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Combined tracer analysis for DESI 2024 BAO

This paper presents a unified analysis pipeline that optimally combines overlapping Luminous Red Galaxies and Emission Line Galaxies from DESI Data Release 1, resulting in an 11% improvement in isotropic BAO constraints and the most precise BAO measurement from the release with a 0.86% distance scale constraint.

Original authors: D. Valcin, M. Rashkovetskyi, H. Seo, F. Beutler, P. McDonald, A. de Mattia, A. J. Rosado-Marín, A. J. Ross, N. Padmanabhan, J. Aguilar, S. Ahlen, U. Andrade, D. Bianchi, D. Brooks, E. Chaussidon, S. C

Published 2026-04-28

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CC BY 4.0

Original authors: D. Valcin, M. Rashkovetskyi, H. Seo, F. Beutler, P. McDonald, A. de Mattia, A. J. Rosado-Marín, A. J. Ross, N. Padmanabhan, J. Aguilar, S. Ahlen, U. Andrade, D. Bianchi, D. Brooks, E. Chaussidon, S. Chen, X. Chen, T. Claybaugh, A. Cuceu, K. S. Dawson, A. de la Macorra, Biprateep Dey, Z. Ding, P. Doel, S. Ferraro, A. Font-Ribera, J. E. Forero-Romero, E. Gaztañaga, S. Gontcho A Gontcho, G. Gutierrez, C. Hahn, K. Honscheid, C. Howlett, M. Ishak, R. Kehoe, D. Kirkby, T. Kisner, A. Kremin, O. Lahav, A. Lambert, M. Landriau, M. E. Levi, M. Manera, A. Meisner, J. Mena-Fernández, R. Miquel, J. Moustakas, S. Nadathur, E. Paillas, N. Palanque-Delabrouille, W. J. Percival, F. Prada, I. Pérez-Ràfols, G. Rossi, R. Ruggeri, L. Samushia, E. Sanchez, C. Saulder, D. Schlegel, M. Schubnell, J. Silber, D. Sprayberry, G. Tarlé, B. A. Weaver, J. Yu, R. Zhou, H. Zou

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, expanding ocean. About 380,000 years after the Big Bang, a "sound wave" traveled through this ocean of matter, leaving behind a specific, repeating pattern in how galaxies are spaced out. This pattern is called Baryon Acoustic Oscillations (BAO). Think of it like a cosmic ruler with a fixed length (about 150 million light-years) that astronomers use to measure how fast the universe is expanding over time.

The Dark Energy Spectroscopic Instrument (DESI) is a massive telescope project in Arizona designed to map millions of these galaxies to measure this cosmic ruler with extreme precision.

This paper is about a specific challenge DESI faced: How do you combine two different types of galaxies that live in the same neighborhood?

The Problem: Two Different Neighborhoods

In the redshift range of 0.8 to 1.1 (a specific slice of cosmic time), DESI is looking at two distinct groups of galaxies:

LRGs (Luminous Red Galaxies): These are like the "old, wealthy residents" of the neighborhood. They are bright, easy to spot, and very numerous.
ELGs (Emission Line Galaxies): These are the "younger, energetic residents." They are fainter and harder to spot. In the first batch of data (DR1), DESI only managed to catch about 25% of them because the telescope's robotic arms (fibers) had to choose between the bright LRGs and the faint ELGs, and the bright ones got priority.

Because the ELGs were so hard to catch, their data was "noisy" (like trying to hear a whisper in a crowded room). If astronomers analyzed the ELGs alone, the results would be shaky and unreliable. If they ignored them, they were throwing away valuable information.

The Solution: The "Team-Up" Strategy

The authors developed a clever method to merge these two groups into a single, unified team before doing the math.

The Analogy: The Choir
Imagine you are trying to measure the pitch of a song.

LRGs are a choir of 100 strong, clear voices.
ELGs are a choir of 500 voices, but they are whispering and some are out of tune.

If you listen to the whispering choir alone, you can't hear the song clearly. If you ignore them, you miss the harmony. The authors' method is like taking the 100 strong voices and the 500 whispering voices and mixing them into one giant choir.

However, you can't just mix them equally. You have to give the strong voices a bit more weight in the mix so they don't get drowned out, but you still include the whispering voices because they add volume and fill in the gaps. The paper describes a mathematical "recipe" (using something called "galaxy bias" as a weight) to blend these two catalogs perfectly.

What They Did

Created a Unified Catalog: They took the data for both galaxy types and merged them into one list, applying the correct "volume knobs" (weights) to each galaxy type.
Tested with Simulations: Before looking at the real universe, they ran this recipe through thousands of computer simulations (mock universes) to make sure it didn't introduce any errors or fake signals.
Applied to Real Data: They applied this method to the actual DESI data from 2024 (Data Release 1).

The Results

The results were a success:

Sharper Ruler: By combining the two groups, the "noise" was reduced. The measurement of the cosmic ruler became 11% more precise for the size of the universe and 7% more precise for how it stretches in different directions.
No New Errors: They checked to see if mixing the two galaxy types created any weird artifacts or biases. It didn't. The combined group acted just like a single, perfect group of galaxies.
The Best Result Yet: This combined method produced the most precise BAO measurement DESI has made so far. They detected the cosmic ruler with a confidence level of 9.1 sigma (which is astronomically high certainty) and measured the distance scale to within 0.86%.

The Bottom Line

Think of this paper as a guide on how to get the most out of a messy dataset. Instead of throwing away the "hard-to-see" galaxies (ELGs) or analyzing them separately where they are too noisy to be useful, the authors showed that by carefully blending them with the "easy-to-see" galaxies (LRGs), you get a clearer, stronger picture of the universe's expansion.

This technique is now the standard for DESI's analysis of this specific slice of the universe, and the authors expect it to become even more powerful as the telescope collects more data and catches more of the faint, whispering galaxies in the future.

1. Problem Statement

The Dark Energy Spectroscopic Instrument (DESI) aims to measure Baryon Acoustic Oscillations (BAO) to map the expansion history of the Universe. In the redshift range $0.8 < z < 1.1$ , DESI observes two distinct types of tracers: Luminous Red Galaxies (LRGs) and Emission Line Galaxies (ELGs).

The Challenge: The ELG sample in Data Release 1 (DR1) suffers from low fiber assignment completeness (35.3%) and lower number density compared to LRGs. This results in high shot noise and a non-Gaussian likelihood distribution, making standalone ELG BAO constraints weak and less robust.
The Goal: To determine the optimal method for combining these overlapping tracers into a unified catalog before BAO analysis. This approach aims to:
1. Increase effective number density and reduce shot noise.
2. Incorporate cross-correlation information (LRG $\times$ ELG) which is lost when analyzing tracers separately.
3. Test for tracer-dependent systematic effects (e.g., relative velocity effects) by comparing results from different tracers within the same volume.
4. Potentially improve the efficiency of density field reconstruction.

2. Methodology

The authors developed a pipeline to create a unified "combined tracer" catalog using galaxy bias as an optimal weighting scheme.

A. Weighting and Catalog Construction

Instead of simply concatenating catalogs, the authors derived an approximate maximum likelihood estimator for the matter density field.

Bias Weighting: Each tracer is weighted by its estimated linear galaxy bias ( $b$ ). The combined overdensity field $\delta_{Combined}$ is constructed as:
$\delta_{Combined} = \frac{b_L(n_L - \bar{n}_L) + b_E(n_E - \bar{n}_E)}{b_L\bar{n}_L + b_E\bar{n}_E}$
where $L$ and $E$ denote LRG and ELG, respectively.
Effective Bias: The effective bias of the combined field is calculated as $b_{eff} = (b_L^2\bar{n}_L + b_E^2\bar{n}_E) / (b_L\bar{n}_L + b_E\bar{n}_E)$ .
FKP Weight Update: The standard Feldman-Kaiser-Peacock (FKP) weights were updated to account for the new effective number density ( $\bar{n}_{eff}$ ) and effective bias of the combined sample.
Renormalization: Random catalogs were re-weighted and renormalized to ensure the data-to-random ratio is consistent for both tracers within the merged catalog, preventing selection function biases.

B. Reconstruction and Analysis

Density Field Reconstruction: The pipeline applied iterative density field reconstruction (using pyrecon) to recover the BAO feature degraded by non-linear growth and redshift-space distortions.
- Crucial Decision: For the combined catalog, the displacement field was estimated strictly within the overlapping redshift range ( $0.8 < z < 1.1$ ) rather than the full LRG range ($0.4-1.1$) or ELG range ($0.8-1.6$), to ensure the bias and growth rate inputs were representative of the specific sample.
Correlation Functions: Two-point correlation functions were computed using the Landy-Szalay estimator for the monopole ( $\ell=0$ ) and quadrupole ( $\ell=2$ ).
BAO Fitting: The BAO scale was constrained using parameters $\alpha_{iso}$ (isotropic dilation) and $\alpha_{AP}$ (Alcock-Paczynski anisotropy) via MCMC sampling and posterior profiling.

C. Validation

The pipeline was tested on two sets of mock catalogs:

Abacus-2 DR1 Mocks: High-resolution N-body simulations (25 realizations) with realistic fiber assignment and survey geometry.
EZmocks: 1,000 realizations based on the Zel'dovich approximation, used to reduce sample variance and box-replication effects for precision gain estimation.

3. Key Contributions

Unified Catalog Pipeline: Developed a robust method to merge distinct tracer populations into a single catalog using bias-based weighting, effectively treating them as a single tracer with optimized signal-to-noise.
Systematic Testing Framework: Established a method to use overlapping tracers as a consistency check. By comparing BAO results from LRGs, ELGs, the cross-correlation (LRG $\times$ ELG), and the combined catalog, the authors can detect tracer-dependent systematics (e.g., relative velocity effects) that might bias standard analyses.
Reconstruction Strategy: Demonstrated that for the current DR1 ELG sample, the primary benefit of combination is the robust integration of low-S/N data, rather than a significant improvement in reconstruction efficiency over LRGs alone (due to ELG noise).

4. Results

A. Mock Catalog Validation

Unbiased Estimates: The combined tracer (LRG+ELG) and the cross-correlation (LRG $\times$ ELG) returned unbiased BAO scale estimates (within $1.7\sigma$ of unity) in mock catalogs, validating the methodology.
Precision Gain:
- Using 1,000 EZmocks, the combined tracer showed a 17% improvement in precision for $\alpha_{iso}$ and 11% for $\alpha_{AP}$ compared to LRGs alone.
- This gain aligns with the increase in effective volume ( $V_{eff}$ ) from 5.0 Gpc $^3$ (LRG) to 6.5 Gpc $^3$ (LRG+ELG).
Reconstruction Efficiency: The reconstruction efficiency of the combined catalog was similar to that of LRGs alone. The noisy ELG displacement field did not significantly degrade the LRG-driven reconstruction, nor did it provide a substantial additional gain in reconstruction efficiency for DR1.

B. Application to DESI DR1 Data

BAO Constraints: Applying the pipeline to real DR1 data yielded:
- $\alpha_{iso}$ : 11% improvement in precision post-reconstruction compared to LRGs alone.
- $\alpha_{AP}$ : $\sim$ 7.0% improvement.
Final Measurement: The combined LRG+ELG analysis produced the most precise BAO measurement in DESI DR1:
- Constraint: 0.86% on the BAO distance scale ( $D_V/r_d$ ).
- Significance: 9.1 $\sigma$ detection of the isotropic BAO feature.
Systematics Check: Comparing the BAO scales derived from LRG, ELG, and the combined catalog in real data showed no significant offsets. The differences were consistent with zero within statistical uncertainties, indicating no evidence of tracer-dependent systematics (such as relative velocity effects) at the current precision level.

5. Significance

Optimal Use of DR1: This analysis validated the decision to use the combined LRG+ELG tracer as the baseline for the DESI DR1 BAO results in the $0.8 < z < 1.1$ bin, maximizing the scientific return from the early data.
Future Prospects: While the current gain is driven by volume and cross-correlation information rather than reconstruction improvements, the authors project that future data releases (DR2 and beyond) with higher ELG completeness will yield even greater gains in reconstruction efficiency and BAO precision.
Robustness: The method provides a powerful tool to cross-check cosmological results against tracer-specific systematics, ensuring the reliability of DESI's dark energy constraints.

In summary, the paper successfully demonstrates that combining overlapping tracers via bias-weighted catalogs is a superior strategy for BAO analysis, yielding tighter constraints and providing a built-in mechanism for systematic error detection.