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The Contribution of Galaxies to the $3.4\,\mathrm{\mu m}$ Cosmic Infrared Background as Measured Using WISE

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

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Pith's one-line read This paper claims that galaxies contribute $I_\nu = 9.0\pm0.5$ kJy/sr to the 3.4 μm extragalactic background light, higher than most prior galaxy-integration estimates but consistent with direct measurements and blazar upper limits.

desk verdict The 9 kJy/sr galaxy EBL at 3.4 microns is a real, reproducible measurement, but the paper's own alternative preferred chain gives ~5 kJy/sr and the quoted 2 kJy/sr systematic bound does not cover that spread, so the headline is less solid than the abstract implies. read the letter →

arxiv 1908.00731 v3 pith:GMFPH32N submitted 2019-08-02 astro-ph.GA astro-ph.CO

Sean E. Lake , Edward L. Wright , Roberto J. Assef , Thomas H. Jarrett , Sara Petty , Spencer A. Stanford , Chao-Wei Tsai This is my paper · ORCID
classification astro-ph.GAastro-ph.CO
keywords extragalacticbackgroundlightcosmicinfraredluminosityfunctionspectralenergydistributionWISEnear-infraredgalaxyevolutionstatistics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to determine how much of the extragalactic background light (EBL) at 3.4 μm was emitted by galaxies. It combines a recently measured galaxy luminosity function at 2.4 μm with an average galaxy spectrum, then integrates the product over cosmic time. The central result is $I_\nu = 9.0 \pm 0.5\,\mathrm{kJy\,sr^{-1}}$ for the galaxy contribution, with systematic errors estimated at no more than about $2\,\mathrm{kJy\,sr^{-1}}$. That value is higher than most previous galaxy-integration estimates, but agrees with direct measurements of the total background and with gamma-ray blazar upper limits. If the result is right, known galaxies produce the bulk of the 3.4 μm background, leaving little room for an unidentified source at this wavelength.

What carries the argument

The central object is the spectro-luminosity functional, which describes how many galaxies occupy each combination of luminosity and spectral energy distribution. The paper never needs the full functional: it uses its first moment, the comoving spectral luminosity density $\rho_\nu$, computed from a Schechter luminosity function $\Phi(L_f,z)$ (a power-law faint end with an exponential cutoff at a characteristic luminosity) and the mean normalized galaxy SED $\mu_\nu$. The load-bearing identity is Equation (5), $d^2 I_\nu / (dz\,dL) = [\mu_\nu([1+z]\nu, L_f, z) / (\Omega_{\rm sky}(1+z))]\,(dD_c/dz)\,L_f\,\Phi(L_f,z)$, which converts the luminosity function into a contribution to the background at each redshift and luminosity. Integrating this over $z$ and $L$ gives $I_\nu$. The luminosity function is an evolving Schechter function whose parameters come from posterior chains of a previous measurement, and the mean SED comes from a separate fit to deep survey photometry; the full posterior distribution of the LF parameters is propagated through the integral to get the uncertainty.

What would settle it

A deep spectroscopic survey measuring the faint-end slope of the 2.4 μm luminosity function at $z \approx 0.5$–$1$ to an uncertainty of $\pm0.1$ would discriminate: if the slope is as steep as $\alpha \lesssim -1.9$, the predicted background falls to roughly $5\,\mathrm{kJy\,sr^{-1}}$. Alternatively, a fully completeness-corrected W1 galaxy count at the faint end would test the model directly, since the paper's own comparison shows the preferred model over-predicting the faint counts.

Watch

Extended reading notes

Core claim

The paper claims that the contribution of galaxies to the 3.4 μm extragalactic background light is $I_\nu = 9.0 \pm 0.5\,\mathrm{kJy\,sr^{-1}}$ ($\nu I_\nu = 8.0 \pm 0.4\,\mathrm{nW\,m^{-2}\,sr^{-1}}$ per e-fold), a value higher than most earlier galaxy-integration estimates. The estimate is built by combining a 2.4 μm galaxy luminosity function, measured from more than half a million galaxies with spectroscopic redshifts, with a mean galaxy spectral energy distribution derived from deep multi-band photometry, and integrating the product over redshift to $z=5$. The paper treats the luminosity-function parameters as a Bayesian posterior and propagates the full chain through the integral, so the quoted error reflects correlated parameter uncertainties. It argues that systematic uncertainties are unlikely to exceed $2\,\mathrm{kJy\,sr^{-1}}$ in either direction, and that the result is consistent with direct sky measurements of the total background and with upper limits set by TeV blazar observations.

Load-bearing premise

The calculation assumes that the adopted evolving Schechter luminosity-function model—with a fixed faint-end slope and a mean galaxy SED that does not change with redshift or luminosity—is the true description of the galaxy population, and a different but defensible version of the same model gives about 5 kJy/sr instead of 9.

Editorial extensions

If this is right

  • At 3.4 μm, known galaxies contribute $I_\nu = 9.0 \pm 0.5\,\mathrm{kJy\,sr^{-1}}$, so ordinary galaxies—not an unidentified source—account for most of the extragalactic background at this wavelength.
  • This galaxy-only value is consistent with both direct measurements of the total EBL and upper limits from TeV blazars, easing the earlier tension among these methods near 3.4 μm.
  • The evolving luminosity density and background tables published with the paper can be used directly to compute the optical depth of the universe to very-high-energy gamma rays.
  • If the model's over-prediction of faint W1 counts is real, deeper completeness-corrected counts will push the estimate toward the 5 kJy/sr alternative; if incompleteness explains the discrepancy, the 9 kJy/sr value will stand.

Reading between the lines

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

  • Editorial inference: If the 9 kJy/sr galaxy contribution survives deeper tests, the 3.4 μm band becomes a place where direct sky measurements, galaxy integration, and gamma-ray opacity constraints agree, which would localize the unresolved near-infrared background controversy to shorter wavelengths.
  • Editorial inference: The published evolving EBL tables could be combined with future TeV blazar spectra to test whether the gamma-ray horizon is explained by galaxies alone or requires extra light from, for example, extended galactic halos.
  • Editorial inference: The faint end is the decisive measurement: if the true faint-end slope $\alpha$ of the luminosity function is near $-2$, the integral requires a low-luminosity cutoff, and the value of that cutoff—not just the slope—determines how much faint-galaxy light is missed.
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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 estimates the contribution of galaxies to the 3.4 μm extragalactic background light (EBL) by integrating a luminosity function (from Lake et al. 2018) with a mean galaxy SED (from Lake & Wright 2016). The headline result is Iν = 9.0±0.5 kJy/sr for z<5, with a claimed systematic uncertainty below 2 kJy/sr. The authors propagate the full MCMC posterior of the LF parameters through the integral, provide machine-readable posterior chains, and compare predicted source counts in WISE and SDSS bands with observed counts. The paper concludes that known galaxies produce most of the 3.4 μm EBL, consistent with direct total-EBL measurements and blazar upper limits.

Significance. If the headline result holds, this is an important measurement: it is higher than most previous galaxy-integration estimates and helps to close the gap between direct EBL measurements and galaxy counts. The methodology has clear strengths: the EBL integral is a forward calculation from independently measured LF and SED quantities, the MCMC uncertainty propagation is statistically sound, the posterior chains are published under a DOI, and the comparison with source counts at multiple wavelengths is a useful diagnostic. The paper also is unusually honest about model limitations, including the non-evolving SED and constant faint-end slope. These strengths make the central claim worth serious consideration, provided the model-selection issue identified below is resolved.

major comments (4)
  1. [Section 3; Figure 3] The choice of the High z Prior chain over the High z Trim Prior chain is the load-bearing step in determining the headline value, but the paper does not provide a quantitative justification. Both chains are explicitly described as preferred, yet their z<5 backgrounds differ by roughly a factor of two (about 9 kJy/sr versus about 5 kJy/sr in Figure 3). The stated reasons for rejecting High z Trim Prior are plausibility arguments: its α = -1.93 is uncomfortably close to the α = -2 divergence, and its implied comoving number density evolution of 1.9±0.7 e-folds per Hubble time is considered too fast. These are not model-independent falsifications, and the same data set produced both chains. As written, the quoted statistical uncertainty of ±0.5 kJy/sr and the systematic bound of 2 kJy/sr do not include this between-chain spread of roughly 4 kJy/sr. The authors should either defend the selection with a quantitative criterion (e.g., a goodness-of-fit comparison or an explicitly motivated prior) or incorporate the chain-to-chain variation into the systematic uncertainty budget.
  2. [Section 4; Table 1; Figure 3] The redshift decomposition of the result exposes a second load-bearing concern. Table 1 shows Inu(z<1) ≈ 4.6 kJy/sr while Inu(z<5) ≈ 9.3 kJy/sr for the High z Prior chain, meaning that roughly half of the headline signal comes from z>1, beyond the redshift range of the LF data (which are limited to z≲1 as stated in Section 3). The z>1 contribution therefore rests entirely on the adopted extrapolation of φ*(z) and L*(z) in Equations 8-10. Because the competing High z Trim Prior chain effectively changes this extrapolation by a factor of two, the paper should quantify how much of the 9 versus 5 kJy/sr discrepancy arises specifically from the high-redshift extrapolation and should present a sensitivity analysis of the EBL integral to the assumed evolution model. Without such an analysis, the claim 'Iν = 9.0±0.5 kJy/sr' is not supported by the internal model spread.
  3. [Section 5; Figures 8-9] The paper uses the source-count comparisons as confirmation of the model, but the text itself weakens that confirmation precisely where the EBL integral is most sensitive. In Section 5, at the end of the flux-count comparison, the authors state that the High z Prior model's over-prediction at the faint end of the W1 counts 'should be viewed as suspect for the purposes of predicting faint galaxy flux counts.' Since the EBL integral is dominated by faint galaxies and high redshifts, this admission directly undermines the use of Figures 8 and 9 as independent checks of the background estimate. The authors need to explain how the faint-end count excess affects the credibility of the EBL integral, or to perform a quantitative test that separates the flux-count information from the EBL normalization. As it stands, the confirmation argument is circular in a way that is acknowledged but not addressed.
  4. [Section 5; last paragraph of Discussion] The systematic uncertainty budget is asserted rather than derived. The sentence 'any modification from the true value caused by the systematic limitations in this work is unlikely be more than about 2 kJy/sr in either direction' is not supported by a quantitative error analysis. The acknowledged limitations include a non-evolving mean SED, a constant faint-end slope, and an uncertain high-redshift L*(z) evolution, each of which could shift the integral by amounts comparable to or larger than the quoted 2 kJy/sr. The authors should either provide a systematic error estimate that combines these effects (e.g., by reweighting the chains or by marginalizing over plausible model extensions) or replace the 2 kJy/sr claim with a more defensible bound.
minor comments (5)
  1. [Section 4, paragraph describing Figure 3] In the phrase 'α = -1.93±-0.04' the sign of the error is garbled; it should read 'α = -1.93±0.04'.
  2. [Section 2, Equation (5) and surrounding text] The notation for LSED and µν is intricate; a short remark explicitly stating that µν is the mean of the normalized SED at fixed Lf and z would help readers who are not already familiar with the spectro-luminosity functional formalism from Lake et al. (2017).
  3. [Section 4, Figure 3 caption and text] The description of the 'High z' versus 'High z Trim' samples is given only in the main text; repeating the definitions in the figure caption would make Figure 3 more self-contained.
  4. [Section 5, Figure 7 caption] The caption does not state that the literature points are adjusted to 3.4 μm assuming Iν is roughly constant, although this is mentioned in the text. Adding this to the caption would prevent misreading.
  5. [Section 1, footnote 2] The WMAP9 parameter URL is given as a footnote; it would be more robust to cite the Hinshaw et al. (2013) parameters in the text as well, particularly because the cosmology affects Dc(z) in Equation (5).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the 3.4 μm EBL result is a forward integral of an independently measured luminosity function and mean galaxy SED, neither of which is fitted to the EBL itself.

full rationale

The paper's derivation chain is explicitly a forward calculation: Equation 5 integrates the luminosity function Φ(L_f,z) from Lake et al. (2018) against the mean SED μ_ν from Lake & Wright (2016) to produce the galaxy contribution to the EBL. The abstract states that the result is 'based on the measurement of the luminosity function in Lake et al. (2018) and the mean spectral energy distribution of galaxies in Lake & Wright (2016),' and there is no step in which the EBL value is used as input to constrain either the LF parameters or the SED. The cited prior works are data-driven measurements from spectroscopic redshift surveys and photometric catalogs, and their stated assumptions do not include the target EBL value, so they constitute independent evidence rather than a self-citation chain. The flux-count comparisons in Figures 8 and 9 partially reuse the same AllWISE and SDSS source catalogs that entered the LF construction, making them consistency checks rather than fully independent validations; however, those counts are not inputs to the EBL integral, so this does not make the central claim circular. The between-chain spread between the 'High z Prior' and 'High z Trim Prior' results is a real model-selection and robustness concern, but it is a scientific vulnerability of the chosen LF evolution model, not a circular reduction, because neither chain was selected or tuned to reproduce the EBL. On the stated criteria, the paper's central 'prediction' is not equivalent to its inputs by construction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

No new entities are introduced. The central claim rests on fitted LF and SED inputs from the authors' prior papers plus explicit modeling assumptions about SED and LF evolution, so the ledger is dominated by inherited fitted parameters and domain assumptions.

free parameters (3)
  • Schechter LF parameters (phi*, R_phi, L*, R_L, alpha, n0) from Lake et al. 2018 = posterior MCMC chains, DOI 10.6084/m9.figshare.4109625
    The EBL integral in Eq. 5 uses LF parameters that were fitted to spectroscopic-redshift galaxy samples in the prior paper; they are inputs here, not re-fit.
  • Mean galaxy SED / template coefficients from Lake & Wright 2016 = fits to zCOSMOS photometry using Assef et al. 2010 templates
    Equation 2 needs the mean normalized SED, mu_nu, which was fit to galaxy photometry in the prior paper.
  • Upper integration redshift z=5 = 5
    Section 4 caps the EBL integral at z=5 to avoid regions where the Gaussian approximation of SED variety breaks down; this truncation is a modeling choice, not a measurement.
assumptions (5)
  • domain assumption Schechter LF with parametric phi* and L* evolution (Eqs. 8-10) describes the galaxy population over z=0 to 5.
    The central integral assumes this analytic form; no non-parametric validation is given in this paper.
  • domain assumption Mean SED does not evolve with luminosity or redshift.
    Acknowledged as a shortcoming in Section 5; if false, high-z and low-luminosity contributions change.
  • domain assumption Faint-end slope alpha is constant.
    Acknowledged in Section 5; steeper alpha would require a low-luminosity cutoff and alter the background.
  • domain assumption Gaussian approximation for SED variety is valid in the integration range used.
    The z=5 truncation is justified by this approximation breaking down beyond that.
  • domain assumption WMAP9 flat LCDM cosmology (Hinshaw et al. 2013) is used for distances and lookback time.
    Distances Dc in Eq. 3 and t0 in Eq. 10 come from this cosmology, cited in Section 1.

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Cite this review

Pith. "Pith review of The Contribution of Galaxies to the $3.4\,\mathrm{\mu m}$ Cosmic Infrared Background as Measured Using WISE." pith.science (2026). https://pith.science/paper/GMFPH32N

@misc{pith2026190800731,
  author       = {Pith},
  title        = {Pith review of: The Contribution of Galaxies to the $3.4\,\mathrm\mu m$ Cosmic Infrared Background as Measured Using WISE},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GMFPH32N}},
  note         = {Machine review of arXiv:1908.00731}
}
abstract

The study of the extragalactic background light (EBL) in the optical and near infrared has received a lot of attention in the last decade, especially near a wavelength of $\lambda\approx 3.4\operatorname{\mu m}$, with remaining tension among different techniques for estimating the background. In this paper we present a measurement of the contribution of galaxies to the EBL at $3.4\operatorname{\mu m}$ that is based on the measurement of the luminosity function (LF) in Lake et al. (2018) and the mean spectral energy distribution of galaxies in Lake & Wright (2016). The mean and standard deviation of our most reliable Bayesian posterior chain gives a $3.4\operatorname{\mu m}$ background of $I_\nu = 9.0\pm0.5 \operatorname{kJy} \operatorname{sr}^{-1}$ ($\nu I_\nu = 8.0\pm0.4 \operatorname{nW} \operatorname{m}^{-2} \operatorname{sr}^{-1} e\operatorname{-fold}^{-1}$), with systematic uncertainties unlikely to be greater than $2\operatorname{kJy} \operatorname{sr}^{-1}$. This result is higher than most previous efforts to measure the contribution of galaxies to the $3.4\operatorname{\mu m}$ EBL, but is consistent with the upper limits placed by blazars and the most recent direct measurements of the total $3.4\operatorname{\mu m}$ EBL.

Figures

Figures reproduced from arXiv: 1908.00731 by the authors.

Figure 1
Figure 1. Mean Galaxy SED with Variety Band The mean SED of galaxies as approximated using fits to the templates in Assef et al. (2010) done in Lake & Wright (2016). The grey lines show the band of 1-σ in SED variety, and the accuracy of the Gaussian approximation is limited to regions where that band is sufficiently narrow compared to the mean SED. The vertical lines are guides to the parts of the mean SED that galaxies at p… view at source ↗
Figure 2
Figure 2. Example EBL Histograms Histograms of EBL posteriors that correspond to different LF posteriors from Lake et al. (2018). The dashed lines are histograms of the z ≤ 1 predictions and the solid lines are of the z ≤ 5. Panel a is based on the High z Prior chain, Panel b is based on the High z Trim Prior chain, and Panel c uses the survey specific chains from WISE/DEIMOS (black) and zCOSMOS (red). Each posterior chain co… view at source ↗
Figure 3
Figure 3. EBL and Uncertainties for Different Chains All of the 3.4 µm EBL predictions made using the posterior chains from Lake et al. (2018). The grey points are the z ≤ 1 backgrounds, and the black points are the z ≤ 5 ones. The dotted lines divides the survey based samples (above) from the combined samples (below). The blue bar highlights background based on the canonical chain from Lake et al. (2018). 100 101 102 Iν [PI… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Induced Prior on the EBL Estimates The relevant part of the EBL prior induced by the priors on the LF parameters in Lake et al. (2018). The black line is the prior for z ≤ 5 backgrounds, and the grey line is for the z ≤ 1 backgrounds. The grey line is shifted to the ri…
Figure 5
Figure 5. Figure 5: Evolving Luminosity Density and Background Panels a and b are 3-dimensional plots of the comoving spectral luminosity density (see Equation 2) and the EBL (Iν) as a function of comoving/coordinate wavelength (λco) and lookback time (tL(z)). The redshifts spanned are fr…
Figure 6
Figure 6. Figure 6: Density of Contributions to the EBL by Redshift and Luminosity Bivariate density of contributions to the 3.4 µm EBL by galaxies according to the mean model from the High z Prior MCMC posterior chain, with the marginal densities abutting. The blue dotted line on the biv…
Figure 7
Figure 7. Figure 7: 3.4 µm EBL Measurements Comparison of different values measured for the EBL for wavelengths near 3.4 µm ordered by year of publication then first author last name. The points plotted as blue circles are direct observations of the EBL, the green triangles are based on i…
Figure 8
Figure 8. Figure 8: WISE Flux Counts Comparisons Comparisons of the predicted source flux counts, g(f) ≡ d 2 N d log10 F d Ω from the MCMC chain mean models of Lake et al. (2018), to observed flux counts (solid black line) in the AllWISE W1, W2, and W3 bands in the top panels. The bottom …
Figure 9
Figure 9. Figure 9: SDSS Flux Counts Comparisons The same comparison as shown in [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.