arxiv: 2605.03502 · v1 · submitted 2026-05-05 · 🌌 astro-ph.SR · astro-ph.IM

Recognition: unknown

Identification and characterization of 15265 super-Nyquist frequencies in 1309 {δ} Scuti stars from Kepler photometry

Jian-Ning Fu, Simon Murphy, Stephane Charpinet, Weikai Zong, Xiao-Yu Ma, Xuan Wang, Yanqi Mo, Zilu Yang

Pith reviewed 2026-05-07 13:53 UTC · model grok-4.3

classification 🌌 astro-ph.SR astro-ph.IM

keywords delta Scuti starssuper-Nyquist frequenciesKepler photometryasteroseismologyLomb-Scargle periodogrampulsation modesfrequency aliasesstellar evolution

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The pith

A sliding Lomb-Scargle periodogram identifies 15265 super-Nyquist frequencies in 1309 Kepler delta Scuti stars.

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

The paper conducts a systematic search for super-Nyquist frequencies across 1838 delta Scuti stars observed by Kepler. It applies a new sliding Lomb-Scargle periodogram method to separate true high-frequency pulsations that alias below the Nyquist limit from other signals. The survey yields 15265 confirmed SNFs in 1309 stars and shows that younger stars exhibit more of them while the fraction rises sharply toward the Nyquist frequency. The authors supply a catalog that labels every detected peak as real or aliased, directly supporting cleaner mode identification in future asteroseismic modeling of these stars.

Core claim

Through a systematic survey of 1838 Kepler delta Scuti stars using a sliding Lomb-Scargle periodogram technique, 15265 confirmed super-Nyquist frequencies are identified in 1309 stars out of a total of 259883 frequencies. The total number of detected frequencies per star shows no trend across the instability strip, yet younger stars display significantly more SNFs; both the number and rate of SNFs decline as stars evolve. The fraction of modes appearing as SNFs increases from roughly 1 percent at 20 microhertz to 23 percent near the Nyquist limit, with the highest underdetection rate among low-amplitude modes. SNF patterns are distinguishable from phase modulations caused by binarity or non-

What carries the argument

sliding Lomb-Scargle periodogram, a technique that tracks frequency modulation patterns to isolate true super-Nyquist aliases from other effects

If this is right

Asteroseismic frequency lists for delta Scuti stars must now treat a substantial fraction of detected peaks as aliases rather than intrinsic modes.
Evolutionary models should predict fewer high-frequency modes in more evolved delta Scuti stars to match the observed decline in SNF rates.
The supplied catalog enables direct searches for regular spacing patterns among the real (non-aliased) pulsation frequencies.
Low-amplitude modes remain the most prone to misclassification, limiting completeness at the faint end of the amplitude distribution.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Applying the same sliding periodogram approach to other long-cadence surveys could systematically correct aliasing in additional classes of pulsating stars.
Accounting for the higher SNF incidence in young stars may tighten constraints on the location of the red edge of the delta Scuti instability strip in theoretical models.

Load-bearing premise

The sliding Lomb-Scargle periodogram technique reliably distinguishes true super-Nyquist aliases from modulation effects such as binarity or nonlinear interactions, with low false-positive rates.

What would settle it

High-cadence photometry of a subset of the same stars that shows many catalogued SNFs to be genuine low-frequency modes or instrumental artifacts would falsify the identifications.

Figures

Figures reproduced from arXiv: 2605.03502 by Jian-Ning Fu, Simon Murphy, Stephane Charpinet, Weikai Zong, Xiao-Yu Ma, Xuan Wang, Yanqi Mo, Zilu Yang.

**Figure 1.** Figure 1: Representative diagnostic plots generated by our automated pipeline. The classification results of four distinct types of view at source ↗

**Figure 2.** Figure 2: Distribution of all 259,883 frequencies in 1,838 view at source ↗

**Figure 3.** Figure 3: Distribution of all frequencies, including recovered SNFs, in the Kepler δ Scuti sample. The vertical dashed line indicates the Kepler long-cadence Nyquist frequency, and the inset panel highlights the SNF region. Note that the discontinuity decreases as SNR increases. In our second validation approach, we applied the technique described by Murphy et al. (2013, 2019), verifying our recovered frequencies… view at source ↗

**Figure 5.** Figure 5: Same as Fig view at source ↗

**Figure 4.** Figure 4: HR diagrams of the 1,776 δ Scuti stars in our sample. The data points are color-coded according to the right-hand colorbars, representing: (a) the total number of detected frequencies; (b) the number of recovered SNFs; and (c) the fraction of SNFs relative to the total number of frequencies. The solid red curves and the black dashed line mark the observational instability strip for δ Scuti stars introduc… view at source ↗

**Figure 6.** Figure 6: Validation of 14,824 SNFs via alias amplitude compar view at source ↗

read the original abstract

The frequency of pressure (p) mode in $\delta$~Scuti stars can exceed the Nyquist limit of \textit{Kepler} long-cadence photometry. {These 'super-Nyquist frequencies' (SNFs) are observed as 'reflected' peaks at lower frequencies, i.e., they are Nyquist aliases that pose} a threat to asteroseismic diagnostics. Their impact on $\delta$~Scuti p modes has yet to be comprehensively explored. We performed a systematic survey to search for SNFs in 1,838 \textit{Kepler} $\delta$~Scuti stars through a novel technique based on sliding Lomb-Scargle periodogram, identifying 15,265 confirmed SNFs in 1,309 stars, from a total of 259,883 frequencies. We observe that the total number of detected frequencies per star remains featureless across the $\delta$~Scuti instability strip; however, young stars pulsate in higher frequencies and so have significantly more SNFs on average. Both the number and the rate of SNFs diminishes accordingly as $\delta$~Scuti stars become more evolved, which is consistent with both observation and stellar models. Furthermore, our method detects a greater fraction of modes as SNFs at higher frequencies, rising from approximately 1\% at 20 $\mu $Hz to 23\% at the Nyquist limit. The rate of underdetection is highest amongst low-amplitude modes. The SNF modulation patterns can be well distinguished from phase modulations induced by binarity or nonlinear mode interactions. We provide a frequency catalog for future asteroseismic studies of $\delta$~Scuti stars, wherein we identify each peak as being real or an alias, enabling further investigations into regular patterns of pulsation modes, linear combination frequencies, and theoretical modeling.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

A sizable public catalog of 15k super-Nyquist frequencies from 1309 delta Scuti stars with clear evolutionary trends, but the sliding Lomb-Scargle identifications rest on unquantified claims about distinguishing aliases from other modulations.

read the letter

The main point is that this paper delivers a large, labeled catalog of super-Nyquist frequencies from Kepler long-cadence data on delta Scuti stars, plus straightforward trends that match basic expectations from stellar evolution. They processed 1838 stars, extracted 259883 frequencies total, and flagged 15265 as confirmed SNFs in 1309 stars. The average number of frequencies per star stays flat across the instability strip, yet younger stars show more high-frequency modes and therefore more SNFs; both the count and the fraction drop as stars evolve. The fraction tagged as SNFs rises from roughly 1 percent at 20 microhertz to 23 percent near the Nyquist limit, with low-amplitude modes hardest to recover. They release the catalog with real-versus-alias labels for each peak. That scale and the public data release are the concrete advance over earlier single-star or small-sample work. The trends are presented plainly and line up with models, which is useful for anyone building frequency lists for asteroseismic modeling. The soft spot is the validation of the sliding Lomb-Scargle technique itself. The abstract states that SNF patterns can be distinguished from binarity or nonlinear interactions, yet supplies no recovery fractions, false-positive rates, injection-test results, or direct comparison to short-cadence data on overlapping stars. Because underdetection is already highest for weak modes, any leakage from other modulation sources would directly affect the reported counts and the frequency-dependent fractions. Without those checks the central numbers remain only moderately supported. This work is aimed at people doing asteroseismology on delta Scuti stars who need cleaned frequency catalogs for mode identification or population studies. A reader who works with Kepler photometry or interior modeling would get immediate use from the data release. The paper shows clear engagement with the observations and prior literature, so it deserves peer review to examine the detection pipeline in detail.

Referee Report

1 major / 1 minor

Summary. The paper reports a systematic survey of super-Nyquist frequencies (SNFs) in 1,838 Kepler δ Scuti stars using a novel sliding Lomb-Scargle periodogram technique on long-cadence photometry. It identifies 15,265 confirmed SNFs in 1,309 stars from 259,883 total frequencies, documents trends showing higher SNF occurrence in younger stars that decreases with evolution, notes the SNF fraction rising from ~1% at 20 μHz to 23% near the Nyquist limit, and supplies a frequency catalog labeling peaks as real or aliases while claiming the method distinguishes SNF patterns from binarity or nonlinear interactions.

Significance. If the identifications prove reliable, the work provides a substantial catalog and statistical characterization of SNFs that could improve asteroseismic modeling of δ Scuti p-modes by mitigating aliasing effects in Kepler data. The large sample size, the reported consistency of evolutionary trends with stellar models, and the public catalog represent clear strengths for future studies.

major comments (1)

The central claim of 15,265 'confirmed' SNFs and the frequency-dependent detection fractions (1% to 23%) rests on the sliding Lomb-Scargle method's ability to separate true SNFs from other modulation effects. No quantitative validation metrics—such as recovery fractions, false-positive rates from controlled injections, or cross-checks against the short-cadence subset—are reported, leaving the false-positive risk unquantified despite the abstract's assertion that patterns 'can be well distinguished' from binarity or nonlinear interactions.

minor comments (1)

The abstract and introduction could more explicitly state the fraction of the 1,838 stars that yielded no SNFs and the total number of stars with short-cadence data available for potential validation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive review and for recognizing the potential value of the catalog and statistical trends for asteroseismology. We address the major comment below.

read point-by-point responses

Referee: The central claim of 15,265 'confirmed' SNFs and the frequency-dependent detection fractions (1% to 23%) rests on the sliding Lomb-Scargle method's ability to separate true SNFs from other modulation effects. No quantitative validation metrics—such as recovery fractions, false-positive rates from controlled injections, or cross-checks against the short-cadence subset—are reported, leaving the false-positive risk unquantified despite the abstract's assertion that patterns 'can be well distinguished' from binarity or nonlinear interactions.

Authors: We agree that the manuscript does not report quantitative validation metrics such as injection-recovery fractions or false-positive rates, and that this leaves the reliability of the identifications less rigorously quantified than the abstract's phrasing suggests. The identifications rest on the distinct 'reflection' signatures produced by the sliding Lomb-Scargle periodogram when a frequency exceeds the Nyquist limit; these signatures differ in both shape and phase behavior from the orbital-phase modulations of binaries and from the specific amplitude and phase relations of nonlinear combination frequencies. Multiple examples of each class are shown in the figures and discussed in the methods. Nevertheless, we acknowledge that visual pattern recognition alone does not constitute a quantitative false-positive assessment. In the revised manuscript we will add a dedicated validation subsection that (i) cross-matches a subset of stars possessing short-cadence data against the long-cadence results and (ii) reports recovery statistics from controlled injections of synthetic SNFs into representative light curves. These additions will directly address the referee's concern and supply the requested metrics. revision: yes

Circularity Check

0 steps flagged

No circularity: direct observational counts from algorithmic application to public data

full rationale

The paper reports counts of super-Nyquist frequencies obtained by applying a sliding Lomb-Scargle periodogram to Kepler long-cadence photometry of 1838 δ Scuti stars. The 15265 confirmed SNFs and associated statistics (frequency-dependent fractions, evolutionary trends) are direct outputs of this data-processing pipeline, not quantities derived from or equivalent to any fitted parameters, self-referential definitions, or prior results by the same authors. No equations, uniqueness theorems, or ansatzes are presented that reduce the reported identifications to inputs by construction. Distinctions from binarity or nonlinear interactions are asserted on the basis of observed modulation patterns in the data, without circular reduction to the detection method itself. This is a standard observational cataloguing exercise whose central claims remain independent of the listed circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions about photometric sampling and the effectiveness of the periodogram method for alias identification, with no new postulated entities.

axioms (2)

standard math Kepler long-cadence photometry has a well-defined Nyquist frequency that causes high-frequency modes to appear as lower-frequency aliases.
This is the physical basis for defining super-Nyquist frequencies.
domain assumption The sliding Lomb-Scargle periodogram can separate SNFs from true low-frequency modes and other effects such as binarity.
Core premise of the novel detection technique described in the abstract.

pith-pipeline@v0.9.0 · 5670 in / 1476 out tokens · 71565 ms · 2026-05-07T13:53:06.954170+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Reference graph

Works this paper leans on

59 extracted references

[1]

2021, Reviews of Modern Physics, 93, 015001

Aerts, C. 2021, Reviews of Modern Physics, 93, 015001

2021
[2]

S., Bowman, D

Antoci, V ., Cunha, M. S., Bowman, D. M., et al. 2019, MNRAS, 490, 4040

2019
[3]

L., et al

Antoci, V ., Handler, G., Campante, T. L., et al. 2011, Nature, 477, 570

2011
[4]

Balona, L. A. 2014, MNRAS, 437, 1476

2014
[5]

Balona, L. A. & Dziembowski, W. A. 2011, MNRAS, 417, 591

2011
[6]

Balona, L. A. & Evers, E. A. 1999, MNRAS, 302, 349

1999
[7]

R., Murphy, S

Barac, N., Bedding, T. R., Murphy, S. J., & Hey, D. R. 2022, MNRAS, 516, 2080

2022
[8]

H., Bedding, T

Barbara, N. H., Bedding, T. R., Fulcher, B. D., Murphy, S. J., & Van Reeth, T. 2022, MNRAS, 514, 2793 Barceló Forteza, S., Michel, E., Roca Cortés, T., & García, R. A. 2015, A&A, 579, A133 Barceló Forteza, S., Roca Cortés, T., & García, R. A. 2018, A&A, 614, A46

2022
[9]

R., Murphy, S

Bedding, T. R., Murphy, S. J., Crawford, C., et al. 2023, ApJ, 946, L10

2023
[10]

R., Murphy, S

Bedding, T. R., Murphy, S. J., Hey, D. R., et al. 2020, Nature, 581, 147

2020
[11]

J., Koch, D., Basri, G., et al

Borucki, W. J., Koch, D., Basri, G., et al. 2010, Science, 327, 977

2010
[12]

Bowman, D. M. & Kurtz, D. W. 2018, MNRAS, 476, 3169

2018
[13]

M., Kurtz, D

Bowman, D. M., Kurtz, D. W., Breger, M., Murphy, S. J., & Holdsworth, D. L. 2016, MNRAS, 460, 1970

2016
[14]

2000, in Astronomical Society of the Pacific Conference Series, V ol

Breger, M. 2000, in Astronomical Society of the Pacific Conference Series, V ol. 210, Delta Scuti and Related Stars, ed. M. Breger & M. Montgomery, 3

2000
[15]

2005, A&A, 435, 955

Breger, M., Lenz, P., Antoci, V ., et al. 2005, A&A, 435, 955

2005
[16]

& Montgomery, M

Breger, M. & Montgomery, M. H. 2014, ApJ, 783, 89

2014
[17]

& Pamyatnykh, A

Breger, M. & Pamyatnykh, A. A. 1998, A&A, 332, 958

1998
[18]

M., Baglin, A., et al

Charpinet, S., Green, E. M., Baglin, A., et al. 2010, A&A, 516, L6

2010
[19]

2022, ApJS, 263, 34

Chen, X., Ding, X., Cheng, L., et al. 2022, ApJS, 263, 34

2022
[20]

J., & Bedding, T

Gatuam, A., Murphy, S. J., & Bedding, T. R. 2026, MNRAS, 545, staf2001

2026
[21]

2024, ApJ, 972, 137

Gootkin, K., Hon, M., Huber, D., et al. 2024, ApJ, 972, 137

2024
[22]

R., Matson, R

Guo, Z., Gies, D. R., Matson, R. A., et al. 2017, ApJ, 837, 114

2017
[23]

R., et al

Handler, G., Arentoft, T., Shobbrook, R. R., et al. 2000, MNRAS, 318, 511

2000
[24]

W., Rappaport, S

Handler, G., Kurtz, D. W., Rappaport, S. A., et al. 2020, Nature Astronomy, 4, 684

2020
[25]

J., Mulders, G

Hippke, M., David, T. J., Mulders, G. D., & Heller, R. 2019, AJ, 158, 143

2019
[26]

M., Caldwell, D

Jenkins, J. M., Caldwell, D. A., Chandrasekaran, H., et al. 2010, ApJ, 713, L87

2010
[27]

Kurtz, D. W. 2022, ARA&A, 60, 31

2022
[28]

W., Handler, G., Rappaport, S

Kurtz, D. W., Handler, G., Rappaport, S. A., et al. 2020, MNRAS, 494, 5118 Lightkurve Collaboration, Cardoso, J. V . d. M., Hedges, C., et al. 2018, Lightkurve: Kepler and TESS time series analysis in Python, Astrophysics Source Code Library, record ascl:1812.013

2020
[29]

2023, A&A, 680, A11

Ma, X.-Y ., Zong, W., Fu, J.-N., et al. 2023, A&A, 680, A11

2023
[30]

M., Angelou, G

Mirouh, G. M., Angelou, G. C., Reese, D. R., & Costa, G. 2019, MNRAS, 483, L28 Article number, page 8 Mo et al.: Super-Nyquist frequencies inδSct stars

2019
[31]

J., Bedding, T

Murphy, S. J., Bedding, T. R., Gautam, A., & Joyce, M. 2023, MNRAS, 526, 3779

2023
[32]

J., Bedding, T

Murphy, S. J., Bedding, T. R., Shibahashi, H., Kurtz, D. W., & Kjeldsen, H. 2014, MNRAS, 441, 2515

2014
[33]

J., Hey, D., Van Reeth, T., & Bedding, T

Murphy, S. J., Hey, D., Van Reeth, T., & Bedding, T. R. 2019, MNRAS, 485, 2380

2019
[34]

J., Moe, M., Kurtz, D

Murphy, S. J., Moe, M., Kurtz, D. W., et al. 2018, MNRAS, 474, 4322

2018
[35]

J., Shibahashi, H., & Kurtz, D

Murphy, S. J., Shibahashi, H., & Kurtz, D. W. 2013, MNRAS, 430, 2986

2013
[36]

& Lampens, P

Neiner, C. & Lampens, P. 2015, MNRAS, 454, L86

2015
[37]

2023, AJ, 166, 43

Niu, J.-S., Liu, Y ., & Xue, H.-F. 2023, AJ, 166, 43

2023
[38]

1975, PASJ, 27, 237 Pamos Ortega, D., García Hernández, A., Suárez, J

Osaki, Y . 1975, PASJ, 27, 237 Pamos Ortega, D., García Hernández, A., Suárez, J. C., et al. 2022, MNRAS, 513, 374

1975
[39]

2019, ApJS, 243, 10

Paxton, B., Smolec, R., Schwab, J., et al. 2019, ApJS, 243, 10

2019
[40]

2009, A&A, 506, 85 Ramón-Ballesta, A., García Hernández, A., Suárez, J

Poretti, E., Michel, E., Garrido, R., et al. 2009, A&A, 506, 85 Ramón-Ballesta, A., García Hernández, A., Suárez, J. C., et al. 2021, MNRAS, 505, 6217

2009
[41]

A., Kurtz, D

Rappaport, S. A., Kurtz, D. W., Handler, G., et al. 2021, MNRAS, 503, 254

2021
[42]

R., Winn, J

Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2015, Journal of Astronomical

2015
[43]

& Breger, M

Telescopes, Instruments, and Systems, 1, 014003 Rodríguez, E. & Breger, M. 2001, A&A, 366, 178

2001
[44]

J., Murphy, S

Scutt, O. J., Murphy, S. J., Nielsen, M. B., et al. 2023, MNRAS, 525, 5235

2023
[45]

& Kurtz, D

Shibahashi, H. & Kurtz, D. W. 2012, MNRAS, 422, 738

2012
[46]

W., & Murphy, S

Shibahashi, H., Kurtz, D. W., & Murphy, S. J. 2015, MNRAS, 450, 3999

2015
[47]

C., Stumpe, M

Smith, J. C., Stumpe, M. C., Van Cleve, J. E., et al. 2012, PASP, 124, 1000

2012
[48]

C., Smith, J

Stumpe, M. C., Smith, J. C., Van Cleve, J. E., et al. 2012, PASP, 124, 985

2012
[49]

Townsend, R. H. D. & Teitler, S. A. 2013, MNRAS, 435, 3406

2013
[50]

2011, A&A, 534, A125

Uytterhoeven, K., Moya, A., Grigahcène, A., et al. 2011, A&A, 534, A125

2011
[51]

2025, A&A, 693, A63

Wang, X., Zong, W., Ma, X.-Y ., et al. 2025, A&A, 693, A63

2025
[52]

Watson, R. D. 1988, Ap&SS, 140, 255

1988
[53]

2024, ApJS, 271, 57

Xing, K., Zong, W., Silvotti, R., et al. 2024, ApJS, 271, 57

2024
[54]

2025, Universe, 11, 246

Yang, Z., Fu, J., Wang, X., Mo, Y ., & Zong, W. 2025, Universe, 11, 246

2025
[55]

2025, Universe, 11, 302

Zhou, A.-Y . 2025, Universe, 11, 302

2025
[56]

& Charpinet, S

Zong, W. & Charpinet, S. 2021, Research Notes of the American Astronomical Society, 5, 41

2021
[57]

2016, A&A, 585, A22

Zong, W., Charpinet, S., Vauclair, G., Giammichele, N., & Van Grootel, V . 2016, A&A, 585, A22

2016
[58]

2015, AJ, 149, 84

Zong, W., Fu, J.-N., Niu, J.-S., et al. 2015, AJ, 149, 84

2015
[59]

2020, A&A, 643, A110 Article number, page 9

Zwintz, K., Neiner, C., Kochukhov, O., et al. 2020, A&A, 643, A110 Article number, page 9

2020