Physically motivated AGN emissivity profiles and their effects on quasar microlensing signatures. 1. Multi-epoch accretion disc size inference

2; (2) SISSA; 3); (3) INAF-OATs; 4) ((1) IFPU; (4) University of Nova Gorica); Carina Fian (3; Scott Hagen (1

REVIEW 2 major objections 6 minor 300 references

Physically motivated AGN emissivity profiles and their effects on quasar microlensing signatures. 1. Multi-epoch accretion disc size inference

T0 review · 2 major / 6 minor · reviewed 2026-07-12 · grok-4.5

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Pith's one-line read Part of the quasar microlensing disc-size excess can come from treating disc-plus-BLR light as a single compact disc.

desk verdict Clean end-to-end mock demonstration that BLR diffuse continuum biases multi-epoch microlensing sizes toward the composite half-light radius, with wavelength dependence set by f_BLR. read the letter →

arxiv 2607.03291 v1 pith:IFZ4YKBP submitted 2026-07-03 astro-ph.GA astro-ph.HE

Scott Hagen (1 , 2 , 3) , Carina Fian (3 , 4) ((1) IFPU , (2) SISSA , (3) INAF-OATs , (4) University of Nova Gorica) This is my paper · ORCID

classification astro-ph.GAastro-ph.HE

keywords quasarmicrolensingaccretiondiscsizebroad-lineregioncontinuumemissivityprofilesdisc-sizeproblemwarmComptonisationhalf-lightradius

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

Microlensing is one of the few ways to measure the physical size of a quasar's optical and ultraviolet continuum. Those sizes often come out larger than a standard thin disc predicts. This paper argues that the mismatch is partly an interpretation problem: the observed light is a mix of a compact accretion disc and much larger-scale diffuse continuum from the broad-line region. The authors build energetically self-consistent disc emissivity maps from a stratified accretion model, add photoionised BLR continuum, convolve the composite sources with realistic magnification maps, and recover sizes from mock multi-epoch light curves. Detailed disc shape is only a second-order effect; the BLR smooths the caustic network and pulls the recovered half-light radius toward the composite effective size, with a strength set by how much flux the diffuse component contributes in the chosen band. A sympathetic reader cares because this offers a wavelength-dependent, physically motivated route to reconciling microlensing sizes with disc theory without discarding the disc.

What carries the argument

Energetically self-consistent bandpass emissivity maps from a radially stratified accretion-flow model, combined with a cloudy-computed diffuse BLR continuum and convolved with source-plane microlensing magnification maps; size is then recovered from the standard-deviation statistics of mock light-curve ensembles.

What would settle it

In multi-band microlensing campaigns, measure the recovered size excess as a function of continuum wavelength and compare it with the independently estimated BLR continuum fraction in each band; the excess should track that fraction and the compact-disc emissivity shape rather than a constant factor or a pure BLR-scale size.

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Extended reading notes

Core claim

When mock multi-epoch microlensing light curves generated from a composite warm-Comptonisation plus BLR source are interpreted with compact-only emissivity models, the recovered half-light radii tend toward the effective half-light radius of the composite emission rather than the true compact-disc size. The bias is set primarily by the fractional BLR contribution to the SED and the radial shape of the compact-disc emissivity, not by the absolute BLR radius itself when that fraction is below half.

Load-bearing premise

The broad-line region is treated as a single constant-density, constant-ionisation cloud in a simple bi-cone, projected as a uniform annular top-hat; if real BLRs have strong gradients or different covering, the diffuse flux fraction and smoothing scale change.

Editorial extensions

If this is right

Part of the reported optical/UV microlensing disc-size excess can be re-read as composite emission rather than a failure of thin-disc theory.
The bias is wavelength-dependent and strongest where the diffuse BLR continuum fraction is highest, so multi-band campaigns can separate disc and BLR contributions.
Compact-only size recovery on BLR-contaminated light curves systematically returns the composite half-light radius, not the pure disc radius.
Detailed shape of the compact-disc emissivity is secondary to the effective half-light radius set by the BLR flux fraction.

Reading between the lines

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

The same composite picture already invoked for continuum reverberation lags should produce correlated wavelength-dependent biases in both lag and microlensing size measurements.
If the BLR continuum fraction can be constrained independently (e.g., from line-free continuum windows or spectral decomposition), microlensing sizes can be corrected rather than discarded.
Future size-recovery pipelines that forward-model a disc-plus-annulus source will be less biased than pure Gaussian or thin-disc templates.

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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

The useful result here is quantitative and controlled: when you generate cosmograil-like light curves from a warm-Comptonisation+BLR composite and recover size with compact-only models, the posterior tracks the composite half-light radius, not the true disc size. The bias is set mainly by the BLR flux fraction and the shape of the compact emissivity (their Eq. 9), not by the absolute BLR radius. That is the concrete step beyond Fian et al. (2023a).

What they did well is the pipeline. They take agnsed, build energetically consistent 2D emissivity maps in chosen bandpasses, feed the SED to cloudy for a diffuse continuum, convolve with positive- and negative-parity maps, draw 100 tracks with realistic cadence/noise/gaps, and recover size from the variability statistic σ_Δm. Same-model recovery (Appendix C) comes back within ~16% of input, so the method is mostly sensitive to characteristic size, as Mortonson et al. already suggested. Cross-model tests (Fig. 5) then show the bias cleanly. Code is released. The claim is carefully hedged (“part of the excess could arise”).

The soft spot is the BLR: single-zone constant density/ionisation, bi-cone projected as a uniform top-hat annulus. That choice sets the quantitative f_BLR and therefore the bias amplitude. Real gradients or different covering will change the numbers. It does not kill the qualitative smoothing argument or the half-light reduction. Free parameters (fc, nH, αl, rh, veff, etc.) are listed; they are not hidden. Detailed disc-profile shape is secondary, which they show rather than assert.

This is for people who actually analyse microlensing sizes or who try to reconcile them with continuum lags. It is not a new observational measurement and does not claim to solve the whole disc-size problem. The math and citation pattern look solid; no circular fitting of real data. I would send it to referees. Worth reading if you work on either microlensing or BLR continuum contamination.

Referee Report

2 major / 6 minor

Summary. The paper constructs energetically self-consistent optical/UV emissivity maps from the radially stratified agnsed framework (standard thin disc and warm-Comptonised disc), adds a diffuse free-bound continuum from a single-zone bi-conical BLR computed with cloudy, and convolves the resulting composite sources with representative positive- and negative-parity microlensing magnification maps. Mock COSMOGRAIL-like multi-epoch light curves are generated and inverted with a variability-amplitude (σ_Δm) size-recovery pipeline. Same-model recovery tests return half-light radii within ~16% of input; when composite disc+BLR mocks are interpreted with compact-only models, recovered sizes track the composite effective half-light radius rather than the true compact-disc size. The bias is argued to be set primarily by the bandpass-dependent BLR flux fraction and the radial shape of the compact emissivity (via the half-light definition, Eq. 9), supporting the claim that part of the microlensing disc-size excess can arise from treating composite emission as a single compact disc.

Significance. If the result holds, it supplies a physically motivated, wavelength-dependent mechanism that can partially reconcile microlensing size measurements with standard disc theory, in close analogy with the BLR-driven lag excess in continuum reverberation. Strengths include: (i) self-consistent SED-to-emissivity mapping from agnsed rather than ad-hoc Gaussians; (ii) controlled forward simulations with explicit same-model recovery checks (Appendix C); (iii) an analytic reduction of the composite half-light radius for f_BLR < 0.5 (Eq. 9); and (iv) public code (AGNmap). The claim is carefully scoped (“part of the excess could arise”) and does not overclaim a full solution of the disc-size problem. The work is a useful, falsifiable contribution to the microlensing and AGN continuum literature.

major comments (2)

§5.3 and Appendix C / Table C.1: Same-model recovery returns sizes systematically larger than input by a mean factor ~1.16 across bands and parities. Fig. 5 is interpreted as showing that recovered sizes “tend toward the effective half-light radius of the input composite model.” Because the recovery pipeline itself is biased high at that level, the quantitative excess relative to the compact-disc half-light radii should be reported after correcting for (or at least subtracting in quadrature / discussing) this baseline offset, so that the BLR-driven bias is not conflated with the recovery systematics.
§3 and Appendix A: The BLR is a single constant-density, constant-ionisation cloudy calculation (fc=0.3, αl=60°, nH=10^11.5 cm−3, NH=10^23 cm−2) projected as a uniform top-hat annulus. The central qualitative claim is robust to this choice, but the quantitative bias amplitudes in Fig. 5 and the wavelength dependence are set by f_BLR, which is model-dependent. Either a short sensitivity test (e.g. varying fc or nH by factors of a few) or an explicit statement in §5.3/§6 that the reported size excesses are for this fiducial BLR only is needed so readers do not over-generalise the numerical factors.

minor comments (6)

Fig. 3: The unconvolved maps and histograms are clear, but the figure caption and main text would benefit from quoting the BLR flux fractions (f_BLR ~30% at 7500 Å, ~1.4% at 1650 Å) next to the corresponding panels so the wavelength dependence is immediately readable.
§5.1: The adopted veff = 600 km s−1 is taken from Mediavilla et al. (2016); a one-sentence note that absolute size scales with the Einstein radius and that relative biases (composite vs compact) are largely velocity-independent would help non-specialists.
Eq. (8)–(9): The monochromatic half-light definition is standard, but the transition from the full integral to the disc-only cumulative form when f_BLR < 0.5 could be flagged more explicitly as an approximation that fails once R_1/2 reaches the BLR annulus (as the text already notes for λ ≳ 10^4 Å).
§2.1: General-relativistic light bending is neglected with a reasoned argument for optical/UV; a brief pointer to the spin/truncation regimes where this would matter (already cited via Hagen & Done 2023a) would complete the caveat.
Typographical / production: “agnsed” and “cloudy” are sometimes set in roman and sometimes not; consistent treatment (e.g. small-caps or monospace for code names) would improve readability. Also “cosmograil” should be capitalised consistently as COSMOGRAIL when referring to the survey.
Appendix B schematic is helpful; ensuring that the published version has sufficient resolution for the likelihood/posterior panels would avoid production issues.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: pure forward-modelling of synthetic light curves; recovered sizes track the input composite half-light radius by the known sensitivity of microlensing to characteristic size, not by re-fitting real data or self-definition of the target claim.

full rationale

The paper constructs energetically self-consistent disc+BLR emissivity maps from agnsed + cloudy, convolves them with independent FMM–IPM magnification maps, draws mock trajectories, and recovers half-light radii from the variability statistic σ_Δm via a joint posterior over an ensemble of tracks. Same-model recovery tests (Appendix C) return sizes consistent with the known input half-light radii (average ratio ~1.16), confirming the procedure is primarily sensitive to characteristic size (as already established by Mortonson et al. 2005). When composite mocks are interpreted with compact-only models, the recovered sizes track the composite R_1/2 (Fig. 5), which follows directly from the monochromatic half-light definition (Eqs. 8–9) once f_BLR is non-zero; this is an expected consequence of the statistic, not a circular re-labelling of a fit. Self-citations (Hagen & Done implementations of agnsed/irradiation, Fian et al. 2023a for the qualitative BLR-smoothing idea, Hagen et al. 2024 for the bi-conical geometry) supply methods and prior motivation; none is a load-bearing uniqueness theorem that forces the present numerical result. No observational sizes are fitted and then re-predicted, no ansatz is smuggled as a theorem, and the central claim remains an independent quantification of bias under stated modelling assumptions. Score 1 only for the minor, non-load-bearing self-citations that are normal in a methods-extension paper.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a chain of standard accretion and photoionisation assumptions plus a set of fiducial numerical choices that fix the BLR flux fraction and geometry. No new physical entities are postulated; the free parameters control the amplitude of the bias rather than its existence. The ledger therefore lists the modelling choices that, if altered substantially, would change the quantitative size overestimation while leaving the qualitative smoothing argument intact.

free parameters (6)

BLR covering fraction fc = 0.3
Fixed at 0.3 following Baskin & Laor (2018); directly sets the absolute BLR luminosity and therefore the flux fraction that drives the half-light-radius bias.
BLR hydrogen density nH and column NH = nH=10^11.5 cm−3, NH=10^23 cm−2
Chosen as 10^11.5 cm−3 and 10^23 cm−2 to produce mostly neutral gas at the mid-radius; control the cloudy-computed diffuse continuum spectrum and its bandpass-dependent fraction.
Launch angle αl and launch radius rl = αl=60°, rl≈5700 RG
αl=60° and rl set so that the geometric-mean BLR radius lies on the Bentz et al. (2013) R–L relation; fix the projected annular size that smooths the caustic network.
Hot-corona truncation radius rh and warm-corona parameters = rh=15, Γw=2.7, kTe,w=0.2 keV
rh=15 RG, kTe,w=0.2 keV, Γw=2.7 (and hot-corona Γh=1.9, kTe,h=100 keV) define the compact emissivity profiles and the ionising SED that powers the BLR.
Black-hole mass, accretion rate, spin = M=1e8 M⊙, ṁ=0.1, a=0
Fiducial M=10^8 M⊙, ṁ=0.1, a=0 set absolute physical scales of both disc and BLR; size recovery later rescales half-light radius without recomputing the SED.
Effective transverse velocity veff = 600 km s−1
Fixed at 600 km s−1 from Mediavilla et al. (2016) to set track lengths on the magnification maps; affects sampling of caustic structure but not the half-light-radius bias itself.

assumptions (5)

domain assumption Accretion flow follows Novikov–Thorne emissivity with radial stratification into standard disc, warm Comptonisation, and hot corona (agnsed framework).
Section 2; supplies the compact emissivity maps and ionising SED. Standard in the field but not uniquely required by the data.
ad hoc to paper BLR is a single bi-conical structure of constant density and ionisation, emitting isotropically into 2π and visible only on the near side.
Section 3 and Appendix A; simplifies cloudy calculation and projection to a top-hat annulus. Real BLRs have gradients.
domain assumption Microlensing size is recoverable from the standard deviation of multi-epoch magnitude variability after convolution with source-plane magnification maps.
Section 5.2; common statistical approach, but omits full light-curve trajectory fitting used in some observational analyses.
domain assumption General-relativistic light bending is negligible for optical/UV microlensing sizes.
Section 2.1; justified by concentration of GR effects at small radii, but remains an approximation.
domain assumption Stellar mass fraction ~20% and microlens mass 0.3 M⊙ produce representative caustic networks whose magnification PDFs are insensitive to the exact mass function.
Section 4.1; standard microlensing literature assumption.

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Pith. "Pith review of Physically motivated AGN emissivity profiles and their effects on quasar microlensing signatures. 1. Multi-epoch accretion disc size inference." pith.science (2026). https://pith.science/paper/IFZ4YKBP

@misc{pith2026260703291,
  author       = {Pith},
  title        = {Pith review of: Physically motivated AGN emissivity profiles and their effects on quasar microlensing signatures. 1. Multi-epoch accretion disc size inference},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IFZ4YKBP}},
  note         = {Machine review of arXiv:2607.03291}
}

read the original abstract

Quasar microlensing is uniquely sensitive to the size-scale of the accretion flow, offering one of the few direct probes of the accretion structure on micro-arcsecond scales. However, microlensing-based measurements in the optical and UV often find sizes systematically larger than expected from standard Shakura-Sunyaev disc theory, commonly referred to as the disc-size problem similar to that seen in continuum reverberation campaigns. But this assumes that all the emission comes from a single compact disc, neglecting the diffuse emission from the BLR which originates on much larger spatial scales. In this paper we directly quantify the effect of large-scale diffuse emission on the observed microlensing signatures. We adapt the physically motivated agnsed model to construct energetically self-consistent emissivity profiles in any given bandpass. Since this also predicts the full SED, we combine these SEDs with cloudy to give a diffuse BLR component. We convolve these models with representative microlensing magnification maps, and generate mock microlensing light curves to directly assess the inferred source size under different physical conditions. While the detailed shape of the disc emissivity profile has only a higher-order effect on the microlensing profile, the inclusion of the BLR makes a significant impact since this naturally smooths out the caustic network over larger scales. This introduces a significant bias when interpreted purely as a compact disc. However, the strength of this bias depends predominantly on the fractional contribution of the diffuse emission to the SED in the bandpass being considered, as this sets the effective half-light radius, giving an important wavelength dependence. We conclude that part of the excess in microlensing-inferred accretion disc sizes could arise from interpreting a composite (disc+BLR) picture as a single compact disc.

Figures

Figures reproduced from arXiv: 2607.03291 by the authors.

**Figure 1.** Top: Model SEDs for the fiducial warm-Comptonised disc model (green solid line) and standard Shakura & Sunyaev (1973) disc model (magenta dashed line). In both cases, the accretion flow truncates into an inner X-ray-emitting plasma below rh = 15, producing the high-energy X-ray tail. The dotted curves show the individual disc and warm-Comptonised disc components. The hatched region marks the unobservable energy ra… view at source ↗

**Figure 2.** Top: Optical/UV portion of the model SED including the diffuse BLR continuum contribution. The intrinsic warmComptonised disc emission is shown as a dashed green line, the diffuse BLR component as a dashed orange line, and the total observed SED as a solid black line. The shaded regions indicate the bandpasses used to extract the radial emissivity profiles shown in the bottom panel and later used to compute the mi… view at source ↗

**Figure 3.** Model convolution results for the positive-parity image (top row) and negative-parity image (bottom row). [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Example simulated light curves. Top row: The left panel shows the input magnification map for the positive-parity image used to generate the light curves. The coloured circles, shown in magenta and yellow, mark the initial disc positions, while the corresponding straig…

**Figure 5.** Figure 5: Recovered half-light radii from simulated microlens [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

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Pith tools

Reviewed July 12, 2026 · model on record in the stance chip above.

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The evolution of soft excess and X-ray continuum

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doi:10.1051/0004-6361/202556654

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Size of the accretion disk in the gravitationally lensed quasar SDSS J1004+4112 from the statistics of microlensing magnifications

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work page Pith review arXiv doi:10.3847/0004-637x/830/2/149

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Estimate of the Accretion Disk Size in the Gravitationally Lensed Quasar HE 0435-1223 using Microlensing Magnification Statistics

Estimate of the Accretion Disk Size in the Gravitationally Lensed Quasar HE 0435-1223 Using Microlensing Magnification Statistics. , keywords =. doi:10.3847/1538-4357/aaeed5 , archivePrefix =. 1811.03312 , primaryClass =

work page Pith review arXiv doi:10.3847/1538-4357/aaeed5

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Revealing the structure of the lensed quasar Q 0957+561. I. Accretion disk size. , keywords =. doi:10.1051/0004-6361/202039854 , archivePrefix =. 2108.05212 , primaryClass =

work page Pith review arXiv doi:10.1051/0004-6361/202039854

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Diffuse emission in microlensed quasars and its implications for accretion-disk physics

Diffuse emission in microlensed quasars and its implications for accretion-disk physics. , keywords =. doi:10.1051/0004-6361/202346766 , archivePrefix =. 2307.14824 , primaryClass =

work page Pith review arXiv doi:10.1051/0004-6361/202346766

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Size is Everything: Universal Features of Quasar Microlensing with Extended Sources

Size Is Everything: Universal Features of Quasar Microlensing with Extended Sources. , keywords =. doi:10.1086/431195 , archivePrefix =. astro-ph/0408195 , primaryClass =

work page Pith review arXiv doi:10.1086/431195

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Probing the dark matter radial profile in lens galaxies and the size of X-ray emitting region in quasars with microlensing

Probing the Dark Matter Radial Profile in Lens Galaxies and the Size of X-Ray Emitting Region in Quasars with Microlensing. , keywords =. doi:10.1088/0004-637X/806/2/251 , archivePrefix =. 1502.00394 , primaryClass =

work page Pith review arXiv doi:10.1088/0004-637x/806/2/251

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The Average Size and Temperature Profile of Quasar Accretion Disks

The Average Size and Temperature Profile of Quasar Accretion Disks. , keywords =. doi:10.1088/0004-637X/783/1/47 , archivePrefix =. 1401.2785 , primaryClass =

work page Pith review arXiv doi:10.1088/0004-637x/783/1/47