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Simulating quasar microlensing light curves: High magnification events

T0 review · 2 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Wide-field surveys should catch about 61 high-magnification quasar microlensing events per year, with saddle images four times more eventful than minima.

desk verdict A solid, reproducible population forecast of quasar microlensing HMEs; the headline rate is model-dependent (thin-disk size), and the quoted error bars omit that systematic, but the paper is a genuinely useful planning tool. read the letter →

arxiv 2507.21973 v1 pith:LPCM2EC4 submitted 2025-07-29 astro-ph.GA astro-ph.CO

Favio Neira , Timo Anguita , Georgios Vernardos This is my paper · ORCID
classification astro-ph.GAastro-ph.CO
keywords accretiondisksgravitationallensing:microquasars:generalhighmagnificationeventsmicrolensinglightcurvescausticcrossings
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks how many high-magnification events—sharp brightening or dimming episodes in the light curves of strongly lensed quasars, produced when stars in the lens galaxy cross the line of sight—the next generation of wide-field ground surveys should detect, and what those events will look like. Working from a realistically simulated population of lensed quasars, it forecasts about 61 events per year with amplitude above 0.3 magnitude in the r-band from systems bright enough and well separated enough for ground-based follow-up in either the northern or southern sky. It also establishes statistical differences between the two types of macro-images: saddle images produce roughly four times as many events as minima, and those events can be one to two magnitudes brighter, while minima have a much higher chance (about half) that the event is a caustic crossing—the sharp feature most useful for probing the accretion disk. The work is meant as a planning tool: it ranks which lensed images should be monitored and estimates how many useful events future monitoring campaigns will capture.

What carries the argument

The machinery is a simulation pipeline that converts a theoretical population of strongly lensed quasars into ten-year microlensing light curves and then into event catalogs. The load-bearing pieces are: a simulated catalog of lens systems with macromodel parameters (convergence and shear from a singular isothermal ellipsoid plus external shear, and a smooth matter fraction assigned from a stellar mass distribution); precomputed inverse-ray-shooting magnification maps and corresponding caustic maps selected per image; an accretion disk size from the standard thin disk model $R_\lambda = 9.7\times10^{15}\,(\lambda_{\rm rest}/\mu\mathrm{m})^{4/3}(M_{\rm BH}/10^9\,M_\odot)^{2/3}(f_E/\eta)^{1/3}$ cm with fixed Eddington ratio $f_E=0.25$ and efficiency $\eta=0.15$; an effective transverse velocity formed by combining observer, lens, source, and stellar velocities; and an event-finding algorithm that defines a high magnification event as any pair of extrema in a light curve whose amplitude exceeds a threshold (0.3 mag in the r-band by default), with the event trimmed to the 5% to 95% flux points. Events are then classified by macro-image parity and by whether the disk crosses or touches a caustic.

What would settle it

Monitor roughly 560 lensed quasars satisfying the selection criteria (image separation at least 1 arcsecond, second-dimmest image at or brighter than 21.5 magnitudes in the i-band) from both hemispheres for one year with a cadence fine enough to catch 0.3-magnitude r-band excursions, and compare the observed event count with the predicted $61.5^{+7.9}_{-8.9}$ per year and the saddle-to-minimum event ratio near four; a count outside the 68% interval or a parity ratio far from four would contradict the forecast. A quicker observational check is to measure accretion disk sizes directly via microlensing or reverberation mapping; if the measured sizes are systematically larger than the thin-disk prediction, the forecast event rate would be an upper limit rather than a central estimate.

Watch

Extended reading notes

Core claim

The authors' central claim is a forecast and a set of event statistics. From the theoretically expected population of lensed quasars that pass ground-based selection (image separation at least 1 arcsecond and second-dimmest image at most 21.5 magnitudes in the i-band, about 560 systems in 20,000 square degrees), they predict $61.5^{+7.9}_{-8.9}$ high magnification events per year with minimum amplitude 0.3 magnitude in the r-band. They further claim that these events are unevenly distributed: saddle images average roughly four times more events than minima, and the events they produce are on average larger in amplitude, with strong caustic crossings up to 1–1.5 magnitudes brighter, because saddle images have deeper de-magnification regions. However, only about 10% of saddle-image events are caustic crossings, whereas about half of minimum-image events are. The authors also find that concentrating monitoring on the top-ranked ~20% of images by expected event count recovers about half of the yearly events, and they argue the forecast is likely an underestimate because observational selection favors high-magnification systems.

Load-bearing premise

The central assumption is that the quasar accretion disks all have the size predicted by the standard thin-disk model with fixed Eddington ratio 0.25 and efficiency 0.15; larger or smaller real disks would respectively lower or raise the predicted event rates and amplitudes.

Editorial extensions

If this is right

  • Wide-field ground surveys should expect a steady supply of roughly sixty high-magnification quasar microlensing events per year, making targeted follow-up a realistic observing program.
  • Saddle images are the most efficient targets for catching frequent, bright events, but minimum images are far more likely to yield a caustic crossing, the feature best suited for probing accretion disk structure.
  • A small fraction of the known lensed images—the top-ranked 20%—produces about half of the yearly events, so monitoring time can be concentrated on a shortlist.
  • Raising the amplitude threshold to 1.0 magnitude cuts the expected r-band yield to about 25 events per year while raising the caustic-crossing fraction by roughly 40 percent, trading event quantity for sharper events.

Reading between the lines

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

  • If the macro-magnification/event-rate correlation holds beyond the simulated catalog, the growth of known lensed quasar samples from next-generation surveys would yield event counts that scale with the number of high-magnification images, not just the total number of systems.
  • A natural testable extension is to repeat the pipeline with accretion disk sizes drawn from the larger measured values; doing so would convert the quoted event rate from a model prediction into a constraint on the disk size distribution.
  • The asymmetry between strong and weak caustic-crossing pairs suggests a practical trigger: monitoring pipelines could flag candidate accretion-disk substructure by looking for asymmetric brightening-dimming pairs in real time.
  • Because the authors adopt face-on disks, including inclination would effectively shrink the projected source and should yield shorter, larger-amplitude events; this could be checked by re-running with random disk orientations.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 6 minor

Summary. This paper uses the OM10 mock catalog of strongly lensed quasars to select ~2800 systems with minimum image separation at least 1 arcsec and second-dimmest i-band magnitude brighter than 21.5, and for each lensed image generates 100,000 ten-year microlensing light curves in six LSST bands using GERLUMPH magnification maps, a standard thin-disk accretion model (Eq. 6), and a velocity model. It defines high magnification events (HMEs) via an extrema-pair algorithm with a 0.3 mag threshold, classifies them by image parity and caustic-crossing type, and reports event statistics. The main forecast is 61.5^{+7.9}_{-8.9} HMEs per year above 0.3 mag in the r-band in either hemisphere, with saddle images hosting about four times as many events as minima and caustic-crossing fractions of roughly 10% (saddles) and 50% (minima).

Significance. If the forecast holds, it provides a concrete, falsifiable target for LSST/Euclid-era monitoring and follow-up of lensed quasars, and the parity/caustic-crossing statistics offer practical guidance for selecting optimal targets. The work is a forward simulation with fixed inputs from the literature and the OM10 catalog; no HME property is used to fit a model parameter, so there is no circularity. The scale of the simulation (about four billion curves) and the public code and online appendix support reproducibility. The bootstrap error bars capture catalog sampling and light-curve variance. The main weakness is the absence of a systematic error from the adopted disk-size model in the headline rate, which the paper itself identifies as the primary parameter controlling microlensing variations.

major comments (2)
  1. [Section 5.2 / Eq. (6) / 5.3.2] The headline forecast (61.5^{+7.9}_{-8.9} HMEs per year) is quoted with error bars that include only OM10 catalog sampling and light-curve variance. The paper identifies the accretion disk size as 'the primary parameter that influences the microlensing variations' (Section 5.3.2), and the Introduction cites reverberation-mapping and microlensing measurements favoring disk sizes larger than the standard thin-disk prediction by factors of roughly 2-3. Since the HME rate is a steep function of the source size relative to the caustic scale, a factor-of-two change in R from Eq. (6) can shift the central rate by more than the quoted +7.9/-8.9 events/yr. The authors should propagate this systematic into the uncertainty budget or explicitly frame the abstract and Section 5.2 numbers as conditional on the thin-disk model, with the error bars denoting statistical precision only. This is load-bearing because the central claim is the rate itself.
  2. [Section 2.2 / 5.3.2 / Fig. 6] The caustic-crossing fractions (Fig. 6) and the parity-dependent amplitude differences (Fig. 7) are computed for a single smooth-matter-fraction model (Salpeter IMF and CASTLES-based Einstein-to-effective-radius ratio). Section 5.3.2 states that the smooth matter fraction is anti-correlated with caustic density, so the other three model combinations of Vernardos (2019) would shift the caustic-crossing rates and possibly the saddle/minimum contrast. Because the abstract quotes the ~10%/~50% caustic-crossing fractions as headline results, the paper should either report how these quantities vary across the four model combinations or explicitly state that the quoted fractions are conditional on the adopted s model.
minor comments (6)
  1. [2.5 (first paragraph)] The phrase 'as well as a touching a caustic curve' contains a doubled article; it should read 'as well as a touching-caustic curve'.
  2. [5.1 (first paragraph)] The sentence 'This is because, the source no longer needs to move through high magnification regions for an event to occur' has an unnecessary comma after 'because'; rephrase for clarity.
  3. [6 (first paragraph)] The summary states that ~4 billion light curves were simulated, but Section 2.5 yields about 1.7 billion light curves (2800 images x 100,000 tracks x 6 bands), or about 3.6 billion curves including the caustic and touching curves; the wording should be corrected.
  4. [Table 1 note] The note that events in redder bands are always identified in bluer bands is relevant to the interpretation of the six band rows and deserves an explanatory sentence in Section 5.4.
  5. [1 (footnote 1)] The footnote 'This number is orders of magnitude lower than other astrophysical phenomena' is vague and could be removed or replaced with a concrete comparison.
  6. [Figs. 3 and 6] The phrase 'the pie chart represents the total area fraction of each histogram' is unclear; the pie chart shows the fraction of images of each parity, and the text should say so directly.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the HME rate forecast is a forward simulation output, not a re-statement of any fitted input.

full rationale

The central prediction (61.5+7.9/-8.9 HMEs/yr, Sec. 5.2) is produced by a forward chain: OM10 mock lensed quasars -> GERLUMPH magnification/caustic maps -> thin-disk sizes from Eq. 6 with externally adopted f_E=0.25, eta=0.15 and virial masses from Eq. 7 -> velocity model from prior literature -> 100,000 light curves per image with the Neira et al. (2020) generator -> event-finder -> bootstrap over a random 1/5 subsample. No HME rate, amplitude, duration, or parity fraction is used to fit any input parameter; the bootstrap only propagates catalog and light-curve sampling noise. Self-citations (Neira et al. 2020 tool, Vernardos et al. GERLUMPH maps, Vernardos & Tsagkatakis 2019 profile-shape insensitivity) supply methodology or data products rather than the target claim, so they are not load-bearing circular support. The paper itself identifies the accretion-disk size as the dominant systematic (Sec. 5.3.2) and warns that larger disks would yield fewer, smaller events; this is a model-dependence caveat, not a circularity. The event definition threshold (0.3 mag) is an explicit convention, not a hidden input masquerading as a prediction. Therefore no circular step can be exhibited.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The forecast depends on a chain of literature-based parameters and model assumptions, the most important being the accretion disk size relation (Eq. 6) and the smooth matter fraction. All are stated explicitly and discussed qualitatively in Section 5.3, and none are fitted to the HME rate itself. The circularity burden is accordingly low.

free parameters (7)
  • Eddington ratio f_E = 0.25
    Fixed typical value from Blackburne et al. 2011, used in the thin disk size relation (Eq. 6). The HME rate is sensitive to disk size.
  • Accretion efficiency eta = 0.15
    Fixed typical value from Blackburne et al. 2011, used in Eq. 6.
  • Microlens mass M = 0.3 M_sun
    Assumed mean of a Salpeter IMF for the microlenses, used in the Einstein radius (Eq. 5). Affects the magnification map scale and event timescales.
  • Velocity dispersion normalization sigma_pec(z=0) = 235 km/s
    From Kochanek 2004, used in the peculiar velocity model (Eq. 10).
  • External shear log-normal parameters = mean 0.05, dispersion 0.2
    Assumed for the magnitude and direction of gamma_ext, following Oguri and Marshall 2010; affects the macromodel and hence map selection.
  • Smooth matter fraction model choice = Salpeter IMF and CASTLES Einstein to effective radius ratio
    One of four possible combinations from Vernardos 2019 is used; affects the smooth matter fraction and caustic density, mainly influencing caustic-crossing fractions rather than the total HME count.
  • Microlens velocity efficiency factor epsilon = 1
    Assumed in the bulk velocity approximation for the microlenses (Eq. 14).
assumptions (6)
  • domain assumption Flat Lambda CDM cosmology with H0 = 72 km/s/Mpc, Omega_m = 0.26, Omega_Lambda = 0.74
    Adopted from the OM10 catalog for angular diameter distances, as stated in Section 2.1.
  • domain assumption Singular isothermal ellipsoid (SIE) macromodel for the lensing galaxy
    Used to compute convergence and shear at image positions (Eqs. 1 and 2), a standard lens model.
  • domain assumption Standard thin disk model (Shakura and Sunyaev)
    Provides the disk size relation (Eq. 6). The central HME rates depend directly on this model, and the introduction notes observational tension with its predictions.
  • domain assumption GERLUMPH magnification maps accurately represent microlensing magnification
    Precomputed inverse ray-shooting maps are selected by kappa, gamma, and s; this is a standard approach in the field.
  • domain assumption Bulk velocity approximation for microlens motion (Wyithe et al. 2000)
    The random motion of individual microlenses is approximated by a bulk velocity with an efficiency factor, simplifying the light curve generation.
  • domain assumption Uniform random sky positions for lens systems
    The OM10 catalog does not constrain sky position, so right ascension and declination are assigned uniformly at random, which sets the observer transverse velocity contribution via the CMB dipole.

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Cite this review

Pith. "Pith review of Simulating quasar microlensing light curves: High magnification events." pith.science (2026). https://pith.science/paper/LPCM2EC4

@misc{pith2026250721973,
  author       = {Pith},
  title        = {Pith review of: Simulating quasar microlensing light curves: High magnification events},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LPCM2EC4}},
  note         = {Machine review of arXiv:2507.21973}
}
abstract

Quasar microlensing can be used to constrain important astrophysical properties, such as the accretion disk size and the amount of stars in the lensing galaxy. The associated brightness variations over time, in particular high magnification events (HMEs) and caustic crossings, can yield precise constraints due to their strong dependence on the relative projected velocities of the components and accretion disk size. The next generation of large sky area surveys, such as The Vera Rubin Observatory (LSST) and Euclid, are expected to find and follow-up thousands of lensed quasars from which such events could be identified and observed. In this work we present a characterization and estimation of all HMEs that could potentially be observed, focusing on systems that could be identified by ground based telescopes. From systems whose minimum image separation is at least 1 arcsec, and their second dimmest image is at least 21.5 magnitudes in the i-band ($\sim560$ in the southern or northern sky), we estimate $\sim60$ HMEs with amplitudes $>0.3$ [mag] in the r-band per year. We find that on average, saddle images are approximately four times more likely to host events than minima, and $\sim10\%$ ($\sim50\%$) of events are caustic crossings for saddles (minima). We also find that HMEs in saddle images can have amplitudes $\sim1-2$ [mag] larger than minima.

Figures

Figures reproduced from arXiv: 2507.21973 by the authors.

Figure 1
Figure 1. Two-dimensional histogram of κ and γ values computed for the selected lensed images from the OM10 catalog. The color in each bin represents the count number. The red solid line indicates where µmacro → ∞ separating minimum (below) from saddle (above) images. We note that κ ≈ γ is due to describing the mass distribution of the lenses with a SIE + γext. mass distribution of the microlenses. Furthermore, the statistics… view at source ↗
Figure 2
Figure 2. Additionally, in Appendix A we show light curve exam￾ples, where we have identified their HMEs and highlighted their corresponding (non-)caustic crossing classification. We do not highlight the parity classification as this pertains to the macro￾model parameters, and not the light curve itself. 4. Results We identify HMEs in the 10-year long simulated light curves in the r-band, which is typically most efficient for… view at source ↗
Figure 4
Figure 4. Duration of all HMEs per image parity. We note that the peak at ∼ 3300 [days] corresponds to events that last longer than the 10 years of the light curves. As per [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: Amplitude of all HMEs per image parity. We note that the larger amplitudes in saddle images are due to their magnification maps having deeper de-magnification regions. amplitudes of caustic crossings, the differences in the duration of caustic crossings between image p…
Figure 6
Figure 6. Figure 6: Fraction of events that are caustic crossings per image parity. Fractions in saddle and minimum images peak at ∼ 0.1 and ∼ 0.5 re￾spectively. As per [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 9
Figure 9. Figure 9: Duration of all non-caustic crossing events for all minimum (top) and saddle (bottom) images. The colors match the scheme classification of non-caustic crossing events shown in [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: Amplitude of all non-caustic crossing events for all minimum (top) and saddle (bottom) images. The colors match the scheme classi￾fication of non-caustic crossing events shown in [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]
Figure 11
Figure 11. Figure 11: Expected number of events with an amplitude >0.3 [mag] in the r band as a function of the fraction the highest ranked (larger expected number of events) over the total number of images. The derivative is plotted in a dashed line. The shaded area corresponds to the 68%…
Figure 12
Figure 12. Figure 12: Expected number of HMEs in 10 years of all the lensed im￾ages as a function of the macro magnification µmacro and compact matter fraction S ⋆. Yellow (purple) indicates a higher (lower) expected num￾ber of HMEs. The expected number of events is strongly correlated wit…

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