pith. sign in

arxiv: 2606.31751 · v1 · pith:2RB4DWK2new · submitted 2026-06-30 · 🌌 astro-ph.EP · astro-ph.IM

Search for L4 Earth Trojan asteroids with the 2.5-meter Wide Field Survey Telescope

Junqiang Lu , Lulu Fan , Shaohan Wang , Minxuan Cai , Bingxue Fu , Xu Kong , Haibin Zhao , Bin Li
show 11 more authors
Qingfeng Zhu Zhen Wan Feng Li Ming Liang Binyang Liu Zheng Lou Jinlong Tang Hairen Wang Jian Wang Yongquan Xue Hongfei Zhang
This is my paper

Pith reviewed 2026-07-01 03:24 UTC · model grok-4.3

classification 🌌 astro-ph.EP astro-ph.IM
keywords Earth Trojan asteroidsL4 Lagrange pointasteroid surveyupper limitnon-detectionWide Field Survey Telescopestable populationsolar system dynamics
0
0 comments X

The pith

Largest L4 survey finds no new Earth Trojan asteroids and sets upper limit of fewer than 19 objects with H less than 19.1

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

The paper reports a wide-field search for asteroids near Earth's L4 Lagrange point using the Wide Field Survey Telescope, covering 236.74 square degrees that represent 33.24 percent of the sky regions where stable L4 Earth Trojans are expected to reside. No new objects were detected. From this non-detection the authors derive a cumulative upper limit of fewer than 19 stable Earth Trojans with absolute magnitude H below 19.1, corresponding to diameters larger than about 520 meters at an assumed albedo of 0.15. A sympathetic reader cares because stable Earth Trojans, if they exist in significant numbers, could preserve material from the earliest solar system; a firm upper bound therefore constrains formation and dynamical models. The result tightens previous limits and is presented as the most stringent constraint available.

Core claim

No new ETAs were detected in our survey. We place a cumulative upper limit of N(H < 19.1) < 19 on the stable population of objects larger than ~520 m (for an assumed albedo of 0.15). This represents the most stringent constraint on the ETA population to date.

What carries the argument

Non-detection in a survey that covers 33.24 percent of the probability-weighted sky area for dynamically stable L4 ETAs, converted to a population upper limit through the assumed albedo and H-to-size relation.

If this is right

  • The number of large stable Earth Trojans is smaller than earlier surveys permitted.
  • Only the two known temporary Earth Trojans are currently confirmed, with no evidence for a substantial stable population at these sizes.
  • Models of early solar-system dynamics must accommodate the scarcity of large objects trapped at L4.
  • Deeper or wider surveys will be required to test whether any stable ETAs exist below the current magnitude threshold.

Where Pith is reading between the lines

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

  • If the limit is correct, any primordial Earth Trojans at L4 were likely removed by dynamical instabilities early in solar-system history.
  • The result can be checked by repeating the survey at fainter magnitudes or with different assumed albedos to see whether the count remains below 19.
  • Connecting the limit to numerical simulations of Trojan stability could show whether L4 is dynamically less hospitable than L5.

Load-bearing premise

The upper limit holds only if the surveyed area truly samples 33.24 percent of the stable L4 probability distribution and if an albedo of 0.15 correctly converts the magnitude limit into physical size.

What would settle it

Discovery of 20 or more stable L4 Earth Trojans brighter than H=19.1 across the full probability region would exceed the reported limit.

Figures

Figures reproduced from arXiv: 2606.31751 by Bingxue Fu, Bin Li, Binyang Liu, Feng Li, Haibin Zhao, Hairen Wang, Hongfei Zhang, Jian Wang, Jinlong Tang, Junqiang Lu, Lulu Fan, Ming Liang, Minxuan Cai, Qingfeng Zhu, Shaohan Wang, Xu Kong, Yongquan Xue, Zheng Lou, Zhen Wan.

Figure 1
Figure 1. Figure 1: Sky coverage of the WFST L4 ETAs survey. The color scale indicates the number of usable exposures per sky position [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: illustrates the spatial variation of ∆, α, and V − H across our L4 survey area. Smaller ∆ and α enhance detectabil￾ity (yielding brighter apparent magnitudes), but ∆ dominates the variation in V − H over our field. Critically, V − H varies by up to ∼1 mag, highlighting the necessity of a spatially resolved detection efficiency model for wide-area ETA surveys. Since detections in different sky regions are i… view at source ↗
Figure 3
Figure 3. Figure 3: Surface probability density of stable L4 ETAs, ex [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Recovery rate Rk(V) of our L4 survey on each of the four nights. The red dashed line shows the recovery rate derived from AVRO data, the blue dotted line from the science catalog, and the black solid line the combined total recovery rate. Error bars are 95% Wilson confidence intervals. angle is given by S n = l 2 cos β = (cos β)/1802 deg2 . Using bi￾linear interpolation, we derived the probability density … view at source ↗
Figure 5
Figure 5. Figure 5: Differential upper limit U(H) on the population of L4 ETAs, expressed as the maximum number per unit absolute mag￾nitude, computed directly from our survey data using Equa￾tions (1) and (10). The flat segment at bright magnitudes (H ≲ 19.5) is limited by geometric coverage, while the steep decline at faint magnitudes (H ≳ 20.5) is driven by the survey’s limiting magnitude. where the slope α adopts values f… view at source ↗
Figure 6
Figure 6. Figure 6: Cumulative upper limits on the L4/L5 ETA population from this work and previous surveys. The blue line and dia￾mond show the result of Whiteley & Tholen (1998), gold line and square show the result of Markwardt et al. (2020), green line and triangle show the result of Lifset et al. (2021), and red line and circle show the result of this work (with N(H < 19.1) ≈ 19). Results from Cambioni et al. (2018) and … view at source ↗
read the original abstract

Earth Trojan asteroids (ETAs) are a mysterious population, and dynamically stable ETAs, if primordial, could be "living fossils" of the early solar system. To date, there are only two known ETAs, but both are temporary ETAs. The aim of our survey is to discover new temporary or stable ETAs; in the absence of detections, we derive upper limits on the population of stable ETAs. We conducted the largest wide-area survey of the Earth's L4 Lagrange point region so far using the Wide Field Survey Telescope, covering about 236.74 deg^2, corresponding to 33.24% of the probability coverage for sky regions where dynamically stable L4 ETAs are likely to reside. No new ETAs were detected in our survey. We place a cumulative upper limit of N(H < 19.1) < 19 on the stable population of objects larger than ~520 m (for an assumed albedo of 0.15). This represents the most stringent constraint on the ETA population to date.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript reports results from the largest wide-area survey to date of the L4 Earth Trojan asteroid region, conducted with the 2.5 m Wide Field Survey Telescope over 236.74 deg². This area is stated to correspond to 33.24% of the probability coverage for dynamically stable L4 ETAs. No new ETAs were detected. From the non-detection the authors derive a cumulative upper limit N(H < 19.1) < 19 on the stable population (corresponding to diameters ≳520 m for an assumed albedo of 0.15) and claim this is the most stringent constraint to date.

Significance. If the dynamical probability coverage fraction, survey completeness, and false-positive rejection are robust, the non-detection supplies a useful new upper bound on the stable ETA population. Such limits help discriminate between models of primordial asteroid retention at Lagrange points and have implications for early solar-system dynamical evolution. The survey strategy and telescope aperture represent a clear observational advance over prior narrower searches.

major comments (2)
  1. [Methods / dynamical coverage calculation] The 33.24% probability coverage fraction (stated in the abstract and used to scale the Poisson upper limit) is derived from dynamical models, yet the manuscript supplies no information on the underlying N-body integrations, initial-condition sampling, integration length, or stability criteria. Because the reported N(H<19.1)<19 scales directly with this fraction, its derivation must be documented in sufficient detail for the limit to be reproducible and falsifiable.
  2. [Data analysis / detection efficiency] Section describing the detection pipeline and completeness: quantitative details on magnitude-dependent detection efficiency, false-positive rates, and how the zero-count result is converted to the stated Poisson upper limit are not provided. These quantities are load-bearing for converting the raw non-detection into the cumulative population limit.
minor comments (2)
  1. [Results] The conversion from H=19.1 to physical size (~520 m) should explicitly state the albedo value and phase function assumptions in the main text as well as the abstract.
  2. [Observations] Figure showing the surveyed footprint would benefit from an overlay of the dynamical probability density contours to allow visual assessment of the 33.24% coverage claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment of the survey's significance and for the constructive major comments. We agree that additional methodological details are required for reproducibility and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Methods / dynamical coverage calculation] The 33.24% probability coverage fraction (stated in the abstract and used to scale the Poisson upper limit) is derived from dynamical models, yet the manuscript supplies no information on the underlying N-body integrations, initial-condition sampling, integration length, or stability criteria. Because the reported N(H<19.1)<19 scales directly with this fraction, its derivation must be documented in sufficient detail for the limit to be reproducible and falsifiable.

    Authors: We agree that the derivation of the 33.24% dynamical probability coverage fraction requires explicit documentation. We will add a dedicated subsection to the Methods section that describes the N-body integrations, including the initial-condition sampling strategy for test particles in the L4 region, the integration length and integrator employed, the stability criteria used to identify long-term stable orbits, and the procedure for computing the sky-position probability coverage within the surveyed area. This addition will allow independent verification of the scaling factor applied to the upper limit. revision: yes

  2. Referee: [Data analysis / detection efficiency] Section describing the detection pipeline and completeness: quantitative details on magnitude-dependent detection efficiency, false-positive rates, and how the zero-count result is converted to the stated Poisson upper limit are not provided. These quantities are load-bearing for converting the raw non-detection into the cumulative population limit.

    Authors: We acknowledge that the current manuscript does not supply the requested quantitative details on detection efficiency, false-positive rejection, and the exact conversion from zero detections to the Poisson upper limit. We will expand the data-analysis section to include the magnitude-dependent completeness (obtained from synthetic source injections), the criteria and measured rates for false-positive rejection, and the step-by-step application of Poisson statistics (including the effective number of trials after accounting for coverage and efficiency) that yields N(H < 19.1) < 19. A plot of the efficiency curve versus magnitude will be added to support the description. revision: yes

Circularity Check

0 steps flagged

No circularity: upper limit follows directly from zero detections scaled by external coverage fraction.

full rationale

The derivation consists of a direct non-detection (zero ETAs found in 236.74 deg²) converted to a Poisson upper bound, then divided by the stated 33.24% probability coverage and scaled by an assumed albedo of 0.15 to obtain N(H < 19.1) < 19. The coverage fraction is presented as an input derived from dynamical models of stable orbits, not fitted or defined from the survey data itself. No equations, self-citations, or ansatzes in the provided text reduce the reported limit to a quantity constructed from the same observations. The chain is therefore independent of its own outputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The reported limit depends on one explicit free parameter (albedo) and one domain assumption (prior dynamical maps of stable L4 regions); no new entities are introduced.

free parameters (1)
  • albedo = 0.15
    Value used to convert absolute magnitude H to physical diameter; set to 0.15.
axioms (1)
  • domain assumption Dynamically stable L4 ETAs occupy sky regions whose probability coverage is known from prior dynamical simulations.
    Invoked to claim the survey covers 33.24% of the relevant area.

pith-pipeline@v0.9.1-grok · 5777 in / 1207 out tokens · 59880 ms · 2026-07-01T03:24:06.083996+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

41 extracted references

  1. [1]

    & Gott Iii, J

    Belbruno, E. & Gott Iii, J. R. 2005, AJ, 129, 1724

    2005

  2. [2]

    1989, Application of Photometric Models to Asteroids

    Bowell, E., Hapke, B., Domingue, D., et al. 1989, Application of Photometric Models to Asteroids. (Tucson, AZ: University of Arizona Press), 524–556

    1989

  3. [3]

    2025, The 2.5-Meter Wide Field Survey Telescope Real-Time Data Processing Pipeline I: From Raw Data to Alert Distribution

    Cai, M., Xu, Z., Fan, L., et al. 2025, The 2.5-Meter Wide Field Survey Telescope Real-Time Data Processing Pipeline I: From Raw Data to Alert Distribution

    2025

  4. [4]

    W., et al

    Cambioni, S., Malhotra, R., Hergenrother, C. W., et al. 2018, in 49th Annual Lunar and Planetary Science Conference, 1149

    2018

  5. [5]

    2011, Nature, 475, 481 ´Cuk, M., Hamilton, D

    Connors, M., Wiegert, P., & Veillet, C. 2011, Nature, 475, 481 ´Cuk, M., Hamilton, D. P., & Holman, M. J. 2012, MNRAS, 426, 3051

    2011

  6. [6]

    2013, PASP, 125, 357

    Denneau, L., Jedicke, R., Grav, T., et al. 2013, PASP, 125, 357

    2013

  7. [7]

    2012, A&A, 541, A127

    Dvorak, R., Lhotka, C., & Zhou, L. 2012, A&A, 541, A127

    2012

  8. [8]

    J., Payne, M

    Holman, M. J., Payne, M. J., Blankley, P., Janssen, R., & Kuindersma, S. 2018, AJ, 156, 135

    2018

  9. [9]

    2022, Universe, 9, 7

    Hu, M., Hu, L., Jiang, J.-a., et al. 2022, Universe, 9, 7

    2022

  10. [10]

    A., Tholen, D

    Hui, M.-T., Wiegert, P. A., Tholen, D. J., & Föhring, D. 2021, ApJL, 922, L25

    2021

  11. [11]

    & Malhotra, R

    Ito, T. & Malhotra, R. 2010, in AGU Fall Meeting Abstracts, V ol. 2010, P53C– 1537

    2010

  12. [12]

    L., Slater, C

    Jones, R. L., Slater, C. T., Moeyens, J., et al. 2018, Icarus, 303, 181

    2018

  13. [13]

    2023, RAA, 23, 035013

    Lei, L., Zhu, Q.-F., Kong, X., et al. 2023, RAA, 23, 035013

    2023

  14. [14]

    J., Yoshida, F., Georgakarakos, N., & Li, X

    Li, J., Xia, Z. J., Yoshida, F., Georgakarakos, N., & Li, X. 2023, A&A, 669, A68

    2023

  15. [15]

    2021, AJ, 161, 282

    Lifset, N., Golovich, N., Green, E., Armstrong, R., & Yeager, T. 2021, AJ, 161, 282

    2021

  16. [16]

    2025, ApJS, 278, 29

    Lin, J., Wang, T., Cai, M., et al. 2025, ApJS, 278, 29

    2025

  17. [17]

    2022, MNRAS, 513, 2422

    Lin, Z., Jiang, N., & Kong, X. 2022, MNRAS, 513, 2422

    2022

  18. [18]

    2023, ApJ, 947, 59

    Liu, Z.-Y ., Lin, Z.-Y ., Yu, J.-M., et al. 2023, ApJ, 947, 59

    2023

  19. [19]

    2025, PASP, 137, 024401

    Lu, J.-Q., Fan, L.-L., Cai, M.-X., et al. 2025, PASP, 137, 024401

    2025

  20. [20]

    K., Masiero, J

    Mainzer, A. K., Masiero, J. R., Abell, P. A., et al. 2023, PSJ, 4, 224

    2023

  21. [21]

    2019, Nat

    Malhotra, R. 2019, Nat. Astron., 3, 193

    2019

  22. [22]

    W., Malhotra, R., et al

    Markwardt, L., Gerdes, D. W., Malhotra, R., et al. 2020, MNRAS, 492, 6105

    2020

  23. [23]

    & Scholl, H

    Marzari, F. & Scholl, H. 2013, Celest. Mech. Dyn. Astron., 117, 91 Nesvorný, D., V okrouhlický, D., & Morbidelli, A. 2013, ApJ, 768, 45 Peña Zamudio, J. & Fuentes, C. 2021, in AAS/Division for Planetary Sciences Meeting Abstracts #53, V ol. 53, 306.03

    2013

  24. [24]

    J., & Turrini, D

    Pirani, S., Johansen, A., Bitsch, B., Mustill, A. J., & Turrini, D. 2019, A&A, 623, A169

    2019

  25. [25]

    & Liu, S.-F

    Rein, H. & Liu, S.-F. 2012, A&A, 537, A128

    2012

  26. [26]

    & Spiegel, D

    Rein, H. & Spiegel, D. S. 2015, MNRAS, 446, 1424

    2015

  27. [27]

    & Tamayo, D

    Rein, H. & Tamayo, D. 2015, MNRAS, 452, 376 Schunová-Lilly, E., Jedicke, R., Vereš, P., Denneau, L., & Wainscoat, R. J. 2017, Icarus, 284, 114

    2015

  28. [28]

    2024, ApJ, 976, 155

    Su, Z.-B., Cai, Z.-Y ., Wang, J.-X., et al. 2024, ApJ, 976, 155

    2024

  29. [29]

    Sutton, P. J. 2009, Classical and Quantum Gravity, 26, 245007

    2009

  30. [30]

    M., Ivezic, Z., Juric, M., & Lupton, R

    Szabo, G. M., Ivezic, Z., Juric, M., & Lupton, R. 2007, MNRAS, 377, 1393

    2007

  31. [31]

    Tabachnik, S. A. & Evans, N. W. 2000, MNRAS, 319, 63

    2000

  32. [32]

    2025, MNRAS, 540, 2863

    Wan, Z., Fan, L., Li, X., et al. 2025, MNRAS, 540, 2863

    2025

  33. [33]

    2025, AJ, 169, 272

    Wang, S.-H., Fu, B.-X., Lu, J.-Q., et al. 2025, AJ, 169, 272

    2025

  34. [34]

    2023, Sci

    Wang, T., Liu, G., Cai, Z., et al. 2023, Sci. China Phys. Mech. Astron., 66, 109512

    2023

  35. [35]

    Whiteley, R. J. & Tholen, D. J. 1998, Icarus, 136, 154

    1998

  36. [36]

    Wilson, E. B. 1927, Journal of the American Statistical Association, 22, 209

    1927

  37. [37]

    & Holman, M

    Wisdom, J. & Holman, M. 1991, AJ, 102, 1528

    1991

  38. [38]

    & Golovich, N

    Yeager, T. & Golovich, N. 2022, ApJ, 938, 9

    2022

  39. [39]

    2024, ApJ, 961, 250

    Yeager, T., Golovich, N., & Pruett, K. 2024, ApJ, 961, 250

    2024

  40. [40]

    2018, in 49th Annual Lunar and Planetary Science Conference, 1771

    Yoshikawa, M., Tsuda, Y ., Watanabe, S., et al. 2018, in 49th Annual Lunar and Planetary Science Conference, 1771

    2018

  41. [41]

    2019, A&A, 622, A97 Article number, page 8

    Zhou, L., Xu, Y .-B., Zhou, L.-Y ., Dvorak, R., & Li, J. 2019, A&A, 622, A97 Article number, page 8

    2019