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REVIEW 4 major objections 9 minor 42 references

Local luminosity functions of galaxies at (sub)millimeter wavelengths from Planck surveys

T0 review · 4 major / 9 minor · reviewed 2026-07-31 · grok-4.5

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Pith's one-line read Planck full-mission maps yield steeper bright-end local (sub)millimeter luminosity functions than earlier catalogs.

desk verdict Solid PCCS2-era remeasurement of local monochromatic submm LFs with a steeper bright end; IR LF and DMF inherit fixed-SED/Td assumptions that the paper itself flags. read the letter →

arxiv 2607.24289 v1 pith:BETNJWQO submitted 2026-07-27 astro-ph.CO astro-ph.GA

Matteo Bonato , Gianfranco De Zotti This is my paper
classification astro-ph.COastro-ph.GA
keywords localluminosityfunctionsubmillimetergalaxiesPlanckdustmassinfrared1/Vmaxkerneldensityestimation
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 rebuilds the local luminosity functions of galaxies at 857, 545, 353, and 217 GHz from the full-mission Planck Compact Source Catalog, restricted to the truly local volume (D < 180 Mpc). Because evolutionary effects are strong at these wavelengths even by z ~ 0.1, a strictly local, all-sky sample is the cleanest benchmark available. Using both classical 1/Vmax binning and a 1/Vmax-weighted kernel density estimator, the authors find a significantly steeper decline above the knee than earlier ERCSC- or Herschel-based estimates, lower high-luminosity space densities, and roughly 35 percent lower luminosity density at 857 GHz. The same samples also supply a total infrared luminosity function and a dust-mass function. The result matters because every evolutionary model of dusty galaxies is normalized to the local luminosity function; a steeper bright end changes the expected abundance of the rarest, most luminous systems.

What carries the argument

The 1/Vmax-weighted kernel density estimator (constant bandwidth 0.25 dex) that produces a continuous luminosity function while still correcting for survey selection; results are cross-checked against classical binned 1/Vmax.

What would settle it

An independent all-sky or large-area local sample at the same frequencies that uses multi-temperature SED fits or energy-balance modeling and recovers a shallower bright-end slope or higher luminosity density would falsify the central claim.

Watch

Extended reading notes

Core claim

With PCCS2+2E photometry and NED-LVS distances inside 180 Mpc, the local luminosity functions at 857, 545, 353, and 217 GHz are mutually consistent between 1/Vmax and KDE and decline more steeply above the knee than previous estimates, yielding lower high-luminosity densities and a ~35 percent lower 857 GHz luminosity density than Marchetti et al. (2016).

Load-bearing premise

K-corrections, total infrared luminosities, and dust masses all rest on one fixed starburst spectral template and fixed dust temperature and opacity; if real SEDs or temperatures change systematically with luminosity, the bright-end shapes shift.

Editorial extensions

If this is right

  • Evolutionary models of dusty galaxies must be renormalized to a lower local high-luminosity density.
  • The total infrared luminosity function shows a power-law rather than Schechter bright-end decline, matching IRAS more closely than many Herschel fits.
  • The dust-mass function declines as a power law at the highest masses, raising the local dust-mass density relative to some H-ATLAS Schechter fits.
  • Future (sub)millimeter surveys can treat these Planck local functions as the zero-redshift anchor free of evolutionary contamination.

Reading between the lines

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

  • If the steeper bright end is real, predictions for the number of ultra-luminous infrared galaxies and strongly lensed submillimeter sources at moderate redshift will decrease.
  • The failure of optical/near-IR energy-balance fits flagged in the paper suggests that aperture mismatches remain a limiting systematic for multi-wavelength local luminosity functions.
  • A joint re-analysis that floats dust temperature with luminosity on the same Planck+IRAS photometry would directly test how much of the steep slope is template-driven.
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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 / 9 minor

Summary. The authors re-derive the local (D < 180 Mpc) galaxy luminosity functions at 857, 545, 353, and 217 GHz using the Second Planck Catalog of Compact Sources (PCCS2+2E), superseding the earlier ERCSC-based work of Negrello et al. (2013), and cross-matching with the NED-LVS local-volume catalog (with HECATE as a cross-check). LFs are computed with both the classical 1/Vmax estimator and a 1/Vmax-weighted kernel density estimator (KDE), with Poisson/Gehrels and bootstrap errors respectively. From the 857 GHz sample they derive a total IR (8–1000 µm) LF via a one-parameter normalization of the Cai et al. (2013) starburst SED, and from the 353 GHz LF a dust mass function via the Hildebrand (1983) relation with fixed Td = 17.7 K and κ850 = 0.77 cm² g⁻¹. Headline results: the two estimators agree; the bright-end decline is steeper than in earlier estimates; the 857 GHz local luminosity density is ~35% below Marchetti et al. (2016); and the high-mass end of the dust mass function declines as a power law rather than an exponential.

Significance. If the results hold, this is the definitive Planck-based benchmark for the local (sub)mm luminosity functions: it uses full-mission data with ~3× better sensitivity and ~10× more sources than the ERCSC-based estimate, exploits essentially complete local galaxy catalogs with redshift-independent distances, and uniquely covers 850 µm and 1.38 mm over the whole high-latitude sky. The paper has several concrete strengths that deserve explicit credit: (i) two largely independent nonparametric estimators that are cross-checked against each other; (ii) careful, documented treatment of contamination (non-galaxy sources removed by name, random-association probability quantified at ~0.17%, multiples explicitly discussed); (iii) full tabulation of the binned LFs and fit parameters (Tables 1, 2, 4–10), making the results directly reusable and falsifiable; (iv) explicit, quantitative comparisons to prior work with proposed physical origins for the discrepancies (Eddington boosting in ERCSC fluxes, evolution in wider-z Herschel samples). The work is descriptive rather than model-dependent at the monochromatic level, which is its main strength.

major comments (4)
  1. [§4.5, eq. (9), Fig. 5, Table 9] §4.5 and Fig. 5: the conclusion that the high-mass end of the dust mass function declines as a power law 'in agreement with Clemens et al. (2013)', in contrast to the exponential Schechter declines of Dunne et al. (2011) and Beeston et al. (2018), is derived from eq. (9) with a single fixed Td = 17.7 K. Because B_λ(T) is exponentially sensitive to Td on the Rayleigh-Jeans side, a modest temperature–luminosity correlation (luminous galaxies are typically warmer) would systematically move the most luminous galaxies out of the highest-mass bins and could steepen an apparent power law into something closer to an exponential — or vice versa. The authors themselves note that Clemens et al. (2013) avoided this by computing a bivariate LF–DMF. Since the power-law-vs-exponential claim is a headline comparison result of §4.5, it needs at minimum a quantitative sensitivity test: e.g., recompute the
  2. [§4.2, Tables 4–5, Fig. 2] §4.2: the total IR LF is built by normalizing a single Cai et al. (2013) starburst SED template (one free parameter), after multi-parameter and energy-balance fits failed. The authors are commendably transparent about this, but the IR LF's bright-end slope (β ≈ 2.1–2.3, Table 5) and the claimed power-law (non-Schechter) decline at high L_IR rest on a mapping in which every galaxy has the same FIR color. A luminosity-dependent SED shape (e.g., warmer dust at higher L_IR, as in the Sanders et al. 2003 template library) would shift galaxies between the top bins of Table 4, where N is 7–26 per bin, and could materially change β. A concrete, tractable test: recompute the IR LF for the subsample with IRAS 60 and 100 µm detections (968/1019 galaxies) using a two-point 60/100 color to set a modified-blackbody temperature, and compare the resulting bright-end slope with Table 5. Alternatively the
  3. [§3 (eq. 6 and following paragraph), §5] §3 (KDE) and §5: the bandwidth h = 0.25 dex was chosen by 'testing a range of bandwidths and comparing the resulting KDEs with the binned 1/Vmax estimates', i.e., tuned against the very estimator the KDE is then compared with. The Discussion's claim that the agreement of the two methods 'confirms the robustness of the derived spatial densities' is therefore partly by construction, and the statement that the empirical optimization 'successfully suppresses Poisson noise without introducing systematic smoothing biases' is not demonstrated — no bias quantification is shown. This matters most at the bright end, where the KDE central estimates sit slightly above 1/Vmax (Figs. 1, 3) and the headline result is precisely the steepness of the decline. The authors should either (a) select h with an objective, 1/Vmax-independent criterion (e.g., likelihood cross-validation as in Yuan et al. 2022, wh
  4. [§4.1, Fig. 1, Table 2] §4.1: 32 sources classified as multiples (30 pairs, 2 triplets) are retained with their total Planck flux, and the authors acknowledge these 'reside' at the bright tail of the LF. Since the significantly steeper bright-end decline relative to Negrello et al. (2013) and Marchetti et al. (2016) is a central result, the contribution of multiples should be quantified rather than only discussed qualitatively: recompute the 857 GHz LF (and the fitted β in Table 2) with the multiples removed or deblended (e.g., splitting flux by NED-LVS member luminosities), and report the effect. If the effect is as small as the text implies ('slightly overestimated'), one number demonstrating it would close the issue.
minor comments (9)
  1. [Table 2] Table 2, 545 GHz / Eq. (8) row: the values log(L*) = 22.850, α = 0.264, β = 2.649 are identical to the 857 GHz / Eq. (8) row (only log Φ* differs by 0.01). This is almost certainly a copy-paste error; please verify and correct, since the Table 3 luminosity density at 545 GHz presumably derives from these parameters.
  2. [§3, eqs. (2) and (4)] Eqs. (2) and (4): index typos. In eq. (2) the sum over j uses V_max,i; in eq. (4) the expression for N_eff sums 1/V_max,i (index i) inside a sum over j. Both should presumably be indexed j.
  3. [§4.3] §4.3: 'we compare them with those of Negrello et al. (2007) and Marchetti et al. (2016)' — the 2007 reference appears to be a typo for Negrello et al. (2013), whose 500 µm LLF is what is plotted in Fig. 3.
  4. [§3, eq. (1)] §3, eq. (1): ω = 2π corresponds to the full |b| ≥ 30° region, but the HFI zone masks (and the |b| cut) remove some additional area. Please state whether ω = 2π is the actual effective area used or an approximation, and if the latter, give the masked effective area and its (small) effect on the normalization.
  5. [§4.5] §4.5: the dust mass density is written as 'log(ρ_dust/L_⊙ Mpc⁻³) = 5.38' — the units should be M_⊙ Mpc⁻³, not L_⊙.
  6. [§4.1] §4.1: the random-association estimate uses '1017 trials' without explanation of where this number comes from (the sample at that point has 1022 objects before additions/removals). Please clarify.
  7. [§5] §5: 'our results agree with those derived from Herschel surveys at 857 and 600 GHz (350 and 500 µm)' — elsewhere the paper consistently converts Marchetti et al.'s 500 µm results to 545 GHz via the 1.35 factor of Maddox et al. (2018); the 600 GHz wording here is slightly inconsistent with that convention.
  8. [Acknowledgements] Acknowledgements thank 'the anonymous referee' in what appears to be a first-version arXiv submission; this is presumably a leftover from a previous submission round and should be checked.
  9. [Table 3, §4.1] Table 3: the 'Marchetti' row lists only two values without a note explaining the empty 353 and 217 GHz columns; a one-line note would help. Also, the 6% difference between the KDE central estimate and the KDE DPL fit mentioned in §4.1 could be included in Table 3 for completeness.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: observational 1/Vmax and KDE luminosity densities from external catalogs, with post-hoc descriptive fits only.

full rationale

This paper measures local (sub)mm luminosity functions from PCCS2+2E photometry cross-matched to NED-LVS (D<180 Mpc), using classical 1/Vmax and 1/Vmax-weighted KDE. The monochromatic LFs are direct number-density estimates against external flux and distance catalogs; they are not derived from a model whose target is reinserted. Double power-law forms (eqs. 7–8) and their parameters (Tables 2, 5, 9) are fitted after the binned/KDE densities are obtained and serve only as descriptive summaries and integrators for luminosity density—they are not claimed as first-principles predictions. KDE bandwidth (h=0.25) is an empirical smoothing choice tuned for visual consistency with 1/Vmax, not a proof that forces the LF shape. Citations to Negrello et al. (2013), Marchetti et al. (2016), and related works are used for comparison of results, not as load-bearing uniqueness theorems or ansatz inputs that define the new densities. Fixed external SED (Cai et al. 2013) and dust parameters (Td, κ) for K-corrections, L_IR, and Mdust are model assumptions that affect systematics, not circular reductions of output to input. The derivation chain is self-contained observational estimation; score 0.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The result is an empirical LF measurement. Load-bearing external inputs are Planck completeness/reliability, NED-LVS completeness and distances inside 180 Mpc, a single SED family for K-corrections and L_IR, and fixed dust emissivity/temperature for Mdust. Free choices include KDE bandwidth, flux thresholds slightly above quoted 90% limits, match radius practice, and which contaminants to drop. No new physical entities are postulated.

free parameters (5)
  • KDE bandwidth h = 0.25 dex in log L
    Constant h=0.25 dex chosen by empirical comparison to binned 1/Vmax to avoid over-smoothing the bright end; not fixed by an external rule.
  • Double power-law LF parameters (Φ*, L*, α, β) = e.g. 857 GHz eq.(8): log Φ*=-1.953, log L*=22.850, α=0.264, β=2.649
    Fitted separately per frequency and estimator (Tables 2, 5, 9) to summarize measured LFs; descriptive, not predictive inputs.
  • Dust temperature Td = 17.7 K
    Fixed Td=17.7 K following Clemens et al. (2013) converts 353 GHz L to Mdust (eq. 9); not fit per galaxy.
  • Dust absorption coefficient κ_850 = 0.77 cm² g⁻¹
    Adopted κ_850=0.77 cm² g⁻¹ following Dunne/Vlahakis/Beeston; scales all dust masses and Ω_dust.
  • Distance and latitude/flux selection thresholds = D<180 Mpc; channel-dependent S_lim
    D_lim=180 Mpc, |b|≥30°, and channel flux floors (e.g. 1 Jy at 857 GHz, 560 mJy at 545 GHz) define the sample; partly motivated by catalog completeness but still analysis choices.
assumptions (7)
  • standard math Classical 1/Vmax and 1/Vmax-weighted KDE give unbiased LF estimates given correct distances, fluxes, and selection function.
    Invoked throughout Sect. 3 (eqs. 1–6) as the estimation framework.
  • domain assumption Flat cosmology with H0=67.7 km s⁻¹ Mpc⁻¹, Ωm=0.31 (with minor NED-LVS H0=69.6 correction) converts distances and volumes correctly.
    Stated in the introduction cosmology paragraph; enters every Vmax.
  • domain assumption NED-LVS is sufficiently complete for bright Planck-detected galaxies at D<180 Mpc, and redshift-independent distances are preferred where available.
    Sect. 1–2 and sample construction; completeness cited from Cook et al. (2023).
  • domain assumption Cai et al. (2013) starburst SED is adequate for K-corrections and single-parameter L_IR fits to sparse FIR/submm photometry.
    Sect. 3 and 4.2; energy-balance full-SED fits were abandoned as incompatible.
  • domain assumption Planck PCCS2/PCCS2E 90% completeness limits and extragalactic-zone reliability cuts define a usable flux-limited sample at |b|≥30°.
    Sect. 2 citing Planck Collaboration XXVI (2016) and BeeP rephotometry.
  • domain assumption Modified blackbody with fixed Td and κ converts monochromatic 850 μm luminosity to dust mass without large luminosity-dependent bias.
    Sect. 4.5 eq. (9); standard but debated in the dust literature.
  • ad hoc to paper Keeping cataloged multiples and removing named non-galaxies/cirrus/AGN-dominated sources yields a fair galaxy LF bright end.
    Explicit cleaning steps in Sects. 4.1–4.6; authors note multiples may slightly overestimate the bright tail.

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Cite this review

Pith. "Pith review of Local luminosity functions of galaxies at (sub)millimeter wavelengths from Planck surveys." pith.science (2026). https://pith.science/paper/BETNJWQO

@misc{pith2026260724289,
  author       = {Pith},
  title        = {Pith review of: Local luminosity functions of galaxies at (sub)millimeter wavelengths from Planck surveys},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BETNJWQO}},
  note         = {Machine review of arXiv:2607.24289}
}
abstract

The Planck all-sky surveys at (sub)millimeter wavelengths enable us to accurately determine the corresponding local luminosity functions up to the highest luminosities. The detected galaxies are strictly local, so evolutionary effects, which are known to be particularly strong at these wavelengths, are not a problem. However, previous studies have so far relied only on the Planck Early Release Compact Source Catalog (ERCSC) for this purpose. Another important improvement over earlier estimates is the availability of complete all-sky catalogs of galaxies within hundreds of megaparsecs, with redshift-independent distances for nearby objects, for which redshifts are not reliable distance estimators. In this paper we re-estimate the (sub)millimeter local luminosity functions using data from the Second Planck Catalog of Compact Sources, which supersedes the previously used ERCSC and contains far more sources and more accurate photometry. We computed the luminosity functions using both the classical $1/V_{\rm max}$ and the nonparametric kernel density estimation (KDE) method, which overcomes limitations of binning techniques. Our implementation of the KDE uses the $1/V_{\max}$ weighting to account for survey selection effects. We obtain Planck-based local luminosity functions at 857, 545, 353, and 217 GHz, as well as the total IR luminosity function and the dust mass function. We find significant differences from earlier estimates and discuss their possible origins.

Figures

Figures reproduced from arXiv: 2607.24289 by the authors.

Figure 1
Figure 1. Local luminosity function at 857 GHz determined using [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Total IR (8–1000 µm) local luminosity function deter￾mined using both the 1/Vmax and the KDE estimators. In the 1/Vmax case we also show the double power-law fits with eqs. (7) and (8). In the KDE case, the solid dark blue line shows the central estimates, while the red line (DPL fit) shows the double power-law fit (eq. (8)). Earlier estimates by Sanders et al. (2003), Gruppioni et al. (2013), Marchetti et al. (2016… view at source ↗
Figure 3
Figure 3. Local luminosity function at 545 GHz determined using [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Local luminosity function at 353 GHz determined us [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Table 9 shows the best-fit values of the double power-law [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Local luminosity function at 217 GHz determined using [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

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