.. _literature_gas:

Gas Benchmark
=============

Compiled ICM/CGM gas measurements for the gas benchmark: X-ray and SZ
scaling relations (Y\ :sub:`SZ`\ –M, Y\ :sub:`X`\ –M, T\ :sub:`X`\ –M,
L\ :sub:`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).

.. contents:: On this page
   :local:
   :depth: 1

----

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\ :sub:`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\ :sub:`X` = M\ :sub:`gas` × T\ :sub:`X`  — the X-ray analog of the SZ signal;
  introduced by `Kravtsov+2006 <https://ui.adsabs.harvard.edu/abs/2006ApJ...650..128K>`_
  as a low-scatter proxy (scatter ~ 5–7%).
* T\ :sub:`X`\ –M — X-ray temperature vs mass; scatter ~15–20%.
* L\ :sub:`X`\ –M — X-ray luminosity vs mass; scatter ~30–40% dominated by
  cool-core clusters.
* Y\ :sub:`SZ` = (σ\ :sub:`T`/m\ :sub:`e`\ c²) ∫ P dV — integrated tSZ Comptonisation;
  the **Universal Pressure Profile** of `Arnaud+2010 <https://ui.adsabs.harvard.edu/abs/2010A&A...517A..92A>`_
  relates the gas pressure profile to Y\ :sub:`SZ` and connects X-ray and SZ.

The **hydrostatic mass bias** (1 − b\ :sub:`hydro`) ~ 0.7–0.85 reconciles
Planck cluster counts with CMB-inferred σ\ :sub:`8`\ : hydrostatic masses
underestimate true masses by 15–30% due to non-thermal pressure support.

**2. Galaxy × tSZ cross-correlations:**
The angular cross-power C\ :sub:`ℓ`\ :sup:`gy` and the real-space w\ :sub:`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\ :sup:`12.5–14` M\ :sub:`☉`\ ) 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\ :sub:`r`/c) τ\ :sub:`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\ :sub:`eff` × f\ :sub:`gas`\ .
* **Projected field** (Schaan+2016): ⟨T(r̂) × v\ :sub:`rec`\ (r̂)⟩ using
  reconstructed large-scale velocity field; higher S/N per galaxy.

Both estimators constrain the effective optical depth
τ\ :sub:`eff` ~ 10\ :sup:`−4`\ –10\ :sup:`−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\ :sub:`X` = M\ :sub:`gas` × T\ :sub:`X` quantity has the lowest intrinsic
scatter (~5–7%) and is the preferred mass proxy for unbiased cosmological
cluster counts from X-ray surveys.

.. list-table::
   :header-rows: 1
   :widths: 26 20 10 10 8 26

   * - Directory
     - Survey
     - z range
     - N\ :sub:`cl`
     - Cites
     - Reference
   * - `Kravtsov2006 <https://ui.adsabs.harvard.edu/abs/2006ApJ...650..128K>`_
     - Chandra archive (sims)
     - 0.0–1.0
     - 17 (sim)
     - ~800
     - ApJ 650, 128 (`arXiv:astro-ph/0603205 <https://arxiv.org/abs/astro-ph/0603205>`_)
   * - `Arnaud2007 <https://ui.adsabs.harvard.edu/abs/2007A&A...474L..37A>`_
     - XMM-Newton REXCESS
     - 0.05–0.2
     - 10
     - ~400
     - A&A 474, L37 (`arXiv:0709.1561 <https://arxiv.org/abs/0709.1561>`_)
   * - `Vikhlinin2009 <https://ui.adsabs.harvard.edu/abs/2009ApJ...692.1060V>`_
     - Chandra CCP
     - 0.02–0.9
     - 85
     - ~1100
     - ApJ 692, 1060 (`arXiv:0812.2720 <https://arxiv.org/abs/0812.2720>`_)
   * - `Pratt2009 <https://ui.adsabs.harvard.edu/abs/2009A&A...498..361P>`_
     - XMM-Newton REXCESS
     - 0.05–0.2
     - 31
     - ~650
     - A&A 498, 361 (`arXiv:0809.3784 <https://arxiv.org/abs/0809.3784>`_)

**Key results:**

* `Kravtsov+2006 <https://ui.adsabs.harvard.edu/abs/2006ApJ...650..128K>`_:
  introduced Y\ :sub:`X` as the lowest-scatter X-ray mass proxy (σ ~ 5%) from
  simulations.  Y\ :sub:`X` ∝ M\ :sup:`5/3` from self-similar evolution.
* `Arnaud+2007 <https://ui.adsabs.harvard.edu/abs/2007A&A...474L..37A>`_:
  first observational confirmation of the Y\ :sub:`X`\ –M relation with XMM;
  scatter 6%.  Established the XMM/REXCESS sample as the X-ray calibration
  reference for Planck.
* `Vikhlinin+2009 <https://ui.adsabs.harvard.edu/abs/2009ApJ...692.1060V>`_:
  comprehensive Chandra scaling relations (T\ :sub:`X`\ –M, L\ :sub:`X`\ –M,
  Y\ :sub:`X`\ –M) for 85 clusters.  Used for Chandra cosmological cluster
  counts yielding σ\ :sub:`8` = 0.80 ± 0.02.
* `Pratt+2009 <https://ui.adsabs.harvard.edu/abs/2009A&A...498..361P>`_:
  L\ :sub:`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\ :sub:`SZ` to cluster mass via the Universal Pressure Profile (UPP).  The
**hydrostatic mass bias** (1 − b) shifts the normalisation of Y\ :sub:`SZ`\ –M
and is a major source of systematic uncertainty in Planck cosmological
analyses.

.. list-table::
   :header-rows: 1
   :widths: 26 20 10 10 8 26

   * - Directory
     - Survey
     - z range
     - N\ :sub:`cl`
     - Cites
     - Reference
   * - `Arnaud2010 <https://ui.adsabs.harvard.edu/abs/2010A&A...517A..92A>`_
     - XMM REXCESS
     - 0.05–0.2
     - 33
     - ~1200
     - A&A 517, A92 (`arXiv:0910.1234 <https://arxiv.org/abs/0910.1234>`_)
   * - `PlanckXI2013 <https://ui.adsabs.harvard.edu/abs/2011A&A...536A..11P>`_
     - Planck all-sky SZ
     - 0.0–1.0
     - 189
     - ~800
     - A&A 536, A11 (`arXiv:1101.2026 <https://arxiv.org/abs/1101.2026>`_)
   * - `Bocquet2015 <https://ui.adsabs.harvard.edu/abs/2015ApJ...799..214B>`_
     - SPT-SZ 2500 deg²
     - 0.25–1.75
     - 100
     - ~350
     - ApJ 799, 214 (`arXiv:1407.2942 <https://arxiv.org/abs/1407.2942>`_)
   * - `deHaan2016 <https://ui.adsabs.harvard.edu/abs/2016ApJ...832...95D>`_
     - SPT-SZ
     - 0.25–1.75
     - 78
     - ~500
     - ApJ 832, 95 (`arXiv:1603.06522 <https://arxiv.org/abs/1603.06522>`_)
   * - `Hilton2021 <https://ui.adsabs.harvard.edu/abs/2021ApJS..253....3H>`_
     - ACT DR5
     - 0.04–1.91
     - 4195
     - ~600
     - ApJS 253, 3 (`arXiv:2009.11043 <https://arxiv.org/abs/2009.11043>`_)
   * - `Chiu2022 <https://ui.adsabs.harvard.edu/abs/2022A&A...661A..11C>`_
     - eROSITA eFEDS × SPT
     - 0.1–0.8
     - 542
     - ~50
     - A&A 661, A11 (`arXiv:2110.09523 <https://arxiv.org/abs/2110.09523>`_)
   * - `Bulbul2024 <https://ui.adsabs.harvard.edu/abs/2024A&A...685A.106B>`_
     - eROSITA eRASS1
     - 0.1–0.8
     - 12247
     - ~50
     - A&A 685, A106 (`arXiv:2402.08452 <https://arxiv.org/abs/2402.08452>`_)

**Key results:**

* `Arnaud+2010 <https://ui.adsabs.harvard.edu/abs/2010A&A...517A..92A>`_:
  derived the **Universal Pressure Profile** (UPP) for galaxy clusters from
  XMM-REXCESS.  The generalized NFW form P(x) = P\ :sub:`0` /
  [(c\ :sub:`500`\ x)\ :sup:`γ`\ (1 + (c\ :sub:`500`\ x)\ :sup:`α`\ )\ :sup:`(β−γ)/α`\ ]
  with P\ :sub:`0` = 8.403, c\ :sub:`500` = 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\ :sub:`SZ`\ –M calibration used in all subsequent Planck analyses.
* `Planck XI 2013 <https://ui.adsabs.harvard.edu/abs/2011A&A...536A..11P>`_:
  first Planck tSZ cluster catalog (ESZ); Y\ :sub:`SZ` calibrated against
  XMM hydrostatic masses; hydrostatic bias (1 − b) ~ 0.80 inferred from
  comparison with Planck cosmological cluster counts.
* `Bocquet+2015 <https://ui.adsabs.harvard.edu/abs/2015ApJ...799..214B>`_:
  SPT-SZ cluster counts with weak-lensing mass calibration;
  Ω\ :sub:`m` = 0.296 ± 0.034, σ\ :sub:`8` = 0.829 ± 0.024.
* `de Haan+2016 <https://ui.adsabs.harvard.edu/abs/2016ApJ...832...95D>`_:
  78-cluster SPT-SZ sample with CMB lensing + WL mass calibration;
  first measurement combining tSZ + kSZ + lensing for mass calibration.
* `Hilton+2021 <https://ui.adsabs.harvard.edu/abs/2021ApJS..253....3H>`_:
  ACT DR5 catalog of 4195 clusters (z up to 1.91); largest mm-wave cluster
  sample pre-eROSITA; mass range 10\ :sup:`13.5`–10\ :sup:`15` M\ :sub:`☉`\ .
* `Chiu+2022 <https://ui.adsabs.harvard.edu/abs/2022A&A...661A..11C>`_:
  joint eROSITA eFEDS × SPT-SZ mass calibration; mass-observable relations
  for 542 clusters in a common footprint.
* `Bulbul+2024 <https://ui.adsabs.harvard.edu/abs/2024A&A...685A.106B>`_:
  eROSITA eRASS1 catalog of 12,247 clusters; largest X-ray cluster sample;
  cosmological constraints yield S\ :sub:`8` = 0.86 ± 0.01 (mild tension
  with galaxy lensing surveys).

**Universal Pressure Profile parameters (Arnaud+2010):**

.. list-table::
   :header-rows: 1
   :widths: 15 15 15 15 15

   * - P\ :sub:`0`
     - c\ :sub:`500`
     - 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\ :sub:`gY`\ (θ) or C\ :sub:`ℓ`\ :sup:`gy`
probes the **gas pressure profile** around galaxies at all scales from the
1-halo (within R\ :sub:`200`\ ) 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.

.. list-table::
   :header-rows: 1
   :widths: 24 22 10 10 8 26

   * - Directory
     - Survey
     - z range
     - N\ :sub:`gal`
     - Cites
     - Reference
   * - `Vikram2017 <https://ui.adsabs.harvard.edu/abs/2017MNRAS.467.2315V>`_
     - DES Y1 × Planck-*y*
     - 0.1–0.9
     - 2.3 M
     - ~200
     - MNRAS 467, 2315 (`arXiv:1608.06295 <https://arxiv.org/abs/1608.06295>`_)
   * - `Pandey2022 <https://ui.adsabs.harvard.edu/abs/2022PhRvD.105l3525P>`_
     - DES Y3 × ACT-*y*
     - 0.1–0.7
     - 10 M
     - ~120
     - PRD 105, 123525 (`arXiv:2108.01600 <https://arxiv.org/abs/2108.01600>`_)
   * - `Tanimura2022 <https://ui.adsabs.harvard.edu/abs/2022MNRAS.509..300T>`_
     - Planck × SDSS LRGs
     - 0.1–0.7
     - 0.5 M
     - ~80
     - MNRAS 509, 300 (`arXiv:2110.08880 <https://arxiv.org/abs/2110.08880>`_)
   * - `Schaan2021_tsz <https://ui.adsabs.harvard.edu/abs/2021PhRvD.103f3513S>`_
     - ACT DR4 × BOSS CMASS
     - 0.4–0.7
     - 0.5 M
     - ~150
     - PRD 103, 063513 (`arXiv:2009.05557 <https://arxiv.org/abs/2009.05557>`_)

**Key results:**

* `Vikram+2017 <https://ui.adsabs.harvard.edu/abs/2017MNRAS.467.2315V>`_:
  9σ detection of g×*y* from DES Y1 × Planck; first joint DES galaxy
  clustering + tSZ constraint on gas pressure HOD.  Pressure bias
  b\ :sub:`P` = 0.49 ± 0.04 at z ~ 0.3.
* `Pandey+2022 <https://ui.adsabs.harvard.edu/abs/2022PhRvD.105l3525P>`_:
  DES Y3 × ACT Compton-*y*; C\ :sub:`ℓ`\ :sup:`gy` measured at
  100 < ℓ < 3000; constraints on AGN + supernova feedback amplitudes from
  joint C\ :sub:`ℓ`\ :sup:`gg` + C\ :sub:`ℓ`\ :sup:`gy`\ .  First
  simultaneous fit of clustering and pressure cross-correlations.
* `Tanimura+2022 <https://ui.adsabs.harvard.edu/abs/2022MNRAS.509..300T>`_:
  stacked Planck Compton-*y* profiles around SDSS LRGs as a function of
  stellar mass; pressure signal detected at 10σ; constrains Y\ :sub:`SZ` vs
  M\ :sub:`★` relation at M\ :sub:`halo` ~ 10\ :sup:`13`\ –10\ :sup:`13.5` M\ :sub:`☉`\ .
* `Schaan+2021 <https://ui.adsabs.harvard.edu/abs/2021PhRvD.103f3513S>`_:
  radial tSZ + kSZ profiles around BOSS CMASS galaxies at 0.4 < z < 0.7 with
  ACT DR4; companion to `Amodeo+2021 <https://ui.adsabs.harvard.edu/abs/2021PhRvD.103f3514A>`_;
  jointly measures the gas pressure (tSZ) and density (kSZ) profiles, the
  ICM equivalent of the ΔΣ + w\ :sub:`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\ :sub:`eff`\ , the mean baryon column density
within the aperture.

.. list-table::
   :header-rows: 1
   :widths: 24 22 10 10 8 26

   * - Directory
     - Survey
     - z range
     - N\ :sub:`gal`
     - Cites
     - Reference
   * - `Hand2012 <https://ui.adsabs.harvard.edu/abs/2012PhRvL.109d1101H>`_
     - ACT × SDSS DR9 CMASS
     - 0.4–0.7
     - 762
     - ~700
     - PRL 109, 041101 (`arXiv:1203.4219 <https://arxiv.org/abs/1203.4219>`_)
   * - `PlanckXXXVII2016 <https://ui.adsabs.harvard.edu/abs/2016A&A...586A.140P>`_
     - Planck × SDSS DR11
     - 0.0–0.7
     - 1.2 M
     - ~400
     - A&A 586, A140 (`arXiv:1504.03339 <https://arxiv.org/abs/1504.03339>`_)
   * - `Schaan2016 <https://ui.adsabs.harvard.edu/abs/2016PhRvD..93h2002S>`_
     - ACT × BOSS CMASS DR10
     - 0.4–0.7
     - 148 k
     - ~300
     - PRD 93, 082002 (`arXiv:1510.06442 <https://arxiv.org/abs/1510.06442>`_)
   * - `Sugiyama2018 <https://ui.adsabs.harvard.edu/abs/2018MNRAS.475.3764S>`_
     - Planck × BOSS LOWZ
     - 0.15–0.43
     - 120 k
     - ~50
     - MNRAS 475, 3764 (`arXiv:1705.07449 <https://arxiv.org/abs/1705.07449>`_)
   * - `Tanimura2021 <https://ui.adsabs.harvard.edu/abs/2021A&A...645A.112T>`_
     - Planck × SDSS photo-z
     - 0.1–0.9
     - 1.5 M
     - ~60
     - A&A 645, A112 (`arXiv:2007.08199 <https://arxiv.org/abs/2007.08199>`_)
   * - `Calafut2021 <https://ui.adsabs.harvard.edu/abs/2021PhRvD.104d3502C>`_
     - ACT DR4 × BOSS DR15
     - 0.2–0.7
     - 0.5 M
     - ~120
     - PRD 104, 043502 (`arXiv:2101.08374 <https://arxiv.org/abs/2101.08374>`_)
   * - `Amodeo2021 <https://ui.adsabs.harvard.edu/abs/2021PhRvD.103f3514A>`_
     - ACT DR4 × BOSS CMASS DR15
     - 0.4–0.7
     - 0.5 M
     - ~180
     - PRD 103, 063514 (`arXiv:2009.05558 <https://arxiv.org/abs/2009.05558>`_)
   * - `Hadzhiyska2024 <https://ui.adsabs.harvard.edu/abs/2025PhRvL.134t1001H>`_
     - ACT DR6 × DESI photo-z
     - 0.1–1.0
     - 5 M
     - ~30
     - PRL 134, 201001 (`arXiv:2407.07152 <https://arxiv.org/abs/2407.07152>`_)
   * - `RiedGuachalla2025 <https://ui.adsabs.harvard.edu/abs/2025PhRvD.112j3512R>`_
     - DESI Y1 LRG × ACT DR6
     - 0.4–1.1
     - 0.8 M
     - ~15
     - PRD 112, 103512 (`arXiv:2503.19870 <https://arxiv.org/abs/2503.19870>`_)
   * - `Qu2026 <https://arxiv.org/abs/2604.19744>`_
     - DESI DR2 LRG × ACT DR6
     - 0.4–1.1
     - 2.4 M
     - ~5
     - arXiv:2604.19744 (preprint)
   * - `Hadzhiyska2026 <https://arxiv.org/abs/2604.19745>`_
     - DESI DR2 BGS+ELG × ACT DR6
     - 0.1–1.6
     - 3 M
     - ~5
     - arXiv:2604.19745 (preprint)

**Key results:**

* `Hand+2012 <https://ui.adsabs.harvard.edu/abs/2012PhRvL.109d1101H>`_:
  **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 <https://ui.adsabs.harvard.edu/abs/2016A&A...586A.140P>`_:
  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 <https://ui.adsabs.harvard.edu/abs/2016PhRvD..93h2002S>`_:
  3.8σ kSZ with the **projected field estimator** ⟨T(r̂) v\ :sub:`rec`\ (r̂)⟩;
  τ\ :sub:`eff` = 1.4 × 10\ :sup:`−4`\ ; baryon fraction ~80% of cosmic mean;
  introduced the standard ACT kSZ methodology.
* `Sugiyama+2018 <https://ui.adsabs.harvard.edu/abs/2018MNRAS.475.3764S>`_:
  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 <https://ui.adsabs.harvard.edu/abs/2021A&A...645A.112T>`_:
  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 <https://ui.adsabs.harvard.edu/abs/2021PhRvD.104d3502C>`_:
  5.4σ pairwise kSZ; ACT DR4 × BOSS DR15; τ\ :sub:`eff` = 1.5 × 10\ :sup:`−4`\ .
* `Amodeo+2021 <https://ui.adsabs.harvard.edu/abs/2021PhRvD.103f3514A>`_:
  6.3σ kSZ radial profile around BOSS CMASS with ACT DR4;
  gas fraction within R\ :sub:`200` = 68% of cosmic baryon fraction; 32% of
  baryons ejected by AGN feedback; best AGN ejection constraint from kSZ at
  group scales.
* `Hadzhiyska+2024 <https://ui.adsabs.harvard.edu/abs/2025PhRvL.134t1001H>`_:
  **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 S\ :sub:`8` lensing tension.
* `Ried Guachalla+2025 <https://ui.adsabs.harvard.edu/abs/2025PhRvD.112j3512R>`_:
  **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 <https://arxiv.org/abs/2604.19744>`_:
  **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
  (10\ :sup:`13`\ –10\ :sup:`14.5`\ M\ :sub:`☉`\ ) and redshifts 0.4 < z < 1.1;
  feedback efficiency exceeds all current simulation predictions.
* `Hadzhiyska+2026 <https://arxiv.org/abs/2604.19745>`_:
  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):**

.. list-table::
   :header-rows: 1
   :widths: 22 20 10 10 18 20

   * - Paper
     - Estimator
     - S/N
     - z\ :sub:`eff`
     - τ\ :sub:`eff` (×10\ :sup:`−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\ :sub:`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\ :sub:`X` ∝ n\ :sub:`e`\ :sup:`2` T\ :sup:`1/2`\ .
Combined with the galaxy × tSZ signal (which probes pressure ∝ n\ :sub:`e` T),
they constrain both n\ :sub:`e` and T independently — the full thermodynamic
state of the gas.

.. list-table::
   :header-rows: 1
   :widths: 24 22 10 10 8 26

   * - Directory
     - Survey
     - z range
     - N\ :sub:`gal`
     - Cites
     - Reference
   * - `Comparat2022 <https://ui.adsabs.harvard.edu/abs/2022A&A...666A.156C>`_
     - eROSITA eFEDS × SDSS/DESI
     - 0.1–0.8
     - 90 k
     - ~30
     - A&A 666, A156 (`arXiv:2201.05169 <https://arxiv.org/abs/2201.05169>`_)
   * - `Croft2023 <https://ui.adsabs.harvard.edu/abs/2023MNRAS.529..3C>`_
     - eROSITA eRASS1 × eBOSS DR16
     - 0.1–1.0
     - 0.9 M
     - ~15
     - MNRAS 529, 3 (`arXiv:2309.05647 <https://arxiv.org/abs/2309.05647>`_)

**Key results:**

* `Comparat+2022 <https://ui.adsabs.harvard.edu/abs/2022A&A...666A.156C>`_:
  stacked eROSITA eFEDS X-ray surface brightness profiles S\ :sub:`X`\ (R)
  around 90 k SDSS/DESI spectroscopic galaxies; resolves the CGM + ICM X-ray
  emission beyond the AGN point source; constrains L\ :sub:`X`\ –M at group
  scales from eROSITA.  First demonstration of eROSITA sensitivity to the
  diffuse CGM.
* `Croft+2023 <https://ui.adsabs.harvard.edu/abs/2023MNRAS.529..3C>`_:
  galaxy × X-ray background angular cross-power C\ :sub:`ℓ`\ :sup:`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\ :sub:`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 R\ :sub:`200`\ ; BAHAMAS predicts 25–35%, ILLUSTRISTNG 15–20%.
  The newer DESI × ACT DR6 results (`Ried Guachalla+2025 <https://ui.adsabs.harvard.edu/abs/2025PhRvD.112j3512R>`_,
  `Hadzhiyska+2024 <https://ui.adsabs.harvard.edu/abs/2025PhRvL.134t1001H>`_,
  `Qu+2026 <https://arxiv.org/abs/2604.19744>`_) 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 S\ :sub:`8` 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\ :sup:`−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 R\ :sub:`500`\ ; deviations in the
  core (r < 0.1 R\ :sub:`500`\ ) reflect cool-core/AGN injection differences.

----

Cosmology conventions
---------------------

.. list-table::
   :header-rows: 1
   :widths: 20 12 12 56

   * - Shorthand
     - H\ :sub:`0`
     - Ω\ :sub:`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\ :sub:`200m` or M\ :sub:`500c` as indicated in each
``paper.json``.  Conversions between M\ :sub:`200c`\ , M\ :sub:`200m`\ , and
M\ :sub:`500c` use the Duffy+2008 NFW concentration–mass relation.