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Electromagnetic counterparts of black hole-neutron star mergers: dependence on the neutron star properties

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Black hole-neutron star mergers produce kilonovae that are systematically dimmer in the blue than neutron star-neutron star mergers, because no hypermassive neutron star forms to drive a neutrino wind that raises the ejecta electron…

desk verdict Careful semi-analytic survey of BHNS EM counterparts with a plausible B-band diagnostic, but the headline brightness ordering leans on ejecta-mass fits pushed outside their calibration range. read the letter →

arxiv 1908.08822 v2 pith:VT62CNJQ submitted 2019-08-23 astro-ph.HE

C. Barbieri , O. S. Salafia , A. Perego , M. Colpi , G. Ghirlanda This is my paper · ORCID
classification astro-ph.HE PACS 04.30.-w26.30.-k97.60.Jd97.60.Lf98.70.Rz
keywords blackhole-neutronstarmergerskilonovagamma-rayburstafterglowtidaldeformabilityneutronequationofstategravitational-wavemultimessengerastronomyr-processnucleosynthesis
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 predicts the electromagnetic light that follows a black hole-neutron star (BHNS) merger and asks which neutron star properties set how bright that light is. The authors build a composite semi-analytical model of the kilonova and the gamma-ray burst afterglow, then survey the neutron star mass $M_\mathrm{NS}$ and tidal deformability $\Lambda_\mathrm{NS}$. Once only $M_\mathrm{NS}$--$\Lambda_\mathrm{NS}$ pairs allowed by a physical equation of state are considered, the brightest counterparts come from binaries with low-mass neutron stars. Using the equation-of-state constraints from GW170817, the predicted kilonova absolute magnitudes fall in a narrow range. The paper also finds BHNS kilonovae are systematically dimmer in the blue B band than neutron star-neutron star kilonovae, because the absence of a hyper/supra-massive neutron star removes the neutrino-driven wind that would raise the ejecta electron fraction; if true, a blue-poor kilonova is a usable electromagnetic fingerprint of a black hole in the binary.

What carries the argument

The load-bearing machinery is a composite semi-analytical model with three outflow components: dynamical ejecta (crescent-shaped, low $Y_e$, high opacity), wind ejecta, and viscous secular ejecta (higher $Y_e$, lower opacity). Ejecta masses come from fitting formulae calibrated on numerical-relativity simulations (Eq. 2 for total mass left outside the black hole, Eq. 3 for dynamical ejecta), with neutron star compactness tied to tidal deformability through the C-Love relation. The decisive mechanism is the wind: in NSNS mergers a transient hyper/supra-massive neutron star emits an intense neutrino wind that raises $Y_e$ and powers blue emission, but in BHNS mergers no such remnant forms, so the model sets the wind fraction to $\xi_w=0.01$ and the blue component is dim.

What would settle it

Run a numerical-relativity simulation of a 3-solar-mass, spin-0.5 black hole merging with a 1.4-solar-mass neutron star and compare the measured ejected mass with Eq. 2; a large discrepancy would remove the basis for the predicted brightness ordering. Observationally, one BHNS kilonova at comparable distance that is as blue as AT2017gfo in the B band would falsify the neutrino-wind-deficit explanation.

Watch

Extended reading notes

Core claim

The central claim is that the electromagnetic counterpart of a BHNS merger carries a fingerprint of the binary's nature. Along any physical equation of state, low-mass neutron stars have the largest tidal deformability and therefore leave the most debris outside the black hole, so fixing the black hole mass and spin makes low-mass $M_\mathrm{NS}\sim 1$--$1.2\,M_\odot$ binaries the brightest kilonovae and afterglow sources. Applying the equation-of-state bracket established by GW170817 compresses the predicted absolute magnitudes into a narrow interval. Compared with the NSNS kilonova AT2017gfo, BHNS light curves are similar in shape and peak time but dimmer in the B band, which the authors attribute to the absence of a hyper/supra-massive NS and its neutrino wind that would otherwise raise the electron fraction $Y_e$ in the ejecta; the $r$ and $K$ bands cannot break the degeneracy.

Load-bearing premise

The brightness ordering rests on trusting the two ejecta-mass fitting formulae beyond the parameter ranges where they were calibrated; if their extrapolated masses are wrong for near-equal-mass black holes or very rigid or soft neutron stars, the predicted ordering and the strength of the blue dimming change.

Editorial extensions

If this is right

  • For fixed black hole mass and spin, kilonovae from BHNS mergers are brighter when the neutron star is less massive, because low-mass neutron stars along a physical equation of state are more deformable and release more debris.
  • With equations of state bracketed by GW170817 (roughly SFHo to DD2), the predicted BHNS kilonova absolute magnitudes cluster in a narrow range for fixed black hole parameters.
  • BHNS kilonovae are consistently dimmer in the B band than the NSNS kilonova AT2017gfo, while r and K band light curves can match it; B-band photometry can therefore break the NSNS/BHNS degeneracy.
  • GRB afterglow brightness follows the same ordering: more deformable neutron stars, and more massive neutron stars at fixed deformability, give brighter afterglows, though degeneracy across black hole mass and spin remains.
  • For unfavourable parameters, such as a low black hole spin of 0.3, the neutron star plunges directly and produces no EM counterpart, so an EM non-detection does not rule out a BHNS origin.

Reading between the lines

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

  • The B-band deficit is a population-level prediction: if it holds, BHNS-origin kilonovae selected through short gamma-ray burst associations should skew redder at early times than NSNS kilonovae, even when r/K light curves look alike.
  • Because the predicted magnitude range is narrow, a future BHNS kilonova significantly bluer or brighter than the SFHo-to-DD2 band would challenge the GW170817 equation-of-state bracket or the assumed small wind fraction, pointing to missing physics in the ejecta model.
  • The same machinery could be run with non-aligned or retrograde black hole spins, which would test how the direct-plunge boundary and the brightness ordering shift with the effective spin entering the dynamical ejecta fit.
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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

4 major / 5 minor

Summary. The paper presents a composite semi-analytical model for the kilonova and GRB afterglow emission from black hole-neutron star (BHNS) mergers, extending earlier work by exploring the NS mass and tidal deformability parameter space for BH masses 3 and 6 M⊙ and spins 0.5 and 0.8. Using numerical-relativity fitting formulae for outflow masses, a three-component kilonova model (dynamical, wind, secular ejecta), and a structured-jet afterglow model, it computes light curves and energy maps. The main claims are: (i) when MNS-ΛNS pairs are restricted to physical EoS, low-mass NSs produce the brightest EM counterparts; (ii) GW170817 EoS constraints compress predicted kilonova magnitudes into a narrow range; (iii) BHNS kilonovae are dimmer in the B band than NSNS kilonovae because no hyper/supra-massive NS forms to drive a neutrino wind; and (iv) light curves resemble NSNS events in the r and K bands. The paper explicitly acknowledges that parts of the explored parameter space lie outside the calibration ranges of the input fitting formulae.

Significance. If the main trends hold, the paper provides a useful multi-messenger guide: the low-mass-NS brightness ordering and the B-band dimming could help distinguish BHNS from NSNS mergers and prioritize follow-up observations. The model is detailed, physically motivated, and anchored to numerical-relativity fits, and the comparison with AT2017gfo is a valuable cross-check. However, the headline claims are model-based predictions resting on extrapolated fitting formulae and on several unquantified input assumptions; the paper would be strengthened by sensitivity tests and by rephrasing the SGRB energy agreement as a consistency check rather than an independent prediction.

major comments (4)
  1. [Sec. 3, Eqs. (2)-(4)] The central brightness ordering that supports the abstract's claim ("brightest EM counterparts ... low mass NSs") is read off Figs. 3-6 and 12-15, but for MBH=3 M⊙ the mass ratio q<3 for every MNS considered, and the Kawaguchi et al. fit (Eq. 3) is calibrated for 3≤q≤7 and 300≤ΛNS≤1500; as the text itself states, these results are "only indicative." The same caveat applies to parameter points with ΛNS above the calibrated range (e.g., the ΛNS=2500 curves in Figs. 8-11) and to any soft/stiff EoS points below ΛNS=300. Because an incorrect extrapolation could change not only the absolute brightness but the relative ordering along an EoS, the authors should either restrict the headline claim to the MBH=6 M⊙ configurations inside the calibration range, or add a quantitative sensitivity test that applies the factor-of-two velocity correction reported from [78] and plausible variations of Mdyn in the q<3 regime and verifies that the low-mass-NS-brightest ordering survives.
  2. [Secs. 5.1 and 5.3] The prompt-emission energy range reported in Sec. 5.3 as a prediction is not independent: ε=0.015 is set in Sec. 5.1 by matching the most energetic observed SGRB (GRB 090510) under assumed beaming and gamma-ray efficiency. With that normalization, the statement that the model "predicts an energy range that reproduces the observed energy range of SGRBs" is a consistency check of the calibration, not an a posteriori prediction. Please rephrase this as a consistency check and discuss how Eiso scales with the assumed ε, jet opening angle, and gamma-ray efficiency η.
  3. [Secs. 4.3 and 6.3.1] The B-band dimming of BHNS kilonovae relative to AT2017gfo is presented as an observational diagnostic, but it is a direct consequence of the assumed wind-ejecta fraction ξw=0.01 (and κw=1 cm² g⁻¹) adopted in Sec. 4.3. The absence of the neutrino-driven wind from a hyper/supra-massive NS is physically plausible, but the magnitude of the B-band suppression is an input, not a derived result. The paper should include a sensitivity test over a plausible range of ξw (e.g., 0.01-0.1) and state whether the conclusion that B-band observations can break the NSNS/BHNS degeneracy survives.
  4. [Sec. 6.3 and Figs. 12-15] The conclusion that GW170817 EoS constraints compress the predicted kilonova magnitudes into a narrow interval is based on a single set of opacities and mass fractions (κdyn=15, κw=1, κs=5 cm² g⁻¹; ξw=0.01, ξs=0.2; f=0.3) with no uncertainty estimate. Because the width of the predicted magnitude interval is comparable to plausible systematic shifts from these choices, the paper should report how the interval broadens under reasonable parameter variations and include the uncertainty on Mout from the fitting formulae (e.g., the residual scatter in [40] and [70]).
minor comments (5)
  1. [Figs. 19-20 captions] The captions of Figs. 19 and 20 read "Same as Fig. 19" and "Same as Fig. 20" respectively; they should refer to the corresponding earlier figures (Figs. 17 and 18).
  2. [Sec. 6.2] In the discussion of χBH=0.3, the sentence stating that ν dL/dν is "∼5–20 times smaller than the χBH=0.3 case" should compare with the χBH=0.5 case.
  3. [Sec. 1] The mass of J0740+6620 is cited as "[?]" in the text; the reference entry needs to be supplied.
  4. [Eq. (1)] The sentence defining the NS compactness CNS is grammatically incomplete; the definition should be written out cleanly.
  5. [Sec. 4.3] The statement that the model was tested on the GW170817 kilonova refers to a "paper in preparation"; please provide a citation or describe the comparison more concretely.

Circularity Check

2 steps flagged · score 6.0 of 10

The afterglow energy-range 'prediction' is partly a fitted normalization, and the B-band dimming restates an assumed small wind fraction; the central low-mass-NS brightness ordering is not circular.

  1. fitted input called prediction [Section 5.1 (Relativistic jet launch, Eq. 49) and Section 5.3 (GRB prompt emission)]
    "Following these arguments we set ϵ = 0.015, corresponding to a maximum possible jet kinetic energy of EK,jet,max≈ 10^52 erg. ... It is interesting to note that our model predicts an energy range that reproduces the observed energy range of SGRBs [101]."

    The dimensionless efficiency ϵ in EK,jet = ϵ(1−ξw−ξs)Mdisc c^2 Ω_H^2 f(Ω_H) (Eq. 49) is calibrated explicitly against the upper extremum of the observed SGRB energy distribution: the most energetic SGRB, GRB 090510, with Eγ,iso∼7.4×10^52 erg, together with assumed 10% gamma-ray efficiency and 5 deg half-opening angle, is used to set ϵ=0.015. The prompt isotropic energy Eiso(θv) in Eq. 51 is proportional to this same kinetic energy, so the statement in Sec. 5.3 that the model 'predicts an energy range that reproduces the observed energy range of SGRBs' is at minimum upper-end-forced by the fitted normalization. The spread across the explored parameter space adds some independent content, but the match to the observed SGRB energy range is not a free prediction.

  2. self definitional [Section 4.3 (Kilonova light curves) and Section 6.3.1 (Comparing BHNS kilonova lightcurves with AT2017gfo)]
    "the wind ejecta is notably a smaller fraction of the disc with respect to the NSNS case. This is due to the lack of a possible intermediate supra- or hypermassive NS state that would produce an intense neutrino wind. ... especially in the B band, the expected kilonova light curves for all the considered BHNS configurations are always dimmer with respect to AT2017gfo. The emission in this band is principally due to high Ye ejecta."

    The model assigns B-band emission to the high-Ye wind ejecta and prescribes the wind mass as a fixed small fraction ξw=0.01 of the disc mass, explicitly because a BHNS merger lacks the hyper/supra-massive NS neutrino wind that would raise Ye in the NSNS case. Therefore the claimed result that BHNS kilonovae are dimmer in B due to the absence of that neutrino wind is a restatement of the assumed input (small ξw) rather than an emergent first-principles prediction. The AT2017gfo comparison provides external illustrative context, but the causal claim in the abstract is not independent of the adopted ξw.

full rationale

The paper's central kilonova claim — that along physically motivated EoS lines the brightest EM counterparts come from low-mass NSs — is not circular: it is read off the ejecta-mass maps built from external numerical-relativity fitting formulae (Foucart et al. 2018; Kawaguchi et al. 2016) combined with the EoS-dependent MNS−ΛNS relation, and the ordering is not identical to any single fitted parameter. The GW170817 EoS restriction to a narrow magnitude range is likewise an externally imposed selection, not a self-referential fit. The two genuinely circular elements are secondary: (1) in Sec. 5.1, ϵ is calibrated to the most energetic observed SGRB and then Sec. 5.3 reports that the model 'predicts' the observed SGRB energy range, so the upper end of that range is forced by construction; and (2) the B-band dimming 'cause' is essentially the assumed small wind fraction ξw=0.01, so presenting it as a derived consequence of the absence of a hyper/supra-massive NS overstates what the model computes. The paper itself flags that the MBH=3 M⊙ and out-of-range ΛNS results rest on extrapolated fits and are 'only indicative'; that is a correctness risk, not circularity. Overall, the core mass-ordering prediction has independent content, but one fitted normalization is presented as a prediction and one abstract-level causal claim re-describes a model input, supporting a partial circularity score of 6.

Assumptions & free parameters 13 free parameters · 6 assumptions · 0 invented entities

The central claim rests on calibrated fitting formulae for outflow masses and on a stack of semi-analytic model assumptions covering kilonova diffusion, crescent geometry, the Blandford-Znajek jet, and annulus-wise afterglow evolution. Most are standard in the field, but the extrapolation beyond fit ranges and the unstated afterglow microphysics parameters make the predictions dependent on choices the reader cannot independently verify.

free parameters (13)
  • Jet efficiency epsilon = 0.015
    Chosen in Sec. 5.1 so that the maximum jet kinetic energy matches the most energetic observed SGRB; this normalization feeds all afterglow light curves.
  • Dynamical ejecta fraction cap f = 0.3
    Set in Sec. 3 from near-equal-mass simulation results as the maximum possible Mdyn/Mout ratio; multiplies all dynamical ejecta masses.
  • Wind ejecta fraction xi_w = 0.01
    Assumed fraction of disc mass ejected in the wind for BHNS systems in Sec. 4.3.
  • Secular ejecta fraction xi_s = 0.2
    Assumed fraction of disc mass ejected by viscous processes in Sec. 4.3.
  • Dynamical ejecta opacity kappa_dyn = 15 cm2/g
    Assumed high opacity for low-Ye r-process ejecta in Sec. 4.3.
  • Wind ejecta opacity kappa_w = 1 cm2/g
    Assumed grey opacity for wind ejecta in Sec. 4.3.
  • Secular ejecta opacity kappa_s = 5 cm2/g
    Assumed grey opacity for secular ejecta in Sec. 4.3.
  • Jet core angle theta_c,E = 0.1 rad
    Educated guess for the angular distribution of jet energy in Sec. 5.2.
  • Jet Lorentz factor parameters Gamma_c and theta_c,Gamma = 100 and 0.2 rad
    Educated guess for the angular Lorentz factor profile in Sec. 5.2.
  • ISM density n = 1e-3 cm^-3
    Constant external density chosen as typical for SGRB afterglows in Sec. 5.4.
  • Viewing angle theta_view = 30 deg
    Fixed for the light curves as the most probable GW orientation in Sec. 6.2.
  • Electron equipartition epsilon_e = 0.1
    Typical value assumed for afterglow microphysics in Sec. 5.4.
  • Magnetic equipartition epsilon_B
    Quoted range [1e-4,0.1] is given in Sec. 5.4, but the exact value used in the calculations is not stated, so reproduction requires guessing this parameter.
assumptions (6)
  • domain assumption The outflow masses and velocities are given by the numerical-relativity fitting formulae of Foucart et al. 2018 (Eq. 2) and Kawaguchi et al. 2016 (Eqs. 3-4), and these remain meaningful outside their calibration ranges.
    Sec. 3 uses the fits for MBH=3 M⊙ (q<3) and Lambda outside [300,1500], while the paper notes these are extrapolations and only indicative.
  • domain assumption The C-Love relation (Eq. 6) maps tidal deformability to compactness for all EoS considered, and the Lattimer-Prakash binding-energy formula (Eq. 8) gives the baryonic mass.
    Sec. 3 uses these EoS-quasi-universal empirical relations as exact for the explored stars.
  • standard math Kilonova emission is described by homologous expansion, grey opacities, blackbody photospheres, and the nuclear heating fit of Korobkin et al. 2012 (Eq. 13).
    Sec. 4 relies on these standard semi-analytic approximations in kilonova modeling.
  • domain assumption Dynamical ejecta have a crescent geometry with half-opening theta_dyn and azimuth phi_dyn~pi, and wind/secular ejecta follow a sin^2(theta) mass distribution.
    Sec. 4.2 and Sec. 5.1 take the geometry from numerical simulations and assume it is independent of BH and NS parameters.
  • domain assumption A Blandford-Znajek jet is launched by the remnant BH-disc system, with magnetic field amplified to a fixed fraction of disc rest-mass energy density, and the jet loses negligible energy crossing the ejecta.
    Sec. 5.1 adopts this jet-launch model and explicitly neglects jet-ejecta interaction.
  • domain assumption The afterglow shock evolves independently in each annulus with no lateral energy exchange, with constant ISM density n=1e-3 cm^-3 and synchrotron emission from a power-law electron distribution.
    Sec. 5.4.1-5.4.3 uses these standard assumptions in semi-analytic afterglow codes.

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Cite this review

Pith. "Pith review of Electromagnetic counterparts of black hole-neutron star mergers: dependence on the neutron star properties." pith.science (2026). https://pith.science/paper/VT62CNJQ

@misc{pith2026190808822,
  author       = {Pith},
  title        = {Pith review of: Electromagnetic counterparts of black hole-neutron star mergers: dependence on the neutron star properties},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VT62CNJQ}},
  note         = {Machine review of arXiv:1908.08822}
}
abstract

Detections of gravitational waves (GWs) may soon uncover the signal from the coalescence of a black hole - neutron star (BHNS) binary, that is expected to be accompanied by an electromagnetic (EM) signal. In this paper, we present a composite semi-analytical model to predict the properties of the expected EM counterpart from BHNS mergers, focusing on the kilonova emission and on the gamma-ray burst afterglow. Four main parameters rule the properties of the EM emission: the NS mass $M_\mathrm{NS}$, its tidal deformability $\Lambda_\mathrm{NS}$, the BH mass and spin. Only for certain combinations of these parameters an EM counterpart is produced. Here we explore the parameter space, and construct light curves, analysing the dependence of the EM emission on the NS mass and tidal deformability. Exploring the NS parameter space limiting to $M_\mathrm{NS}-\Lambda_\mathrm{NS}$ pairs described by a physically motivated equations of state (EoS), we find that the brightest EM counterparts are produced in binaries with low mass NSs (fixing the BH properties and the EoS). Using constraints on the NS EoS from GW170817, our modeling shows that the emission falls in a narrow range of absolute magnitudes. Within the range of explored parameters, light curves and peak times are not dissimilar to those from NSNS mergers, except in the B band. The lack of an hyper/supra-massive NS in BHNS coalescences causes a dimming of the blue kilonova emission in absence of the neutrino interaction with the ejecta.

Figures

Figures reproduced from arXiv: 1908.08822 by the authors.

Figure 1
Figure 1. NS dimensionless tidal deformability parameter ΛNS as a func￾tion of the NS mass MNS for a set of selected EoS. The softest con￾sidered EoS is 2B (blue), while the stiffest one is MS1 (pink). Vertical dashed lines represent the estimated ranges for NS masses coming from GW170817 analysis (black for the primary component, gray for the secondary). where Mb NS is the NS baryonic mass, η = q/(1+q) 2 is the sym￾metric ma… view at source ↗
Figure 2
Figure 2. Dynamical ejecta (left) and disc masses (right) produced during the merger in the MBH − χBH parameter space, assuming a NS with MNS = 1.4 M and ΛNS = 330 (corresponding to SFHo EoS). EoS, we find that the optimal condition to produce massive dy￾namical ejecta and discs fixing MBH and χBH is having a low mass NS. Indeed, as shown in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Dynamical ejecta (left) and disc masses (right) produced dur￾ing the merger in the MNS −ΛNS parameter space, assuming a BH with MBH = 3 M and χBH = 0.5. The NS compactness is computed assum￾ing the C-Love relation. Gray symbols show the ΛNS − MNS relation for a set of EoS. The match of any point with the underlying shaded area corresponds to the estimated value of the dynamical ejecta and disc masses. 1.0 1.5 2.0 2.… view at source ↗
Figures from the paper (13 more)
Figure 6
Figure 6. Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: Schematic division of a section of dynamical ejecta (assumed to have a crescent-like geometry). The decreasing ejecta density in the outward direction is represented qualitatively by the colouring. The equatorial plane is at z = 0. We identify three regions, delimited …
Figure 8
Figure 8. Figure 8: Kilonova (top) and GRB afterglow (bottom) light curve dependence on NS tidal deformability (left - for MNS = 1.4 M ) and mass (right - for Λ = 330), considering a BH with MBH = 3 M and χBH = 0.5. For the kilonova we show the absolute magnitude vs time, while for the GR…
Figure 9
Figure 9. Figure 9: Same as [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: Same as [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]
Figure 11
Figure 11. Figure 11: Same as [PITH_FULL_IMAGE:figures/full_fig_p016_11.png]
Figure 12
Figure 12. Figure 12: Kilonova light curve dependence on NS mass and EoS, considering a BH with MBH = 3 M and χBH = 0.5. We show the absolute magnitude VS time. Linestyles indicate the two different adopted EoS reported in the central legend, while colours indicate different NS masses. We …
Figure 13
Figure 13. Figure 13: Same as [PITH_FULL_IMAGE:figures/full_fig_p017_13.png]
Figure 14
Figure 14. Figure 14: Same as [PITH_FULL_IMAGE:figures/full_fig_p018_14.png]
Figure 15
Figure 15. Figure 15: Same as [PITH_FULL_IMAGE:figures/full_fig_p018_15.png]
Figure 16
Figure 16. Figure 16: Total energy emitted in kilonova in the MBH − χBH param￾eter space. We assumed a NS with MNS = 1.4 M and ΛNS = 330, corresponding to SFHo EoS). 1.0 1.5 2.0 2.5 MNS [M ] 10 2 10 3 10 4 NS 2B SFHo MS1 DD2 46 46.5 47 47.5 48 48.5 EKN [erg] [PITH_FULL_IMAGE:figures/full_…
Figure 19
Figure 19. Figure 19: Same as [PITH_FULL_IMAGE:figures/full_fig_p019_19.png]
Figure 20
Figure 20. Figure 20: Same as [PITH_FULL_IMAGE:figures/full_fig_p020_20.png]

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Forward citations

Cited by 3 Pith papers

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