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The caustic method applied to The Three Hundred: prospects for upcoming CATARSIS and other surveys

This paper investigates the expected uncertainties and systematic errors in recovering galaxy cluster mass profiles using the caustic technique on upcoming spectroscopic survey data, specifically focusing on the CATARSIS survey's potential to mitigate biases through deep redshift measurements and iterative corrections for velocity anisotropy.

Original authors: B. Callejas Córdoba, P. Sánchez Blázquez, A. Gil de Paz, A. Knebe, W. Cui, C. Catalán Torrecilla, R. Dave

Published 2026-06-03

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CC BY 4.0

Original authors: B. Callejas Córdoba, P. Sánchez Blázquez, A. Gil de Paz, A. Knebe, W. Cui, C. Catalán Torrecilla, R. Dave

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 is filled with giant, invisible cosmic webs made of dark matter. At the intersections of these webs sit galaxy clusters—massive cities of hundreds or thousands of galaxies held together by gravity. Astronomers want to know exactly how heavy these cities are, but since we can't put a cluster on a scale, they have to guess the weight by watching how the galaxies inside move.

This paper is like a dress rehearsal for a new telescope survey called CATARSIS. The authors are using a super-powerful computer simulation (called "The Three Hundred") to test if their new method for weighing these clusters will work correctly before they actually point their telescope at the sky.

Here is a breakdown of their findings using simple analogies:

1. The Problem: The "Trumpet" and the "Speed Limit"

To weigh a cluster, astronomers use a technique called the Caustic Method.

The Analogy: Imagine a group of cars driving on a highway that curves around a mountain. If you look at the cars from the side, you see a "trumpet shape" forming: cars near the center are moving fast, and as you get further out, the fastest cars are still moving fast, but the average speed drops off.
The Method: The "Caustic" is the outer edge of this trumpet shape. It represents the speed limit of the universe for that specific spot. If a galaxy is moving faster than this limit, it will fly away forever. By measuring this speed limit at different distances from the center, astronomers can calculate how much mass (gravity) is holding the cluster together.

2. The Old Way vs. The New Way (The "Anisotropy" Issue)

The old way of doing this calculation made a big assumption: it assumed that galaxies move in a perfectly uniform way in all directions, like a swarm of bees buzzing evenly.

The Reality: In reality, galaxies are like cars on a racetrack. Some are zooming straight toward the center, while others are circling around. This difference is called velocity anisotropy.
The Mistake: Assuming everyone moves the same way is like guessing the weight of a crowd by assuming everyone is standing still, when some are actually running. This led to the old method often overestimating the mass of the cluster (thinking it was heavier than it really was).
The Fix: The authors developed a new iterative method (a "try, check, and fix" loop). Instead of guessing the movement pattern once, they calculate the mass, check the movement pattern, and then recalculate the mass with the new, more accurate movement data.
The Result: This new loop reduced the error significantly. It's like switching from a rough guess to a precise measurement, cutting the mistake down from a 16% overestimate to just a 6% underestimate.

3. The Survey: CATARSIS (The "Blind" Photographer)

The paper focuses on a future survey called CATARSIS, which will use a special camera (an Integral Field Spectrograph) on a telescope in Spain.

The Old Surveys: Many previous surveys were like taking photos of a party but only looking at the people wearing red shirts (Red-Sequence galaxies). They ignored the people in blue or green.
- The Problem: The "red shirt" people tend to hang out in the center of the room. By ignoring everyone else, the survey missed the fast-moving people on the edges, leading to an underestimation of the cluster's total weight.
The CATARSIS Advantage: CATARSIS is a blind survey. It doesn't care what color the galaxies are; it takes a picture of everyone in the field of view, from the brightest stars to the faintest, dusty ones.
- The Benefit: By capturing the "whole party," they get a much more accurate picture of the cluster's true mass.

4. The "Magnitude Limit" (How Deep Can You See?)

The authors also tested what happens if the camera isn't sensitive enough to see the faintest galaxies.

The Analogy: Imagine trying to count the weight of a pile of rocks, but your scale can only see the big boulders and misses the pebbles.
The Finding: If you only look at the brightest galaxies (the big boulders), you tend to overestimate the mass. If you set the bar too high for how bright a galaxy must be to be counted, you miss the faint, fast-moving ones on the edges, which throws off the calculation.
The CATARSIS Solution: The survey is designed to be very "deep," meaning it can see very faint galaxies (down to a specific brightness limit). This ensures they don't miss the crucial "pebbles" on the edge of the cluster, keeping the mass estimate accurate.

5. Comparison with Other Surveys

The paper compares CATARSIS to other upcoming surveys (like WEAVE, HeCS, and CHANCES):

WEAVE: Good for low redshift (nearby), but its "camera lens" is too small for distant clusters, so it can't see the outer edges needed for this method.
HeCS & CHANCES: These are excellent and very similar to what CATARSIS will do.
eROSITA: It can see very far, but it doesn't get enough "snapshots" (spectra) of individual galaxies to use this specific weighing method.
CATARSIS: It hits the "sweet spot." It has a wide view, goes deep enough to see faint galaxies, and covers the right distance range to weigh these clusters perfectly.

Summary

The paper concludes that by using a smarter calculation method (the iterative loop) and a camera that doesn't ignore the faint or colorful galaxies (CATARSIS), astronomers will be able to weigh galaxy clusters with much higher precision. This is a crucial step because knowing the exact weight of these cosmic cities helps us understand the nature of Dark Matter and the expansion of the Universe.

In short: They tested a new, smarter way to weigh cosmic cities using a computer simulation, and they found that their new method, combined with a super-sensitive, "blind" camera, will give us the most accurate weights yet.

Technical Summary: The Caustic Method Applied to The Three Hundred

Problem Statement
The observational determination of galaxy cluster mass profiles is critical for understanding structure growth and constraining cosmological models. While the caustic technique offers a dynamical method to estimate masses at large radii without assuming hydrostatic equilibrium, it is subject to systematic uncertainties. These arise primarily from assumptions regarding the velocity anisotropy profile ( $\beta(r)$ ), the choice of smoothing kernel parameters in phase-space reconstruction, and observational selection biases (e.g., magnitude limits, red-sequence selection, and flux cuts). Previous studies indicate that adopting a constant anisotropy or insufficient sampling can lead to mass overestimates of 30–70% in inner regions and significant scatter. This paper investigates these uncertainties using cosmological simulations to assess the prospects for upcoming spectroscopic surveys, specifically the CATARSIS survey.

Methodology
The authors utilize the "The Three Hundred" (The300) project, a suite of 324 cluster-scale zoom-in simulations based on the MultiDark-Planck 2 (MDPL2) cosmology. The analysis focuses on the GIZMO-Simba hydrodynamical run, which provides resolved galaxy populations down to stellar masses of $M_\star \gtrsim 10^8 M_\odot$ and includes realistic galaxy colors and luminosities.

The study applies the caustic technique to the simulated galaxy catalogs, reconstructing mass profiles from the "trumpet-shaped" envelope in projected phase space ( $r, v_{los}$ ). Key methodological steps include:

Center Determination: Cluster centers are estimated using a Kernel Density Estimation (KDE) approach on galaxy positions (both unweighted and luminosity-weighted) to mimic observational constraints, rather than using the simulation's potential minimum.
Kernel Optimization: The impact of the smoothing kernel size ( $s$ ) and the ratio between velocity and position kernels ( $q$ ) is systematically tested. The authors explore a grid of parameters to determine if optimal values correlate with cluster properties like mass or richness.
Iterative Anisotropy Correction: To address the bias introduced by assuming a constant anisotropy, the authors propose an iterative method. This involves:
- Deriving an initial mass profile assuming a constant anisotropy.
- Fitting a Navarro–Frenk–White (NFW) profile to obtain a concentration parameter.
- Recomputing the caustic profile using either a data-driven empirical $\beta(r)$ profile or the analytical Mamon & Łokas (2005) prescription.
Selection Bias Analysis: The study simulates observational constraints by applying cuts to the galaxy samples:
- Restricting to Red-Sequence (RS) galaxies.
- Applying apparent magnitude limits ( $m_r$ ) and H $\alpha$ flux limits to mimic the detection capabilities of the TARSIS instrument and other surveys.
Survey Comparison: The performance of the caustic method is evaluated against the expected capabilities of the CATARSIS survey and compared with other ongoing/future surveys (WEAVE, HeCS, CHANCES, eROSITA).

Key Contributions and Results

Iterative Method Efficacy: The standard non-iterative approach using a constant anisotropy factor ( $F_\beta = 0.65$ ) systematically overestimates cluster masses by a median of 16% ( $M_{200,c}/M_{200,true} = 1.16$ ) with a scatter of 0.23. The proposed iterative method significantly reduces this bias to $-6\%$ ( $M_{200,c}/M_{200,true} = 0.94$ ) and reduces the scatter to 0.18. The improvement is particularly notable for low-mass systems, where non-iterative methods can overestimate masses by factors of 1.5–2.
Kernel Sensitivity: The study finds that the optimal smoothing kernel parameters ( $s, q$ ) vary significantly from cluster to cluster and do not correlate strongly with global cluster properties (mass or richness). No single pair of parameters yields optimal results for all clusters, suggesting that a "one-size-fits-all" kernel approach is insufficient for high-precision mass recovery.
Selection Biases:
- Red-Sequence Selection: Restricting the sample to Red-Sequence galaxies consistently leads to an underestimation of cluster masses (median bias of $-14\%$ ) because these galaxies are overrepresented in the dense central regions.
- Magnitude and Flux Limits: Bright magnitude cuts ( $m_r < 20.5$ ) tend to overestimate masses, while flux cuts (excluding low H $\alpha$ emitters) increase the scatter in mass estimates.
CATARSIS Prospects: The CATARSIS survey, designed to obtain redshifts for galaxies down to $m_{AB,r} < 22$ within $2 \times R_{200,c}$ using blind integral-field spectroscopy, is projected to mitigate the biases associated with magnitude limits and Red-Sequence selection. By capturing fainter, dust-reddened, and star-forming members, CATARSIS aims to provide a more complete dynamical tracer population.

Significance and Claims
The paper claims that while the caustic technique is a powerful tool for mass estimation, its reliability is heavily dependent on the treatment of velocity anisotropy and the completeness of the galaxy sample. The authors demonstrate that an iterative correction for anisotropy can reduce systematic biases by approximately 20% compared to standard methods.

Regarding the CATARSIS survey, the paper positions it as a uniquely promising instrument for cluster mass reconstruction. By combining deep, blind spectroscopy with wide spatial coverage, CATARSIS is expected to minimize the selection biases (specifically the underestimation from RS-only samples and overestimation from bright magnitude cuts) that plague other surveys. The authors conclude that CATARSIS will enable the derivation of dynamical mass profiles with precision comparable to benchmark surveys like HeCS, while providing essential complementary data to weak-lensing studies, thereby improving the calibration of cluster masses for cosmological constraints. The work emphasizes that these findings are based on the specific capabilities of the GIZMO-Simba run and the planned CATARSIS strategy, serving as a preparatory assessment for the upcoming observational campaign.