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REVIEW 4 major objections 4 minor 65 references

Luminosity function of quasars at $1.0<z<3.5$ from SDSS and DESI

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A uniform color-selected quasar census at $1<z<3.5$ revises the faint end upward and the $z>2.5$ bright end upward.

desk verdict A careful, well-documented QLF measurement with a genuinely new completeness strategy, but the headline offsets from prior work rest on an unverified representativeness assumption that could shift the normalization by roughly the size of the claimed differences. read the letter →

arxiv 2608.06000 v1 pith:SLKF6SDP submitted 2026-08-06 astro-ph.GA

Gaocheng Yin , Linhua Jiang , Zhiwei Pan , Paul Martini , Wei-Jian Guo , Siwei Zou , Shengxiu Sun , Swayamtrupta Panda
show 49 more authors
Abhijeet Anand Benjamin Alan Weaver Aaron Meisner Andrei Cuceu Arjun Dey Axel de la Macorra Christophe Magneville David Brooks David Kirkby David Schlegel David Sprayberry Davide Bianchi Dick Joyce Enrique Gaztañaga Eusebio Sanchez Francisco Javier Castander Francisco Prada Gaston Gutierrez Graziano Rossi Gregory Tarlé Hiram K. Herrera-Alcantar Hu Zou Ignasi Pérez-Ràfols Jaime E. Forero-Romero Jessica Nicole Aguilar John Moustakas Joseph Harry Silber Klaus Honscheid Laurent Le Guillou Marc Manera Martin Landriau Michael Schubnell Mustapha Ishak Nathalie Palanque-Delabrouille Peter Doel Ramon Miquel Robert Kehoe Satya Gontcho A Gontcho Seshadri Nadathur Simone Ferraro Stephanie Juneau Steven Ahlen Theodore Kisner Todd Claybaugh Will Percival Anthony Kremin Claire Lamman Claire Poppett Rongpu Zhou
This is my paper · ORCID
classification astro-ph.GA
keywords quasarluminosityfunctiontype1quasarsevolutionoptical-infraredcolorselectionredshiftto3.5puredensityspectroscopiccompleteness
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 attempts to settle disagreements among previous quasar luminosity function measurements at the peak epoch of quasar activity, $1.0

What carries the argument

The central object is a spectroscopically confirmed quasar library, a list of all known quasars in two well-observed sky regions, independent of how each was originally targeted. The library calibrates two simple color-color cuts that convert the photometric catalog into a uniformly selected sample: $u-r$ versus $r-K$ for $1.0<z<2.5$, and $g-i$ versus $i-W1$ for $2.5<z<3.5$. The selection function $p(M,z)$ combines four completeness corrections (morphology, cross-matching, color selection, and spectral coverage) and enters both the $1/V_a$ binned estimator and the maximum-likelihood double power-law fits. Three evolution models (pure luminosity, pure density, and luminosity-plus-density evolution) are then compared on the fitted QLFs.

What would settle it

Take a small patch of sky where every point source brighter than the survey limit has been observed spectroscopically with no color preselection, count quasars with $1.0<z<3.5$ in bins of $M_{1450}$ and $z$, and compare those counts with the QLF predicted here; any mismatch larger than the quoted uncertainties would show the completeness corrections are not representative.

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Extended reading notes

Core claim

The paper claims that a uniformly color-selected sample of 62,426 type 1 quasars at $1.0<z<3.5$ yields quasar luminosity functions that are slightly higher at the faint end than previous measurements in most redshift bins and higher at the bright end for $2.5<z<3.5$. Binned estimators corrected by a multi-term selection function, fitted as double power laws, show no clear redshift evolution in the bright- or faint-end slopes, while the characteristic magnitude declines and the density normalization rises with cosmic time. The authors state that the QLF evolution from $1.0<z<2.5$ is well described by pure luminosity evolution, and that between $2.5<z<3.5$ either pure luminosity or pure density evolution works, with the simpler pure density model preferred because it has one fewer parameter.

Load-bearing premise

The load-bearing premise is that the pre-existing quasar library assembled from two large surveys is a representative census of all quasars in the surveyed fields, and that point sources without spectra contain the same fraction of quasars as those with spectra; if either fails, the color-selection completeness and thus the QLF normalization are biased.

Editorial extensions

If this is right

  • The faint end of the QLF at $1.0<z<3.5$ is slightly higher than in earlier measurements, so the integral quasar number density is larger than previously counted.
  • At $2.5<z<3.5$ the bright end is higher, meaning the most luminous quasars at the activity peak are more common than inferred from earlier surveys.
  • At $1.0<z<2.5$ pure luminosity evolution fits well, so the quasar population's number density is approximately constant while its characteristic luminosity declines.
  • At $2.5<z<3.5$ pure density evolution is sufficient, so the rise in quasar numbers over that interval can be attributed mainly to increasing number density.
  • A uniform optical-infrared color selection recovers roughly 1.5 times as many spectroscopically confirmed quasars at $2.5<z<3.0$ as an optical-only selection in the same region, with the extra objects systematically redder.

Reading between the lines

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

  • A step the paper leaves implicit is that applying the same library-plus-color-cut strategy to fainter magnitude limits or to $z>3.5$ would test whether the upward faint-end revision continues beyond the current survey depth.
  • An external check that would settle the absolute normalization is a patch with near-complete spectroscopy for every point source; if those counts disagree with the predicted QLF, the completeness model is not representative.
  • The preference for pure density evolution over pure luminosity evolution at $2.5<z<3.5$ rests on only two redshift bins; splitting that interval into three or four bins would distinguish the models more cleanly.
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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 / 4 minor

Summary. This paper measures the optical quasar luminosity function (QLF) at 1.0<z<3.5 using a new strategy: rather than defining a quasar survey from its own target selection, the authors start from a library of spectroscopically confirmed SDSS DR16 and DESI Year~3 quasars, apply simple optical--infrared color cuts over two footprints (a ~265 deg^2 deep region and a ~1690 deg^2 wide region), and estimate completeness by comparing the color-selected library quasars with the full library. The final sample contains 62,426 quasars. The authors apply four completeness corrections (morphology, cross-matching, color selection, and spectral coverage), compute binned QLFs with the 1/Va estimator, fit double power laws, and test pure luminosity evolution, pure density evolution, luminosity evolution + density evolution, and a fully free evolution model. The main claims are that the QLF is slightly higher at the faint end than previous determinations and also higher at the bright end at 2.5<z<3.5, and that PLE describes 1.0<z<2.5 while either PLE or PDE describes 2.5<z<3.5.

Significance. If the systematic corrections are sound, this is a potentially valuable contribution: it applies a uniform color selection over a larger area than many previous QLF studies, exploits the large SDSS/DESI spectroscopic library, uses the standard 1/Va estimator and maximum-likelihood double power-law fits, includes a simqso simulation check of the color selection, and makes the data products available on Zenodo. The comparison with Ross et al. (2013) in §4.2, including the recovery of additional red quasars at z~2.7, is informative. However, the central claims about the faint-end normalization and the bright-end excess depend directly on completeness corrections whose most uncertain ingredient, the spectral completeness assumption, is not independently tested and could shift the QLF by an amount comparable to the claimed differences from previous work.

major comments (4)
  1. [§3.1, spectral completeness] The spectral completeness correction assumes that sources without spectra have the same fraction of quasars as sources with spectra, as stated explicitly in §3.1. Because SDSS/BOSS/DESI spectroscopy was obtained by targeting quasar-like objects, the quasar fraction among untargeted, unobserved color-selected sources is expected to be lower than the fraction among observed spectra. For the wide region at 2.5<z<3.5, where the spectral completeness is 87.1% (Table 1), the resulting overcorrection is roughly 0.03 dex if the true quasar fraction among unobserved sources is half the observed fraction and up to ~0.06 dex if it is near zero; these shifts are comparable to the reported offset from Ross et al. (2013). Please test this assumption with an independent estimate (e.g., photometric classification of the non-spectroscopic color-selected sources, or a small spectroscopic follow-up) and propagate the resulting uncertainty into the QLF normalization.
  2. [§3.1, Table 1] The morphology and cross-matching completeness corrections appear to enter p(M,z) as region-wide scalars, even though the text states that cross-matching completeness is lower for fainter quasars and that faint point sources may be misclassified as extended. If the true morphology and cross-matching completeness decline toward the faint end, applying a single average correction per region biases the faint-end slope of the QLF and therefore the claim of a higher faint end relative to previous results. Please parameterize these corrections as functions of apparent magnitude or M1450 rather than as global constants, or justify quantitatively that the magnitude dependence is negligible within the fitted range.
  3. [§3.1, uncertainty budget] The uncertainty assigned to each completeness fraction is derived from the ad hoc rule that the missed fraction or contaminant fraction corresponds to a 2-sigma uncertainty (e.g., 96% completeness gives 1-sigma = 2%). Since the final binned QLF errors Delta-Phi in Table 2 are formed by adding these completeness uncertainties to the statistical errors, the quoted error bars are not measurement uncertainties in the usual statistical sense. The paper should either derive these uncertainties from a Poisson or bootstrap calculation over the library, or show explicitly how the size of the claimed faint-end and bright-end offsets depends on reasonable alternative completeness values.
  4. [§2.2, §3.1, color completeness] Color-selection completeness is measured using the SDSS DR16 + DESI Year 3 quasar library, but the paper does not establish that this library is a representative census of all quasars in the survey footprints. If the library under-represents red or unusual SED quasars near z~2.7, the color completeness is overestimated and the bright-end QLF at 2.5<z<3.5 can be biased upward. Please validate the color completeness against an independent selection that does not rely on the same SDSS/DESI targeting, for example X-ray-selected or variability-selected quasars in Stripe 82, and quantify the impact on the bright-end result.
minor comments (4)
  1. [Figure 4] Panel (d) is labeled '2.0<z<3.0' in the caption; from the text and the other panels it should be '2.5<z<3.0'.
  2. [Figure 6, §4.2] There is an inconsistency between the text, which specifies integration limits M=-24, -25, and -26, and the caption, which states M1450<-25, -26, and -27 for the blue, green, and red lines; please align the notation and values.
  3. [Table 4, §4.1] All fitted evolution models have reduced chi-square values well below unity, especially for the 2.5<z<3.5 range; this suggests possible overfitting or overestimated errors, and the comparison among PLE, PDE, and LEDE should be supplemented with a note on this limitation or an information criterion such as AIC.
  4. [Table 3, Table 4] The symbols Ms and Phi*(z=z_p) are not defined in the table captions; please define them explicitly and state the units of Phi*.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the QLF is measured from spectroscopic counts with explicit completeness corrections, and the evolutionary-model fits are made to those independently measured binned QLFs.

full rationale

The derivation is self-contained. Binned QLFs are computed from observed quasar counts using the 1/V_a estimator (Section 3.2, Eqs. 1-3), with the selection function p(M,z) assembled in Section 3.1 from four explicitly stated completeness corrections (morphology, cross-matching, color, and spectral completeness). The double power-law fit (Eq. 4) and the PLE/PDE/LEDE evolution-model fits (Eqs. 6-10) are fits to these independently measured binned QLFs, not to parameters already contained in the data. The Section 2.3 simulation uses the Ross et al. (2013) model only as a selection-efficiency check and is not used to set QLF parameters. The only self-citation, Pan et al. (2022), appears alongside the external Kim & Im (2021) reference as motivation for testing the PDE model; the paper's PDE conclusion rests on its own chi-squared comparison (Table 4), so the self-citation is not load-bearing. The spectral-completeness assumption that 'sources without spectra have the same fraction of quasars as those with spectra' is a potential systematic bias in the absolute normalization, but it is an explicit assumption rather than an equation that reduces to a fitted value, so it does not constitute circularity.

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

The QLF rests on standard 1/Va methodology plus four empirical completeness corrections. The main non-standard inputs are the color cuts (chosen by inspection), the use of the SDSS/DESI spectroscopic library as the ground truth for completeness, the assumption that unobserved candidates have the same quasar fraction as observed candidates, and an ad hoc assignment of 2-sigma uncertainty equal to the complement of each completeness fraction. These are listed below.

free parameters (3)
  • Optical-IR color selection cuts for low-z and high-z quasars = u-r<1.5, 1.1<r-K<3.5, r-K>0.8(u-r)+1.1 for 1.0<z<2.5; g-i<2.0, i-W1<(g-i)+1.9 for 2.5<z<3.5
    Chosen by inspecting color-color diagrams in section 2.2; they define the sample and therefore enter every completeness and QLF calculation.
  • Double power-law QLF parameters per redshift bin (alpha, beta, M*, log Phi*) = Table 3: e.g., alpha=-1.44, beta=-3.11, M*=-23.98, logPhi*=-5.79 at 1.0<z<1.5
    Fitted to the binned QLFs by maximum likelihood MCMC in section 3.3; the paper's characterization of the QLF shape depends on these 20 numbers.
  • Evolution model coefficients (k1, k2, and base values for PLE, PDE, LEDE, and free case) = Table 4: e.g., PLE k1=0.98, k2=-0.19 for 1.0<z<2.5; PDE k1=-0.32 for 2.5<z<3.5
    Fitted to the derived QLFs in section 4.1; the conclusion that PLE works at z<2.5 and PDE suffices at z>2.5 is determined by these coefficients.
assumptions (5)
  • domain assumption The SDSS DR16 plus DESI Year 3 spectroscopic quasar library is a representative census of quasars in the two survey regions.
    Invoked in sections 2 and 3.1 as the reference for computing color-selection completeness and purity; if this library inherits any targeting bias, the QLF normalization and shape inherit it too.
  • ad hoc to paper Sources without spectra contain the same fraction of quasars as sources with spectra.
    Stated in section 3.1 as the basis for the spectral completeness correction; it is not tested against an independent sample.
  • ad hoc to paper The complement of a completeness fraction is a 2-sigma uncertainty (e.g., 96% completeness gives 1-sigma = 2%).
    Used in section 3.1 to propagate completeness uncertainties into QLF error bars.
  • standard math Adopted flat LCDM cosmology (H0=70 km/s/Mpc, Omega_m=0.3, Omega_Lambda=0.7) and the Richards et al. 2006 K-correction recipe.
    Standard volume and absolute-magnitude conversions in sections 3.1 and 3.2; consistent with the literature the paper compares against.
  • domain assumption Zero-point offsets between SDSS, UKIDSS, VISTA, and WISE photometric systems are negligible.
    Section 2.2 states 'Zero-point corrections are not applied in this work'; small systematics here would shift colors and slightly move the selection boundaries.

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Cite this review

Pith. "Pith review of Luminosity function of quasars at $1.0<z<3.5$ from SDSS and DESI." pith.science (2026). https://pith.science/paper/SLKF6SDP

@misc{pith2026260806000,
  author       = {Pith},
  title        = {Pith review of: Luminosity function of quasars at $1.0<z<3.5$ from SDSS and DESI},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SLKF6SDP}},
  note         = {Machine review of arXiv:2608.06000}
}
abstract

We present a study of the evolution of type 1 quasars at $1.0<z<3.5$, covering the peak epoch of quasar activity. The quasar evolution has been extensively explored by a variety of previous works and the derived quasar luminosity functions (QLFs) are not well consistent with each other, presumably due to the complexities introduced by different quasar selection techniques and associated completeness corrections. We use a new strategy to construct QLFs based on a library of all known quasars. We focus on a wide region of $\sim$1700 deg$^2$ and a deep field of $\sim$265 deg$^2$ that have rich spectroscopic data primarily from SDSS and DESI. We then apply traditional color cuts in the rest-frame UV/optical to select quasar candidates and use the quasar library to identify them. Our final sample consists of 62,426 quasars at $1.0<z<3.5$, with a high completeness ($\sim$96%) and a high purity ($\sim$93%) in the color selection. Simple color cuts can potentially minimize selection biases for the study of quasar evolution. We derive binned QLFs and characterize them using a double power-law model. Sample incompleteness and contamination are considered as part of the uncertainties in the calculation. Compared to previous results, our QLFs are slightly higher at the faint end, and also higher at the bright end at $2.5<z<3.5$. The QLFs suggest that the quasar evolution at $1.0 < z < 2.5$ can be well described by the pure luminosity evolution model, while at $2.5 < z < 3.5$, it can be described by either the pure luminosity evolution or the pure density evolution model.

Figures

Figures reproduced from arXiv: 2608.06000 by the authors.

Figure 1
Figure 1. Our color selection criteria. Panels (a) and (b) show the selection of quasars at 1.0 < z < 2.5 in the deep region and wide region, respectively. The magnitude range of the objects is 15.0 < r < 21.5 mag in (a) and 15.0 < r < 20.5 mag in (b). The light grey dots represent point sources without spectra. Quasars at 1.0 < z < 2.5 are marked by the red dots, and other quasars are represented by the green dots. Stars and… view at source ↗
Figure 2
Figure 2. Color-color diagrams of our simulated quasars. Panel (a) displays the redshift range of 1.0 < z < 2.5 and covers a magnitude range of 15.0 < r < 21.5. Panel (b) shows the redshift range of 2.5 < z < 3.5 and covers a mag￾nitude range of 15.0 < i < 21.5. The purple dots represent the simulated quasars. For the convenience of comparison, we also plot the true distributions of point-like stars and galaxies with the blue… view at source ↗
Figure 3
Figure 3. Distribution of the quasar selection function p(M, z). Panel (a) shows the distribution of p(M, z) in the deep region. A magnitude limit of 15.0 < r < 21.5 mag is adopted for 1.0 < z < 2.5, while a magnitude limit of 15.0 < i < 21.5 mag is adopted for 2.5 < z < 3.5. Panel (b) shows the distribution of p(M, z) in the wide region. A magnitude limit of 15.0 < r < 20.5 mag is adopted for 1.0 < z < 2.5, while a magnitude… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: QLFs at 1.0 < z < 3.5. The black solid dots represent the binned QLFs in the deep region, and the red solid dots represent the binned QLFs in the wide region. The orange dashed line represents the result of fitting the parameterized luminosity function using the maximu…
Figure 5
Figure 5. Figure 5: Comparison of QLFs with others. The solid orange line represents the QLFs using the PLE model for the redshift range 1.0 < z < 2.5 and the PDE model for the redshift range 2.5 < z < 3.5. For comparison, the solid cyan line represents the results from Ross et al. (2013)…
Figure 6
Figure 6. Figure 6: Cumulative density evolution of quasars at 1.0 < z < 3.5. The blue, green, and red lines represent magnitude ranges M1450 < −25, −26, and −27 mag, respec￾tively. Square points and solid lines are our results. For comparison, the dashed line represents the results from …

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