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REVIEW 3 major objections 5 minor 171 references

A new constraint on galaxy-halo connections of [O II] emitters via HOD modelling with angular clustering and luminosity functions from the Subaru HSC survey

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper establishes that a halo occupation distribution model embedding a double-power-law luminosity-to-halo-mass relation can jointly reproduce the angular clustering and luminosity functions of [O II] emission-line galaxies, giving…

desk verdict A useful HOD extension for [O II] emitters that joins ACFs and luminosity functions, but the added value of the LF constraint is asserted more than demonstrated. read the letter →

arxiv 2412.19898 v2 pith:N66DJB6Y submitted 2024-12-27 astro-ph.GA astro-ph.CO

Shogo Ishikawa , Teppei Okumura , Masao Hayashi , Tsutomu T. Takeuchi This is my paper · ORCID
classification astro-ph.GAastro-ph.CO
keywords halooccupationdistributionemission-linegalaxies[OII]emittersluminosityfunctionangularcorrelationgalaxy–haloconnectiondarkmatterhalos
topics 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

This paper argues that the connection between [O II] emission-line galaxies (ELGs) and their host dark matter halos can be captured more completely by folding galaxy luminosity directly into the halo occupation distribution (HOD). The authors introduce a double-power-law luminosity-to-halo-mass relation (LHMR) that assigns each halo a predicted line luminosity, which lets the model predict luminosity functions as well as angular correlation functions. Applied to [O II] emitters at z = 1.193 and z = 1.471 from narrow-band imaging, the joint fit reproduces both measured angular clustering (reduced chi-squared around 0.8) and the observed luminosity functions. If correct, this yields a smoother, more gradual occupation of dark halos than earlier ELG models, characteristic halo masses around $10^{11}$.6 $h^{-1}$ solar masses, and satellite fractions of about 0.2–0.3. The authors further use the inferred halo masses to argue that the z ~ 1.4 emitters are plausible progenitors of present-day Milky-Way-like halos.

What carries the argument

The load-bearing object is the luminosity-to-halo-mass relation (LHMR), a double power law f_LHMR(M_h) = (L_0/2)[(M_h/M_trans)^β + (M_h/M_trans)^γ] (Eq. 11), which converts a halo mass into the predicted [O II] line luminosity of its central galaxy. This relation is embedded in the central occupation N_c(M_h | > L_th) (Eq. 10) through a Gaussian term plus an error-function term, and its inverse sets the satellite mass scale (Eq. 14). Inserting the occupation into Eq. 21 yields the model luminosity function, so the likelihood (Eq. 36) includes both the angular correlation function and the LF. The double-power-law shape, with positive slopes 0 < β < γ, is motivated by the stellar-to-halo-mass relation and observed ELG luminosity–halo-mass correlations; it is what allows the model to predict the LF without prescribing a Schechter or other analytic form.

What would settle it

One could measure the [O II] luminosities of central galaxies in halos of known mass (e.g., via galaxy groups or weak lensing) at z ~ 1.2–1.5 and check whether the relation follows a double power law; a plateau, strong redshift dependence, or significant scatter would falsify the model. Alternatively, a deeper survey constraining the bright end of the [O II] luminosity function at these redshifts would test the extrapolation: a bright-end excess or deficit relative to the double-power-law prediction would rule out the assumed LHMR shape.

Watch

Extended reading notes

Core claim

The central claim is that a deterministic double-power-law relation between [O II] line luminosity and halo mass, f_LHMR(M_h) = (L_0/2)[(M_h/M_trans)^β + (M_h/M_trans)^γ], when inserted into the HOD central occupation function, gives the model enough information to predict the differential luminosity function without assuming a functional form for it. Fitting jointly to the angular correlation function and the luminosity function of [O II] emitters at two redshifts (z = 1.193 and z = 1.471) yields reduced chi-squared values of 0.79 and 0.86, with the best-fitting luminosity functions fully consistent with observations. The inferred median halo masses of central ELGs are log10(M_LF^min / $h^{-1}$ M_sun) = 11.60 (+0.19, -0.20) and 11.66 (+0.18, -0.19) for the two samples, and satellite fractions are 0.31 ± 0.08 and 0.20 ± 0.06. The paper shows that the Gaussian component of the central occupation is negligible, so a simplified model without it fits equally well, and it interprets the smooth occupation as a more realistic representation of ELG environments compared with a sharp mass threshold.

Load-bearing premise

The load-bearing premise is that the true relation between [O II] line luminosity and halo mass is exactly the deterministic double power law of Eq. 11, with no scatter and no assembly bias, and that its parameters can be learned from the same luminosity function data used in the likelihood.

Editorial extensions

If this is right

  • If the model is right, ELG clustering analyses gain a new constraint: the luminosity function carries differential number-density information that the integrated number density alone does not, making halo-mass inferences less degenerate.
  • The inferred occupation is smooth rather than sharply thresholded, implying ELGs populate halos across a broad mass range rather than switching on abruptly at a single mass.
  • The characteristic halo masses of about 10^11.6 h^-1 M_sun and satellite fractions of 0.2–0.3 at z ~ 1.2–1.5 provide calibration targets for ELG mock catalogues for upcoming redshift surveys.
  • Extrapolating the inferred halo masses forward with the extended Press–Schechter formalism suggests the z ~ 1.5 [O II] emitters evolve into Milky-Way-sized halos by z = 0.
  • The measured satellite fraction at z ~ 1.47 is more than 1σ below the IllustrisTNG simulation prediction, hinting that the simulation may overproduce star-forming satellites at that epoch.

Reading between the lines

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

  • The framework is naturally extendable to other line tracers (Hα, Lyα) or broad-band-selected populations: one only needs to replace the LHMR with the appropriate luminosity–halo-mass calibration, and the LF constraint becomes available.
  • A direct test of the deterministic LHMR is to compare the model's predicted zero scatter in central luminosity with measurements from group or weak-lensing samples; adding a lognormal scatter is a straightforward generalization.
  • The joint ACF+LF likelihood may break degeneracies that clustering alone leaves unresolved, especially between the satellite occupation amplitude and the central–satellite boundary, which could sharpen forecasts for ELG redshift-space distortion analyses.
  • The model ignores assembly bias by construction; hydrodynamical or high-resolution N-body simulations that introduce formation-time dependence could shift the inferred M_LF^min and satellite fractions, so quantifying that sensitivity would be a useful next step.
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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 / 5 minor

Summary. The paper proposes a new HOD framework for [O II] emission-line galaxies in which the central occupation is tied to a double-power-law luminosity-to-halo-mass relation (LHMR, Eq. 11). This allows the model to predict luminosity functions as well as angular correlation functions. The authors fit the model jointly to ACFs and LFs of HSC NB816 and NB921 [O II] emitters at z=1.193 and z=1.471, compare with the Geach et al. (2012) HOD model, and report good fits (best-fit reduced chi2 around 0.8-0.9 in Table 3, with a text value of 0.79/0.86 in Section 4.3.2). They infer characteristic halo masses log10(M_LF^min/h^-1 Msun) ~ 11.5-11.7, satellite fractions ~0.2-0.3, and use extended Press-Schechter evolution to argue that the z~1.4 sample may evolve into Milky-Way-like halos. The paper also compares derived LHMR, baryon conversion efficiency, and SHMR with literature and with IllustrisTNG satellite fractions.

Significance. If the central claim is sustained, the framework is a useful step toward ELG HOD models that connect line luminosity to halo mass, with clear applications to mock catalogues for PFS, DESI, Euclid, and Rubin. The observational analysis is careful in several respects: jackknife covariance matrices with Hartlap correction, integral-constraint correction, explicit contamination modelling via f_ELG(M_h), and consistency checks against spectroscopic contamination estimates and IllustrisTNG. The public availability of the underlying halomod and emcee infrastructure also aids reproducibility. However, the load-bearing claim that the LF constraint makes the HOD constraints 'more robust' is not demonstrated by an ablation, and the luminosity-function fit is not an independent validation because the same data enter the likelihood that generates the model LF. These gaps prevent the paper from fully establishing its headline claim, although they are addressable with additional analysis.

major comments (3)
  1. [§3.3.3, Eq. (21)] The Gaussian term in the central occupation (Eq. 10) is independent of the threshold L_th, so it cancels exactly in the LF difference N_tot,ELG(M_h|>L1) - N_tot,ELG(M_h|>L2). Consequently the LF likelihood in Eq. (38) provides no constraint on F_Gauss, L_Gauss, or sigma_logM_h; those parameters are constrained only by the ACF (and the abundance through f_ELG). The text should state this limitation explicitly and discuss what the LF actually constrains: the error-function transition, the massive-end decay phi_d(M_h), and the satellite term. This is not fatal because the Gaussian component turns out to be small, but it is essential for the paper's claim that luminosity information makes the central occupation more robust.
  2. [§4.3.2 and §4.4] The central claim that joint ACF+LF fitting provides 'more robust constraints' than ACF+number-density fitting is not demonstrated by any ablation. The comparison with the Geach et al. (2012) model changes both the HOD parameterisation and the data entering the likelihood, so it cannot isolate the effect of the LF. I request an ablation in which the proposed HOD model is fitted (a) to the ACF plus the observed number density with a Gaussian penalty analogous to Eq. (33), and (b) to the ACF plus the LF, with a comparison of posterior widths and pulls for M_LF^min, f_sat, and b_g. In addition, the statement that the best-fitting LFs are 'fully consistent with the observed LFs' is not an independent check: the same observed LF data enter Eq. (38) and are generated by Eq. (21) from the fitted LHMR. A posterior-predictive or cross-validation test, such as predicting the NB921 LF from the NB816 fit or vice versa, would materially support the claim that the LF constraint adds information.
  3. [§5.1.1, Fig. 11] The Milky-Way-descendant conclusion follows from M_LF^min (Eq. 39) evolved with EPS. M_LF^min is derived from the central occupation built on the deterministic double power-law LHMR of Eq. (11), with no explicit scatter and a functional form that is not validated independently. The paper itself notes in Section 5.2.1 that the bright/massive end of the LHMR is statistically difficult to constrain. A different LHMR shape, a redshift-dependent LHMR, or intrinsic scatter degenerate with sigma_logL could shift the inferred M_LF^min and therefore the z=0 descendant masses. Please test the sensitivity of M_LF^min and the Milky-Way connection to (i) an alternative LHMR parametrisation and (ii) scatter about the LHMR, or compare the predicted central occupation against hydrodynamical ELG catalogues (e.g., IllustrisTNG or MillenniumTNG) to bound the systematic error.
minor comments (5)
  1. [§4.3.2 vs Table 3] The text states minimum reduced chi2 = 0.79 (NB816) and 0.86 (NB921), whereas Table 3 reports best-fit chi2/dof = 6.93/15 = 0.46 and 12.50/14 = 0.89 for the model with Gaussian central occupation. Please reconcile these values.
  2. [§3.1, Eq. (11)] The text says the two power-law slopes satisfy 0<β<γ, but the no-Gaussian best fit for NB816 in Table 3 has β=1.03 and γ=1.03. Please clarify whether this inequality is a prior assumption actually imposed in the MCMC or an expectation stated after the fit.
  3. [§4.3.1] The variation of the fixed ELG fraction endpoints (f_min_ELG and f_max_ELG) is described as having little impact, but no results are shown. A short table or appendix giving the tested range and the resulting changes in M_LF^min, f_sat, and b_g would strengthen this claim.
  4. [Figure 13] The y-axis range of the LHMR plot spans 38-52 in log10(L_ELG/erg/s), which is much wider than the data and literature points; narrowing the axis would improve readability.
  5. [Abstract] The abstract contains the phrase 'mock catalogues of for future surveys'; please correct this typo.

Circularity Check

1 steps flagged · score 4.0 of 10

The LF is used both as a fitting constraint and as a claimed output, so the reported agreement of the model LFs with the observed LFs is a refit, not an independent prediction.

  1. fitted input called prediction [Abstract; Section 3.3.3 (Eq. 21); Section 4.3.1 (Eq. 38); Section 4.3.2]
    "This innovation enables prediction of galaxy luminosity functions (LFs) and facilitates joint analyses using both angular correlation functions (ACFs) and LFs. ... The best-fitting results of the LFs are fully consistent with the observed LFs."

    The HOD-predicted LF is built from the fitted HOD parameters via Eq. 21, and Eq. 38 adds chi2_LF = sum_{i,j} (Phi_obs(L_i) - Phi_HOD(L_i)) C^{-1}_{ij,LF} (Phi_obs(L_j) - Phi_HOD(L_j)) directly to the likelihood. The observed LF is therefore an input to the parameter fit, not an independent target. 'Predicting' the LF and then reporting that the best fit is 'fully consistent' with it is a refit: the agreement is produced by minimizing chi2_LF, so it cannot serve as validation of the LF-prediction capability or of the assumed double-power-law LHMR. The inference itself remains a legitimate joint fit of ACF+LF, but the LF consistency claim is circular in the framing.

full rationale

The main circular step is the treatment of the luminosity function as both a constraint and a reproduced prediction. Equation 38 explicitly fits Phi_HOD to Phi_obs, so the 'fully consistent' LFs in Section 4.3.2 are guaranteed by construction rather than by an out-of-sample test. This is a real but partial circularity, because the paper's central parameter inference is a standard joint fit to ACF and LF; the ACF fit, the comparison to the Geach HOD model, and the external comparisons of LHMR/BCE/SHMR provide independent content. The Gaussian central occupation term in Eq. 10 is independent of the luminosity threshold and cancels in the LF difference in Eq. 21, further weakening the claim that the LF constraint strongly reaches the full central occupation, though this is a structural limitation rather than circularity. The M_LF^min and Milky-Way-descendant statements are model-derived quantities that depend on the assumed double-power-law LHMR, but the paper does not claim to derive that shape from first principles; it is an explicitly stated ansatz justified by external literature. Self-citations such as Hayashi et al. (2020) and Okumura et al. (2021) set sample definitions and prior choices but are not used to force the central conclusion in a circular way. Overall, the derivation is not equivalent to its inputs, but one prominent 'prediction' reduces by construction; score 4.

Assumptions & free parameters 17 free parameters · 7 assumptions · 0 invented entities

The central claim is carried by 15 free parameters in the fiducial no-Gaussian model (17 including the hand-fixed f_min_ELG and f_max_ELG, or 20 if the Gaussian component is included), plus external calibrations for the halo mass function, bias, concentration, and the M_cut-M_sat relation. The most consequential unmeasured premise is the double-power-law LHMR, whose parameters are fitted to the same LF data that the model is said to predict. No new physical entities are introduced.

free parameters (17)
  • f_min_ELG = fixed to 0.70
    Hand-chosen lower limit for the ELG fraction sigmoid, set to the sample completeness threshold in Section 4.3.1.
  • f_max_ELG = fixed to 1.00
    Hand-chosen upper limit for the ELG fraction sigmoid, set to full completeness in Section 4.3.1.
  • F_erf = 0.75 +/- 0.19 (NB816 posterior mean, no-Gaussian HOD)
    Amplitude of the error-function central occupation term in Eq. 10.
  • sigma_logL = 0.26 +/- 0.18 (NB816)
    Width of luminosity scatter in the error-function central occupation.
  • F_d = 0.59 +/- 0.30 (NB816)
    Amplitude of the high-mass decay in central occupation, Eq. 12.
  • log10(M_d) = 13.18 +/- 0.62 (NB816, h^-1 Msun)
    Characteristic mass where central ELG occupation decays.
  • sigma_d = 0.52 +/- 0.32 (NB816)
    Width of the high-mass decay transition.
  • log10(L0) = 42.24 +/- 0.91 (NB816, erg/s)
    Normalization of the double-power-law LHMR in Eq. 11.
  • log10(Mtrans) = 12.26 +/- 0.81 (NB816, h^-1 Msun)
    Transition halo mass of the LHMR double power law.
  • beta = 0.88 +/- 0.24 (NB816)
    Massive-end slope of the LHMR.
  • gamma = 1.67 +/- 0.74 (NB816)
    Low-mass slope of the LHMR.
  • F_s = 0.56 +/- 0.29 (NB816)
    Amplitude of the satellite power-law occupation, Eq. 13.
  • B_sat = 1.02 +/- 0.41 (NB816)
    Normalization of the satellite mass-scale relation, Eq. 14.
  • beta_sat = 1.35 +/- 0.47 (NB816)
    Power-law slope relating satellite mass scale to halo mass derived from the inverse LHMR.
  • alpha_sat = 0.46 +/- 0.18 (NB816)
    Power-law slope for the number of satellite ELGs.
  • log10(M_h,ELG) = 11.42 +/- 0.30 (NB816, h^-1 Msun)
    Transition halo mass of the ELG fraction sigmoid, Eq. 18.
  • alpha_ELG = 2.73 +/- 1.58 (NB816)
    Width of the ELG fraction sigmoid transition.
assumptions (7)
  • domain assumption Tinker et al. (2008) halo mass function, Tinker et al. (2010) halo bias, Duffy et al. (2008) concentration, NFW profile, CAMB transfer function, and revised Halofit non-linear power spectrum are valid.
    These external prescriptions are used to compute ACFs and halo-weighted quantities in Section 4.1; they are assumed accurate at the redshifts and mass scales considered.
  • domain assumption The LHMR is a deterministic double power law (Eq. 11) with 0 < beta < gamma, with no assembly bias and no explicit redshift evolution within each narrow slice.
    This shape is fitted to the same LF data used in the likelihood. If the true relation differs, the central occupations and LF predictions would be biased. Introduced in Eq. 11, Section 3.1.
  • ad hoc to paper The ELG fraction f_ELG(Mh) is a sigmoid with f_min_ELG = 0.70 and f_max_ELG = 1.00, and contaminants are homogeneously distributed.
    The fixed amplitude values are set to the sample completeness threshold (Section 4.3.1), not measured directly. Contamination correction assumes homogeneous fake sources and uses (1-f_fake)^2 in Eq. 20.
  • domain assumption The satellite cutoff mass M_cut is tied to M_sat through log10 M_cut = 0.76 log10 M_sat + 2.3 (Eq. 15), taken from Conroy et al. (2006).
    Imported from abundance-matching-based fits; not re-fitted in this work.
  • domain assumption Redshift distribution is constant within each narrow Delta-z ~ 0.03 slice.
    Tested by Okumura et al. (2021); they report at most ~7% effect on ACF amplitudes, so the assumption has some support.
  • domain assumption Dust corrections calibrated with local SDSS Balmer decrements apply at z ~ 1.2-1.5 (Eqs. 8-9).
    The intrinsic line luminosities used for LF fitting and LHMR inference depend on this extrapolation; if wrong, the fitted luminosity scale shifts.
  • domain assumption The extended Press-Schechter formalism correctly predicts halo mass growth from z ~ 1.2-1.5 to z = 0.
    Used for the Milky-Way-descendant claim in Section 5.1.1; it is a standard but approximate model of merger-driven halo growth.

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Cite this review

Pith. "Pith review of A new constraint on galaxy-halo connections of [O II] emitters via HOD modelling with angular clustering and luminosity functions from the Subaru HSC survey." pith.science (2026). https://pith.science/paper/N66DJB6Y

@misc{pith2026241219898,
  author       = {Pith},
  title        = {Pith review of: A new constraint on galaxy-halo connections of [O II] emitters via HOD modelling with angular clustering and luminosity functions from the Subaru HSC survey},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/N66DJB6Y}},
  note         = {Machine review of arXiv:2412.19898}
}
abstract

Establishing a robust connection model between emission-line galaxies (ELGs) and their host dark haloes is of paramount importance in anticipation of upcoming redshift surveys. We propose a novel halo occupation distribution (HOD) framework that incorporates galaxy luminosity, a key observable reflecting ELG star-formation activity, into the galaxy occupation model. This innovation enables prediction of galaxy luminosity functions (LFs) and facilitates joint analyses using both angular correlation functions (ACFs) and LFs. Using physical information from luminosity, our model provides more robust constraints on the ELG-halo connection compared to methods relying solely on ACF and number density constraints. Our model was applied to [O II]-emitting galaxies observed at two redshift slices at $z=1.193$ and $1.471$ from the Subaru Hyper Suprime-Cam PDR2. Our model effectively reproduces observed ACFs and LFs observed in both redshift slices. Compared to the established \citeauthor{geach12} HOD model, our approach offers a more nuanced depiction of ELG occupation across halo mass ranges, suggesting a more realistic representation of ELG environments. Our findings suggest that ELGs at $z\sim1.4$ may evolve into Milky-Way-like galaxies, as their inferred halo masses evolve accordingly based on the extended Press--Schechter formalism, highlighting their role as potential building blocks in galaxy formation scenarios. By incorporating the LF as a constraint linking galaxy luminosity to halo properties, our HOD model provides a more precise understanding of ELG-host halo relationships. Furthermore, this approach facilitates the generation of high-quality ELG mock catalogues of for future surveys. As the LF is a fundamental observable, our framework is potentially applicable to diverse galaxy populations, offering a versatile tool for analysing data from next-generation galaxy surveys.

Figures

Figures reproduced from arXiv: 2412.19898 by the authors.

Figure 1
Figure 1. The ELG fraction as a function of dark halo mass parameterized by equation 17. This function is characterised by the standard sigmoid function described in equation 18. The lower and upper limit of the ELG fraction at the less-massive and massive end are controlled by 𝑓 min ELG and 𝑓 max ELG parameters, respectively. The median halo mass and the width of the transition scale are represented by 𝑀ℎ,ELG and 𝛼ELG parame… view at source ↗
Figure 2
Figure 2. The HOD-model fitting results for observed ACFs at 𝑧 = 1.193 (NB816; blue) and 𝑧 = 1.471 (NB921; red) predicted by the HOD model proposed by Geach et al. (2012, left panel) and this study (middle and right panels). Circles with error bars represent the observed ACFs of [O ii]-emitting galaxies. The solid lines depict the best-fitting results obtained through the entire MCMC fitting process, and the shaded regions in… view at source ↗
Figure 3
Figure 3. The constrained HOD parameters of the HOD model proposed by Geach et al. (2012) obtained through the HOD-model fittings for [O ii] emitting galaxies at 𝑧 = 1.193 (NB816; blue) and 𝑧 = 1.471 (NB921; red). The diagonal panels show 1D posterior probability distributions for each HOD parameter, whereas contours in other panels depict marginalised 2D posterior distributions. Dark and light-coloured regions of the contour… view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: The posterior mean occupation functions of [O ii]-emitting galaxies for NB816 (upper panels) and NB921 (lower panels) are shown as a function of host dark halo mass. The left, middle, and right panels display the results obtained using the HOD models proposed by Geach …
Figure 6
Figure 6. Figure 6: The HOD-model fitting results for observed luminosity functions at 𝑧 = 1.193 (NB816; blue) and 𝑧 = 1.471 (NB921; red) using our HOD model. Left panels show the results using our HOD model with the Gaussian central occupation (Section 4.3.2), whereas right panels are re…
Figure 7
Figure 7. Figure 7: Similar to [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: Similar to [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]
Figure 9
Figure 9. Figure 9: Similar to [PITH_FULL_IMAGE:figures/full_fig_p015_9.png]
Figure 11
Figure 11. Figure 11: Halo masses and their redshift evolution of our [O ii]-emitting galaxies observed through NB816 (blue) and NB921 (red) filters. Shaded regions represent the 1𝜎 confidence intervals of halo mass evolution predicted by the extended Press–Schechter formalism. For compari…
Figure 12
Figure 12. Figure 12: Comparison of the satellite fractions for our [O ii]-emitting galax￾ies at 𝑧 = 1.193 (blue star) and 𝑧 = 1.471 (red star) with other galaxy populations at various redshifts as a function of stellar mass limit. The solid lines with shaded regions show the theoretical p…
Figure 13
Figure 13. Figure 13: This figure illustrates the relationship between the line luminosi￾ties of ELGs and their host halo masses, referred to as the LHMR in this study. Our [O ii] emitter samples observed through NB816 (blue, 𝑧 = 1.193) and NB921 (red, 𝑧 = 1.471) are presented with both po…
Figure 14
Figure 14. Figure 14: The baryon conversion efficiencies of ELGs as a function of halo mass. The results for our [O ii] samples are plotted in the same manner as in [PITH_FULL_IMAGE:figures/full_fig_p020_14.png]
Figure 15
Figure 15. Figure 15: The stellar-to-halo mass relationship of ELGs as a function of halo mass. The results for our [O ii] samples are plotted in the same manner as in [PITH_FULL_IMAGE:figures/full_fig_p021_15.png]

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    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

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