Gravitational Microlensing of the Galactic Centre $\gamma$-Ray Excess: A New Test for Point-Like or Extended Emission?

Florian List; Geraint Lewis; Nada Salama

REVIEW 3 major objections 5 minor 65 references

Gravitational Microlensing of the Galactic Centre $\gamma$-Ray Excess: A New Test for Point-Like or Extended Emission?

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Gravitational microlensing can tell whether the Galactic Centre gamma-ray excess comes from point-like pulsars or smooth dark matter—provided future detectors gain enough sensitivity.

desk verdict A genuinely new temporal test of the GCE origin, with a sound qualitative conclusion but several load-bearing numerical inconsistencies that must be fixed before the event rates can be trusted. read the letter →

arxiv 2508.19577 v1 pith:3PPFP2R5 submitted 2025-08-27 astro-ph.HE astro-ph.COastro-ph.GA

Nada Salama , Florian List , Geraint Lewis This is my paper · ORCID

classification astro-ph.HEastro-ph.COastro-ph.GA

keywords galacticcentreexcessgravitationalmicrolensingmillisecondpulsarsdarkmatterannihilationgamma-rayastronomycausticcrossingdetectorsensitivitytimevariability

topics Dark Matter

open problems Dark Matter

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 proposes a temporal test to decide whether the gamma-ray excess at the Galactic Centre comes from annihilating dark matter or from a population of unresolved millisecond pulsars. The test exploits gravitational microlensing by ordinary stars along the line of sight: a stellar-mass lens magnifies a point-like source by roughly the ratio of the Einstein radius to the source size, so a 10-km pulsar can flash with magnification factors up to about 8700 during caustic crossings, whereas dark-matter annihilation emission, smooth over au scales, is effectively unaltered. The authors simulate populations of 500, 5000, and 100,000 identical pulsars and find that detecting these flashes requires detector sensitivity improvements over Fermi-LAT of about 26x, 200x, and 18,000x, respectively, all beyond the planned Advanced Particle-physics Telescope. The result turns the unresolved point-like-versus-extended debate into a question a future gamma-ray observatory could answer by watching the bulge for the predicted flicker.

What carries the argument

The load-bearing object is the Einstein radius in the source plane, $R_E = \sqrt{\frac{4GM}{c^2}\frac{D_{os}D_{ls}}{D_{ol}}}$, about 8.1 au for a solar-mass lens toward the Galactic Bulge. The key identity is the point-source magnification $\mu = \frac{y^2+2}{y\sqrt{y^2+4}}$, whose spike at a binary-lens caustic crossing is capped by the finite source radius as $\mu_{\max} \sim 2R_E/r_s$; for a 10-km pulsar this yields the ~8700-fold flashes that the paper uses as its primary signature. The argument runs on the contrast between point sources and extended sources: a pulsar is eight orders of magnitude smaller than $R_E$ and therefore gets magnified, while dark-matter annihilation emission is smooth on au scales and is essentially unmodified. The caustic-crossing events come from the 6% of lenses that are binaries, 70% of which produce caustic crossings, and the paper converts the optical depth $\tau \sim 3\times10^{-6}$ into event rates via the area swept out by moving lenses.

What would settle it

A concrete check: inject the predicted twin-peak caustic-crossing lightcurve into one resolution element of synthetic Fermi-LAT data with photon counts scaled by $10^{1.41}$ (26x sensitivity) and run the paper's 3-day sliding-window Poisson significance search; if the twin peaks are not recovered with p ≤ 0.01, the detection threshold is too optimistic. On the observational side, a single clean measurement of the ~8700-amplification double peak separated by ~70 days from the Galactic Centre would rule out smooth dark-matter annihilation as the source of that flux, while a decade-long null search with a 26x detector in the 500-source scenario would start to constrain the compact-source fraction.

Watch

Extended reading notes

Core claim

The central claim is that gravitational microlensing supplies a new, template-independent discriminant between the two leading explanations of the Galactic Centre excess: if the excess is produced by millisecond pulsars, the gamma-ray flux from a small patch of the bulge will occasionally show sharp temporal magnifications, while a smooth dark-matter signal will be temporally flat. The physical basis is the size-dependence of the Einstein magnification: for a point source of radius $r_s$, the maximum magnification is about $2 R_E / r_s$, and with a 10-km pulsar and a stellar lens $R_E \sim$ au, this reaches about $2.4\times10^8$ in perfect alignment and about 8700 at the caustic crossing of a typical binary-lens event. On this basis the paper predicts two characteristic signatures—twin caustic-crossing peaks roughly 70 days apart, and single-lens bumps lasting weeks—and simulates Poisson photon arrivals to find the detector sensitivity needed to see them. The required improvement in effective area over Fermi-LAT is a factor of $10^{1.41}$ for a population of 500 bright sources, $10^{2.31}$ for 5000 sources, and $10^{4.26}$ for 100,000 faint sources. None of these thresholds is met by Fermi-LAT or the planned Advanced Particle-physics Telescope, so the authors present the test as a tool for future observations rather than a resolution of the current debate.

Load-bearing premise

The load-bearing premise is that the pulsar population behind the GCE can be modelled as a set of identical, steady point sources emitting at a single constant photon rate (Section 3, Eq. 11); in reality the source-count distribution is poorly constrained, and a bright tail of sources or intrinsic flaring—which the authors acknowledge as a concern in Section 5—would change both the event rates and the detector sensitivity needed to see the predicted flashes.

Editorial extensions

If this is right

If a small population of ~500 bright MSPs produces the excess, a detector with about 26 times Fermi-LAT's effective area could detect caustic-crossing flashes, but such events are expected only once every ~1500 years.
If the population is intermediate (~5000 sources), a ~200x sensitivity detector would see one microlensing flash every ~150 years, while a ~18,000x detector would see several per year for the 100,000-source case—though each flash from faint sources is very hard to catch.
A single clean detection of the predicted twin-peak lightcurve would break the degeneracy between dark matter and pulsar interpretations, and the observed event rate would constrain the number of MSPs contributing to the excess.
Because the test looks at time variability rather than sky templates, it avoids the main systematic that has plagued spatial and spectral studies: mismodelling of the diffuse background and of the source template.

Reading between the lines

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

The same size-discrimination argument could be turned around: even before reaching the detection thresholds, a decade-long gamma-ray lightcurve of the bulge with a future detector could place an upper limit on the compact-source fraction of the GCE from the absence of flicker, making a null result physically informative.
The thresholds are sensitive to the assumed 3.5% caustic-crossing fraction and to the binary fraction of lenses; if the true binary fraction is closer to the 23% found in recent population fits, caustic-crossing events would be several times more common, lowering the sensitivity needed for the bright-population cases.
A matched-filter search over the full lightcurve, rather than a sliding 3-day Poisson window, might recover the faint caustic-crossing peaks at lower sensitivity than the paper's thresholds, since it would use the known twin-peak shape; this is a testable modelling improvement not explored in the paper.
The same method could be applied to unresolved source populations elsewhere in the Galaxy, such as globular clusters or the Galactic plane, where future detectors could use microlensing flicker to measure the compact-object content independently of spectral template fits.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things you should know. First, the core suggestion is new: use gravitational microlensing of the Galactic Centre as a temporal discriminator between a smooth dark-matter GCE and a population of point-like MSPs. That is not in the prior morphology/spectrum/statistics literature, and the paper surveys that literature fairly. Second, the printed quantitative predictions are not internally consistent, so treat the event rates as illustrative until corrected.

What the paper does well: it gets the basic physics right (Einstein radius vs source size; caustic magnification limits ~8700), builds a plausible forward simulation with Poisson photon noise, and reports detection thresholds as a function of detector sensitivity rather than pretending current instruments can see anything. The qualitative conclusion—Fermi-LAT and even the APT are far from detecting this, with only the bright-population caustic-crossing case within an order of magnitude of a future instrument—is robust to the arithmetic problems below.

Where it gets soft. Table 1 says lenses move at 0.28 RE/day for 200 km/s; with RE = 8.1 au, 200 km/s is 0.0143 RE/day, a factor of about 20 smaller. That inflates the swept area in Equations (15)–(17) and therefore the reported event frequencies. Independently, Table 1 lists Nlens=6.3e4 in a region of radius 4e7 RE, which gives optical depth ~4e-11, not the stated 3e-6; a self-consistent population would need ~5e9 lenses. And the text says 6% binaries × 70% caustic-crossing = 3.5%, but that product is 4.2%. The paper quotes one CC event per ~1500 years for Ns=500; plugging their own y<2 criterion and v=0.28 RE/day into Equation (17) gives ~146 years, about a factor of 10 more frequent. So either the velocity, the lens count, or the quoted rates are wrong.

The detection-threshold curves in Section 4.2 are less sensitive to these errors because they are computed from injected single-event lightcurves, but the "multiple times a year" claim for 1e5 sources and the rate comparison between cases should not be quoted until the parameters are reconciled. The source-count model (identical, steady sources) is crude, but the authors acknowledge it and it is a reasonable first cut. No code or data are shipped, and the logistic thresholds lack confidence intervals; both would strengthen the paper.

Who this is for: anyone working on the GCE origin or on microlensing applications to compact object populations. It deserves a serious referee; the idea is worth publishing even if the numbers need major revision. I would send it to review and ask for a corrected Table 1, re-derived event rates, code/data release, and confidence intervals on the threshold values.

Referee Report

3 major / 5 minor

Summary. This paper proposes a new observational test of the origin of the Galactic Centre gamma-ray excess (GCE). If the GCE arises from a population of millisecond pulsars, gravitational microlensing by stellar-mass lenses along the bulge line of sight will produce time-dependent magnifications, including rare caustic-crossing spikes with peak magnification about 8700; if the GCE arises from smooth dark-matter annihilation, the emission is extended on AU scales and effectively immune. The authors model three source populations (Ns = 1e5, 500, 5000), simulate lens configurations and Poisson photon light curves, and compute the detector sensitivity (scaled by a relative to Fermi-LAT) needed to identify microlensing events. They find that Fermi-LAT cannot detect these events and that even the proposed APT (log10 a about 1) is insufficient; for a bright 500-source population, caustic-crossing events could be seen with log10 a about 1.4 but are extremely rare, and for a faint 1e5-source population detection would need log10 a about 4.3. The paper concludes that microlensing is not a near-term discriminator but could constrain point-source populations in future observations.

Significance. The proposed test is conceptually novel and forward-modeled from standard microlensing physics. The distinction between point-like MSP emission and extended emission via finite-source magnification is physically sound, and the conclusion that current and near-future instruments lack sensitivity is robust to the quantitative errors discussed below. The paper provides a clearly described simulation pipeline (source placement, binary-lens caustic-crossing light curves, Poisson significance tests) and gives explicit detection thresholds. It also candidly acknowledges limitations: identical-source assumption, unknown source-count distribution, intrinsic flaring, and look-elsewhere corrections. However, the quantitative event rates rest on internally inconsistent lens parameters, so the numerical predictions in Sections 4.2.1 and 4.2.2 and the abstract's 'multiple times a year' statement need correction; the central methodological claim is not invalidated.

major comments (3)

[Section 4.1, Table 1 and Eq. (17)] The lens population in Table 1 is internally inconsistent with the stated optical depth. For a circular region of radius R_region = 4e7 R_E, the optical depth is tau = N_lens / (R_region/R_E)^2; with N_lens = 6.3e4 this gives tau about 4e-11, not 3e-6. Matching tau = 3e-6 requires N_lens about 4.8e9. The simulations therefore do not generate a lens distribution that realizes the assumed optical depth, and the event rates computed from Eq. (17) and the counts in Figure 7 are not grounded in the simulated lens field.
[Section 2.2 and Table 1; Eq. (15)] The stated conversion of the lens velocity is wrong by a factor of about 20. With R_E = 8.1 au for a solar-mass lens, v = 200 km/s corresponds to 0.0143 R_E/day, not 0.28 R_E/day. This overestimates the swept-area factor in Eq. (15), which also appears to be evaluated as 74 rather than about 36 given the stated inputs. The error propagates into Eq. (17), so all event-rate claims—the CC rates of one per 1500 and 150 years in Section 4.2.1, the per-century color bars in Figure 7, and the abstract's statement that a large population would produce 'events multiple times a year'—must be recomputed.
[Section 4.2.1] Even using the published Table 1 inputs, the quoted CC event rates do not follow from Eq. (17). For Ns = 500, y = 2, tau = 3e-6, v = 0.28 R_E/day, and DeltaT = 11 years, Eq. (17) gives about 2 events with y < 2 in the survey, or about 0.07 CC events after the 3.5% fraction; this corresponds to one CC per about 150 years, not one per 1500 years. The analogous discrepancy affects the Ns = 5000 rate. The rates need to be reconciled with the equations and with the corrected velocity and lens-number inputs; the detection thresholds in Figure 6 are less affected because they use injected events, but they do not rescue the event-rate claims.

minor comments (5)

[Section 3, Eq. (15)] The fiducial value 74 for the swept-area factor is not consistent with v = 200 km/s and R_E = 8.1 au; please state the actual numeric value and use it consistently throughout.
[Section 4.2.1] The relationship between the 70-day in-caustic plateau magnification of 'an order of magnitude' and the caustic-crossing spikes with mu about 8700 should be clarified; the detection algorithm appears to use only the two peaks, while the rate statement about 4 photons in a 70-day period uses the plateau.
[Figure 1] Figure 1 would benefit from labeling which panel corresponds to the q = 1, s = 1 configuration used in all CC simulations, since the reader cannot otherwise identify the lightcurve shape adopted in Section 4.
[Section 4.2.2, Case 1] The text refers to 'Figure 5' for the minimum log10(a) as a function of maximum magnification, but the actual figure is Figure 7; correct the cross-reference.
[Table 1 and Section 4.1, step 3] The stated threshold ymax = 4 R_E yields a maximum single-lens magnification of about 1.006, i.e. a 0.6% enhancement, not 'approximately 6%'; please correct the numerical value.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the derivation is forward-modeled from standard microlensing physics and literature-based source populations.

full rationale

The paper does not fit a parameter to a target conclusion and then rename it a prediction. Its central derivation chain is forward: standard point-mass and binary-lens magnification equations (Eqs. 2-9) are combined with literature-based source populations (Gautam et al. 2022; Lee et al. 2016) and externally measured microlensing event statistics (OGLE/MACHO binary and caustic-crossing fractions) to simulate lightcurves (Section 4.1), and only then are detector-sensitivity thresholds extracted by Poisson-significance logistic fits (Section 4.2). The claimed thresholds log10(a)=1.41, 2.31, 4.26 are derived from injected lightcurves, not from the assumed Ns values alone. The MSP peak magnification ~8700 is imported from observed OGLE caustic events via Eq. (10), so it is an external input, not a fitted output. Self-citations to List et al. (2020, 2021, 2025) appear only in the GCE literature review and do not carry the lensing derivation. The numerical inconsistencies in the lens velocity and lens-number normalization (Table 1 vs Eq. 3/optical depth) are correctness/consistency concerns, not circularity: correcting them would change event-rate numbers but would not make the derivation depend on its own conclusion. The paper's own caveats about source-count distribution, intrinsic flaring, and look-elsewhere effects are acknowledged uncertainties rather than hidden circular inputs. No equation is defined in terms of the quantity it is supposed to predict.

Assumptions & free parameters 9 free parameters · 7 assumptions · 0 invented entities

No new physical entities are introduced. The numbers the central quantitative claims rest on are the adopted optical depth, the three source-population scenarios, the binary/caustic fractions, and the derived MSP peak magnification; several of these are uncertain or inconsistently printed.

free parameters (9)

Microlensing optical depth τ = 3×10^-6
Adopted from bulge microlensing surveys; sets the number of lenses and all event-rate normalizations.
Number of GCE sources Ns (Case 1) = 10^5
Scenario from Gautam et al. (2022) for a large faint MSP population.
Number of GCE sources Ns (Case 2) = 500
Scenario from the NPTF bright-population analysis of Lee et al. (2016).
Number of GCE sources Ns (Case 3) = 5000
Intermediate scenario chosen by the authors.
Binary lens fraction = 6%
Adopted from microlensing surveys; 6% of events due to binary lenses.
Caustic-crossing fraction among binaries = 70%
Adopted from surveys; 70% of binary events are caustic crossings (paper prints 3.5% for the product).
CC configuration parameters q, s = 1, 1
All caustic-crossing events assumed to have identical binary geometry for simplicity.
Peak CC magnification µMSP = ~8700
Derived from OGLE stellar caustic events via Equation (10), scaling by sqrt(rstar/rMSP).
Detectable impact parameter limit ymax = 4 RE
Chosen as the threshold for a detectable microlensing event.

assumptions (7)

standard math Standard point-mass and binary microlensing equations (Eqs. 2-10)
Used to compute magnifications and caustic-crossing light curves.
domain assumption The GCE is either smooth dark matter annihilation or a population of unresolved MSPs
Central dichotomy the test is designed to resolve.
domain assumption MSP gamma-ray emission is point-like on au scales (source radius ~10 km)
Needed for the large magnifications; if the emitting region were much larger the test would weaken.
domain assumption Dark matter annihilation emission is smooth on au scales
Makes DM emission immune to microlensing.
domain assumption Lenses are uniformly distributed in a 2D plane with the adopted optical depth
Simulation prescription; the printed Nlens is inconsistent with τ (see red flags).
domain assumption Source-count normalizations from Gautam et al. (2022) and Lee et al. (2016) apply
Sets the per-source photon rates for Cases 1 and 2.
domain assumption Advanced Particle-astrophysics Telescope will provide log10(a)=1 sensitivity improvement
Taken from Buckley et al. (2022); used as the reference future detector.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Gravitational Microlensing of the Galactic Centre $\gamma$-Ray Excess: A New Test for Point-Like or Extended Emission?." pith.science (2026). https://pith.science/paper/3PPFP2R5

@misc{pith2026250819577,
  author       = {Pith},
  title        = {Pith review of: Gravitational Microlensing of the Galactic Centre $\gamma$-Ray Excess: A New Test for Point-Like or Extended Emission?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3PPFP2R5}},
  note         = {Machine review of arXiv:2508.19577}
}

abstract

We present a potential test of the origin of the $\gamma$-ray Galactic Centre Excess (GCE). We demonstrate how gravitational microlensing by stellar mass objects along the line of sight to the Galactic Bulge can distinguish between the possibility of extensive emission due to dark matter self-annihilation from more prosaic astrophysical sources, namely millisecond pulsars. Such an astrophysical origin would result in emission from a population of small, currently unresolved point-like sources - in contrast to the expected smoother emission resulting from dark matter annihilation. Given that the scale of gravitational microlensing, that is, the Einstein radius for stellar mass lenses, and hence, the degree of induced magnification, is sensitive to the size of the emitting region, such microlensing will induce time variability in the emission of astrophysical sources, whereas $\gamma$-ray emission from dark matter annihilation will effectively be immune to such influences. However, we find that detecting microlensing-induced variability requires significantly greater sensitivity than that of current or planned $\gamma$-ray detectors. For a small population of bright GCE sources, more than an order-of-magnitude increase in effective area over Fermi-LAT would be required, with events remaining extremely rare. For a large population of faint sources, events would occur multiple times a year, but would only be detectable with a four-order-of-magnitude improvement. Whilst microlensing might not be a definitive test of the origin of the GCE, in future observations, it may prove useful in determining the properties of any point-like source population.

Figures

Figures reproduced from arXiv: 2508.19577 by the authors.

**Figure 1.** First and third columns (Left) - binary lens configurations. The lenses are shown as black dots, with their relative sizes representing their mass. The source trajectories are the coloured straight lines. The critical curve is in red, and the caustic is the spiky blue curve. Second and fourth columns (Right) - lightcurve for the respective lens configuration. The coloured lines represent the corresponding source tra… view at source ↗

**Figure 2.** An illustration of the simulation process for a single lens. Left - We generated a few sources (coloured dots), their magnitude represented by the size of the dots. A lens moves across our line of sight, its trajectory shown by the black line. Centre - We compute the distance between each source and lens every dt, and calculate the magnification over time, using Equation (4). Right - We sum all the source lightcurve… view at source ↗

**Figure 4.** Simulated lightcurve of the entire Galactic Centre containing 105 sources. The lightcurve is normalised to the total luminosity of 105 identical sources. The inset shows the two consecutive CC events at ∼ 9500 days. may contain more than 1 source. We note that other event selections are also possible; for instance, lowering the requirements on the reconstructed direction would result in a larger photon number, at t… view at source ↗

Figures from the paper (4 more)

**Figure 3.** Figure 3: Examples of time-scaled lightcurves for SL (top) and BL (bottom) events. Depending on the impact parameter of the lensing event, we should see different maximum magnifications for the SL case. ing events, we randomly designate 6% as originating from BLs. Following the …

**Figure 5.** Figure 5: Average number of sources per resolution element as a function of distance from the Galactic Centre for a population of 105 MSPs. The shaded region is the standard error. The dashed (dotted) line indicates the radius beyond which 75% (50%) of MSPs are located. We artif…

**Figure 6.** Figure 6: Correct peak detections for a CC event as a function of log10(a) - the log increase in efficiency from the LAT, with the number of sources contributing to the GCE indicated on each plot. A logistic curve is fit to each of these, with the inflection defining the detecto…

**Figure 7.** Figure 7: log10(a) at the inflection point for the event identification curve of the SL lightcurve, as a function of maximum amplification of the SL peak. We also show a fit to these points, where the events with log10(a) = 0 in the central panel are omitted from the fits. The c…

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

65 extracted references · 52 canonical work pages

[1]

Abazajian, K. N. 2011, J. Cosmology Astropart. Phys., 2011, 010

2011
[2]

N., Canac, N., Horiuchi, S., & Kaplinghat, M

Abazajian, K. N., Canac, N., Horiuchi, S., & Kaplinghat, M. 2014, Phys. Rev. D, 90, 023526

work page 2014
[3]

S., Lu, J

Abrams, N. S., Lu, J. R., Lam, C. Y., et al. 2025, ApJ, 980, 103

work page 2025
[4]

2013, ApJ, 771, 57

Ackermann, M., Ajello, M., Albert, A., et al. 2013, ApJ, 771, 57

work page 2013
[5]

B., et al

Ajello, M., Albert, A., Atwood, W. B., et al. 2016, ApJ, 819, 44

work page 2016
[6]

A., Alves, D., et al

Alcock, C., Allsman, R. A., Alves, D., et al. 2000, ApJ, 541, 270

work page 2000
[7]

B., Abdo, A

Atwood, W. B., Abdo, A. A., Ackermann, M., et al. 2009, ApJ, 697, 1071

2009
[8]

2016, Phys

Bartels, R., Krishnamurthy, S., & Weniger, C. 2016, Phys. Rev. Lett., 116, 051102

work page 2016

Show all 65 references

[9]

2018, Nature Astronomy, 2, 819

Bartels, R., Storm, E., Weniger, C., & Calore, F. 2018, Nature Astronomy, 2, 819

2018
[10]

J., & Kumar, J

Baxter, E. J., & Kumar, J. 2023, arXiv e-prints, arXiv:2310.01724

2023 arXiv
[11]

E., & Seljak, U

Bayer, A. E., & Seljak, U. 2020, J. Cosmology Astropart. Phys., 2020, 009

2020
[12]

2022, in 37th International Cosmic Ray Conference, 655

Buckley, J., Adapt, Alnussirat, S., et al. 2022, in 37th International Cosmic Ray Conference, 655

2022
[13]

L., Safdi, B

Buschmann, M., Rodd, N. L., Safdi, B. R., et al. 2020, Phys. Rev. D, 102, 023023

2020
[14]

Calore, F., Cholis, I., & Weniger, C. 2015, J. Cosmology Astropart. Phys., 2015, 038

2015
[15]

2021, Phys

Calore, F., Donato, F., & Manconi, S. 2021, Phys. Rev. Lett., 127, 161102, publisher: American Physical Society

2021
[16]

Caron, S., Eckner, C., Hendriks, L., et al. 2023, J. Cosmology Astropart. Phys., 2023, 013

2023
[17]

A., Hendriks, L., & Ruiz de Austri, R

Caron, S., Gómez-Vargas, G. A., Hendriks, L., & Ruiz de Austri, R. 2018, J. Cosmology Astropart. Phys., 2018, 058

2018
[18]

J., Mishra-Sharma, S., Lisanti, M., et al

Chang, L. J., Mishra-Sharma, S., Lisanti, M., et al. 2020, Phys. Rev. D, 101, 023014

2020
[19]

A., Scott, P., Trotta, R., & Lewis, G

Clark, H. A., Scott, P., Trotta, R., & Lewis, G. F. 2018, J. Cosmology Astropart. Phys., 2018, 060

2018
[20]

2020, MN- RAS, 495, 3350

Coleman, B., Paterson, D., Gordon, C., Macias, O., & Ploeg, H. 2020, MN- RAS, 495, 3350

2020
[21]

P., Hooper, D., et al

Daylan, T., Finkbeiner, D. P., Hooper, D., et al. 2016, Physics of the Dark Universe, 12, 1

2016
[22]

T., & Slatyer, T

Dinsmore, J. T., & Slatyer, T. R. 2022, J. Cosmology Astropart. Phys., 2022, 025

2022
[23]

S., & Petters, A

Gaudi, B. S., & Petters, A. O. 2002, ApJ, 574, 970

2002
[24]

M., Ferrario, L., et al

Gautam, A., Crocker, R. M., Ferrario, L., et al. 2022, Nature Astronomy, 6, 703

2022
[25]

2009, arXiv e-prints, arXiv:0910.2998

Goodenough, L., & Hooper, D. 2009, arXiv e-prints, arXiv:0910.2998

2009 arXiv
[26]

2013, Phys

Gordon, C., & Macías, O. 2013, Phys. Rev. D, 88, 083521

2013
[27]

K., Gould, A., et al

Han, C., Jung, Y. K., Gould, A., et al. 2023, A&A, 672, A8

2023
[28]

M., & Slatyer, T

Hooper, D., Cholis, I., Linden, T., Siegal-Gaskins, J. M., & Slatyer, T. R. 2013, Phys. Rev. D, 88, 083009

2013
[29]

2011, Physics Letters B, 697, 412

Hooper, D., & Goodenough, L. 2011, Physics Letters B, 697, 412

2011
[30]

2011, Phys

Hooper, D., & Linden, T. 2011, Phys. Rev. D, 84, 123005

2011
[31]

2002, Acta Astron., 52, 39

Jaroszynski, M. 2002, Acta Astron., 52, 39

2002
[32]

2004, Acta Astron., 54, 103

Jaroszynski, M., Udalski, A., Kubiak, M., et al. 2004, Acta Astron., 54, 103

2004
[33]

2006, Acta Astron., 56, 307 Jaroszyński, M., Skowron, J., Udalski, A., et al

Jaroszynski, M., Skowron, J., Udalski, A., et al. 2006, Acta Astron., 56, 307 Jaroszyński, M., Skowron, J., Udalski, A., et al. 2010, Acta Astron., 60, 197

2006
[34]

2024, ApJ, 968, 44

Joffre, S., Torres-Albà, N., Ajello, M., Kocevski, D., & Buehler, R. 2024, ApJ, 968, 44

2024
[35]

Kuang, R., Mao, S., Wang, T., Zang, W., & Long, R. J. 2021, MNRAS, 503, 6143

2021
[36]

K., & Slatyer, T

Leane, R. K., & Slatyer, T. R. 2019, arXiv e-prints, arXiv:1904.08430 —. 2020a, Phys. Rev. Lett., 125, 121105 —. 2020b, Phys. Rev. D, 102, 063019

2019 arXiv
[37]

K., Lisanti, M., Safdi, B

Lee, S. K., Lisanti, M., Safdi, B. R., Slatyer, T. R., & Xue, W. 2016, Phys. Rev. Lett., 116, 051103

2016
[38]

Lewis, G. F. 2004, MNRAS, 355, 106

2004
[39]

L., Safdi, B

Linden, T., Rodd, N. L., Safdi, B. R., & Slatyer, T. R. 2016, Phys. Rev. D, 94, 103013

2016
[40]

L., Schoen, E., & W olf, F

List, F., Park, Y., Rodd, N. L., Schoen, E., & W olf, F. 2025, arXiv e-prints, arXiv:2507.17804

2025
[41]

L., & Lewis, G

List, F., Rodd, N. L., & Lewis, G. F. 2021, Phys. Rev. D, 104, 123022

2021
[42]

L., Lewis, G

List, F., Rodd, N. L., Lewis, G. F., & Bhat, I. 2020, Phys. Rev. Lett., 125, 241102

2020
[43]

Malyshev, D. V. 2025, Phys. Rev. D, 111, 043033

2025
[44]

2024, Phys

Manconi, S., Calore, F., & Donato, F. 2024, Phys. Rev. D, 109, 123042

2024
[45]

D., Zhong, Y.-M., & Cholis, I

McDermott, S. D., Zhong, Y.-M., & Cholis, I. 2023, MNRAS, 522, L21

2023
[46]

2022, Phys

Mishra-Sharma, S., & Cranmer, K. 2022, Phys. Rev. D, 105, 063017

2022
[47]

L., & Safdi, B

Mishra-Sharma, S., Rodd, N. L., & Safdi, B. R. 2017, AJ, 153, 253

2017
[48]

2024, Symmetry, 16, 201

Misiaszek, M., & Rossi, N. 2024, Symmetry, 16, 201

2024
[49]

2020, Annual Review of Nuclear and Particle Science, 70, 455

Murgia, S. 2020, Annual Review of Nuclear and Particle Science, 70, 455

2020
[50]

M., Silk, J., Libeskind, N

Muru, M. M., Silk, J., Libeskind, N. I., Gottlöber, S., & Hoffman, Y. 2025, arXiv e-prints, arXiv:2508.06314

2025 arXiv
[51]

F., Frenk, C

Navarro, J. F., Frenk, C. S., & White, S. D. M. 1997, ApJ, 490, 493 O’Leary, R. M., Kistler, M. D., Kerr, M., & Dexter, J. 2015, arXiv e-prints, arXiv:1504.02477

1997 arXiv
[52]

1986, ApJ, 304, 1 —

Paczynski, B. 1986, ApJ, 304, 1 —. 1991, ApJ, 371, L63 12 Nada Salama et al. Petrović, J., Serpico, P. D., & Zaharijas, G. 2015, J. Cosmology Astropart. Phys., 2015, 023

1986
[53]

Ploeg, H., Gordon, C., Crocker, R., & Macias, O. 2020, J. Cosmology As- tropart. Phys., 2020, 035

2020
[54]

Schneider, P., Ehlers, J., & Falco, E. E. 1992, Gravitational Lenses (Springer), doi:10.1007/978-3-662-03758-4

1992 doi
[55]

2007, Acta Astron., 57, 281

Skowron, J., Jaroszynski, M., Udalski, A., et al. 2007, Acta Astron., 57, 281

2007
[56]

2024, MNRAS, 530, 4395

Song, D., Eckner, C., Gordon, C., et al. 2024, MNRAS, 530, 4395

2024
[57]

R., Udalski, A., et al

Sumi, T., W oźniak, P. R., Udalski, A., et al. 2006, ApJ, 636, 240

2006
[58]

P., Bond, I

Sumi, T., Bennett, D. P., Bond, I. A., et al. 2013, ApJ, 778, 150

2013
[59]

1997, MNRAS, 284, 172

Wambsganss, J. 1997, MNRAS, 284, 172

1997
[60]

Witt, H. J. 1990, A&A, 236, 311

1990
[61]

J., & Mao, S

Witt, H. J., & Mao, S. 1995, ApJ, 447, L105

1995
[62]

2015, ApJ, 802, 124

Yuan, Q., & Ioka, K. 2015, ApJ, 802, 124

2015
[63]

2016, ApJS, 225, 18

Zechlin, H.-S., Cuoco, A., Donato, F., Fornengo, N., & Vittino, A. 2016, ApJS, 225, 18

2016
[64]

2024, Phys

Zhong, Y.-M., & Cholis, I. 2024, Phys. Rev. D, 109, 123017

2024
[65]

D., Cholis, I., & Fox, P

Zhong, Y.-M., McDermott, S. D., Cholis, I., & Fox, P. J. 2020, Phys. Rev. Lett., 124, 231103

2020

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

Abazajian, K. N. 2011, J. Cosmology Astropart. Phys., 2011, 010

2011

[2] [2]

N., Canac, N., Horiuchi, S., & Kaplinghat, M

Abazajian, K. N., Canac, N., Horiuchi, S., & Kaplinghat, M. 2014, Phys. Rev. D, 90, 023526

work page 2014

[3] [3]

S., Lu, J

Abrams, N. S., Lu, J. R., Lam, C. Y., et al. 2025, ApJ, 980, 103

work page 2025

[4] [4]

2013, ApJ, 771, 57

Ackermann, M., Ajello, M., Albert, A., et al. 2013, ApJ, 771, 57

work page 2013

[5] [5]

B., et al

Ajello, M., Albert, A., Atwood, W. B., et al. 2016, ApJ, 819, 44

work page 2016

[6] [6]

A., Alves, D., et al

Alcock, C., Allsman, R. A., Alves, D., et al. 2000, ApJ, 541, 270

work page 2000

[7] [7]

B., Abdo, A

Atwood, W. B., Abdo, A. A., Ackermann, M., et al. 2009, ApJ, 697, 1071

2009

[8] [8]

2016, Phys

Bartels, R., Krishnamurthy, S., & Weniger, C. 2016, Phys. Rev. Lett., 116, 051102

work page 2016