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A Bayesian Approach to Inferring Accretion Signatures in Young Stellar Objects: A Case Study with VIRUS

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper claims that a Bayesian fitting tool called nuts-for-ysos can derive reliable accretion luminosities and mass accretion rates for young stellar objects from low-resolution optical spectra, with full posterior uncertainties, and…

desk verdict A genuinely useful public Bayesian fitting tool for YSO accretion, whose 'verification' is really a consistency check because the line calibrations and literature comparisons share the same slab-model bolometric correction. read the letter →

arxiv 2501.10500 v2 pith:EGE7FFOB submitted 2025-01-17 astro-ph.SR astro-ph.GAastro-ph.IM

Lauren Halstead Willett , Joe P. Ninan , Suvrath Mahadevan , Gregory R. Zeimann , Steven Janowiecki , Gary J. Hill This is my paper · ORCID
classification astro-ph.SRastro-ph.GAastro-ph.IM
keywords youngstellarobjectsaccretionluminositymassrateBayesianinferenceNoU-TurnSamplerVIRUSspectrographBalmercontinuumphotospherictemplates
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

The paper develops a Bayesian framework, packaged as nuts-for-ysos, to fit a simple accretion model to the blue-optical continuum of young stellar objects and to extract accretion luminosities and mass accretion rates with complete uncertainty distributions. It applies this framework to 15 YSOs observed with the VIRUS spectrograph. The derived accretion rates agree with independent estimates from emission-line luminosities and with published results for the Lupus, Chamaeleon I, and NGC1333 regions. This matters because accretion rates connect disk evolution and planet formation, and the method offers a path to analyze large spectroscopic surveys of star-forming regions while quantifying parameter degeneracies.

What carries the argument

The load-bearing mechanism is a seven-parameter composite model of a YSO's blue-optical continuum: an isothermal hydrogen LTE slab (parameters Tslab, ne, tau0, and scaling Kslab) added to a scaled class III photospheric template (effective temperature Teff and scaling Kphot), then reddened by extinction AV. The argument is carried by the No-U-Turn Sampler, which explores the posterior over these parameters; to make Teff continuous, the code linearly interpolates between 23 observed class III templates whose fluxes and luminosities have been rescaled to follow a smooth polynomial relation. This machinery converts the previous discrete-grid chi-squared fitting approach into a full Bayesian inference that can report covariances and per-object uncertainty distributions for Lacc and Macc.

What would settle it

Take a set of YSOs with accretion luminosities measured independently from space-based ultraviolet spectra, fit the same VIRUS-resolution spectra with nuts-for-ysos, and check whether the posterior distributions for Lacc overlap the independent values: a systematic exclusion would show that the slab-model bolometric correction, the paper's load-bearing assumption, is biased.

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Extended reading notes

Core claim

The central claim is that a Bayesian implementation of the standard continuum model can reliably recover the accretion luminosity and mass accretion rate of a young stellar object from a single low-resolution (R~800) optical spectrum, demonstrated on 15 YSOs observed with VIRUS. The method treats all seven model parameters as random variables and samples their joint posterior with the No-U-Turn Sampler, so that uncertainties in distance, extinction, template luminosity, spectral type, and the accretion model itself propagate into Lacc and Macc as full probability distributions. The derived values agree with emission-line-based accretion luminosities using the Alcalá et al. (2017) relations and occupy the same range as published results for Lupus, Chamaeleon I, and NGC1333. The authors further report that the slab parameters are largely nuisance parameters, that Lacc correlates strongly with extinction AV, and that five of the fifteen objects have accretion components consistent with zero and are therefore reported as upper limits.

Load-bearing premise

The results hinge on the assumption that integrating the isothermal hydrogen slab flux over 500-25000 Å gives the correct bolometric correction for the true accretion luminosity, even though the slab model is not physically tied to magnetospheric accretion.

Editorial extensions

If this is right

  • With nuts-for-ysos, the same fitting procedure can be applied to spectra from other spectrographs by changing the spectral feature set; the authors demonstrate runs on HST STIS and X-Shooter spectra.
  • Because the tool outputs posterior distributions for Lacc and Macc, future studies can quantify degeneracies such as the AV-Lacc correlation instead of quoting approximate 0.25 dex uncertainties.
  • The method can identify weak accretors: five objects in the sample have slab components consistent with zero and are reported as upper limits, including two class II objects.
  • Applied to larger VIRUS or other survey samples, the framework could populate the M*-Macc plane across many star-forming regions, which the authors argue is needed to understand the scatter in the mass-accretion relation.

Reading between the lines

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

  • If the slab bolometric correction is biased, the emission-line check inherits the same bias because the Alcalá et al. (2017) Lline-Lacc relations were calibrated with the same slab method; an independent calibration would be required to break that circularity.
  • The strong AV-Lacc correlation implies that for blue-limited, low-resolution spectra, extinction uncertainty sets a floor on how precisely any single-epoch accretion rate can be measured; adding longer-wavelength photometry should reduce it, which is a testable expectation.
  • The same template-interpolation and posterior machinery could be transferred to other continuum-excess problems in YSO physics, such as veiling at higher resolution or near-infrared excesses, where similar degeneracies are present.
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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 / 4 minor

Summary. The paper presents nuts-for-ysos, a Bayesian (NUTS-based) framework that fits a simple isothermal LTE hydrogen-slab accretion model plus a class III photospheric template to low-resolution VIRUS spectra of 15 YSOs, simultaneously inferring Teff, AV, stellar luminosity, accretion luminosity, and mass accretion rate with full posterior uncertainties. The authors apply the code to archival VIRUS parallel observations, derive Lacc and Macc for the sample (with upper limits for five objects), and test the results against emission-line-based accretion luminosities using the Alcalá et al. (2017) Lline-Lacc relations and against literature values from Lupus, Chamaeleon I, and NGC 1333. The paper emphasizes that the Bayesian approach quantifies parameter covariances and uncertainties more completely than previous grid-based direct-method analyses, and it publicly releases the code and a Zenodo archive.

Significance. If the inferred accretion luminosities are reliable, the paper is a useful proof of concept: it demonstrates that a Bayesian sampler can be applied to the standard slab-plus-template continuum-fitting method, that the resulting posteriors expose degeneracies (notably AV-Lacc) that grid methods obscure, and that the tool can be transferred to other spectrographs. The public release of nuts-for-ysos and the explicit convergence checks (Rhat <= 1.1, thinning, posterior simulation) are strengths, as is the careful construction of the sample from HETVIPS data. The central limitation is that the verification is largely consistency testing rather than independent validation: the emission-line relations and most literature comparisons inherit the same slab-model bolometric correction, so a systematic bias in Lacc would propagate through the apparent agreement. The paper is honest about the slab model's lack of physical basis, but does not quantify the resulting systematic uncertainty in the final Macc values.

major comments (3)
  1. [Section 6 and Section 7.2] The validation is not independent of the fitting method. The Lline-Lacc relations from Alcalá et al. (2017) were calibrated using Lacc values obtained with the same slab-model continuum-fitting approach (Manara et al. 2013a), and the literature comparisons in Section 7.2 are dominated by studies that use the same direct slab method or, for Object 14, the Alcalá et al. (2017) relations. Thus the approximate 1:1 agreement in Figure 15 and the overlap in Figures 18 and 20 demonstrate self-consistency within the slab-model framework, not independent confirmation that the slab bolometric correction is correct. The paper should either add a genuinely independent test (e.g., shock-model-based Lacc estimates, or spectrally resolved Balmer-continuum studies) or explicitly reframe the claims of 'reliability' as consistency checks within the standard method.
  2. [Section 5.2 and Section 7.1] The derivation of Lacc integrates the slab flux over 500-25000 A, but the paper's own justification for the slab model is limited to agreement with shock models at wavelengths below about 3000 A, and the cited literature (Ingleby et al. 2013) shows that the slab and shock models diverge at longer wavelengths. If the bolometric correction from the isothermal LTE slab is biased over this full range, every Lacc and Macc in Tables 5 and 6 is biased in the same direction, and the emission-line and literature checks in Section 6 inherit that bias. The authors should quantify the sensitivity of Lacc to the integration range and to the choice of slab versus shock-model spectral shape, or present the bolometric-correction uncertainty as a dominant systematic term.
  3. [Section 4.3.1] The procedure of rescaling all photospheric template fluxes and luminosities so that their median fluxes follow a fourth-degree polynomial is an ad hoc renormalization that could affect the inferred Teff, Kphot, and hence Lstar and Mstar. The paper asserts that this 'does not fundamentally change the nature of the results' but provides no test of that assertion. Since Teff and Lstar feed into the mass and accretion-rate estimates via the evolutionary-track interpolation, the authors should demonstrate with a sensitivity analysis (e.g., fitting with and without the polynomial rescaling, or comparing against the original template grid) that the derived physical parameters are robust to this choice.
minor comments (4)
  1. [Section 6] The text states that the Alcalá et al. (2017) relations are 'completely independently derived' from the present data; this is true in the sense that they were calibrated on a different sample, but it is misleading because they were calibrated using the same slab-based direct method. Please rephrase to make the distinction between independence of data and dependence on the same accretion model clear.
  2. [Section 6, Object 12 discussion] The sentence 'the class III Object 12, which has Lacc,line = 0.36' appears to be missing a logarithm or a unit; presumably log(Lacc,line/Lsun) is meant. Please correct and ensure the value is shown with the same convention as in Table 5.
  3. [Table 5] For Objects 4 and 13, the table lists approximate values without uncertainties for several entries, while for other objects uncertainties are given. Please include a note or symbols indicating which quantities are approximate due to the Teff boundary issue, and consider providing the full posterior summaries for these objects in the appendix.
  4. [Section 4.3.2 and Section 5] The prior table lists the effective-temperature uncertainty as a bounded Normal distribution, but the text does not fully explain how this prior interacts with the template interpolation when Teff is near the grid edges. A sentence clarifying the behavior at the edges would help the reader assess the two boundary cases reported in Section 5.

Circularity Check

3 steps flagged · score 4.0 of 10

The central Bayesian Lacc fit is not circular, but the emission-line and literature verifications share the slab-model calibration used to build the comparison relations, so the validation is only partly independent.

  1. fitted input called prediction [Sections 4.1 and 6 (Alcalá et al. 2017 calibration description)]
    "We use a slab of isothermal hydrogen in local thermodynamic equilibrium (LTE) ... This approach has been used numerous times in the past to derive accretion luminosities (e.g. ... Manara et al. (2013a); Alcalá et al. (2014, 2017)). ... Alcalá et al. (2017) studied X-shooter spectra of 81 class II or transition disk YSOs in Lupus, using the 'direct' method on each YSO by fitting the continuum model to each spectrum. They then updated empirical linear relationships between Lline and Lacc to calibrate the 'indirect' method."

    The paper calls the emission-line check 'independently derived,' but the Alcalá et al. (2017) Lline-Lacc relations were calibrated against Lacc obtained with the same isothermal LTE slab 'direct' method that nuts-for-ysos uses. Applying those relations to VIRUS line luminosities therefore produces Lacc,line values that track slab-model Lacc by construction. A systematic error in the slab bolometric correction (e.g., from integrating the slab over 500-25000 Å when the model is justified mainly at <3000 Å) would appear on both sides of Figure 15, so the 1:1 agreement does not validate the model's absolute scale.

  2. other [Section 7.2, comparison with Lupus, Chamaeleon I, and NGC1333]
    "With our small sample we can at least note that our results for the L∗-Lacc plot (Figure 8) and M∗-Macc plots (Figures 11 and 12) occupy a similar range as previous studies of various star-forming regions. ... Figure 18 shows that the L∗ and Lacc of our class II sample follow a loose linear relationship in agreement with these three star-forming regions."

    The comparison values are not independent of the slab model: the Lupus (Alcalá et al. 2017) and Chamaeleon I (Manara et al. 2016) studies derive Lacc with the same direct slab-continuum method, and the NGC1333 comparison (Fiorellino et al. 2021) uses Pa-beta/Br-gamma relations from Alcalá et al. (2017), themselves slab-calibrated. Agreement with these samples therefore confirms consistency with earlier applications of the same model, but cannot detect a shared systematic bias in the slab bolometric correction.

1 more flagged steps
  1. other [Section 6, extinction correction of line fluxes]
    "We correct the emission line fluxes for extinction using the AV derived from the continuum-fitting process in Section 4. We use the same AV so that the the direct and indirect methods can be consistently compared."

    Both the continuum-derived Lacc and the line-derived Lacc,line are corrected with the same fitted AV posterior. If AV is biased, the two estimators shift together, so part of the Figure 15 agreement is inherited from this shared fitted input rather than from an independent measurement. This couples the two sides of the 'verification' without making the central fit definitional.

full rationale

The central derivation is not circular: nuts-for-ysos fits the slab plus photospheric template to continuum features (Section 4), then computes Lacc by integrating the fitted slab flux over 500-25000 Å (Section 5.2). That Lacc is a function of the fitted model, not an input, and the code was also tested for compatibility on HST ULYSSES and X-Shooter data. The circularity is confined to the validation layer. The paper explicitly describes the emission-line check as 'independently derived,' but the Alcalá et al. (2017) relations were calibrated on Lacc from the same isothermal LTE slab 'direct' method, and the paper itself notes the slab has no basis in the magnetospheric accretion picture (Sections 4.1 and 7.1). Consequently, the near-1:1 agreement in Figure 15 and the agreement with literature samples in Figures 18 and 20 are partly guaranteed by shared model assumptions and shared fitted AV, so they cannot validate the slab's bolometric correction. This is a real limitation of the verification, but the Bayesian estimation machinery, uncertainty propagation, and parameter-correlation results still have independent content. Score 4 (partial circularity in validation, not in the main derivation).

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

The central result relies on the slab model for the bolometric correction, the template library for the photosphere, and a set of priors for distances and template uncertainties. No new physical entities are introduced.

free parameters (8)
  • Tslab = posterior, bounded 5000-11000 K
    Slab electron temperature; fitted with uniform prior.
  • ne = posterior, bounded 1e10-1e16 cm-3
    Slab electron density; fitted with log-uniform prior.
  • tau0 = posterior, bounded 0.01-5.0
    Slab optical depth at 300 nm; fitted with uniform prior.
  • Kslab = posterior, >0
    Scale factor of the accretion slab; fitted with HalfFlat prior.
  • Kphot = posterior, >0
    Scale factor of the photospheric template; fitted with HalfFlat prior.
  • Teff = posterior, bounded 2615-5550 K
    Effective temperature from interpolated template; fitted with uniform prior plus a bounded normal uncertainty term.
  • AV = posterior, bounded 0-10 mag
    Extinction toward the target; fitted with uniform prior plus a Half-Normal template AV term.
  • Fourth-degree polynomial for template flux rescaling = coefficients from fit to 23 template median fluxes
    The templates are rescaled to make Teff interpolable; this data-driven adjustment is not propagated as an uncertainty.
assumptions (6)
  • domain assumption Isothermal hydrogen LTE slab model represents the accretion excess continuum
    Used in Section 4.1; the paper notes the slab is a simplified empirical model without basis in the magnetospheric accretion paradigm.
  • domain assumption Class III YSO spectra are valid photospheric templates for class II YSOs
    Section 4.1; templates from Manara et al. (2013b) and Manara et al. (2017a) with AV close to zero.
  • domain assumption Cardelli et al. (1989) reddening law with R_V=3.1 applies
    Used to redden model spectra and correct line fluxes.
  • domain assumption Bailer-Jones et al. (2021) geometric distances with generalized gamma prior are correct
    Section 4.3.2; distances used to convert flux to luminosity.
  • domain assumption PMS evolutionary tracks (Baraffe+15, Siess+00) map Teff and L* to mass
    Section 5.3; used for M* and Macc.
  • domain assumption Alcala et al. (2017) Lline-Lacc relations apply to these targets
    Section 6; used for the emission-line validation, but calibrated with the same direct method.

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Cite this review

Pith. "Pith review of A Bayesian Approach to Inferring Accretion Signatures in Young Stellar Objects: A Case Study with VIRUS." pith.science (2026). https://pith.science/paper/EGE7FFOB

@misc{pith2026250110500,
  author       = {Pith},
  title        = {Pith review of: A Bayesian Approach to Inferring Accretion Signatures in Young Stellar Objects: A Case Study with VIRUS},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EGE7FFOB}},
  note         = {Machine review of arXiv:2501.10500}
}
abstract

The mass accretion rates of young stellar objects (YSOs) are key to understanding how stars form, how their circumstellar disks evolve, and even how planets form. We develop a Bayesian framework to determine the accretion rates of a sample of 15 YSOs using archival data from the VIRUS spectrograph ($R \sim 800$, 3500-5500\r{A}) on the Hobby-Eberly Telescope. We are publicly releasing our developed tool, dubbed nuts-for-ysos, as a Python package which can also be applied to other spectroscopic datasets. The nuts-for-ysos code fits a simple accretion model to the near-UV and optical continuum of each VIRUS spectrum. Our Bayesian approach aims to identify correlations between model parameters using the No U-Turn Sampler (NUTS). Moreover, this approach self-consistently incorporates all parameter uncertainties, allowing for a thorough estimation of the probability distribution for accretion rate not accomplished in previous works. Using nuts-for-ysos, we derive accretion rates of each YSO. We then verify the reliability of our method by comparing to results separately derived from only the spectral emission lines, and to results from earlier studies of the Lupus, Chamaeleon I, and NGC1333 regions. Finally, we discuss what qualitative trends, covariances, and degeneracies were found among model parameters. The technique developed in this paper is a useful improvement that can be applied in the future to larger samples of YSOs observed by VIRUS or other spectrographs.

Figures

Figures reproduced from arXiv: 2501.10500 by the authors.

Figure 1
Figure 1. The median values of each photospheric template flux, after being multiplied by its squared distance. A fourth￾degree polynomial is fit to the medians, and the template fluxes and respective luminosities are then rescaled to match this polynomial. tral flux of an inputted template grid, such as those acquired from FRAPPE. 4.3.2. Priors After making the adjustment so the Tef f parameter is continuous rather than disc… view at source ↗
Figure 2
Figure 2. A diagram illustrating the components of the YSO model. Parameters which are fitted for are highlighted in yellow. The shape of each prior is shown using Kruschke-style plots. Each prior has a color-coded arrow indicating whether it belongs to the slab portion, the photospheric portion, or to the entire composite model (black, green, and blue, respectively) [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. The median model fit resulting from testing nuts-for-ysos on HST STIS G430L and G750L data of Sz97, considering 14 different continuum features between ∼ 3300˚A and ∼ 6000˚A [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (46 more)
Figure 4
Figure 4. Figure 4: Object 16 (ATO J052.3580+31.4444), the one YSO in our current sample for which we were unable to fit a model including accretion. Instead, we fit the spectrum (red) with only a reddened Class III template (green) having Teff ≈ 5500K and AV ≈ 3.2. that goes all the way …
Figure 5
Figure 5. Figure 5: The YSO model fit to VIRUS spectra of class II and class III YSOs. On the top left of each plot is the object ID originating in Tables 1 and 10. The VIRUS spectrum (red) has a model fit to its continuum (blue), which is the sum of the hydrogen accretion slab (black) an…
Figure 6
Figure 6. Figure 6: Comparison of Kslab posteriors (expressed as log(106 ∗ Kslab)) for Object 8 vs. Object 10. In blue is the original Kslab posterior, using the uniform prior for Kslab that was introduced in Section 4.3.2 and [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 7
Figure 7. Figure 7: An example corner plot for the fit of an accreting YSO model to the spectrum of Object 11 (2MASS J03285101+3118184). Included are the model parameters as well as the log(L∗) and log(Lacc) posteriors. The corner plots for all fits are in the in Appendix B [PITH_FULL_I…
Figure 8
Figure 8. Figure 8: Plot of log(Lacc) vs. log(L∗) for the class II and class III YSO targets. Class II YSOs are plotted in black, and the class III objects are plotted in green. Upper limits on logLacc are denoted with downward arrows instead of errorbars. Object 12 has an upper limit for…
Figure 9
Figure 9. Figure 9: Hertzsprung-Russell diagram for the total sample, plotted over evolutionary tracks (blue lines) and isochrones (dashed red lines) from Baraffe et al. (2015). Class II YSOs are plotted in black, and class III YSOs in green. Objects 4 and 13 have only approximate L∗ and …
Figure 10
Figure 10. Figure 10: Hertzsprung-Russell diagram for the total sample, plotted over evolutionary tracks (blue lines) and isochrones (dashed red lines) from Siess et al. (2000). Plotting conventions are the same as in [PITH_FULL_IMAGE:figures/full_fig_p021_10.png]
Figure 11
Figure 11. Figure 11: Plot of log(Macc) vs. log(M∗) for our YSO sample, using masses derived from the Baraffe et al. (2015) evolutionary model. Class II YSOs are shown in black, and class III YSOs in green. Objects are annotated with their indices according to 10. Upper limits on log(Macc)…
Figure 12
Figure 12. Figure 12: Plot of log(Macc) vs. log(M∗) for our YSO sample, using masses derived from the Siess et al. (2000) evolutionary model. Plotting conventions are the same as 11. Object 13 does not fall within the mass range of Siess et al. (2000) and is not included in this plot. Obje…
Figure 13
Figure 13. Figure 13: Continuum-derived accretion luminosity Lacc of both the class II and class III sample plotted against line luminosity for a variety of emission lines studied in Alcal´a et al. (2017). Each emission line is labeled on the top left of the plot. For the class II YSOs, de…
Figure 14
Figure 14. Figure 14: Continuum-derived accretion luminosity Lacc of both the class II and class III sample plotted against line luminosity for a variety of emission lines studied in Alcal´a et al. (2017). The plot conventions are the same as [PITH_FULL_IMAGE:figures/full_fig_p024_14.png]
Figure 15
Figure 15. Figure 15: The average Lacc,line plotted against the continuum-derived Lacc for the class II stars (black) as well as Object 13, a class III star (green). Lacc,line is derived us￾ing emission line luminosities and the relations from Alcal´a et al. (2017). Objects 4 and 13, havin…
Figure 17
Figure 17. Figure 17: The overlaid posteriors for log(Lacc) and log(L∗) versus AV , for every object in our sample in which log(Lacc) is not an upper limit or is approximated. A strong correlation can be seen between AV and log(Lacc) in particular. the model: Tslab, ne, and τ0. This is tru…
Figure 18
Figure 18. Figure 18: Plot of the continuum-derived log(Lacc) vs. log(L∗) for the class II targets of our sample, compared to the results for class II YSOs from Lupus (Alcal´a et al. 2017), Chamaeleon I (Manara et al. 2016), and NGC1333 (Fiorellino et al. 2021). These three sets are plotte…
Figure 19
Figure 19. Figure 19: Plot of log(Macc) vs. the spectral index α used for YSO classification in Section 3. Class II YSOs are plotted in black, and Class III YSOs are plotted in green. Upper limits in Macc are denoted by downward triangles. Objects 4 and 13, having only an approximate Macc,…
Figure 20
Figure 20. Figure 20: Plot of log(Macc) vs. log(M∗) for the class II targets of our current sample, compared to the results for class II YSOs from Lupus (Alcal´a et al. 2017), Chamaeleon (Manara et al. 2016), and NGC1333 (Fiorellino et al. 2021). These three sets are plotted in magenta, bl…
Figure 21
Figure 21. Figure 21: The median model fit for Object 1 and the parameter posteriors below (the median parameters marked with a vertical gray dotted line) [PITH_FULL_IMAGE:figures/full_fig_p037_21.png]
Figure 22
Figure 22. Figure 22: The corner plot for Object 1, for model parameters and the log(L∗) and log(Lacc) posteriors [PITH_FULL_IMAGE:figures/full_fig_p037_22.png]
Figure 23
Figure 23. Figure 23: The median model fit for Object 2 and the parameter posteriors with the same plotting convention as [PITH_FULL_IMAGE:figures/full_fig_p038_23.png]
Figure 24
Figure 24. Figure 24: The corner plot for Object 2, for model parameters and the log(L∗) and log(Lacc) posteriors [PITH_FULL_IMAGE:figures/full_fig_p038_24.png]
Figure 25
Figure 25. Figure 25: The median model fit for Object 3 and the parameter posteriors with the same plotting convention as [PITH_FULL_IMAGE:figures/full_fig_p039_25.png]
Figure 26
Figure 26. Figure 26: The corner plot for Object 3, for model parameters and the log(L∗) and log(Lacc) posteriors [PITH_FULL_IMAGE:figures/full_fig_p039_26.png]
Figure 27
Figure 27. Figure 27: The median model fit for Object 4 and the parameter posteriors with the same plotting convention as [PITH_FULL_IMAGE:figures/full_fig_p040_27.png]
Figure 28
Figure 28. Figure 28: The corner plot for Object 4, for model parameters and the log(L∗) and log(Lacc) posteriors [PITH_FULL_IMAGE:figures/full_fig_p040_28.png]
Figure 29
Figure 29. Figure 29: The median model fit for Object 5 and the parameter posteriors with the same plotting convention as [PITH_FULL_IMAGE:figures/full_fig_p041_29.png]
Figure 30
Figure 30. Figure 30: The corner plot for Object 5, for model parameters and the log(L∗) and log(Lacc) posteriors [PITH_FULL_IMAGE:figures/full_fig_p041_30.png]
Figure 31
Figure 31. Figure 31: The median model fit for Object 6 and the parameter posteriors with the same plotting convention as [PITH_FULL_IMAGE:figures/full_fig_p042_31.png]
Figure 32
Figure 32. Figure 32: The corner plot for Object 6, for model parameters and the log(L∗) and log(Lacc) posteriors [PITH_FULL_IMAGE:figures/full_fig_p042_32.png]
Figure 33
Figure 33. Figure 33: The median model fit for Object 7 and the parameter posteriors with the same plotting convention as [PITH_FULL_IMAGE:figures/full_fig_p043_33.png]
Figure 34
Figure 34. Figure 34: The corner plot for Object 7, for model parameters and the log(L∗) and log(Lacc) posteriors [PITH_FULL_IMAGE:figures/full_fig_p043_34.png]
Figure 35
Figure 35. Figure 35: The median model fit for Object 8 and the parameter posteriors with the same plotting convention as [PITH_FULL_IMAGE:figures/full_fig_p044_35.png]
Figure 36
Figure 36. Figure 36: The corner plot for Object 8, for model parameters and the log(L∗) and log(Lacc) posteriors [PITH_FULL_IMAGE:figures/full_fig_p044_36.png]
Figure 37
Figure 37. Figure 37: The median model fit for Object 9 and the parameter posteriors with the same plotting convention as [PITH_FULL_IMAGE:figures/full_fig_p045_37.png]
Figure 38
Figure 38. Figure 38: The corner plot for Object 9, for model parameters and the log(L∗) and log(Lacc) posteriors [PITH_FULL_IMAGE:figures/full_fig_p045_38.png]
Figure 39
Figure 39. Figure 39: The median model fit for Object 10 and the parameter posteriors with the same plotting convention as [PITH_FULL_IMAGE:figures/full_fig_p046_39.png]
Figure 40
Figure 40. Figure 40: The corner plot for Object 10, for model parameters and the log(L∗) and log(Lacc) posteriors [PITH_FULL_IMAGE:figures/full_fig_p046_40.png]
Figure 41
Figure 41. Figure 41: The median model fit for Object 11 and the parameter posteriors with the same plotting convention as [PITH_FULL_IMAGE:figures/full_fig_p047_41.png]
Figure 42
Figure 42. Figure 42: The corner plot for Object 11, for model parameters and the log(L∗) and log(Lacc) posteriors [PITH_FULL_IMAGE:figures/full_fig_p047_42.png]
Figure 43
Figure 43. Figure 43: The median model fit for Object 12 and the parameter posteriors with the same plotting convention as [PITH_FULL_IMAGE:figures/full_fig_p048_43.png]
Figure 44
Figure 44. Figure 44: The corner plot for Object 12, for model parameters and the log(L∗) and log(Lacc) posteriors [PITH_FULL_IMAGE:figures/full_fig_p048_44.png]
Figure 45
Figure 45. Figure 45: The median model fit for Object 13 and the parameter posteriors with the same plotting convention as [PITH_FULL_IMAGE:figures/full_fig_p049_45.png]
Figure 46
Figure 46. Figure 46: The corner plot for Object 13, for model parameters and the log(L∗) and log(Lacc) posteriors [PITH_FULL_IMAGE:figures/full_fig_p049_46.png]
Figure 47
Figure 47. Figure 47: The median model fit for Object 14 and the parameter posteriors with the same plotting convention as [PITH_FULL_IMAGE:figures/full_fig_p050_47.png]
Figure 48
Figure 48. Figure 48: The corner plot for Object 14, for model parameters and the log(L∗) and log(Lacc) posteriors [PITH_FULL_IMAGE:figures/full_fig_p050_48.png]
Figure 49
Figure 49. Figure 49: The median model fit for Object 15 and the parameter posteriors with the same plotting convention as [PITH_FULL_IMAGE:figures/full_fig_p051_49.png]
Figure 50
Figure 50. Figure 50: The corner plot for Object 15, for model parameters and the log(L∗) and log(Lacc) posteriors [PITH_FULL_IMAGE:figures/full_fig_p051_50.png]

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Reviewed August 10, 2026 · model on record in the stance chip above.