-Neptune planet transiting a 3700 K, 0.493R⊙ M1V dwarf star with i = 90.0 ◦ and P = 2 d. The starspot prope…
Figure 8
Figure 8. Figure 8: Nine simulated transit light curves, generated by PRISM, showing the smallest detected starspot for three trends, Teff: top row; λobs: middle row; P: bottom row. (Top row) simulations of a 1.5R⊕ super-Earth planet transiting a 3200 K, 0.155R⊙ M4V dwarf star with i = 90…
Figure 9
Figure 9. Figure 9: Example of a single data point describing the apex of a starspot anomaly. Using a 1.0R⊕ Earth-sized planet transiting a 3200 K, 0.155R⊙ M4V dwarf star with i = 90.0 ◦ and P = 2 d. The starspot prop￾erties are: θ = 0 ◦ , φ = 90◦ , rspot = 0.061R∗ and Tspot = 3150 K. The…
Figure 10
Figure 10. Figure 10: Example of multiple data points describing the plateau of a starspot anomaly. Using a 1.75R⊕ super-Earth planet transiting a 3200 K, 0.155R⊙ M4V dwarf star with i = 90.0 ◦ and P = 2 d. The starspot properties are: θ = 0 ◦ , φ = 90◦ , rspot = 0.061R∗ and Tspot = 3150 K…
Figure 11
Figure 11. Figure 11: Plot of ∆Fp and ∆Fspot calculated from Eq. 4 & 7 combined with the best fitting model (solid black line). The blue data points represent the M4V host star results. The red data points represent the M1V host star results, while, the green data points represent the K5V …
Figure 12
Figure 12. Figure 12: Plot of log10  1 ∆Fp  and ∆Fspot calculated from Eq. 4 & 7 com￾bined with the best fitting model (solid black line). The blue data points represent the M4V host star results. The red data points represent the M1V host star results, while, the green data points repre…

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