Calibrating optical galaxy cluster projection effects with sparse spectroscopic samples: A clustering redshift approach

arXiv:2604.00420 · astro-ph.CO · Submitted 2026-04-01 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: We're looking at the paper: "Calibrating optical galaxy cluster projection effects with sparse spectroscopic samples".

Jocelyn: Here's the gist of the paper. The gist A clustering redshift approach is developed to calibrate optical galaxy cluster projection effects by cross-correlating cluster members with sparse, non-cluster-targeted spectroscopic galaxy samples.

Vera: Wide-field optical imaging surveys are efficient at identifying galaxy clusters, but optically identified clusters suffer from projection effects — physically unassociated galaxies along the line of sight can be misidentified as cluster members due to distance uncertainties <ref:2604.00420#pg2> Previous studies have used spectroscopic follow-up observations of cluster members to quantify projection effects; however, such follow-up efforts cannot keep pace with the rapidly growing cluster samples <ref:2604.00420#pg2> On the other hand, spectroscopic surveys designed for large-scale structure studies collect tens of millions of spectra but tend to have sparse spectra in cluster regions <ref:2604.00420#pg2> To bridge this gap, we develop a clustering redshift approach that cross-correlates cluster members with sparse, non-cluster-targeted spectroscopic galaxy samples <ref:2604.00420#pg2>.

Jocelyn: The core idea involves using the clustering-redshift method (clustering-z hereafter; also known as the cross-correlation redshift to cross-correlate cluster members with a non-cluster-targeted spectroscopic sample.

Vera: This method allows one to infer the true redshift distribution of an unknown sample by cross-correlating it with a reference sample at a known redshift.

Title and authors: Vera: So, to recap, this paper introduces a method called clustering redshift that uses sparse spectroscopic samples to fix those projection errors when we look at galaxy clusters using big optical surveys.

Jocelyn: Right, so the core idea is cross-correlating the known cluster members with these other galaxies at their known redshifts to figure out the true distribution of the unknown sample.

Subrahmanyan: And they use these bins—narrow ones and wide ones—to make sure they get a good estimate of how many real members are actually there versus just line-of-sight noise.

Vera: The results are interesting because this method works whether you use luminous red galaxies or emission line galaxies as your reference sample, which means it's pretty robust against the specific way you choose your reference data.

Jocelyn: Exactly, and they found that by fitting a double-Gaussian model to the measured redshift distribution, they can actually pull out parameters like fproj and sigma proj.

Subrahmanyan: That fproj parameter is what tells you how much of the projected galaxies are actually physically associated members versus just being line-of-sight accidents in the paper.

Vera: And what's particularly compelling is seeing how this projection fraction grows with redshift, increasing from about zero point fourteen at z equal to zero point three up to zero point sixty-five at z equal to zero point seven five.

Jocelyn: That evolution of fproj across cosmic time suggests that the way clusters are projected onto each other gets more significant as we look further back in history.

Subrahmanyan: From a structure formation perspective, that means the statistical noise from projection effects is not constant; it changes with the scale and depth of the universe you're looking at.

Vera: The authors also pointed out some things they didn't do, like ignoring how galaxy bias evolves because their unknown sample only covers a small redshift range of delta z less than zero point two.

Jocelyn: And they also noted that magnification and redshift-space distortions are probably not big issues here because of how fine their redshift binning is in cluster regions.

Subrahmanyan: So the real implication is this method gives us a common tool to assess projection effects across different clusterfinding techniques, which is super useful when you're planning for bigger surveys like the LSST or Euclid.

Vera: It's a solid piece of work, and we can see how this framework could help us assess projection effects across different cluster finding methods independently of the available spectroscopic follow-ups.

The paper's summary: Tom: So, we're talking about how these authors are looking at ways to make this clustering redshift method even better, right?

Vera: They suggest improving cluster mass calibration by using this same cross-correlation approach, but they emphasize that it should be "insensitive to the selection of the spectroscopic sample," which is a big win.

Jocelyn: That means we don't have to worry so much about whether we use LRGs or ELGs as our reference data; the method should still give us consistent results.

Subrahmanyan: The improvement here is moving toward a more robust way to measure cluster mass, which is crucial for linking these observations back to cosmological models.

Vera: They also talk about how they can enhance redshift distribution recovery by using this cross-correlation approach, fitting a double-Gaussian model to infer those projection effect parameters.

Jocelyn: So instead of just measuring the noise, they're using the data to actually map out what's physically there versus what's just projected onto us.

Subrahmanyan: That mapping is important because it allows us to get a clearer picture of the actual mass distribution within those clusters, not just a projection artifact.

Vera: They show how you can quantify these projection effects by fitting that double-Gaussian model, getting those numbers for fproj and sigma proj using the jackknife covariance matrix.

Jocelyn: And they highlight that they are mapping the evolution of these parameters across redshift, showing how fproj increases as you go to higher z.

Subrahmanyan: That redshift dependence is key because it tells us about the growth of structure in the universe and how those projection effects change as we look deeper into time.

Vera: The authors also flag a limitation: they haven't accounted for galaxy bias evolution because their unknown sample only spans a redshift range of delta z less than zero point two.

Jocelyn: That means if you want to apply this method to samples spanning larger redshift gaps, like those in future surveys, you might need to account for that bias evolution.

Subrahmanyan: So the next step is applying this framework to much bigger datasets like LSST and Euclid, where they'll have massive overlap with existing spectroscopic surveys like DESI.

Vera: They plan to use this approach on photometric surveys that overlap with BOSS or DESI, like the DECADE survey.

Jocelyn: It's a great way to get a common framework for assessing projection effects across different clusterfinding methods, regardless of what spectroscopic follow-ups are available.

Subrahmanyan: If we can use this to get cleaner cluster measurements, it helps us better constrain cosmological models like lambda c d m and how dark matter structures grow over time.

The paper's improvements: Vera: So we're wrapping up this discussion on "Calibrating optical galaxy cluster projection effects with sparse spectroscopic samples: A clustering redshift approach," by summarizing what this paper actually achieves for us, right?

Jocelyn: Basically, they developed a method using cross-correlation with sparse spectroscopic samples to fix those tricky projection errors in optical galaxy clusters.

Subrahmanyan: It's an important tool because it gives us a way to get a more reliable picture of what's actually inside those clusters when we only have photometric data.

Vera: They showed that this method works regardless of whether you use luminous red galaxies or emission line galaxies as your reference sample, which makes it pretty robust against those selection choices.

Jocelyn: And they found that by fitting a double-Gaussian model to the measured redshift distribution, they can pull out parameters like fproj and sigma proj.

Vera: The most telling result is seeing how this projection fraction grows with redshift, increasing from about zero point fourteen at z equal to zero point three up to zero point sixty-five at z equal to zero point seven five.

Subrahmanyan: From a structure formation perspective, that means the statistical noise from projection effects isn't constant; it changes with the scale and depth of the universe you't looking at.

Vera: The authors also flagged that they didn't account for galaxy bias evolution because their unknown sample only covers a small redshift range of delta z less than zero point two.

Vera: This paper, "Calibrating optical galaxy cluster projection effects with sparse spectroscopic samples: A clustering redshift approach," gives us a way to calibrate those projection effects without needing massive follow-up for every single cluster member.

Jocelyn: It gives us a way to get the true redshift distribution of photometric samples and quantify the projection effect parameters like fproj and sigma proj.

Subrahmanyan: And it shows that these projection effects evolve with redshift, increasing as you look at higher redshifts when using this method, connecting directly to how structure forms in the universe.

Vera: It's a solid piece of work that provides a common framework for assessing projection effects across different cluster finding methods independently of the available spectroscopic follow-ups.

Jocelyn: It opens up the door for applying this technique to other large photometric surveys that overlap with data from DESI or BOSS.

Conclusion: Vera: So to wrap up, this paper, "Calibrating optical galaxy cluster projection effects with sparse spectroscopic samples: A clustering redshift approach," gives us a way to calibrate those projection effects without needing massive follow-up for every single cluster member.

Jocelyn: Right, so they use cross-correlation with sparse spectroscopic samples to get the true redshift distribution of photometric samples and quantify parameters like fproj and sigma proj.

Subrahmanyan: It's an important tool because it gives us a way to get a more reliable picture of what's actually inside those clusters when we only have photometric data.

Jocelyn: And they found that by fitting a double-Gaussian model to the measured redshift distribution, they can pull out parameters like fproj and sigma proj.

Subrahmanyan: That fproj parameter is what tells you how much of the projected galaxies are actually physically associated members versus just line-of-sight accidents in the paper.

Jocelyn: That evolution of fproj across cosmic time suggests that the way clusters are projected onto each other gets more significant as we look further back in history.

Vera: The authors also flagged that they didn't account for galaxy bias evolution because their unknown sample only spans a redshift range of delta z less than zero point two.

Jocelyn: That means if you want to apply this method to samples spanning larger redshift gaps, like those in future surveys, you might need to account for that bias evolution.

Subrahmanyan: So the next step is applying this framework to much bigger datasets like LSST and Euclid, where they'll have massive overlap with existing spectroscopic surveys like DESI.

Vera: They plan to use this approach on photometric surveys that overlap with BOSS or DESI, like the DECADE survey.

Jocelyn: It's a great way to get a common framework for assessing projection effects across different cluster finding methods, regardless of what spectroscopic follow-ups are available.

Subrahmanyan: If we can use this to get cleaner cluster measurements, it helps us better constrain cosmological models like lambda c d m and how dark matter structures grow over time.

Jocelyn: It gives us a way to get the true redshift distribution of photometric samples and quantify the projection effect parameters like fproj and sigma proj.

Jocelyn: It opens up the door for applying this technique to other large photometric surveys that overlap with data from DESI or BOSS.

Subrahmanyan: If we can use this to get cleaner cluster measurements, it helps us better constrain cosmological models like lambda c d m and how dark matter structures grow over time.

Lei Yang, *, Hao-Yi Wu, †Tesla Jeltema, Chun-Hao To, Ross Cawthon, Shulei Cao

Department of Physics, Southern Methodist University · Physics Department, University of California, Santa Cruz Institute for Particle Physics Santa Cruz Institute for Particle Physics Department of Astronomy and Astrophysics University of Chicago Oxford College of Emory University

astro-ph.CO

Submitted: 2026-04-01

Updated: 2026-10-21

Comments: 8 pages, 4 figures. Published in PRD

DOI: 10.1103/j128-fvwd

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 83/100

The gist: The gist A clustering redshift approach is developed to calibrate optical galaxy cluster projection effects by cross-correlating cluster members with sparse, non-cluster-targeted spectroscopic galaxy

Key concepts

Clustering Redshift Method (Clustering-z): This technique infers the true redshift distribution of an unknown galaxy sample by cross-correlating it with a known reference sample at a specific redshift. It uses pair counting estimators to relate the density distributions of the two samples, allowing researchers to map out the underlying physical structure.
Projection Effects: These occur when galaxies that are not physically part of a cluster along the line of sight are mistakenly identified as members due to distance uncertainties. The method quantifies this by fitting a double-Gaussian model to the measured redshift distribution, separating physically associated members from those that are merely projected.
Reference Samples (LRGs and ELGs): The study uses two distinct spectroscopic samples—Luminous Red Galaxies (LRGs) and Emission Line Galaxies (ELGs)—as external references. The key finding is that the clustering-z method yields consistent results regardless of which reference sample is used, proving the technique's robustness against sample selection.
Projection Parameters ($f_{proj}$ and $\sigma_{proj}$): These parameters describe the degree of projection. $f_{proj}$ represents the fraction of cluster members that are physically associated with the cluster, while $\sigma_{proj}$ describes their redshift extent. The analysis shows that both these parameters evolve with redshift, increasing as clusters get farther away.

Terminology

Clustering — 2× in this paper · explained in 2 episodes

Summary

The gist

A clustering redshift approach is developed to calibrate optical galaxy cluster projection effects by cross-correlating cluster members with sparse, non-cluster-targeted spectroscopic galaxy samples.

Motivation and Problem

Wide-field optical imaging surveys are efficient at identifying galaxy clusters, but optically identified clusters suffer from projection effects — physically unassociated galaxies along the line of sight can be misidentified as cluster members due to distance uncertainties <ref:2604.00420#pg2> Previous studies have used spectroscopic follow-up observations of cluster members to quantify projection effects; however, such follow-up efforts cannot keep pace with the rapidly growing cluster samples <ref:2604.00420#pg2> On the other hand, spectroscopic surveys designed for large-scale structure studies collect tens of millions of spectra but tend to have sparse spectra in cluster regions <ref:2604.00420#pg2> To bridge this gap, we develop a clustering redshift approach that cross-correlates cluster members with sparse, non-cluster-targeted spectroscopic galaxy samples <ref:2604.00420#pg2>.

Methodology Overview

The core idea involves using the clustering-redshift method (clustering-z hereafter; also known as the cross-correlation redshift to cross-correlate cluster members with a non-cluster-targeted spectroscopic sample. This method allows one to infer the true redshift distribution of an unknown sample by cross-correlating it with a reference sample at a known redshift.

The implementation involves three types of redshift bins for cluster members: reference bins, narrow unknown bins, and wide unknown bins.

Narrow unknown bins are chosen with a size of Δzcl = 0.0025.
Wide unknown bins are formed by combining adjacent narrow bins to achieve a size of Δzcl = 0.05.

Pair counting is performed using the Davis-Peebles estimator, which is given by wˆ ur(z′) = DuDr(z′)NRr / DuRr(z′)NDr - 1. The redshift distribution estimator is then derived by assuming that phiˆu (z) ∝ wˆ ur(z), which is normalized to derive the redshift distribution estimator.

Simulation and Validation

The approach is validated using the Cardinal simulation, where clusters are identified by the redMaPPer cluster finder. The simulation uses a flat ΛCDM cosmology with specific parameters such as Ωm = 0.286, Ωb = 0.047, and h = 0.7.

Two distinct spectroscopic galaxy samples are used as reference samples:

Luminous Red Galaxies (LRGs) are selected from the redMaGiC sample, which is based on the red-sequence model calibrated by redMaPPer.
Emission Line Galaxies (ELGs) are selected following criteria optimized for spectroscopic redshift measurements, and they are expected to preferentially reside in filaments and low-density environments rather than in clusters.

Results on Redshift Distributions and Projection Effects

The clustering-z method successfully recovers the spectroscopic redshift distribution of cluster galaxies using both LRGs and ELGs as reference samples, demonstrating that the method is insensitive to sample selection. The measured redshift distributions are modeled using a double-Gaussian function.

The projection effect parameters, specifically the fraction of projected members (fproj) and their redshift extent (sigmaproj), are derived by fitting this model to the measured phiˆu by minimizing the chi2 defined with the jackknife covariance matrix. The results show that both LRGs and ELGs recover spectroscopic results, indicating insensitivity to reference sample selection. The fraction of projected members increases with redshift, as fproj increases from 0.14 (zcl = 0.3) to 0.65 (zcl = 0.75).

Discussion and Systematics

The results are consistent with previous studies on projection effects, such as those by Sunayama [32] and Lee et al. [85], which found that the ratio wp,cg/wp,gg increases with pimax until pimax ≈ 150 h−1Mpc. The paper discusses systematic uncertainties, noting that galaxy bias evolution is ignored because the unknown sample spans a redshift range Δz ≲ 0.2. Furthermore, the impact of magnification and redshift-space distortions is expected to be negligible in this study due to the nature of cluster regions and fine redshift binning.

This approach provides a common framework for assessing projection effects across different clusterfinding methods, independent of the available spectroscopic follow-ups. The method is planned for application to upcoming data sets such as the LSST and Euclid, which will provide substantial overlap with existing spectroscopic surveys like DESI.

The developed clustering-z approach has been validated using the redMaPPer clusters from the Cardinal simulation. The use of LRGs and ELGs as reference samples confirms that our method is insensitive to sample selection. The low number density of clusters necessitates using two levels of redshift bins for clusters: narrow bins for calculating pair counts between members and spectroscopic galaxies, and wide bins for combining clusters at different redshifts. This method is planned to be applied to photometric surveys that have substantial overlap with BOSS and DESI, such as the DECADE survey. It will also be applicable to several upcoming data sets. The LSST data will overlap with DESI for at least 4,000 square degrees. The HLWAS from Roman will obtain spectra for approximately 2,000 square degrees. Although we use redMaPPer as a case study, we plan to apply our clustering-z approach to clusters identified by other algorithms. Our approach provides a common framework for assessing projection effects across different clusterfinding methods, independent of the available spectroscopic follow-ups. The computation of this study has been performed on the M3 high-performance computing cluster provided by the Office of Information Technology (OIT) and the O’Donnell Data Science and Research Computing Institute of Southern Methodist University.

Improvements for AI systems

Improved Cluster Mass Calibration for Wide-Field Surveys: The system can calibrate cluster mass calibration by cross-correlating cluster members with sparse, non-cluster targeted spectroscopic galaxy samples, which is insensitive to the selection of the spectroscopic sample.
Enhanced Redshift Distribution Recovery: The AI can recover the true redshift distribution of photometric samples by using a clustering redshift approach that cross-correlates cluster members with a non-cluster targeted spectroscopic sample and fitting a double-Gaussian model to infer projection effect parameters.
Robust Projection Effect Quantification: The system can quantify projection effects by fitting a double-Gaussian model to the measured redshift distribution, where the first Gaussian describes physically associated members and the second describes projected members, yielding parameters like fproj and sigma proj.
Sample Selection Independence: The improved AI system is designed to be robust against reference sample selection, as shown by demonstrating that its results are insensitive to sample selection when comparing LRGs and ELGs as reference samples.
Redshift Dependence Mapping: The system can map the evolution of projection effect parameters across redshift by showing how the fproj parameter increases with redshift, confirming that the projection fraction increases with redshift.

Calibrating optical galaxy cluster projection effects with sparse spectroscopic samples: A clustering redshift approach

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