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Accretion disc reverberation mapping of the quasar 3C 273

T0 review · 3 major / 6 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read Reverberation mapping of quasar 3C 273 shows its accretion disc is 2–7 times larger than thin-disc theory predicts.

desk verdict First dedicated disc RM for 3C273, but the size-problem claim hinges on a black-hole mass choice the paper waves away, and the near-IR/BLR story is an extrapolation, not a measurement. read the letter →

arxiv 2502.08366 v1 pith:QFMUG72O submitted 2025-02-12 astro-ph.GA

James P. Thorne , Hermine Landt , Jiamu Huang , Juan V. Hernandez Santisteban , Keith Horne , Edward M. Cackett , Hartmut Winkler , David Sanmartim This is my paper · ORCID
classification astro-ph.GA
keywords accretiondiscreverberationmappingquasar3C273inter-bandcontinuumlagssizeproblemthinmodelbroadlineregiondustyoutflow
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 reports the first dedicated accretion-disc reverberation-mapping campaign on the quasar 3C 273, using four seasons of high-cadence light curves in seven optical filters from the Las Cumbres Observatory. The inter-band time delays, recovered independently with the Javelin and PyROA fitting algorithms, agree with each other and place the emitting regions 2–7 times farther out than the Shakura–Sunyaev thin-disc model predicts, making 3C 273 one of the brightest, highest-luminosity objects yet to show the 'accretion disc size problem.' The slope of the lag–wavelength relation still matches the thin-disc exponent β = 4/3, and a 'flat disc with a steep rim' geometry can simultaneously reproduce the lags and the spectral energy distribution of the variations. Extrapolating the optical lag spectrum into the near-infrared gives radii of 100–200 light-days for putative dust-forming disc regions, consistent with the measured broad-line-region size and the rim's outer edge, suggesting the disc may extend far enough to be dusty and that the BLR could form in a dusty outflow.

What carries the argument

The central object is the lag–wavelength (reverberation) spectrum tau($\lambda$), the light-travel delay between continuum variations at different photometric bands; it is measured with Javelin (a damped-random-walk Gaussian-process fit with a top-hat transfer function) and PyROA (a running-optimal-average fit with a delta-function transfer function), and cross-checked against thin-disc predictions tau ∝ (X $\lambda$)^(4/3) with Wien factor X = 4.96 or 2.49. The argument then turns on two extensions of this spectrum: a 'flat disc with steep rim' model, a finite-height power-law disc H(r) = H_out (r/r_out)^k with k > 1 irradiated by a lamp-post, which fits both the lags and the variable SED, and a power-law extrapolation from the measured optical lags to the roughly 1000 K dust-forming region at J, H, and K band wavelengths.

What would settle it

A dedicated near-infrared reverberation campaign measuring J-, H-, and K-band lags in 3C 273: if those lags do not fall in the 100–200 day range, or if the lag spectrum flattens or steepens beyond the optical bands, the claim that the disc extends to dust-forming radii and feeds the BLR is ruled out. A shorter-term test is to measure an absolute B-band lag independently (for example via X-ray or UV to optical cross-correlation) and check whether tau_0 = 19.7 days holds.

Watch

Extended reading notes

Core claim

3C 273's accretion disc is a factor of about 2–7 larger than predicted by the standard geometrically thin, optically thick disc model, based on inter-band continuum lags measured with two independent reverberation-mapping codes. The lag spectrum follows tau ∝ $\lambda$^$\beta$ with $\beta$ consistent with 4/3, so the disc matches the thin-disc temperature profile in shape but not in absolute size. A disc with a flat interior and a steep irradiated rim, parametrised following Starkey et al., fits both the observed lags and the variable-flux SED, placing the outer rim at roughly 120–150 light-days. Extrapolating the measured optical power law to the about 1000 K dust-sublimation region yields near-infrared lags of about 100–200 days, which match the BLR radius measured by near-infrared interferometry and the rim's outer edge; the paper therefore argues that the disc in 3C 273 may extend into dust-forming territory, so the broad-line region could emerge from a dusty disc wind.

Load-bearing premise

The dusty-disc and BLR conclusions assume that the lag–wavelength relation measured in the optical continues unchanged as the same power law out to about 2 microns, and that the back-calculated B-band reference lag of 19.7 days is the correct absolute zero-point.

Editorial extensions

If this is right

  • 3C 273 becomes a high-luminosity, near-Eddington data point in the 'accretion disc size problem', showing that the discrepancy is not confined to low-luminosity AGN.
  • The consistency of Javelin and PyROA lags, despite very different assumptions about the driving variability, suggests the measured disc sizes are robust to the choice of variability model for this data set.
  • If the steep-rim geometry is correct, the outer disc rim at roughly 120–150 light-days should shine at about 5000 K and produce a small near-infrared excess that can be searched for in the SED.
  • If the dusty-disc extension is right, the inner edge of the BLR in 3C 273 should coincide with the dust-sublimation temperature, providing a testable site for dusty-outflow BLR formation models.
  • For a rim at radius r_out, the mean rim lag scales as (r_out/c)(1 + (2/3) sin i), giving about 120 days face-on and about 180 days at inclination 45 degrees, so future near-infrared RM can also constrain the disc inclination.

Reading between the lines

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

  • The paper notes that a dedicated near-infrared RM campaign on 3C 273 has been completed by some of the authors with results forthcoming; if those measured JHK lags fall outside 100–200 days, the dusty-disc and BLR-connection conclusions would be directly falsified.
  • The absolute B-band reference lag of 19.7 days is itself back-calculated from the relative optical lags and the thin-disc normalisation; an independent absolute lag measurement, for example from X-ray or UV to optical cross-correlation, would test whether the extrapolated radii are an artefact of that zero-point.
  • Because the structure-function analysis finds a decorrelation timescale above roughly 300 days, monitoring longer than a decade is needed to distinguish the apparent ~3-year quasi-periodic trend from red noise; a confirmed periodicity would strengthen the disc-dominated variability interpretation.
  • The dusty-disc idea implies a continuous transition from accretion disc to torus, predicting that the hot-dust radius from near-infrared RM (about 400–900 light-days) is physically connected to the ~100–200 light-day disc rim, a relation testable with joint optical and near-infrared RM campaigns.
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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

3 major / 6 minor

Summary. The paper presents the first dedicated accretion disc reverberation mapping campaign of the quasar 3C 273, using seven optical bands from Las Cumbres Observatory over four observing seasons. Inter-band lags are measured with two independent codes, Javelin and PyROA, and the main analysis focuses on the third season, which has the largest variability amplitude. The claimed findings are: (i) the two codes give mutually consistent lags; (ii) the lags exceed thin-disc predictions by factors of ~2-7, placing 3C 273 in the 'accretion disc size problem' class; (iii) power-law fits tau ~ lambda^beta and nu f_nu ~ nu^beta are consistent with beta = 4/3; (iv) a flat disc with a steep rim can reproduce both the lags and the variable SED; and (v) extrapolating the optical lags to near-infrared wavelengths gives 100-200 light-day radii, matching the BLR radius and supporting a dusty-disc/BLR connection. Flux variation gradient and structure function analyses are used to argue that the variability is disc-dominated.

Significance. If the lags are robust, this is a valuable addition to the accretion disc RM sample because 3C 273 is a high-luminosity, near-Eddington quasar, whereas the 'disc size problem' has mostly been studied in lower-luminosity AGN. The paper has clear strengths: it presents season-resolved lag tables and MCMC corner plots for both codes, it uses a contemporaneous spectrum to estimate broad-line contamination, it checks the disc-variability assumption with two independent methods, and it makes an explicit, testable prediction for a near-infrared RM campaign. However, the headline size-problem claim is sensitive to the adopted black hole mass and the chosen Wien factor convention, and the near-infrared/BLR inference is an extrapolation based on the same optical lag data. These issues are correctable but affect the central conclusions as currently stated.

major comments (3)
  1. [Section 4.3, Table 3] The mass dependence of the predicted lags is misstated. Equation (5) gives tau0 proportional to M^(2/3) mdot^(1/3), and since mdot = L_acc/L_Edd with L_Edd proportional to M, for fixed L_acc one has mdot proportional to M^(-1) and hence tau0 proportional to M^(1/3). The claim in Section 4.1 that increasing the black hole mass to the Li et al. (2022) value of 1.15e9 M_sun makes the changes 'roughly cancel' is therefore not correct. Using M = 1.15e9 M_sun instead of 3e8 M_sun raises the predicted lags by (1.15/0.3)^(1/3) ~ 1.56. Applying this to the Year 3 lags in Table 5 lowers the X = 4.96 observed/predicted ratios from ~2-3 to roughly 1.0-1.9 (for example, the PyROA g-band ratio drops from ~3.0 to ~1.9, V from ~2.0 to ~1.3, and r from ~2.4 to ~1.5). The abstract's 'factor ~2-7' and the statement that 3C 273 joins the size-problem sample depend on the adopted mass, so the analysis should propagate the mass uncertainty and report the discrepancy under both the GRAVITY and Li et al. masses and both X conventions.
  2. [Section 5.4, Table 9] The decision to base the remaining analysis on Year 3 alone was made after inspecting the season-by-season results. The PyROA lags in Years 1 and 2 do not show the size excess claimed for Year 3: for example, Year 2 gives z = 6.2 days against an X = 4.96 prediction of 15.7 days, and Year 1 gives r = 5.0 days against 6.3 days. Only Year 3 shows the large lags used in Tables 5 and 8. Javelin lags are more stable across seasons, but the quoted uncertainties are internal to a single season and do not include season-to-season scatter. The paper also notes in Section 4.3 that the variability amplitude falls below the ~10% threshold recommended for RM. The authors should either report the all-season comparison in the size-problem analysis or justify the Year 3 choice with a clear, objective variability-based criterion rather than selecting the season that produces the desired lag pattern.
  3. [Section 5.4, Table 9] The near-infrared 'predictions' in Table 9 are not independent measurements or independent theoretical predictions. The absolute lags are computed by taking tau0 = 19.7 days, which is the average of values back-calculated from the observed optical differential lags in Table 5, and then extrapolating a fitted power law to 1.2-2.2 microns. This assumes that tau ~ lambda^beta continues unchanged beyond the observed bands. That assumption is directly challenged by the steep-rim model in Section 5.3, which predicts the rim response to become increasingly important at redder wavelengths. If the lag spectrum flattens or steepens beyond the i/z bands, the inferred 100-200 light-day dusty disc radii and the BLR connection would not follow. The BLR/FRADO conclusion should therefore be presented as a model-dependent consistency check rather than a measured result, and the abstract's causal 'therefore' should be softened accordingly.
minor comments (6)
  1. [Section 4.3, Table 3] The PyROA Year 4 lags (e.g., g = 52.9 days, z = 99.0 days) are close to or at the 100-day upper prior. The text calls these 'unrealistically large' but should state explicitly that they are prior-dominated, since this is part of the justification for excluding Year 4.
  2. [Section 4.2.2] The phrase 'Bayesian Information Criterion loss function' is imprecise; BIC is a model comparison criterion, not a loss function in the usual sense. Consider rewording to 'Bayesian Information Criterion penalty' or similar.
  3. [Section 5.4, Table 9] Table 9 quotes integer values for the extrapolated absolute lags without uncertainties. Since both beta and tau0 carry uncertainties, the JHK predictions should include propagated errors or at least a sensitivity range.
  4. [Section 5.3, Figure B4] The text reports k = 160 as the best-fit disc shape index, but the corner plot shows that log k flattens beyond log k ~ 2. The parameter k is therefore effectively a lower limit on the rim steepness, and the paper should describe it as such rather than as a tightly constrained index.
  5. [Appendix A] The outlier-rejection threshold chi^2 > 70 is presented without justification or a sensitivity test. A brief demonstration that the fitted lags are stable under different thresholds would strengthen confidence in the cleaned light curves.
  6. [Section 4.5, Eq. (16)] The structure function likelihood treats the N(N-1)/2 magnitude pairs as independent even though they share the same light curve. The quoted parameter uncertainties may therefore be underestimated; this should be acknowledged or tested with a bootstrap.

Circularity Check

1 steps flagged · score 4.0 of 10

Near-IR 'lag predictions' are calibrated from the same optical lags; the central size-problem comparison remains externally benchmarked and not circular.

  1. fitted input called prediction [Section 5.4, Table 9; Section 4.1 Eq. 4; Table 5 last column]
    "We have converted to rest-frame absolute values using the average of τ0 = 19.7 days from the estimated B-band rest-frame reference lags, excluding the u band, as listed in the last column of Table 5, which are required to bring the observations in agreement with theoretical predictions."

    The absolute near-IR lag 'predictions' in Table 9 are not derived from first principles. The zero-point τ0=19.7 d is the average of per-filter B-band reference lags obtained by forcing each observed optical differential lag (Table 5) onto the assumed τ∝λ^β relation (Eq. 4), while the slope β is fitted to the same observed lags in Section 5.2. Evaluating that fitted relation at JHK wavelengths therefore returns a deterministic rescaling of the already-measured optical lags, not an independent prediction of the dusty-disc model. The subsequent comparison to the GRAVITY BLR radius (145±35 d) is an external benchmark and does provide independent support, so the circularity is partial rather than total.

full rationale

The paper's central 'accretion disc size problem' claim is not circular: the observed differential lags (Table 5) are compared with predicted lags from Eq. 5, whose inputs (M_BH=3e8 Msun from GRAVITY, mdot_Edd=1.2 from an independent SED fit, and X=4.96 or 2.49) are external to the lag measurements. The beta≈4/3 checks are also external comparisons against a theoretical exponent. However, Section 5.4's near-IR 'predictions' (Table 9) are a calibrated extrapolation: τ0=19.7 days is the average of B-band reference lags 'required to bring the observations in agreement with theoretical predictions' (Table 5 last column), and β is fitted to the same observed lags, so the JHK values are deterministic rescalings of the optical data, not independent predictions. The comparison to the GRAVITY BLR radius is an external benchmark, so the paper's dusty-BLR inference retains independent support. The dismissal of the Li et al. (2022) mass as 'roughly canceling' is arithmetically questionable (Eq. 5 gives τ0 ∝ M^{1/3} at fixed L_acc, raising predicted lags by ~1.56 for M=1.15e9 Msun and reducing the quoted discrepancy factors), but that is a robustness/correctness concern, not circularity. Self-citations to Starkey et al. (2023) and Landt et al. (2011) are not load-bearing: the former is a model applied as a fit, not a uniqueness theorem, and the latter is a luminosity estimate.

Assumptions & free parameters 17 free parameters · 6 assumptions · 0 invented entities

The ledger separates standard AGN model inputs from parameters fitted or chosen in this paper. The predicted lag scale in Eq. (5) depends on externally measured black hole mass and Eddington ratio, and on the chosen Wien factor X. The steep-rim model contributes eight fitted parameters. The near-IR lag predictions require a fitted power-law beta and a back-calculated B-band reference lag tau0. No new particles or forces are introduced.

free parameters (17)
  • Black hole mass M_BH = 3e8 M_sun (GRAVITY 2018)
    Input to Eq. (5) that sets the thin-disc lag normalization; a mass of 1.15e9 M_sun (Li et al. 2022) would raise predicted lags by roughly 50 percent and reduce the size-problem factor.
  • Eddington ratio mdot_Edd = 1.2 (from L_acc = 4.5e46 erg/s)
    Estimated from fitting the continuum in the MIKE spectrum; enters Eq. (5) via mdot_Edd.
  • Wien factor X = 4.96 and 2.49
    Chosen blackbody prescriptions convert wavelength to disc radius; the choice changes predicted lags by about a factor of 2.5 and hence contributes to the reported 2-7x size-problem range.
  • Lag power-law index beta (free fit) = 1.01 +/- 0.39 PyROA; 1.59 +/- 0.29 Javelin; 1.17 +/- 0.25 combined
    Fitted to observed optical lags in Section 5.2 and used to extrapolate to near-IR in Table 9.
  • B-band reference lag tau0 = 19.7 days
    Back-calculated from observed relative lags by assuming tau ~ lambda^(4/3); used to convert relative lags into absolute near-IR lag predictions.
  • Steep-rim accretion rate = ~1.6 M_sun/yr (i=0); ~3.0 M_sun/yr (i=45)
    MCMC parameter in the steep-rim SED plus lag fit, Section 5.3.
  • Lamp-post efficiency eps_LP = 1
    Fitted dimensionless reprocessing efficiency in the steep-rim model.
  • Lamp-post height H_LP = 4 r_g
    Fitted height of the irradiating lamp-post above the disc.
  • Inner disc radius r_in = ~r_g (near ISCO)
    Fitted inner radius; the paper notes inner-disc parameters are less reliable because relativistic and Compton effects are ignored.
  • Outer disc radius r_out = 120-150 light-days
    Fitted outer edge of the steep-rim disc; compared with the BLR radius in Section 5.4.
  • Rim height H_out/r_out = ~0.8%
    Fitted scale height at the outer radius.
  • Disc shape index k = 160
    Fitted power-law index for the disc height profile; posterior flattens for log k > 2.
  • SED model uncertainty sigma_SED = 10%
    Fitted uncertainty added to the SED model, Section 5.3.
  • Disc inclination = 0 or 45 degrees
    Fixed by hand in the model fits; affects the mean rim lag by a factor 1 + (2/3) sin i.
  • Javelin DRW timescale prior = 50 < tau_d < 300 days
    Imposed in Section 4.2.1 to constrain the fits; influences the modelled driving light curve.
  • PyROA smoothing width Delta = 20-30 days
    Uniform prior chosen to prevent overfitting; controls the flexibility of the running optimal average.
  • Outlier rejection threshold = chi^2_threshold = 70
    Chosen in Appendix A to remove outliers from the structure-function-based rejection.
assumptions (6)
  • domain assumption Shakura-Sunyaev geometrically thin, optically thick disc with local blackbody emission and T(r) proportional to r^(-3/4)
    Used in Section 4.1 to derive lag predictions Eq. (4)-(5); this is the standard model being tested, so the size-problem claim is relative to it.
  • domain assumption Reverberation lags are dominated by light-travel time, tau = r/c, with a linear echo model Eq. (3)
    Stated in the introduction and used by Javelin and PyROA; if variability propagates rather than reprocesses, inferred radii change.
  • domain assumption Wien factor X maps blackbody temperature and wavelength to radius, Eq. (6)
    Converts each filter's effective wavelength to a characteristic disc radius; different X values give factor-2.5 normalization shifts.
  • domain assumption A compact lamp-post X-ray source irradiates the disc and drives the optical variability
    Used in the steep-rim model Section 5.3; the lamp-post is not directly observed and the paper notes the X-ray-driving picture is debated.
  • domain assumption The broad-line flux contamination in each filter, estimated from one MIKE spectrum, is correct
    Used to interpret lag biases and to omit u and i bands from fits; a single epoch spectrum may not represent time-varying line flux.
  • domain assumption The variable component of the light curves follows a single linear response model with additive host-galaxy flux
    Flux-flux analysis Eq. (12) assumes a non-varying host plus a varying disc; diffuse BLR continuum can also contribute to the non-varying component.

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Pith. "Pith review of Accretion disc reverberation mapping of the quasar 3C 273." pith.science (2026). https://pith.science/paper/QFMUG72O

@misc{pith2026250208366,
  author       = {Pith},
  title        = {Pith review of: Accretion disc reverberation mapping of the quasar 3C 273},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QFMUG72O}},
  note         = {Machine review of arXiv:2502.08366}
}
read the original abstract

We present accretion disc size measurements for the well-known quasar 3C 273 using reverberation mapping (RM) performed on high-cadence light-curves in seven optical filters collected with the Las Cumbres Observatory (LCO). Lag estimates obtained using Javelin and PyROA are consistent with each other and yield accretion disc sizes a factor of ~2-7 larger than `thin disc' theoretical expectations. This makes 3C 273 one of a growing number of active galactic nuclei (AGN) to display the so-called `accretion disc size' problem usually observed in low-luminosity AGN. Power-law fits of the form tau~lambda^beta to the lag spectrum, and nufnu ~ nu^beta to the spectral energy distribution (SED) of the variations, both give results consistent with the `thin disc' theoretical expectation of beta=4/3. The Starkey et al. `flat disc with a steep rim' model can fit both the lag estimates and the SED variations. Extrapolating the observed optical lags to putative dust-forming regions of the disc gives r~100-200 light-days. These radii are consistent with the size of the broad line region (BLR) as determined by near-infrared interferometric studies as well as with the best-fit location of the outer edge for the `flat disc with a steep rim' model. Therefore, the accretion disc in 3C 273 might be sufficiently extended to be dusty, allowing the BLR to emerge from it in a dusty outflow. A flux variation gradient analysis and the structure function of our LCO light-curves confirm that the optical variability in 3C 273 is dominated by the accretion disc rather than its radio jet.

Figures

Figures reproduced from arXiv: 2502.08366 by the authors.

Figure 1
Figure 1. Multi-band LCO light-curves of 3C 273 between 2019 Jan and 2022 Apr. Flux units are in mJy and time is represented as modified Julian date. MNRAS 000, 1–18 (2025) [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Contemporaneous optical spectrum of 3C 273 obtained with the high-resolution echelle spectrograph MIKE. Overplotted are the photometric filter centres and widths used to obtain our light-curve data. Here the reference level ¯𝑓C, typically a mean or median of the con￾tinuum light curve, corresponds to a mean flux ¯𝑓L in the lagged echo light curve. The ‘transfer function’ 𝜓(𝜏), a distribution over time de￾lay 𝜏, desc… view at source ↗
Figure 3
Figure 3. Javelin fits to the detrended Year 3 light-curves observed for 3C 273. Fluxes are in mJy and time is represented as modified Julian date. MNRAS 000, 1–18 (2025) [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: PyROA fits of the model 𝐹(𝜆, 𝑡) = 𝐵(𝜆) + 𝐴(𝜆) 𝑋(𝑡 − 𝜏 (𝜆) ) to the detrended Year 3 light-curves observed for 3C 273. Fluxes are in mJy and time is represented as modified Julian date. The light-curve shape 𝑋(𝑡) is a running optimal average over all the data, with a Ga…
Figure 5
Figure 5. Figure 5: Flux-flux analysis of 3C 273 based on correlated variations in 3- band UV fluxes from Swift and 7-band optical fluxes from LCO. Fluxes at different brightness levels are plotted against the model driving light-curve 𝑋0 (𝑡) (running optimal average fitted with PyROA). T…
Figure 6
Figure 6. Figure 6: SEDs for the host galaxy (red) and the AGN component in faint (orange) and bright (blue) state inferred from the flux-flux analysis shown in [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: Structure function (SF) analysis of the 𝑢-band light-curve. Each blue dot corresponds to the change in the magnitude Δ𝑚𝑖 𝑗 for a pair of data points separated in (rest-frame) time by Δ𝑡 = (𝑡𝑗 −𝑡𝑖 )/(1+𝑧) with 𝑡𝑗 > 𝑡𝑖 . The grey shaded area shows the fit to the SF varia…
Figure 8
Figure 8. Figure 8: Structure function fitting results for the 10-day rms amplitude 𝐴(𝜆) (coloured circles) compared with the rms variability amplitude, Δ𝐹𝜈 (coloured triangles) from the flux-flux analysis (see [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 10
Figure 10. Figure 10: Spectrum of 3C 273 taken from the MIKE spectrograph plotted in a logarithmic form. A power law is fit which returns a measured power law exponent 𝛽 = 1.35 ± 0.13 monochromatic luminosity 𝜈 𝐿𝜈. Also shown is a power-law model (black dashed line) that traces the spectra…
Figure 9
Figure 9. Figure 9: Power-law models, 𝜏 ∝ 𝜆 𝛽 , fit to the RM lag results from [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]
Figure 11
Figure 11. Figure 11: Simultaneous fit to the SED and delay spectrum of 3C 273. Upper left: Geometry of the accretion disc with the fitted parameters. The black curve shows an nearly-flat discs with a relatively steep rim that rises to 𝐻out = 𝐻 (𝑟out) ≈ 1 light days (𝐻/𝑟 ≈ 0.8%) at the out…
Figure 12
Figure 12. Figure 12: Extrapolation of the 𝜏 ∝ 𝜆 𝛽 power law fit to the combined PyROA and Javelin RM results into the near-infrared 𝐽𝐻𝐾 regime. This allowed the lag predictions in [PITH_FULL_IMAGE:figures/full_fig_p016_12.png]
Figure 13
Figure 13. Figure 13: LCO light-curves each fitted with a sinusoidal function. The light-curves have been colour-coded according to their photometric band. For reference, the maximum of each sine wave is also plotted (diamonds) [PITH_FULL_IMAGE:figures/full_fig_p017_13.png]
Figure 14
Figure 14. Figure 14: The lag spectrum for the fitted trends in [PITH_FULL_IMAGE:figures/full_fig_p017_14.png]

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