Gas Benchmark

Compiled ICM/CGM gas measurements for the gas benchmark: X-ray and SZ scaling relations (Y_SZ–M, Y_X–M, T_X–M, L_X–M) and cross-correlations of galaxy positions with thermal SZ Compton-y, kinematic SZ, and X-ray surface brightness.

Selection criteria: publications since 2000; data from dedicated CMB experiments (Planck, ACT, SPT) and X-ray observatories (Chandra, XMM-Newton, eROSITA); citation count > 30 (recent eROSITA papers excepted).

Physics overview 

The hot baryonic gas in and around galaxy groups and clusters is the most massive component of the baryonic budget in the Universe. It emits bremsstrahlung X-rays (observable as extended X-ray emission, luminosity L_X), imprints spectral distortions on the CMB via inverse Compton scattering (thermal SZ: Compton-y; kinematic SZ: kSZ temperature shift), and through its pressure profile sets the amplitude of the tSZ power spectrum.

Three families of observables are benchmarked here:

1. Scaling relations (cluster scale): Relate cluster mass M to X-ray and SZ observables. The key quantities are:

Y_X = M_gas × T_X — the X-ray analog of the SZ signal; introduced by Kravtsov+2006 as a low-scatter proxy (scatter ~ 5–7%).
T_X–M — X-ray temperature vs mass; scatter ~15–20%.
L_X–M — X-ray luminosity vs mass; scatter ~30–40% dominated by cool-core clusters.
Y_SZ = (σ_T/m_ec²) ∫ P dV — integrated tSZ Comptonisation; the Universal Pressure Profile of Arnaud+2010 relates the gas pressure profile to Y_SZ and connects X-ray and SZ.

The hydrostatic mass bias (1 − b_hydro) ~ 0.7–0.85 reconciles Planck cluster counts with CMB-inferred σ₈: hydrostatic masses underestimate true masses by 15–30% due to non-thermal pressure support.

2. Galaxy × tSZ cross-correlations: The angular cross-power C_ℓ^gy and the real-space w_gY(θ) between galaxy density and the Compton-y map probes the pressure of hot gas at the locations of galaxies. Measured at group and cluster scales (M ~ 10^12.5–14 M_☉) it directly constrains the gas pressure profile normalisation and AGN/SN feedback energy.

3. Galaxy × kSZ cross-correlations: The kSZ effect shifts photon energies by ΔT/T = −(v_r/c) τ_e, proportional to the radial velocity and the electron optical depth. Two estimators are in common use:

Pairwise kSZ (Hand+2012): ⟨(T₁−T₂) sign(v₁−v₂)⟩ over galaxy pairs; sensitive to the pairwise momentum, scales as τ_eff × f_gas.
Projected field (Schaan+2016): ⟨T(r̂) × v_rec(r̂)⟩ using reconstructed large-scale velocity field; higher S/N per galaxy.

Both estimators constrain the effective optical depth τ_eff ~ 10⁻⁴–10⁻³, i.e. the total gas column within the aperture, and the baryon ejection fraction by AGN feedback.

X-ray–Mass Scaling Relations 

The X-ray–mass scaling relations calibrate the mass proxy chain. The Y_X = M_gas × T_X quantity has the lowest intrinsic scatter (~5–7%) and is the preferred mass proxy for unbiased cosmological cluster counts from X-ray surveys.

Directory	Survey	z range	N_cl	Cites	Reference
Kravtsov2006	Chandra archive (sims)	0.0–1.0	17 (sim)	~800	ApJ 650, 128 (arXiv:astro-ph/0603205)
Arnaud2007	XMM-Newton REXCESS	0.05–0.2	10	~400	A&A 474, L37 (arXiv:0709.1561)
Vikhlinin2009	Chandra CCP	0.02–0.9	85	~1100	ApJ 692, 1060 (arXiv:0812.2720)
Pratt2009	XMM-Newton REXCESS	0.05–0.2	31	~650	A&A 498, 361 (arXiv:0809.3784)

Key results:

Kravtsov+2006: introduced Y_X as the lowest-scatter X-ray mass proxy (σ ~ 5%) from simulations. Y_X ∝ M^5/3 from self-similar evolution.
Arnaud+2007: first observational confirmation of the Y_X–M relation with XMM; scatter 6%. Established the XMM/REXCESS sample as the X-ray calibration reference for Planck.
Vikhlinin+2009: comprehensive Chandra scaling relations (T_X–M, L_X–M, Y_X–M) for 85 clusters. Used for Chandra cosmological cluster counts yielding σ₈ = 0.80 ± 0.02.
Pratt+2009: L_X–M from REXCESS with CC/NCC separation; scatter 34% for full sample, 14% for NCC-only. Sets the baseline scatter model for eROSITA predictions.

SZ–Mass Scaling Relations 

The SZ–mass scaling relations connect the integrated Compton-y parameter Y_SZ to cluster mass via the Universal Pressure Profile (UPP). The hydrostatic mass bias (1 − b) shifts the normalisation of Y_SZ–M and is a major source of systematic uncertainty in Planck cosmological analyses.

Directory	Survey	z range	N_cl	Cites	Reference
Arnaud2010	XMM REXCESS	0.05–0.2	33	~1200	A&A 517, A92 (arXiv:0910.1234)
PlanckXI2013	Planck all-sky SZ	0.0–1.0	189	~800	A&A 536, A11 (arXiv:1101.2026)
Bocquet2015	SPT-SZ 2500 deg²	0.25–1.75	100	~350	ApJ 799, 214 (arXiv:1407.2942)
deHaan2016	SPT-SZ	0.25–1.75	78	~500	ApJ 832, 95 (arXiv:1603.06522)
Hilton2021	ACT DR5	0.04–1.91	4195	~600	ApJS 253, 3 (arXiv:2009.11043)
Chiu2022	eROSITA eFEDS × SPT	0.1–0.8	542	~50	A&A 661, A11 (arXiv:2110.09523)
Bulbul2024	eROSITA eRASS1	0.1–0.8	12247	~50	A&A 685, A106 (arXiv:2402.08452)

Key results:

Arnaud+2010: derived the Universal Pressure Profile (UPP) for galaxy clusters from XMM-REXCESS. The generalized NFW form P(x) = P₀ / [(c₅₀₀x)^γ(1 + (c₅₀₀x)^α)^(β−γ)/α] with P₀ = 8.403, c₅₀₀ = 1.177, γ = 0.31, α = 1.05, β = 5.49. Provides the mapping from X-ray pressure to tSZ Compton-y and defines the Y_SZ–M calibration used in all subsequent Planck analyses.
Planck XI 2013: first Planck tSZ cluster catalog (ESZ); Y_SZ calibrated against XMM hydrostatic masses; hydrostatic bias (1 − b) ~ 0.80 inferred from comparison with Planck cosmological cluster counts.
Bocquet+2015: SPT-SZ cluster counts with weak-lensing mass calibration; Ω_m = 0.296 ± 0.034, σ₈ = 0.829 ± 0.024.
de Haan+2016: 78-cluster SPT-SZ sample with CMB lensing + WL mass calibration; first measurement combining tSZ + kSZ + lensing for mass calibration.
Hilton+2021: ACT DR5 catalog of 4195 clusters (z up to 1.91); largest mm-wave cluster sample pre-eROSITA; mass range 10^13.5–10¹⁵ M_☉.
Chiu+2022: joint eROSITA eFEDS × SPT-SZ mass calibration; mass-observable relations for 542 clusters in a common footprint.
Bulbul+2024: eROSITA eRASS1 catalog of 12,247 clusters; largest X-ray cluster sample; cosmological constraints yield S₈ = 0.86 ± 0.01 (mild tension with galaxy lensing surveys).

Universal Pressure Profile parameters (Arnaud+2010):

P₀	c₅₀₀	γ (inner)	α (pivot)	β (outer)
8.403	1.177	0.31	1.05	5.49

Galaxy × tSZ Cross-Correlations 

The galaxy × tSZ cross-correlation w_gY(θ) or C_ℓ^gy probes the gas pressure profile around galaxies at all scales from the 1-halo (within R₂₀₀) to the 2-halo regime (cosmic web filaments and sheets). It is sensitive to the total thermal energy of the gas and provides constraints on feedback processes complementary to X-ray measurements.

Directory	Survey	z range	N_gal	Cites	Reference
Vikram2017	DES Y1 × Planck-y	0.1–0.9	2.3 M	~200	MNRAS 467, 2315 (arXiv:1608.06295)
Pandey2022	DES Y3 × ACT-y	0.1–0.7	10 M	~120	PRD 105, 123525 (arXiv:2108.01600)
Tanimura2022	Planck × SDSS LRGs	0.1–0.7	0.5 M	~80	MNRAS 509, 300 (arXiv:2110.08880)
Schaan2021_tsz	ACT DR4 × BOSS CMASS	0.4–0.7	0.5 M	~150	PRD 103, 063513 (arXiv:2009.05557)

Key results:

Vikram+2017: 9σ detection of g×*y* from DES Y1 × Planck; first joint DES galaxy clustering + tSZ constraint on gas pressure HOD. Pressure bias b_P = 0.49 ± 0.04 at z ~ 0.3.
Pandey+2022: DES Y3 × ACT Compton-y; C_ℓ^gy measured at 100 < ℓ < 3000; constraints on AGN + supernova feedback amplitudes from joint C_ℓ^gg + C_ℓ^gy. First simultaneous fit of clustering and pressure cross-correlations.
Tanimura+2022: stacked Planck Compton-y profiles around SDSS LRGs as a function of stellar mass; pressure signal detected at 10σ; constrains Y_SZ vs M_★ relation at M_halo ~ 10¹³–10^13.5 M_☉.
Schaan+2021: radial tSZ + kSZ profiles around BOSS CMASS galaxies at 0.4 < z < 0.7 with ACT DR4; companion to Amodeo+2021; jointly measures the gas pressure (tSZ) and density (kSZ) profiles, the ICM equivalent of the ΔΣ + w_p decomposition for dark matter.

Galaxy × kSZ Cross-Correlations 

The kinematic SZ effect measures the radial momentum of gas along the line of sight. Cross-correlating the CMB temperature with the galaxy density weighted by the reconstructed velocity gives a signal proportional to the electron optical depth τ_eff, the mean baryon column density within the aperture.

Directory	Survey	z range	N_gal	Cites	Reference
Hand2012	ACT × SDSS DR9 CMASS	0.4–0.7	762	~700	PRL 109, 041101 (arXiv:1203.4219)
PlanckXXXVII2016	Planck × SDSS DR11	0.0–0.7	1.2 M	~400	A&A 586, A140 (arXiv:1504.03339)
Schaan2016	ACT × BOSS CMASS DR10	0.4–0.7	148 k	~300	PRD 93, 082002 (arXiv:1510.06442)
Sugiyama2018	Planck × BOSS LOWZ	0.15–0.43	120 k	~50	MNRAS 475, 3764 (arXiv:1705.07449)
Tanimura2021	Planck × SDSS photo-z	0.1–0.9	1.5 M	~60	A&A 645, A112 (arXiv:2007.08199)
Calafut2021	ACT DR4 × BOSS DR15	0.2–0.7	0.5 M	~120	PRD 104, 043502 (arXiv:2101.08374)
Amodeo2021	ACT DR4 × BOSS CMASS DR15	0.4–0.7	0.5 M	~180	PRD 103, 063514 (arXiv:2009.05558)
Hadzhiyska2024	ACT DR6 × DESI photo-z	0.1–1.0	5 M	~30	PRL 134, 201001 (arXiv:2407.07152)
RiedGuachalla2025	DESI Y1 LRG × ACT DR6	0.4–1.1	0.8 M	~15	PRD 112, 103512 (arXiv:2503.19870)
Qu2026	DESI DR2 LRG × ACT DR6	0.4–1.1	2.4 M	~5	arXiv:2604.19744 (preprint)
Hadzhiyska2026	DESI DR2 BGS+ELG × ACT DR6	0.1–1.6	3 M	~5	arXiv:2604.19745 (preprint)

Key results:

Hand+2012: first detection of the kSZ effect from a spectroscopic galaxy sample (2.9σ pairwise); introduced the pairwise kSZ estimator p(r) = ⟨(T₁ − T₂) sign(v₁ − v₂)⟩; foundational for the field.
Planck Collaboration XXXVII 2016: Planck confirmation of pairwise kSZ at 1.8σ with 1.2 M SDSS galaxies; lower significance than ACT due to larger Planck beam (5′ vs 1.4′).
Schaan+2016: 3.8σ kSZ with the projected field estimator ⟨T(r̂) v_rec(r̂)⟩; τ_eff = 1.4 × 10⁻⁴; baryon fraction ~80% of cosmic mean; introduced the standard ACT kSZ methodology.
Sugiyama+2018: 3.2σ kSZ with BOSS LOWZ + Planck; extends kSZ to lower redshifts and demonstrates improved velocity reconstruction from photo-z + spec-z hybrid.
Tanimura+2021: 4.5σ pairwise kSZ using 1.5 M photometric SDSS galaxies with Planck; shows kSZ is accessible without spectroscopic redshifts (relevant for LSST).
Calafut+2021: 5.4σ pairwise kSZ; ACT DR4 × BOSS DR15; τ_eff = 1.5 × 10⁻⁴.
Amodeo+2021: 6.3σ kSZ radial profile around BOSS CMASS with ACT DR4; gas fraction within R₂₀₀ = 68% of cosmic baryon fraction; 32% of baryons ejected by AGN feedback; best AGN ejection constraint from kSZ at group scales.
Hadzhiyska+2024: 13σ kSZ from 5 million photometric DESI galaxies × ACT DR6; gas extends beyond dark matter haloes; baryonic feedback exceeds ILLUSTRISTNG predictions, contributing to resolution of the S₈ lensing tension.
Ried Guachalla+2025: 10σ kSZ radial profile around 0.8 M DESI Y1 LRGs × ACT DR6; gas halos extend beyond dark matter at 99.5% confidence; favours FLAMINGO/BAHAMAS high-feedback models. Direct successor to Amodeo+2021 with 3× more galaxies.
Qu+2026: 18σ kSZ — most significant detection to date — from 2.4 M DESI DR2 LRGs × ACT DR6; gas profiles shallower than dark matter at all halo masses (10¹³–10^14.5M_☉) and redshifts 0.4 < z < 1.1; feedback efficiency exceeds all current simulation predictions.
Hadzhiyska+2026: first high-significance kSZ for BGS (9σ, z < 0.4) and ELG (7.5σ, 0.8 < z < 1.6) tracers; ELGs retain more gas than LRGs at fixed halo mass, consistent with weaker AGN feedback in star-forming systems.

Detection significance timeline (kSZ):

Paper	Estimator	S/N	z_eff	τ_eff (×10⁻⁴)	Notes
Hand+2012	Pairwise	2.9σ	0.55	~1.3	First detection
Planck+2016	Pairwise	1.8σ	0.4	~1.0	Low S/N (Planck beam)
Schaan+2016	Projected field	3.8σ	0.55	1.4 ± 0.3	Introduced PF method
Calafut+2021	Pairwise	5.4σ	0.45	1.5 ± 0.3	ACT DR4 benchmark
Tanimura+2021	Pairwise	4.5σ	0.5	1.2 ± 0.3	Photometric z
Amodeo+2021	Projected field	6.3σ	0.55	~1.6	Radial profile; f_gas
Hadzhiyska+2024	Projected field	13σ	0.5	—	Photo-z; gas beyond DM
Ried Guachalla+2025	Projected field	10σ	0.7	—	DESI Y1 LRG; 99.5% gas beyond DM
Qu+2026	Projected field	18σ	0.7	—	DESI DR2; highest S/N ever

Galaxy × X-ray Cross-Correlations 

Galaxy × X-ray cross-correlations probe the density of hot gas through the X-ray bremsstrahlung emissivity ε_X ∝ n_e² T^1/2. Combined with the galaxy × tSZ signal (which probes pressure ∝ n_e T), they constrain both n_e and T independently — the full thermodynamic state of the gas.

Directory	Survey	z range	N_gal	Cites	Reference
Comparat2022	eROSITA eFEDS × SDSS/DESI	0.1–0.8	90 k	~30	A&A 666, A156 (arXiv:2201.05169)
Croft2023	eROSITA eRASS1 × eBOSS DR16	0.1–1.0	0.9 M	~15	MNRAS 529, 3 (arXiv:2309.05647)

Key results:

Comparat+2022: stacked eROSITA eFEDS X-ray surface brightness profiles S_X(R) around 90 k SDSS/DESI spectroscopic galaxies; resolves the CGM + ICM X-ray emission beyond the AGN point source; constrains L_X–M at group scales from eROSITA. First demonstration of eROSITA sensitivity to the diffuse CGM.
Croft+2023: galaxy × X-ray background angular cross-power C_ℓ^gX at 50 < ℓ < 2000 from eROSITA eRASS1 × eBOSS (LRG, ELG, QSO); 8σ detection; separates AGN and diffuse ICM/WHIM contributions; constraints on the X-ray bias b_X and hot gas fraction across halo masses.

Comparison with simulations 

The gas benchmarks directly constrain hydrodynamic simulations. Key comparisons are:

Y:sub:`SZ`–M normalisation — BAHAMAS (McCarthy+2017) and ILLUSTRISTNG (Springel+2018) bracket the observed normalisation, with BAHAMAS tuned to match cluster gas fractions. SIMBA (Davé+2019) overshoots at low mass due to stronger AGN feedback.
kSZ baryon ejection and gas profiles — Amodeo+2021 constrains 32% ejection from within R₂₀₀; BAHAMAS predicts 25–35%, ILLUSTRISTNG 15–20%. The newer DESI × ACT DR6 results (Ried Guachalla+2025, Hadzhiyska+2024, Qu+2026) find gas profiles shallower than dark matter at 99.5% confidence and feedback efficiency exceeding all current simulation predictions including BAHAMAS and FLAMINGO high-feedback variants. This finding is consistent with the lensing S₈ tension and suggests simulations underpredict the extent of AGN-driven gas ejection.
Galaxy × tSZ amplitude — Pandey+2022 find the DES Y3 × ACT signal is consistent with BAHAMAS but 15–20% above the raw ILLUSTRISTNG prediction at scales R ~ 1–5 h⁻¹ Mpc, suggesting ILLUSTRISTNG under-heats the diffuse gas.
Universal Pressure Profile — the UPP of Arnaud+2010 is well reproduced by BAHAMAS and ILLUSTRISTNG at R > 0.2 R₅₀₀; deviations in the core (r < 0.1 R₅₀₀) reflect cool-core/AGN injection differences.

Cosmology conventions 

Shorthand	H₀	Ω_m	Used by
Planck15	67.3–67.8	0.307–0.315	Arnaud+2010 (H₀=70), Planck XI+XXXVII (H₀=67.3), most ACT papers
Planck18	67.4	0.315	Bulbul+2024, Chiu+2022, Amodeo+2021, Calafut+2021
WMAP	70–71	0.27–0.30	Kravtsov+2006, Hand+2012

All halo masses are M_200m or M_500c as indicated in each paper.json. Conversions between M_200c, M_200m, and M_500c use the Duffy+2008 NFW concentration–mass relation.