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Quantifying the Limits of TESS Stellar Rotation Measurements with the K2-TESS Overlap

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read TESS rotation periods are 70–80% reliable out to 10 days, then collapse beyond 12 days.

desk verdict A solid, practically useful calibration of TESS rotation periods against K2 and Kepler, with the main caveat that the headline reliability numbers inherit any errors in the K2 benchmark and the abstract overstates precision at 10 days. read the letter →

arxiv 2504.13262 v1 pith:GRGHB7AF submitted 2025-04-17 astro-ph.SR astro-ph.EPastro-ph.IM

Andrew W. Boyle , Andrew W. Mann , Jonathan Bush This is my paper · ORCID
classification astro-ph.SRastro-ph.EPastro-ph.IM
keywords stellarrotationTESSK2periodreliabilityLomb-Scargleperiodogramcausalpixelmodelgyrochronologylightcurves
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 asks when a stellar rotation period measured from TESS light curves can be trusted, and it answers with an empirical calibration against K2, a prior space mission with longer observing windows. Using roughly 23,000 stars observed by both missions, it finds that a standard Lomb-Scargle period analysis of single-sector TESS data recovers the K2 rotation period 70–80 percent of the time for periods out to 10 days, even without quality cuts, with fractional uncertainties below 3 percent for periods under 5 days. Beyond about 12 days—roughly half a TESS sector—reliability collapses, many detections become half-period aliases, and stitching consecutive sectors does not restore accuracy. The payoff is a quantitative map of reliability and completeness as a function of rotation period, signal strength, brightness, and signal-to-noise ratio, which lets studies of stellar ages and young associations decide which periods to trust and how to count non-detections.

What carries the argument

The load-bearing apparatus is an empirical calibration set: 22,986 stars observed by both TESS and K2, with K2 rotation periods from Reinhold & Hekker (2020) treated as ground truth; after cuts on binaries, contamination, and completeness, 16,752 stars carry the analysis. On the TESS side, the pipeline is a causal pixel model (CPM) light curve, built with a non-parametric model of instrumental systematics using pixels outside the target aperture, followed by a Lomb-Scargle periodogram. The match criterion—a TESS period within $3\sigma$ of the K2 period using the fitted fractional uncertainty relation—defines reliability, and completeness counts matches against the full sample. These definitions turn raw period measurements into reliability and completeness maps as functions of period, Lomb-Scargle power, TESS magnitude, and signal-to-noise ratio.

What would settle it

Verify the benchmark itself: take a random subset of the K2-TESS overlap stars, measure their rotation periods from long-baseline ground-based photometry or an independent K2 pipeline, and compare. If the independently verified stars show that below-10-day TESS periods match truth less than about 70 percent of the time—or that more than a few percent of the RH20 periods are wrong—the central reliability claim would need substantial revision.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that TESS rotation periods extracted with a causal pixel model and a Lomb-Scargle periodogram are empirically calibrated quantities: they are accurate to about 70–80 percent reliability below 10 days, degrade sharply near 12 days, and are barely better than random beyond 15 days. The fitted single-sector fractional uncertainty is below 3 percent for periods under 5 days and grows roughly linearly to about 6 percent at 12 days, following $\sigma(\%) = 0.005577\,P_{\rm rot} + 0.001768$. There is a systematic bias of about 10 percent toward too-short periods in the 10–14 day range, attributed to the 27-day sector window. Stitching sectors reduces period uncertainty by up to a factor of two at long periods but does not improve reliability or completeness, because persistent systematics such as the 13.7-day scattered-light signal are reinforced by merging.

Load-bearing premise

The calibration treats the K2 rotation periods of Reinhold & Hekker (2020) as the true rotation periods; if a substantial share of those benchmark values are wrong or systematically biased, every reliability and completeness number in the paper shifts.

Editorial extensions

If this is right

  • Single-sector TESS rotation periods can be used as gyrochronology inputs for periods below 10 days, with Lomb-Scargle power thresholds setting the trade-off between reliability and completeness.
  • Periods measured beyond about 12 days should not be treated as secure detections, since many are half-period aliases; long-period TESS-only rotation statistics need priors or independent confirming data.
  • Stitching TESS sectors buys precision but not accuracy, so studies seeking slow rotators should analyze sectors separately and keep the highest-power period rather than merging light curves.
  • The fitted uncertainty relation and the released code let any user assign per-star period errors and compute reliability or completeness for arbitrary cuts on signal power, brightness, and signal-to-noise ratio.
  • Applied to young associations, the reliability map identifies roughly 7–14 unreliable rotation measurements per cluster and predicts about 5–17 missed detections per cluster, so cluster rotation sequences built from TESS alone should carry these probabilities.

Reading between the lines

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

  • If the reliability map transfers to TESS-only samples, then catalogs of TESS rotation periods should report more than a single period: each star needs a reliability and a completeness value, and age or membership analyses should marginalize over aliased and missed periods.
  • A natural extension is to use TESS continuous-viewing-zone stars observed across many sectors to map how systematics grow with sector count; the paper does not do this, but such a map could predict exactly when stitching starts to hurt.
  • The 13.7-day scattered-light signal and its 6.85-day half-alias likely explain part of the inflated error at 6–8 and 10–14 days, so testing whether removing scattered-light contamination before stitching raises reliability would be a direct follow-up.
  • Because machine-learning period finders are improving long-period recovery, the reliability maps in this paper provide a clean benchmark for deciding whether such methods genuinely beat a Lomb-Scargle periodogram beyond 12 days.
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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

3 major / 5 minor

Summary. This paper quantifies the reliability, completeness, and precision of stellar rotation periods derived from TESS light curves, using a cross-matched sample of roughly 23,000 stars observed by both TESS and K2. Light curves are extracted with the unpopular causal pixel model (CPM) and rotation periods are measured with a Lomb-Scargle periodogram, with RH20 K2 periods treated as the benchmark truth. The main results are an empirical fractional period uncertainty relation (Equation 1), a match-based reliability metric (Equation 2), and completeness estimates as functions of period, Lomb-Scargle power, TESS magnitude, and signal-to-noise ratio. The authors report that single-sector TESS periods are roughly 70-80% reliable out to 10 days, with uncertainties below 3% for periods under 5 days, and that reliability and completeness drop sharply beyond about 12 days. They also find that stitching consecutive TESS sectors reduces period uncertainties but does not improve reliability or completeness. The paper includes an application to three young associations and an appendix repeating the reliability analysis with a Kepler benchmark (R13).

Significance. If the results hold, this paper provides a useful empirical calibration of TESS rotation period measurements that many stellar rotation and gyrochronology studies can adopt. The study has notable strengths: a large overlap sample, a carefully documented pipeline based on CPM light curves and Lomb-Scargle periodograms, a second independent benchmark check against Kepler rotation periods in Appendix A, and release of code for computing reliability and completeness for user-defined cuts. The framework connecting reliability and completeness to explicit quality cuts is directly applicable to ongoing TESS-based surveys. The central qualitative conclusions, especially the sharp drop in reliability beyond roughly 10-12 days and the modest gain from stitching sectors, are physically expected and appear robust. The quantitative headline numbers, however, need correction and additional sensitivity testing, as detailed below.

major comments (3)
  1. [Abstract and Section 4.1, Equation (1)] The abstract's claim that uncertainties are "typically below 3% for stars with periods < 10 days" is inconsistent with Equation (1), which gives roughly 5.8% at 10 days; the text itself states that uncertainties are below 3% only for Prot < 5 days. Please revise the abstract and any summary statements so that all quoted uncertainty numbers agree with Equation (1) and Figure 4.
  2. [Section 4.2, Equation (2)] The match criterion in Equation (2) uses a 3-sigma window derived from the empirical uncertainty relation of Equation (1), which is itself fitted to the same TESS-K2 comparison data. This makes the reported reliability fractions partly self-referential: outliers that inflate the fitted sigma widen the matching window, potentially masking failures. Please quantify the sensitivity of the headline reliability values to alternative match definitions, such as a fixed fractional tolerance (e.g., 10% or 20%) or uncertainties taken from the TESS-TESS comparison, and report how much the 70-80% reliability claim changes.
  3. [Sections 2 and 4.2] The analysis treats RH20 K2 periods as ground truth, but the internal re-analysis reported in Section 4.2, which found RH20 to be wrong for roughly 1% of the overlap sample, was performed on a random subset of mismatches in a regime of high Lomb-Scargle power, short periods, and bright stars. It does not constrain the RH20 error rate among faint, low-power, or long-period stars, which are precisely the stars that dominate the reliability drop beyond 10 days. Appendix A reproduces the qualitative trend with a Kepler benchmark but does not quantify the mismatch rate in the same reliability framework. Please add a sensitivity test that perturbs a plausible fraction of benchmark periods, or restricts the analysis to the highest-confidence RH20 subset (e.g., HPeak > 0.5), and report how the headline reliability numbers change.
minor comments (5)
  1. [Figure 10 caption] The caption ends with "using the relation of ." followed by a blank; this appears to be an incomplete reference and should be fixed.
  2. [References] Several references are duplicated in the bibliography, including Curtis et al. (2020), Douglas et al. (2019), and Rampalli et al. (2021a); please consolidate duplicate entries.
  3. [Section 7.2] The phrase "It also exudes rapidly-rotating stars" should read "It also excludes rapidly-rotating stars."
  4. [References] The name "Vowell" is typeset as "V owell" in the reference list; please correct the spacing.
  5. [Figure 4] The legend labels such as "1 (TESS-RH20)" appear to contain a typographical artifact; the label should presumably read "sigma (TESS-RH20)" for clarity.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the calibration is an empirical measurement against external K2 and Kepler benchmarks, with only a minor in-sample definitional link between the fitted uncertainty relation and the match criterion.

full rationale

The paper's central claims are empirical characterizations rather than first-principles derivations. The uncertainty relation (Eq. 1) is fitted to the distribution of TESS-vs-K2 period differences, and the recovery definition (Eq. 2) uses that fitted sigma as a 3-sigma match threshold. This creates a mild self-referential element: the reliability fractions are defined relative to a scatter fitted from the same sample. However, the reported reliability values are not forced by the fit; they are the measured fractions of stars falling inside the 3-sigma core, and the paper separately shows that chance matching would produce far lower fractions at short periods. The qualitative conclusions (high reliability below about 10 days, sharp drop near 12 days, better performance of LS-power cuts) are independently supported by Appendix A, where the same analysis is repeated using rotation periods from the original Kepler mission (Reinhold et al. 2013) as the benchmark. The benchmark dependence on RH20 is explicitly acknowledged as a limitation in Section 7.2, and the paper does not present the benchmark as an internally derived truth. There is no load-bearing self-citation: the cited K2-reliability support and pipeline references are external or methodological, and the core comparison rests on the RH20 catalog and the independent Kepler check. No prediction is shown to reduce by construction to a fitted parameter, and no uniqueness theorem or ansatz is imported from the authors' own prior work. The only concern is the in-sample definition of the match criterion, which is transparent and does not undermine the central, externally validated findings.

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

The central calibration depends on a benchmark (RH20 K2 periods), two fitted constants for the uncertainty relation, a hand-chosen match threshold, and a hand-set regularization parameter. No new physical entities are introduced.

free parameters (4)
  • Uncertainty relation slope = 0.005577 per day
    Fitted via least squares to the binned relative difference distributions in Section 4.1; enters the reliability match criterion via Equation 1 and Equation 2.
  • Uncertainty relation intercept = 0.001768 (fractional)
    Fitted in the same least-squares procedure in Section 4.1.
  • Match threshold (sigma multiplier) = 3
    Hand-selected in Equation 2 to define a match; directly sets which fraction of measurements count as reliable.
  • CPM L2 regularization = 0.1
    Hand-set in Section 3.1 for the unpopular light-curve model; authors state results are robust to modest variations.
assumptions (4)
  • domain assumption K2 rotation periods from RH20 are reliable enough to serve as a benchmark truth.
    All comparisons treat P_RH20 as P_true (Sections 2 and 4.1); supported by prior validation and a ~1% re-analysis but not fully re-derived.
  • domain assumption CPM (unpopular) systematic correction removes instrumental signals while preserving astrophysical signals.
    Section 3.1 assumes non-aperture and aperture pixels are linked only by non-astrophysical signals; if false, periods could be biased, especially in stitched light curves.
  • domain assumption Stars' rotation periods are stable enough between K2 and TESS epochs that differences represent measurement error plus predictable spot and wavelength effects.
    Section 4.1 folds all differences into an empirical uncertainty; real period changes would inflate the claimed uncertainty.
  • domain assumption The Lomb-Scargle periodogram is an appropriate method for rotation-period estimation on these light curves.
    The choice of LS over autocorrelation or machine learning can affect reliability numbers; the authors note this in Section 7.2.

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Pith. "Pith review of Quantifying the Limits of TESS Stellar Rotation Measurements with the K2-TESS Overlap." pith.science (2026). https://pith.science/paper/GRGHB7AF

@misc{pith2026250413262,
  author       = {Pith},
  title        = {Pith review of: Quantifying the Limits of TESS Stellar Rotation Measurements with the K2-TESS Overlap},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GRGHB7AF}},
  note         = {Machine review of arXiv:2504.13262}
}
read the original abstract

The Transiting Exoplanet Survey Satellite (TESS) has provided stellar rotation periods across much of the sky through high-precision light curves, but the reliability and completeness of these measurements require careful evaluation. We assess the accuracy of TESS-derived rotation periods by leveraging a cross-matched sample of ~23,000 stars observed by both TESS and the K2 mission, treating K2 periods as a benchmark. Using causal pixel models to extract light curves and the Lomb-Scargle (LS) periodogram to identify rotation signals, we quantify the empirical uncertainties, reliability, and completeness of TESS rotation period measurements. We find that uncertainties on TESS-derived rotation periods are typically below 3% for stars with periods < 10 days. Rotation periods are generally reliable out to 10 days, with >80% of measurements matching the K2 benchmark. Completeness and reliability drop dramatically for periods beyond ~12 days due to the 27-day sector limitation. Stricter cuts on TESS magnitude and LS power improve reliability; the highest LS power tested (>0.2) ensures >90% reliability below 10 days but removes over half of potential detections. Stitching consecutive-sector light curves reduces period uncertainties but does not improve overall reliability or completeness due to persistent systematics. Our findings and code provide a framework for interpreting TESS-derived rotation periods and inform the selection of quality cuts to optimize studies of stellar rotation, young associations, and gyrochronology.

Figures

Figures reproduced from arXiv: 2504.13262 by the authors.

Figure 1
Figure 1. The RH20-TESS overlap. Characteristics of the 23,000-star RH20-TESS overlap sample used in this study. On top, we show the sky position of targets colored by the number of TESS sectors available as of January 2024. The bottom left panel shows the rotation period distribution (as measured by K2) for the subset of stars that comprise our final sample used for analysis (cf. Section 3.2). Effective temperatures are calc… view at source ↗
Figure 2
Figure 2. Different pipelines have different systematics. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Distribution of the difference between the measured pe￾riod from TESS data and the benchmark period - taken from K2 data (RH20; yellow) or the best (highest LS power) sector of data from TESS (red). The histograms show the fractional difference between the rotation periods, broken into six period bins. The black lines show fits assuming a Gaussian distribution with a constant offset to account for non-matches (which… view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Period uncertainty (%) on Prot, CPM as a function of Prot, CPM. The points are derived from the bins shown in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Single-sector reliability results. The left column shows the match fractions for Lomb-Scargle power, T, and SNR, while the right column shows the same analysis for aliases. The blue line shows the reliability fraction without cuts, and the gray line represents that cha…
Figure 7
Figure 7. Figure 7: Single-sector completeness results. The left column shows the match fractions for Lomb-Scargle power, T, and SNR, while the right column shows the same analysis for aliases. The gray line represents that chance that a randomly chosen rotation period will match the RH20…
Figure 8
Figure 8. Figure 8: Consecutive-sector reliability results. Same as [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: Consecutive-sector completeness results. [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]
Figure 10
Figure 10. Figure 10: Application to young associations. The recovery, match, and alias probability of rotation periods measured by TESS for three benchmark associations: α Persei (t ∼ 80 Myr), Pisces-Eridanus (t ∼ 130 Myr), and Group X (t ∼ 300 Myr). Effective temperatures were estimates …
Figure 11
Figure 11. Figure 11: Single- and consecutive-sector comparison. [PITH_FULL_IMAGE:figures/full_fig_p016_11.png]
Figure 12
Figure 12. Figure 12: Reliability analysis with Kepler rotation periods. Our results show the same trends as in our earlier K2-TESS overlap, namely that the reliability of TESS rotation periods remains high out to ∼10 days and drops sharply thereafter. Aliases increase as rotation period i…
Figure 13
Figure 13. Figure 13: ROC curves for LS power, T, and SNR. The gray line represents a model that does no better than guessing at differentiating between true and false positives and is included for reference. The point closest to the top-left corner of each plot — typically considered the …

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