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The 3D clustering of Lyman Alpha Emitters measured with DESI

This paper presents a clustering analysis of Lyman- $\alpha$ emitters using DESI spectroscopic data and IBIS imaging, determining their linear bias, characterizing their connection to dark matter halos via HOD modeling, and quantifying non-perturbative effects to improve future cosmological analyses.

Original authors: Haruki Ebina, Martin J. White, Rongpu Zhou, Arjun Dey, David Schlegel, Jessica Nicole Aguilar, Steven Ahlen, Davide Bianchi, David Brooks, Francisco Javier Castander, Todd Claybaugh, Kyle S. Dawson, A

Published 2026-06-24

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CC BY 4.0

Original authors: Haruki Ebina, Martin J. White, Rongpu Zhou, Arjun Dey, David Schlegel, Jessica Nicole Aguilar, Steven Ahlen, Davide Bianchi, David Brooks, Francisco Javier Castander, Todd Claybaugh, Kyle S. Dawson, Axel de la Macorra, Peter Doel, Simone Ferraro, Andreu Font-Ribera, Jaime E. Forero-Romero, Satya Gontcho A Gontcho, Alma Xochitl Gonzalez-Morales, Gaston Gutierrez, Julien Guy, ChangHoon Hahn, Hiram K. Herrera-Alcantar, Mustapha Ishak, David Kirkby, Anthony Kremin, Ofer Lahav, Martin Landriau, Dustin Lang, Laurent Le Guillou, Michael E. Levi, Marc Manera, Paul Martini, Aaron Meisner, Ramon Miquel, Seshadri Nadathur, Nathalie Palanque-Delabrouille, Will J. Percival, Francisco Prada, Ignasi Pérez-Ràfols, Ashley J. Ross, Graziano Rossi, Eusebio Sanchez, Michael Schubnell, Hee-Jong Seo, Gregory Tarlé, Benjamin Alan Weaver

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

The Big Picture: Mapping the Cosmic "Ghost Town"

Imagine the universe as a giant, dark city. Most of the "buildings" (galaxies) are lit up, but there is a specific type of building that is hard to see because it's very dim and only glows in a specific, faint color (Lyman-alpha light). These are called Lyman-alpha Emitters (LAEs).

Astronomers want to map where these "ghost buildings" are located in 3D space. Why? Because by seeing how they cluster together, we can learn how the universe grew and expanded over time. However, these ghost buildings are tricky to find and even trickier to measure accurately because the light they emit bounces around like a pinball in a foggy room before it reaches our telescopes.

This paper is a "dress rehearsal" for a future, massive survey called DESI-II. The authors used a smaller, current telescope setup (DESI) to test if they can successfully map these faint galaxies, measure how they clump together, and understand the "fog" that distorts their light.

1. The Tools: The Net and the Flashlight

To find these galaxies, the team used two main tools:

The Net (IBIS/DECam): They used a special camera on a telescope in Chile equipped with "medium-band" filters. Think of these filters like colored sunglasses that only let through a specific slice of the rainbow. By looking through these specific slices, they could spot the faint glow of the LAEs against the dark background.
The Flashlight (DESI): Once they spotted candidates with the camera, they used the Dark Energy Spectroscopic Instrument (DESI). This machine has 5,000 tiny robotic fibers (like optical needles) that can be moved to point at specific galaxies. It acts like a flashlight, capturing the actual light spectrum to confirm exactly what the object is and how far away it is.

The Challenge: The team had to be very careful. If the "fibers" (needles) are too close together, they can't both point at a galaxy at the same time (like two people trying to sit in the same chair). The authors proved that for their specific sample, they got such a high success rate (98.6% of targets were measured) that this "chair-sharing" problem didn't mess up their data.

2. The Measurement: The "Clumpiness" Test

The main goal was to measure clustering. Imagine dropping a handful of marbles on a table. Do they scatter randomly, or do they form little piles?

The Monopole (The Pile Size): This measures the overall strength of the clumping. It tells the team how "biased" these galaxies are. In simple terms, do these faint galaxies live in the biggest, most massive dark matter "cities," or do they hang out in the small, quiet suburbs?
- Result: They found these galaxies are biased, meaning they live in specific types of dark matter halos, with a bias factor of about 2.3 to 2.6.
The Quadrupole (The Stretch): Because the universe is expanding and galaxies are moving, the 3D map looks slightly stretched or squashed depending on the angle you look at it. This is called the Redshift Space Distortion (RSD).
- Result: By measuring this stretch, they could estimate how fast the universe's structure is growing. This is the first time this specific "stretch" has been measured for this type of galaxy.

3. The "Fog" Problem: Radiative Transfer

Here is the tricky part. The light from these galaxies (Lyman-alpha) has to travel through a fog of neutral hydrogen gas surrounding the galaxy.

The Analogy: Imagine shouting in a dense fog. Your voice (the light) doesn't travel in a straight line; it scatters, bounces off water droplets, and takes a weird path. This scattering can make the galaxy look like it's in a slightly different spot or moving differently than it actually is.
The Paper's Claim: The authors tried to measure how much this "fog" (Radiative Transfer) messed up their map. They found that while the fog could distort the map, the data they have right now isn't strong enough to say for sure if the distortion is happening. It's consistent with there being no distortion, but they can't rule it out completely yet. They set a limit on how bad the fog could be, which is crucial for future, bigger surveys.

4. The "Fingers of God": The Cosmic Stretch

When galaxies are inside a tight cluster (like a galaxy cluster), they are moving around wildly, like bees in a hive. When we look at them, this motion makes the cluster look like a long, stretched-out finger pointing toward us. This is called the Fingers of God (FoG) effect.

The Finding: The authors checked if this effect was ruining their measurements. They found that for these specific faint galaxies, the "Fingers" are actually quite short. The galaxies aren't moving as wildly as some feared. This is good news! It means the data is "cleaner" and easier to use for precise cosmology.

5. The Simulation: The "Virtual Universe"

To make sure their math was right, the team built a virtual universe (a simulation) inside a computer. They populated this virtual world with fake galaxies using different rules (models) to see which rules made the fake galaxies look like the real ones they observed.

They tested three different rulebooks:
1. Standard: Galaxies live in halos based on simple rules.
2. HMQ: A rule where very heavy halos stop hosting these galaxies (like a "mass quenching" rule).
3. Velocity Bias: A rule where the galaxies move differently than the dark matter they live in.
The Winner: The Standard model worked best. It was the simplest and fit the data well, suggesting these galaxies are mostly "central" residents of their dark matter homes, with very few "satellite" neighbors.

Summary of Results

Success: They successfully mapped the 3D clustering of these faint galaxies for the first time using spectroscopic data.
Bias: They confirmed these galaxies live in dark matter halos with a bias of roughly 2.3–2.6.
Growth: They provided the first measurement of the growth rate of structure for this specific galaxy type.
Fog: They found that the "fog" (radiative transfer) might be present but is likely small enough not to ruin future big surveys.
Fingers: The "Fingers of God" effect is weak, meaning the data is very reliable.

The Bottom Line: This paper is a "proof of concept." It tells the astronomers running the future DESI-II survey: "We have a working map, we know how to measure these faint galaxies, and the data looks clean enough to trust us with the big job of mapping the entire universe's history."

Technical Summary: The 3D Clustering of Lyman Alpha Emitters Measured with DESI

Problem and Motivation
Current Stage IV spectroscopic surveys have mapped the large-scale structure (LSS) of the universe with high precision up to redshifts of $z \lesssim 2$ . However, extending precision cosmology to higher redshifts ( $z \gtrsim 2$ ) is essential for accessing larger comoving volumes, longer cosmic time lever arms for growth-rate measurements, and more (quasi-)linear modes. At these redshifts, the primary probe of LSS has been the Ly $\alpha$ forest, which is limited by the sparsity of background quasars and continuum fitting contaminants. Galaxy tracers offer a denser, independent sampling of the matter field. The Dark Energy Spectroscopic Instrument (DESI) and its proposed successor, DESI-II, plan to utilize Lyman Alpha Emitters (LAEs) as key tracers.

A critical prerequisite for using LAEs in cosmological analyses is a robust characterization of their clustering properties, specifically their linear bias and the reliability of theoretical models in the redshift space. Previous measurements of LAE bias relied on angular clustering or projected correlation functions, which suffer from reduced signal-to-noise due to projection effects and cannot access the redshift-space distortion (RSD) quadrupole ( $\xi_2$ ), a key observable for constraining the growth rate ( $f\sigma_8$ ). Furthermore, LAE clustering is complicated by radiative transfer (RT) effects, where the scattering of Ly $\alpha$ photons by neutral hydrogen can introduce scale-dependent distortions that mimic RSD signals. This paper presents the first measurement of the full 3D redshift-space correlation function multipoles ( $\xi_0$ and $\xi_2$ ) and power spectrum for LAEs selected via medium-band imaging, providing essential calibration for future high-redshift surveys.

Methodology
The analysis utilizes spectroscopic observations from the Dark Energy Spectroscopic Instrument (DESI) targeting LAE candidates selected from the Intermediate Band Imaging Survey (IBIS) using the Dark Energy Camera (DECam) on the Blanco telescope. The IBIS survey employs five adjacent medium-band filters (4000–5300 Å) to isolate Ly $\alpha$ emission.

Sample Selection: The target selection combines a "peak excess" cut (identifying flux excess in a medium band relative to a synthetic continuum) with broadband color cuts (using HSC-SSP data) to reject low-redshift interlopers. The sample is restricted to the COSMOS field (tertiary54 program) to ensure high fiber completeness.
Spectroscopy: DESI observations achieved a fiber completeness of 98.6% within the analysis footprint (0.3 deg < $r$ < 1.4 deg from the field center), effectively eliminating the need for fiber-assignment corrections that typically plague small-scale clustering measurements. The final sample contains 5,087 LAEs with secure redshifts in the range $2.26 < z < 3.41$ , divided into two bins: $z \approx 2.5$ and $z \approx 3.0$ .
Clustering Measurement: The authors measured the two-point correlation function ( $\xi$ ) and the anisotropic power spectrum ( $P(k)$ ) multipoles ( $\ell=0, 2, 4, 6$ ) in both configuration and Fourier space. Cross-correlations with DESI DR2 quasars (QSOs) were also computed to break degeneracies in bias and RT modeling.
Modeling:
- HOD Fits: Halo Occupation Distribution (HOD) models were fitted to the correlation function multipoles using mock catalogs generated from the AbacusSummit N-body suite. Three models were tested: a standard HOD, a Halo Mass Quenching (HMQ) model, and a model including velocity bias.
- Fourier-Space Fits: Effective Field Theory (EFT) formalism was used to fit the power spectrum multipoles. This approach allows for a clear separation of scales and the inclusion of counterterms to model small-scale physics. The analysis incorporated a parametrized model for Radiative Transfer (RT) effects and cross-correlated LAEs with QSOs to constrain the RT parameter.
- FoG Analysis: The strength of Fingers-of-God (FoG) effects was investigated using anisotropic correlation functions, high multipoles in the power spectrum, and comparisons between data and HOD simulations.

Key Results

Linear Bias: The analysis yields tight constraints on the linear bias of medium-band selected LAEs. Using EFT modeling, the linear bias is measured as $b_1 = 2.31 \pm 0.23$ at $z=2.5$ and $b_1 = 2.62 \pm 0.20$ at $z=3.0$ . These results are consistent with HOD model fits ( $b \sim 2.2$ and $2.55$) and previous literature within $0.5\sigma$ .
Radiative Transfer (RT): The study places the first constraints on the strength of RT effects using a one-parameter distortion model ( $\alpha$ ). The results show a deviation from zero at less than $2\sigma$ significance ( $\alpha = -0.64 \pm 0.63$ at $z=2.5$ and $\alpha = -0.95 \pm 0.55$ at $z=3.0$ ). While the data allows for order-unity distortions, the results are consistent with negligible RT effects, and the AIC does not strongly favor the inclusion of RT in the model.
Fingers-of-God (FoG): The analysis indicates that FoG effects in the LAE population are relatively weak. The zero-crossing of the quadrupole occurs at high wavenumbers ( $k \gtrsim 0.45 \, h \, \text{Mpc}^{-1}$ ), and the line-of-sight power spectrum suppression is minimal. Both data and HOD simulations suggest that the FoG contribution is sub-dominant to perturbative terms up to the non-linear scale ( $k_{nl} \sim 0.5 \, h \, \text{Mpc}^{-1}$ ).
HOD Characteristics: The standard HOD model is preferred over HMQ and velocity bias models due to having fewer parameters (lowest AIC). The analysis suggests LAEs reside in halos with masses around $10^{11.75} \, h^{-1} M_\odot$ and have a low satellite fraction, consistent with their identification as young, low-mass galaxies.

Significance and Claims
The paper claims to provide the first measurement of the 3D redshift-space correlation function multipoles ( $\xi_0, \xi_2$ ) for LAEs at $2.2 \lesssim z \lesssim 3.5$ . This represents a significant advancement over previous angular or projected analyses, enabling direct constraints on the growth rate ( $f\sigma_8$ ) and rigorous testing of theoretical clustering models.

The authors emphasize that the high fiber completeness of the DESI tertiary54 sample allows for clustering measurements without fiber-assignment corrections, a critical systematic for small-scale analysis. The derived bias constraints and the characterization of RT and FoG effects provide essential inputs for forecasting and optimizing future high-redshift surveys like DESI-II and Spec-S5. The results confirm that LAEs are robust cosmological probes, with clustering signals that are largely linear and minimally affected by non-perturbative effects or radiative transfer distortions at the current level of precision. The paper concludes that while HOD models provide a good phenomenological fit, future work should explore more physically motivated models and complex RT scenarios as datasets grow.