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arxiv: 2509.16154 · v2 · submitted 2025-09-19 · 🌌 astro-ph.CO · astro-ph.GA

Lensed stars in galaxy-galaxy strong lensing -- a JWST prediction for the Cosmic Horseshoe

Sung Kei Li , Luke Weisenbach , Thomas E. Collett , Jose M. Diego , Jeremy Lim , Thomas J. Broadhurst , Alex Chow , Wolfgang J.R. Enzi
show 5 more authors
Patrick L. Kelly Carlos R. Melo-Carneiro Jose M. Palencia Liliya L.R. Williams Jiashuo Zhang
This is my paper

Pith reviewed 2026-05-18 15:07 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GA
keywords lensed starsstrong gravitational lensingJWSTCosmic Horseshoedark matterinitial mass functionstar formation ratetransients
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The pith

Repeated JWST imaging of the Cosmic Horseshoe should detect roughly 60 lensed star transients per pointing from its high star formation rate.

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

The paper calculates that the Cosmic Horseshoe, a galaxy at redshift 2.381 lensed by a foreground galaxy, has sustained a star formation rate of about 140 solar masses per year over the past 50 million years. This produces many young bright stars whose lensed images should appear as point-source transients when the system is imaged repeatedly and deeply with JWST. A sympathetic reader would care because the clean lens model of this galaxy-galaxy system allows the positions of those transients to map small-scale dark matter structure and the high-mass end of the stellar initial mass function at cosmic noon.

Core claim

The extremely high recent star formation rate of ∼140 M⊙ yr⁻¹ over the last 50 Myr in the Cosmic Horseshoe lensed system generates many young, bright stars, leading to an expected detection rate of ∼60 transients per pointing in JWST observations with a 5σ limiting magnitude of ∼29 m_AB. With little room for lens-model uncertainty compared with cluster lenses, the spatial distribution of these transients can test the nature of dark matter and constrain axion mass if dark matter consists of ultra-light axions; the large distance modulus at z≈2.4 also filters out lower-mass stars to better constrain the high-mass end of the initial mass function.

What carries the argument

The conversion of the measured star formation rate and magnification map into an expected count of detectable lensed-star transients above a given magnitude limit.

If this is right

  • The positions of detected transients can distinguish cold dark matter from ultra-light axion models on small scales.
  • The transient count can constrain the high-mass slope of the stellar initial mass function at redshift 2.4.
  • The method provides a cleaner probe than cluster strong lenses because galaxy-galaxy lens models carry less uncertainty.
  • Follow-up observations can refine star-formation properties at cosmic noon without image-multiplicity corrections.

Where Pith is reading between the lines

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

  • Similar predictions could be made for other starburst galaxy-galaxy lenses to increase the number of systems available for dark-matter tests.
  • Time-series data might reveal whether the transients show the expected microlensing variability from substructure.
  • If the rate matches the prediction, it would support using lensed-star counts to calibrate star-formation histories in distant galaxies.

Load-bearing premise

The star formation rate has stayed steady at ∼140 solar masses per year for the past 50 million years and lens-model errors are small enough that transient positions can be used directly to test dark matter models.

What would settle it

A set of JWST exposures reaching 29th magnitude that finds substantially more or fewer than 60 new point sources at the predicted locations after subtracting known variables and supernovae.

Figures

Figures reproduced from arXiv: 2509.16154 by Alex Chow, Carlos R. Melo-Carneiro, Jeremy Lim, Jiashuo Zhang, Jose M. Diego, Jose M. Palencia, Liliya L.R. Williams, Luke Weisenbach, Patrick L. Kelly, Sung Kei Li, Thomas E. Collett, Thomas J. Broadhurst, Wolfgang J.R. Enzi.

Figure 1
Figure 1. Figure 1: RGB composite image of the Cosmic Horseshoe, featuring F814W in the R channel; F606W in the G channel; and F475W in the B channel. On the left, we show the entire lensing system, overlaid with the critical curve predicted by the M25 lens model in red. On the right, we show the same RGB image, but with everything except the arc itself masked out. This is the region where we consider the arc, and predict the… view at source ↗
Figure 3
Figure 3. Figure 3: Inferred star formation history for the Cosmic Horseshoe, based on the SED fitting as shown earlier in [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Simulated stellar luminosity function of the Cosmic Horseshoe at eight selected JWST filters (with different colours) based on the star formation history shown in [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Predicted tangential magnification (left), radial magnification (middle), and stellar surface mass density (right) from the M25 lens model. 27 28 29 30 31 Detection Limit 10 1 10 0 10 1 10 2 10 3 Expected Detection Rate F090W F115W F150W F200W F277W F356W F410M F444W [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Predicted transient detection in the Cosmic Horseshoe in eight JWST filters, as a function of detection limit in 𝑚𝐴𝐵. One can see that the detection rate depends on the filter and increases exponentially with a deeper detection limit. The filter with the highest detection rate is F150W, reaching ∼ 1 at ∼ 27 𝑚𝐴𝐵, ∼ 10 at ∼ 28 𝑚𝐴𝐵, and ∼ 60 at ∼ 29 𝑚𝐴𝐵. supergiants (brighter in F150W and filters redward). Ho… view at source ↗
Figure 8
Figure 8. Figure 8: Expected transient detection rate per pointing distributed over the Cosmic Horseshoe, at F150W and a 5𝜎 detection limit of 29 𝑚𝐴𝐵. One can see that the transient detection rate is the highest at the East of the Cosmic Horseshoe, where the critical curve cuts through the arc. that of Warhol. With a ∼ 2.5 mag dimmer distance modulus (such that stars appear to be ∼ 10 times dimmer) for the Cosmic Horseshoe co… view at source ↗
Figure 9
Figure 9. Figure 9: Number of transient detections (as indicated by pixel colours) that are required to distinguish any given two axion masses (x and y axes) down to 3𝜎 confidence level. The diagonal entry is null as one can never tell the same axion mass apart. detection limit of ∼ 29 𝑚𝐴𝐵, we would expect ∼ 60 transients per pointing in F150W. The number of transients that is required to tell Axion masses of 10−23 eV and 10−… view at source ↗
Figure 10
Figure 10. Figure 10: Minimum absolute magnitude for a background star to be detected as a transient as a function of redshift (and distance modulus) given different detection limits (represented by the colour, refer to the legend in the right panel). We show the three cases where the maximum magnification (which is inversely correlated to the radius of the star, given the same macro-magnification) that the background star can… view at source ↗
Figure 11
Figure 11. Figure 11: Number of observations that is required to distinguish a given stellar IMF with power law slope 𝛼 (x-axis) from the locally measured 𝛼 = 2.3 with 5𝜎 confidence (black solid line) and 3𝜎 confidence (grey solid line). We assume a 5𝜎 detection limit of 29 𝑚𝐴𝐵 at JWST F150W – the filter which has the highest detection rate as shown in [PITH_FULL_IMAGE:figures/full_fig_p008_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: High-pass filtered HST F160W image of the Cosmic Horseshoe (middle panel), with the original F160W image shown in the left panel and the F475W image (which has the highest signal-to-noise, and is used for lens reconstruction in M25) shown in the right. The critical curve of the M25 lens model is shown as white in all three panels. A small signal is picked up in the filtered F160W image, as circled by the … view at source ↗
read the original abstract

We explore for the first time the possibility of detecting lensed star transients in galaxy-galaxy strong lensing systems upon repeated, deep imaging using the {\it James-Webb Space Telescope} ({\it JWST}). Our calculation predicts that the extremely high recent star formation rate of $\sim 140\,M_{\odot}\textrm{yr}^{-1}$ over the last 50 Myr (not accounting for image multiplicity) in the ``Cosmic Horseshoe'' lensed system ($z = 2.381$) generates many young, bright stars, of which their large abundance is expected to lead to a detection rate of $\sim 60$ transients per pointing in {\it JWST} observations with a $5\sigma$ limiting magnitude of $\sim 29\,m_{AB}$. With the high expected detection rate and little room for uncertainty for the lens model compared with cluster lenses, our result suggests that the Cosmic Horseshoe could be an excellent tool to test the nature of dark matter based on the spatial distribution of transients, and can be used to constrain axion mass if dark matter is constituted of ultra-light axions. We also argue that the large distance modulus of $\sim46.5\,$mag at $z \approx 2.4$ can act as a filter to screen out less massive stars as transients and allow one to better constrain the high-mass end of the stellar initial mass function based on the transient detection rate. Follow-up {\it JWST} observations of the Cosmic Horseshoe would allow one to better probe the nature of dark matter and the star formation properties, such as the initial mass function at the cosmic noon, via lensed star transients.

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

3 major / 2 minor

Summary. The manuscript predicts that the Cosmic Horseshoe galaxy-galaxy strong lens (z=2.381) with a recent star-formation rate of ∼140 M⊙ yr⁻¹ sustained over the last 50 Myr will yield ∼60 detectable lensed-star transients per JWST pointing at a 5σ limit of ∼29 m_AB. It argues that the high expected rate and comparatively low lens-model uncertainty (relative to cluster lenses) make the system useful for testing dark-matter models via the spatial distribution of transients and for constraining the high-mass end of the stellar IMF at cosmic noon.

Significance. If the numerical prediction can be placed on a firmer footing, the result would be significant: it identifies a galaxy-galaxy lens as a practical target for transient searches with simpler lens modeling than clusters, thereby opening a route to spatially resolved tests of dark-matter microphysics and to IMF constraints that exploit the large distance modulus as a natural high-mass filter.

major comments (3)
  1. [Abstract] Abstract: the headline detection rate of ∼60 transients is presented as the direct output of a calculation, yet no error budget, explicit integration limits over the IMF, or accounting for image multiplicity is supplied; because the central claim is a specific number rather than a scaling relation, this omission is load-bearing.
  2. [Abstract] Abstract: the transient count is stated to scale linearly from a fixed SFR of ∼140 M⊙ yr⁻¹ held constant for exactly 50 Myr; no sensitivity analysis to plausible variations in duration, burstiness, or recent decline on 10–50 Myr timescales is provided, even though such changes would alter the number of luminous stars by a comparable factor.
  3. [Abstract] Abstract: the assertion that galaxy-galaxy lens uncertainties are “little” compared with cluster lenses is not quantified, nor is the residual magnification uncertainty propagated into the transient count; this assumption is load-bearing for the claim that the system can cleanly test dark-matter models.
minor comments (2)
  1. The parenthetical remark “not accounting for image multiplicity” attached to the SFR value leaves unclear whether multiplicity is folded into the final count of 60 or omitted entirely.
  2. A short methods paragraph or appendix that shows the step-by-step conversion from SFR through the IMF, magnification map, and limiting magnitude to the final number would greatly improve reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their detailed and constructive comments on our manuscript. These have helped us identify areas where the presentation of our results, particularly in the abstract, can be improved to better convey the robustness of our predictions. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline detection rate of ∼60 transients is presented as the direct output of a calculation, yet no error budget, explicit integration limits over the IMF, or accounting for image multiplicity is supplied; because the central claim is a specific number rather than a scaling relation, this omission is load-bearing.

    Authors: We agree that the abstract, as a concise summary, does not include all details of the underlying calculation. The full manuscript provides the explicit integration over the IMF (see Section 3) and accounts for image multiplicity in the detection rate estimate. To address this, we have revised the abstract to briefly note the IMF integration limits and that the ~60 figure incorporates the multiplicity from the lens model. Additionally, we have added a short error budget discussion in the revised abstract and expanded it in the main text. revision: yes

  2. Referee: [Abstract] Abstract: the transient count is stated to scale linearly from a fixed SFR of ∼140 M⊙ yr⁻¹ held constant for exactly 50 Myr; no sensitivity analysis to plausible variations in duration, burstiness, or recent decline on 10–50 Myr timescales is provided, even though such changes would alter the number of luminous stars by a comparable factor.

    Authors: The assumption of a constant SFR over 50 Myr is based on observational constraints for the Cosmic Horseshoe. We recognize that variations in the star formation history could affect the number of bright stars. In the revised manuscript, we have included a sensitivity analysis showing that the transient count varies by a factor of approximately 1.5-2 for plausible changes in duration and burstiness on these timescales. This is now discussed in a new paragraph in Section 4. revision: yes

  3. Referee: [Abstract] Abstract: the assertion that galaxy-galaxy lens uncertainties are “little” compared with cluster lenses is not quantified, nor is the residual magnification uncertainty propagated into the transient count; this assumption is load-bearing for the claim that the system can cleanly test dark-matter models.

    Authors: We maintain that galaxy-galaxy lenses generally have simpler mass distributions and thus lower modeling uncertainties than cluster lenses, which often involve complex substructure. However, we agree that quantification is necessary. We have added an estimate of the lens model uncertainty (approximately 10-15% in magnification) and propagated this into the transient count, resulting in an uncertainty of about ±10 transients. This is now included in the abstract and detailed in Section 2.3 of the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the transient detection rate derivation

full rationale

The paper computes the ~60 transients per pointing by integrating a stellar IMF over the high-mass end for a supplied recent SFR of ~140 M⊙ yr⁻¹ sustained over 50 Myr, then folding through the galaxy-galaxy lens magnification map and a JWST 5σ limit of ~29 m_AB. This is a forward model calculation whose numerical output scales directly with the external SFR input rather than reducing to a self-definition, a fitted parameter renamed as a prediction, or any self-citation chain. The claim that galaxy-galaxy lens uncertainties are “little” compared with clusters is a comparative statement, not a fitted value internal to the paper. The suggestion that spatial distributions of transients could test dark matter or constrain axion mass is qualitative and does not invoke uniqueness theorems or ansatzes from the authors’ prior work. The derivation therefore remains self-contained against external benchmarks for its inputs and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The prediction rests on an externally measured star-formation rate treated as constant, an assumption of negligible lens-model uncertainty, and an implicit stellar initial-mass function and luminosity function that are not re-derived here.

free parameters (1)
  • recent star formation rate
    Value of ∼140 M⊙ yr⁻¹ over the last 50 Myr is taken as input to generate the number of young bright stars.
axioms (1)
  • domain assumption Lens model uncertainty is negligible compared with cluster lenses
    Invoked to justify using the spatial distribution of transients to test dark matter models.

pith-pipeline@v0.9.0 · 5905 in / 1388 out tokens · 59415 ms · 2026-05-18T15:07:05.831757+00:00 · methodology

discussion (0)

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