CHEX-MATE: Cluster Multi-Probes in Three Dimensions (CLUMP-3D) II. Combined Gas and Dark Matter Analysis from X-ray, SZE, and WL

Adriana Gavidia; Dominique Eckert; Elena Rasia; Federico De Luca; Gabriel Pratt; Herve Bourdin; Jack Sayers; Junhan Kim; Keiichi Umetsu; Lorenzo Lovisari

REVIEW 4 major objections 6 minor 136 references

CHEX-MATE: Cluster Multi-Probes in Three Dimensions (CLUMP-3D) II. Combined Gas and Dark Matter Analysis from X-ray, SZE, and WL

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Modeling Abell 1689 as elongated along the line of sight lowers its weak-lensing mass by about 30 percent relative to a spherical fit.

desk verdict The 30% triaxial mass reduction is not yet robust because the RLP systematic error is an order of magnitude larger than the quoted statistical uncertainty, but the pipeline itself is a solid methods contribution. read the letter →

arxiv 2507.10857 v1 pith:R7LFSKWI submitted 2025-07-14 astro-ph.CO

Adriana Gavidia , Junhan Kim , Jack Sayers , Mauro Sereno , Loris Chappuis , Dominique Eckert , Keiichi Umetsu , Herve Bourdin

show 10 more authors

Federico De Luca Stefano Ettori Massimo Gaspari Raphael Gavazzi Scott Kay Lorenzo Lovisari Pasquale Mazzotta Gabriel Pratt Elena Rasia Mariachiara Rossetti

This is my paper · ORCID

classification astro-ph.CO

keywords galaxyclusterstriaxialmodelingweakgravitationallensingSunyaev-ZeldovicheffectX-rayastronomyAbell1689non-thermalpressureclustermassbias

open problems Dark Matter

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

Galaxy clusters are triaxial, not spherical, so fitting them as spheres can bias the masses measured from weak lensing. This paper builds a multiprobe triaxial analysis that combines X-ray surface brightness and temperature, Sunyaev-Zeldovich effect, and weak-lensing shear in a single geometric model, and applies it to the massive cluster Abell 1689. It finds the cluster is stretched along the line of sight, with elongation $\mathcal{R}_{LP} = 1.27 \pm 0.02$, which lowers the weak-lensing mass from about $17.8 \times 10^{14}$ to $13.7 \times 10^{14}$ solar masses relative to an otherwise identical spherical fit. The paper argues that the cluster's unusually high concentration is not a projection artifact, and it derives a non-thermal pressure fraction rising from about 20 percent at 600 kpc to near 30 percent at the largest radius. If the approach is correct, spherical models systematically overestimate the masses of line-of-sight elongated clusters by tens of percent.

What carries the argument

The central object is the triaxial ellipsoidal radius $\zeta$ defined by $\zeta^2 = x_1^2/q_1^2 + x_2^2/q_2^2 + x_3^2$, with two axial ratios $q_1$ and $q_2$ and three Euler angles relating the ellipsoid to the observer. All ICM and gravitational-potential profiles are written as functions of $\zeta$, and the projection integral $F_{2D}(x_\xi) = 2 l_p e_\parallel \int_{x_\xi}^\infty F_{3D}(x_\zeta) x_\zeta / \sqrt{x_\zeta^2 - x_\xi^2} \, dx_\zeta$ converts them into predicted two-dimensional maps of X-ray surface brightness, Compton-$y$, and lensing potential. The mass model works through the gravitational potential $\Phi(\zeta)$, which is assumed to have the same ellipsoidal shape and orientation as the X-ray gas; Poisson's equation is inverted numerically to connect $\Phi$ to the total density, characterized by $M_{200c}$ and $c_{200c}$. The elongation parameter $\mathcal{R}_{LP}$ (ratio of line-of-sight extent to average projected extent) sets the projection correction, and the generalized hydrostatic-equilibrium equation $dP_{tot}/d\zeta = -\rho_{gas}\,d\Phi/d\zeta$ is integrated outside the fit to obtain the non-thermal pressure fraction.

What would settle it

Measure the cluster's three-dimensional shape with an independent tracer that does not assume $q_{pot} = q_{ICM}$, for example strong-lensing arc positions combined with central-galaxy stellar kinematics, and check whether the inferred potential axial ratio matches the gas axial ratio. If the potential is significantly rounder, the 30 percent mass correction is an overestimate; alternatively, repeat the fit using the two-dimensional temperature map instead of the one-dimensional profile, which the appendix says shifts $\mathcal{R}_{LP}$ by about 0.20, and see whether the mass difference disappears.

Watch

Extended reading notes

Core claim

The paper's central claim is that combining X-ray, SZ, and weak-lensing observations with a triaxial ellipsoidal model removes a major projection bias in cluster mass measurement. For Abell 1689, the fit yields $M_{200c} = (13.69_{-1.41}^{+1.56}) \times 10^{14}\,M_\odot$ with concentration $c_{200c} = 8.55_{-1.61}^{+2.20}$, whereas a spherical fit to the same weak-lensing data gives $M_{200c} = (17.77_{-1.75}^{+2.00}) \times 10^{14}\,M_\odot$ and $c_{200c} = 9.99_{-1.78}^{+2.26}$. The mass difference is attributed to the cluster's line-of-sight elongation $\mathcal{R}_{LP} = 1.27 \pm 0.02$. Because the triaxial fit retains the high concentration, the paper concludes that the high concentration is intrinsic rather than a projection effect. The analysis also uses the triaxial gravitational potential, assumed to share the gas axial ratios, to derive the non-thermal pressure support, which runs from roughly 20 percent at intermediate radii to near 30 percent at the edges of the fitted range, at about $\pm5$ percent precision. The pipeline was first tested on mock observations with known input parameters, and it recovered masses consistent with the inputs within noise.

Load-bearing premise

The mass and projection correction assume the dark-matter potential has exactly the same axial ratios as the X-ray gas and is aligned with it; if the potential is rounder or tilted, the inferred line-of-sight elongation and the mass shift change.

Editorial extensions

If this is right

Spherical weak-lensing fits overestimate the mass of line-of-sight elongated clusters by roughly 30 percent for a cluster like Abell 1689, and the size of the bias tracks the elongation $\mathcal{R}_{LP}$.
The unexpectedly high concentration of Abell 1689 is intrinsic to the cluster rather than a viewing-angle artifact.
The multiprobe triaxial pipeline recovers input masses in mock observations, so it can be applied to the rest of the CHEX-MATE sample to map orientation biases.
Abell 1689 carries roughly 20–30 percent of its pressure in non-thermal form over 0.18–1.37 Mpc, with about $\pm5$ percent precision.

Reading between the lines

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

If the potential is rounder than the gas, as some simulations suggest, the quoted mass correction is an upper limit; a rounder potential would produce a smaller triaxial-versus-spherical mass difference.
The appendix's sensitivity tests show individual modeling choices shift $\mathcal{R}_{LP}$ by up to about 0.20, so the quoted statistical uncertainty of 0.02 likely understates the real uncertainty; a systematic shift that large would move the mass by several $\times 10^{13}\,M_\odot$.
Applying this pipeline to a full sample should reveal a population-level correlation between inferred $\mathcal{R}_{LP}$ and the spherical-versus-triaxial mass offset, which can be checked against independent shape indicators such as strong-lensing morphology.

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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

First: the headline result—triaxial mass about 30% lower than spherical—is not yet robust. The quoted RLP = 1.27 ± 0.02 carries only statistical error, but Appendix A shows that switching between 1D and 2D temperature weighting moves RLP by ~0.20, the ARF choice by ~0.07, and several other modeling choices by similar amounts. The shifts happen to cancel in the final value, but cancellation is not a systematic error budget. Since the mass ratio 17.77/13.69 ≈ 1.30 is essentially RLP, a ±0.2 uncertainty in RLP translates into a ±2 × 10^14 M_sun change in M200c—comparable to or larger than the quoted uncertainty. The mock validation doesn't cover this, because the mocks use the same modeling choices.

What the paper does well: it integrates WL into the K24 gas-only triaxial formalism, applies it to A1689, validates mass recovery on mocks, and produces a non-thermal pressure profile consistent with Chappuis et al. and simulations. The comparison with prior triaxial analyses is thorough. This is a real pipeline that will be used on the CHEX-MATE sample.

The fixable problems: (1) The abstract says the spherical fit 'otherwise employs the same methodology,' but Section 6 shows it uses WL only. That is misleading. (2) The concentration result is prior-dominated—the log-normal prior centered on the Diemer & Joyce relation sets the posterior's upper edge, and a flat prior hits the boundary. So the claim that the high concentration is intrinsic is not supported. (3) The RLP systematic must be quantified, either by marginalizing over the weighting/response choices or by reporting an error an order of magnitude larger than 0.02.

The qpot = qICM assumption is a separate dependency that the mocks don't stress-test; it's secondary to the RLP issue.

Who this is for: cluster cosmologists and anyone doing triaxial multi-probe fitting. It's a methods demonstration on one cluster, not a cosmological result. I'd send it to peer review, but the revision must address the systematic error budget and the spherical-fit comparison honestly.

Referee Report

4 major / 6 minor

Summary. The paper presents an extension of the triaxial cluster modeling pipeline of Kim et al. (2024) to include weak-lensing shear data, and applies it to Abell 1689 using X-ray surface brightness and temperature, SZ maps from Planck/ACT, and Subaru weak-lensing maps. The main results are an inferred line-of-sight elongation R_LP = 1.27 +/- 0.02, a triaxial mass M_200c = (13.69^{+1.56}_{-1.41}) x 10^14 Msun, a concentration c_200c = 8.55^{+2.20}_{-1.61}, and a non-thermal pressure fraction of roughly 20-30% between 0.18 and 1.37 Mpc. The paper reports that the spherical-fit mass is (17.77^{+2.00}_{-1.75}) x 10^14 Msun and interprets the difference as a projection bias. A mock-data validation of the mass and concentration recovery is included.

Significance. If the central claims hold, the paper would provide a valuable demonstration that joint triaxial modeling of X-ray, SZ, and WL data can remove orientation-dependent bias in weak-lensing mass estimates of individual clusters. The work uses a rich, publicly available CHEX-MATE dataset, documents its methodological updates transparently in Appendix A, and includes mock validation with full instrumental response. However, several load-bearing aspects of the analysis currently prevent full confidence in the headline results: the spherical comparison is not apples-to-apples, the concentration measurement is prior-dominated, and the elongation parameter carries unquantified modeling systematics that are comparable to the quoted statistical uncertainties.

major comments (4)

[Abstract and Section 6] The abstract states that the spherical fit 'otherwise employs the same methodology' as the triaxial fit, but Section 6 says the spherical fit was performed 'to the WL data' only. The triaxial mass, in contrast, comes from a joint X-ray, SZ, and WL fit. The comparison of M_200c = 17.77 vs 13.69 therefore conflates a change in geometry with a change in the data used in the fit, and the claim that the mass difference is due to line-of-sight elongation is not established by this comparison. Please either rerun the spherical fit on the full multi-probe dataset or state clearly that the spherical reference is WL-only and discuss the implications.
[Sections 2.5.1, 4, and 6] The concentration measurement c_200c = 8.55 is dominated by the informative log-normal prior centered on the Diemer & Joyce (2019) mass-concentration relation. The paper itself states in Section 6 and Figure 5 that the upper edge of the posterior is set by the prior and that a flat prior returns a posterior that hits the prior boundary. The mock tests in Section 4 (Table 2) also show a measurable prior-induced bias for input values c_200c = 2 and 10. The conclusion that the high concentration is intrinsic and 'not due to triaxiality and orientation' is therefore not supported by the data. Please present the flat-prior result and limit the concentration claim to what the data actually constrain.
[Appendix A and Section 6] The quoted elongation R_LP = 1.27 +/- 0.02 is a statistical uncertainty only. Appendix A documents that alternative modeling choices shift R_LP by up to 0.20 (1D vs 2D temperature profile), 0.18 (APEC normalization), 0.07 (ARF), 0.05 (X-ray SB profile method), and 0.03 (integration tolerance). Because the mass ratio M_200c,sph / M_200c,triax ~ 1.30 closely tracks R_LP, an unquantified R_LP systematic of +/-0.2 changes the triaxial mass by roughly +/-2 x 10^14 Msun, comparable to or larger than the quoted mass uncertainty. The mock validation in Section 4 does not address this, since the mocks are generated with the same modeling choices. Please provide a systematic error budget for R_LP or weaken the claim that the triaxial mass is 'significantly lower' than the spherical value.
[Section 2.3.1] The assumption that the gravitational potential has exactly the same axial ratios and orientation as the ICM (q_pot = q_ICM, co-aligned) is load-bearing for the triaxial mass estimate, but it is not stress-tested. The mock observations in Section 4 were generated from the same model, so they cannot validate this assumption. If the potential is rounder than the gas or is misaligned, the projected WL signal and the inferred M_200c will change. A sensitivity test with a rounder or misaligned potential, or at least a quantitative discussion of the expected bias based on simulations, is needed before the mass comparison can be considered robust.

minor comments (6)

[Introduction] There is a typo 'Custer Lensing And Supernovae survey' and 'hearafter' should be 'hereafter'.
[Section 2.2.2] The sentence 'A grid of values for Lambda(Te,Z) is precalculated using using the Python package pyproffit' contains a duplicated 'using'.
[Section 2.3.1] The phrase 'an the initial spherically-symmetric rho(r)' is ungrammatical and should be revised.
[Section 2.4] The word 'Arbritary' before Eq. (17) should be 'Arbitrary'.
[Section 6] The sentence 'We see that for the Compton-y and X-ray SB profiles, the model follows the the data closely' contains a duplicated 'the'.
[Appendix A] The heading 'Logrithmically-Spaced LOS Projection Integral' should be 'Logarithmically-Spaced'.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the triaxial mass reduction follows from the fitted geometry and is disclosed, the concentration prior is informative but not self-fulfilling, and the RLP systematics in Appendix A are a robustness concern rather than a circular reduction.

full rationale

The central derivation chain is not circular. The paper explicitly separates the constraints on geometry from those on mass: 'the three ICM observables constrain the parameters associated with the three-dimensional geometry. Given this geometry, the parameters of the total matter density are constrained entirely by the WL data' (Sec. 2.5). The elongation RLP=1.27 is fitted from the X-ray and SZ data, and the lower triaxial WL mass is presented transparently as a consequence: 'As a result, the WL mass obtained from our triaxial fit... is significantly lower than the value... obtained from a spherically-symmetric fit' (Abstract). This is a model comparison driven by the projection equation (Eq. 25), not a hidden prediction fitted to the same data. The informative log-normal c200c prior is centered on the low values of 4-6.5 from Diemer & Joyce (2019), whereas the recovered c200c=8.55 lies above that center, so the high-concentration conclusion is not manufactured by the prior; the paper even notes that the prior may bias c200c downward and reports that a flat prior pushes the posterior to the prior boundary, which is a prior-sensitivity limitation rather than a circular reduction. The assumption qpot=qICM with co-alignment (Sec. 2.3.1) is an explicit modeling assumption, not a self-referential derivation. Appendix A documents RLP shifts from modeling choices (0.05, 0.20, 0.03, 0.02, 0.18, 0.07) that affect the robustness of the quoted 0.02 uncertainty, but systematic uncertainty is a correctness risk, not circularity. The self-citations to K24 and Sereno et al. (2017) provide the pipeline and are externally published methods, and the mock validation in Sec. 4 is a self-consistency check rather than the source of the target claims. No step in the paper reduces to its inputs by construction, so the circularity score is low.

Assumptions & free parameters 15 free parameters · 7 assumptions · 0 invented entities

The model introduces no new physical entities. It relies on a parametric gas description, a potential-shape assumption, a spherical NFW starting point, generalized hydrostatic equilibrium, and an informative concentration prior. The central mass is constrained by WL data, but the concentration and non-thermal pressure are partly shaped by the prior and by the same fitted profiles.

free parameters (15)

q_ICM,1 = 0.75 +- 0.01
Minor-to-major axial ratio of the ICM distribution; fitted to X-ray and SZ data.
q_ICM,2 = 0.82 +- 0.01
Intermediate-to-major axial ratio of the ICM distribution; fitted.
cos(theta) = 0.99 +- 0.01
Cosine of the inclination angle of the ellipsoid major axis to the line of sight; fitted.
phi
Second Euler angle; fitted but not reported in the summary.
psi
Third Euler angle; fitted but not reported in the summary.
n0 = 2.99e-2 cm^-3
Central electron density normalization; fitted to X-ray surface brightness.
zeta_c = 60.1 kpc
Core radius of the electron density profile; fitted.
zeta_t = 0.61 Mpc
Truncation radius of the electron density profile; fitted.
beta_e = 0.43
Intermediate slope of the electron density profile; fitted.
eta_e = 0.24
Inner slope of the electron density profile; fitted.
gamma_e = 1.19
Outer slope of the electron density profile; fitted.
P0 = 21.3
Normalization of the gNFW pressure profile; fitted to SZ data.
alpha_p = 1.03
Intermediate slope of the pressure profile; fitted.
M200c = 13.69e14 Msun
Total mass within R200c; the primary WL-constrained parameter.
c200c = 8.55
Concentration; the posterior is strongly influenced by the log-normal prior from Diemer & Joyce (2019).

assumptions (7)

domain assumption The ICM gas density and pressure follow the parametric forms of Eqs. 3 and 4.
The Vikhlinin-type density and gNFW pressure profiles are assumed to describe the true gas distribution; systematic errors in these forms propagate directly into the recovered geometry and mass.
domain assumption The gravitational potential has the same axial ratios as the ICM and is co-aligned with it (qpot = qICM).
Invoked in Sec 2.3.1; if the potential is rounder or misaligned, the triaxial mass and the projection correction are biased.
domain assumption The starting density for the Poisson inversion is a spherical NFW profile (Eq. 10).
The potential is constructed from a spherical NFW, then evaluated on an ellipsoidal grid; the resulting density is not NFW, but the mass and concentration are defined through spherical integrals of that density.
domain assumption Generalized hydrostatic equilibrium: dPtot/dzeta = -rho_gas dPhi/dzeta (Eq. 34).
Used to define the total pressure and derive Pnt/Ptot; assumes the cluster is fully virialized and that non-thermal pressure is the only additional support.
domain assumption The X-ray spectroscopic temperature is approximated by the Mazzotta et al. (2004) weighting (Eq. 7).
The conversion from the 3D temperature to the projected spectroscopic temperature affects the SZ/X-ray deprojection and hence RLP; alternative weightings can shift results.
ad hoc to paper The c200c prior is log-normal centered on the Diemer & Joyce (2019) mass-concentration relation.
The concentration posterior is largely set by this prior; a flat prior yields a posterior that hits the upper boundary, so the reported c200c is not data-driven.
domain assumption Fixed gNFW pressure parameters c500 = 1.4, gamma_p = 0.3, and beta_p = 5.4 are adopted from Sayers et al. (2023).
These fixed values reduce the pressure profile freedom; if they are wrong for Abell 1689, the gas pressure and RLP inference change.

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Cite this review

Pith. "Pith review of CHEX-MATE: Cluster Multi-Probes in Three Dimensions (CLUMP-3D) II. Combined Gas and Dark Matter Analysis from X-ray, SZE, and WL." pith.science (2026). https://pith.science/paper/R7LFSKWI

@misc{pith2026250710857,
  author       = {Pith},
  title        = {Pith review of: CHEX-MATE: Cluster Multi-Probes in Three Dimensions (CLUMP-3D) II. Combined Gas and Dark Matter Analysis from X-ray, SZE, and WL},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/R7LFSKWI}},
  note         = {Machine review of arXiv:2507.10857}
}

abstract

Under the standard model of hierarchical structure formation, the overall geometry of galaxy clusters is better described by a triaxial ellipse than a sphere. As a result, applying spherically-symmetric models can result in significant biases. These biases can be mitigated by fitting a triaxial model, requiring deep multiprobe data and a set of physically motivated models to describe them. Here we present a multiprobe triaxial analysis methodology based on the data available for galaxy clusters in the Cluster Heritage project with XMM-Newton - Mass Assembly and Thermodynamics at Endpoint of structure formation (CHEX-MATE), which includes X-ray data from XMM-Newton, SZ data from Planck and ACT, and WL data from Subaru. This work builds on our previous development of a gas-only X-ray and SZ triaxial fitting formalism in Paper I. We apply our approach to the CHEX-MATE cluster PSZ2 G313.33+61.13 (Abell 1689) and find that it is elongated along the line of sight relative to the plane of sky by a factor of $\mathcal{R}_{LP} = 1.27 \pm 0.02$. As a result, the WL mass obtained from our triaxial fit, $\text{M}_{200c}=(13.69_{-1.41}^{+1.56})\times10^{14} \text{M}_{\odot}$, is significantly lower than the value of $(17.77_{-1.75}^{+2.00})\times10^{14} \text{M}_{\odot}$ obtained from a spherically-symmetric fit that otherwise employs the same methodology. Our triaxial fit finds a concentration of $c_{200c}=8.55_{-1.61}^{+2.20}$, consistent with the spherically-symmetric value of $9.99_{-1.78}^{+2.26}$, which suggests that the unexpectedly high concentration in Abell 1689 is not due to triaxiality and orientation. We also measure the non-thermal pressure fraction at radii between 0.18-1.37 Mpc, finding a minimum of approximately 20 per cent at intermediate radii increasing to near 30 per cent at both the smallest and largest radii, and with a typical measurement precision of $\pm$5 per cent.

Figures

Figures reproduced from arXiv: 2507.10857 by the authors.

**Figure 1.** The posterior distribution of M200c and c200c obtained from fits to mock observations. The shaded region for each posterior represents the 68 per cent credible region. The corresponding input values are indicated by the × symbol. In all cases the recovered M200c value is consistent with the input, within noise fluctuations. This is also true for c200c when the input value is c200c= 3.8, as this value is close to the… view at source ↗

**Figure 2.** Radial plots of the non-thermal pressure fraction (Pnt/Ptot) recovered from fits to mock observational data, generated with a range of M200c and c200c values. The solid purple line represents the best fit model and the shaded purple region is the corresponding 68 per cent credible region calculated from the accepted MCMC samples. The dashed blue line is the non-thermal pressure fraction calculated from the input par… view at source ↗

**Figure 3.** SZ, X-ray and WL data for the CHEX-MATE galaxy cluster PSZ2 G313.33+61.13 (Abell 1689). The ACT DR6 Compton-y map (top left), the X-ray SB map (top middle), X-ray SB radial profile (top right), two component WL shear maps (bottom left and middle), and radial profile of X-ray temperature are shown. The grayed out portions of the maps are data that are excluded from the fit. For the SZ and X-ray portion of the analysi… view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Radial profiles of the model SZ (top left), X-ray SB (top right), X-ray temperature (bottom left) and tangential shear (bottom right) obtained from the accepted samples from the MCMC. For the two dimensional SZ and X-ray model maps, the radial profiles were obtained vi…

**Figure 5.** Figure 5: Posterior distributions of the mass and concentration obtained for a fit to Abell 1689 using SZ, X-ray SB and temperature, and WL data assuming a triaxial geometry (in green, labeled as M200c,triax and c200c,triax) and using only WL data, assuming a spherical geometry …

**Figure 7.** Figure 7: Gas mass fraction computed from our fits to the gas and total mass density compared to the ensemble average profile obtained from simulated galaxy clusters from The300 used in the analysis of Rasia et al. (2025). The 68 per cent credible region and intrinsic scatter ar…

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

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, " * write output.state after.block = add.period write newline

ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 ...

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write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....

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