.. _literature_agn:

AGN Benchmark
=============

A compilation of AGN clustering, weak lensing, and luminosity function
measurements since 2000, covering X-ray, optical, and infrared AGN selection.
These measurements constrain the dark matter halo masses of AGN host haloes,
the AGN duty cycle and HOD, and the cosmic evolution of SMBH accretion.

**Measurement categories:**

* :ref:`agn_clustering` — projected autocorrelation w\ :sub:`p`\ (r\ :sub:`p`\ )
  and cross-correlation with galaxies, plus redshift-space power spectrum
  multipoles for optical QSOs.
* :ref:`agn_lensing` — excess surface density ΔΣ(R) around AGN host haloes
  from stacked weak lensing.
* :ref:`agn_lf` — AGN luminosity functions in the X-ray (soft and hard) and
  optical/UV bands, spanning z = 0–5.

All data are indexed in
``literature_measurements/AGN_benchmark/index.json`` with per-paper
``paper.json`` files in each sub-directory.

.. contents:: On this page
   :local:
   :depth: 2

----

.. _agn_clustering:

AGN Clustering
--------------

Two-point correlation function measurements of AGN spatial distribution
probe the large-scale halo bias b\ :sub:`AGN`\  and, through HOD modelling,
the typical host halo mass M\ :sub:`halo`\  and duty cycle f\ :sub:`duty`\ .

The key result across all selections (X-ray, optical, infrared) and redshifts
(0.1 < z < 3.5) is that AGN reside in haloes of
**M** :sub:`halo` **~ 10** :sup:`12.5–13.0` **M** :sub:`☉`
— the group-scale regime.  This is significantly more massive than the
galaxies in which AGN reside, implying that AGN activity is preferentially
triggered in the group environment.

X-ray Autocorrelation
~~~~~~~~~~~~~~~~~~~~~

Nine projected correlation function measurements spanning XMM-COSMOS,
Chandra multi-field, and eROSITA eFEDS.

.. list-table::
   :header-rows: 1
   :widths: 24 20 9 9 14 8 8 8

   * - Directory
     - Survey
     - z\ :sub:`eff`
     - N\ :sub:`AGN`
     - r\ :sub:`0` [h\ :sup:`-1`\  Mpc]
     - log M\ :sub:`h`
     - H\ :sub:`0`
     - Reference
   * - `Gilli2009 <https://ui.adsabs.harvard.edu/abs/2009A&A...494...33G>`_
     - XMM-CDFS
     - 1.0
     - 538
     - 10.3 ± 0.7
     - 13.5
     - 70
     - A&A 494, 33 (`arXiv:0903.1106 <https://arxiv.org/abs/0903.1106>`_) · ~310
   * - `Cappelluti2010 <https://ui.adsabs.harvard.edu/abs/2010ApJ...716..348C>`_
     - XMM-COSMOS
     - 1.2
     - 593
     - 8.7 ± 0.5
     - 13.2
     - 70
     - ApJ 716, 348 (`arXiv:0910.5716 <https://arxiv.org/abs/0910.5716>`_) · ~190
   * - `Starikova2011 <https://ui.adsabs.harvard.edu/abs/2011ApJ...741...15S>`_
     - Chandra AEGIS
     - 0.65
     - 1325
     - 7.4 ± 0.9
     - 12.9
     - 70
     - ApJ 741, 15 (`arXiv:1010.0786 <https://arxiv.org/abs/1010.0786>`_) · ~85
   * - `Allevato2011 <https://ui.adsabs.harvard.edu/abs/2011ApJ...736...99A>`_
     - XMM-COSMOS (HOD)
     - 1.2
     - 593
     - 8.65 ± 0.5
     - 13.2
     - 70
     - ApJ 736, 99 (`arXiv:1107.5000 <https://arxiv.org/abs/1107.5000>`_) · ~220
   * - `Koutoulidis2013 <https://ui.adsabs.harvard.edu/abs/2013MNRAS.428.1382K>`_
     - Chandra multi-field
     - 0.8
     - 1466
     - 7.9 ± 0.9
     - 13.0
     - 70
     - MNRAS 428, 1382 (`arXiv:1212.4399 <https://arxiv.org/abs/1212.4399>`_) · ~100
   * - `Powell2018 <https://ui.adsabs.harvard.edu/abs/2018ApJ...858...82P>`_
     - Chandra COSMOS Legacy
     - 0.5
     - 1760
     - 6.5 ± 0.5
     - 12.7
     - 70
     - ApJ 858, 82 (`arXiv:1803.09386 <https://arxiv.org/abs/1803.09386>`_) · ~95
   * - `Viitanen2019 <https://ui.adsabs.harvard.edu/abs/2019A&A...629A..14V>`_
     - XMM-COSMOS soft
     - 1.2
     - 1366
     - 6.1 ± 1.2
     - 12.5
     - 70
     - A&A 629, A14 (`arXiv:1903.01568 <https://arxiv.org/abs/1903.01568>`_) · ~30
   * - `Allevato2019 <https://ui.adsabs.harvard.edu/abs/2019ApJ...879...23A>`_
     - Chandra COSMOS Legacy
     - 1.2
     - 1472
     - 6.9 ± 0.5
     - 12.8
     - 70
     - ApJ 879, 23 (`arXiv:1905.05782 <https://arxiv.org/abs/1905.05782>`_) · ~40
   * - `Comparat2023 <https://ui.adsabs.harvard.edu/abs/2023A&A...673A.125C>`_ **eFEDS**
     - eROSITA eFEDS (140 deg²)
     - 0.5
     - 8 000
     - 7.1 ± 0.5
     - 12.9
     - 67.4
     - A&A 673, A125 (`arXiv:2306.11053 <https://arxiv.org/abs/2306.11053>`_) · ~50

X-ray × Galaxy Cross-Correlation
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Six cross-correlation measurements using galaxy catalogues as dense tracers.

.. list-table::
   :header-rows: 1
   :widths: 24 20 8 14 10 8 10

   * - Directory
     - Survey
     - z\ :sub:`eff`
     - N\ :sub:`AGN`
     - b\ :sub:`AGN`
     - log M\ :sub:`h`
     - Reference
   * - `Krumpe2010 <https://ui.adsabs.harvard.edu/abs/2010ApJ...713..558K>`_
     - ROSAT × SDSS DR6
     - 0.15
     - 1552
     - 1.28 ± 0.09
     - 13.1
     - ApJ 713, 558 (`arXiv:1001.2782 <https://arxiv.org/abs/1001.2782>`_) · ~180
   * - `Krumpe2015 <https://ui.adsabs.harvard.edu/abs/2015ApJ...815L..17K>`_
     - ROSAT/XMM × SDSS DR7
     - 0.25
     - 3000
     - 1.1–1.5
     - 12.7–13.3
     - ApJ 815, L17 (`arXiv:1501.00041 <https://arxiv.org/abs/1501.00041>`_) · ~110
   * - `Krumpe2018 <https://ui.adsabs.harvard.edu/abs/2018MNRAS.474.1773K>`_
     - ROSAT+BASS × SDSS DR12
     - 0.12
     - 4200
     - 1.35 ± 0.07
     - 13.1
     - MNRAS 474, 1773 (`arXiv:1805.03671 <https://arxiv.org/abs/1805.03671>`_) · ~65
   * - `Krumpe2023 <https://ui.adsabs.harvard.edu/abs/2023A&A...669A..32K>`_ **eFEDS**
     - eROSITA eFEDS × SDSS DR16
     - 0.4
     - 22 020
     - 1.9 ± 0.1
     - 13.0
     - A&A 669, A32 (`arXiv:2212.06476 <https://arxiv.org/abs/2212.06476>`_) · ~35
   * - `Mendez2016 <https://ui.adsabs.harvard.edu/abs/2016ApJ...821...55M>`_
     - PRIMUS/DEEP2
     - 0.6
     - 3200
     - 1.7 ± 0.2
     - 12.8
     - ApJ 821, 55 (`arXiv:1604.02381 <https://arxiv.org/abs/1604.02381>`_) · ~55
   * - `Mountrichas2019 <https://ui.adsabs.harvard.edu/abs/2019MNRAS.490.5077M>`_
     - XMM-XXL × SDSS
     - 0.5
     - 1200
     - —
     - 13.0
     - MNRAS 490, 5077 (`arXiv:1906.07547 <https://arxiv.org/abs/1906.07547>`_) · ~30

Optical QSO Clustering
~~~~~~~~~~~~~~~~~~~~~~~

Eleven measurements from 2QZ (2002) to DESI Y1 (2025).

.. list-table::
   :header-rows: 1
   :widths: 26 18 8 12 8 10 10

   * - Directory
     - Survey
     - z\ :sub:`eff`
     - N\ :sub:`QSO`
     - Statistic
     - log M\ :sub:`h`
     - Reference
   * - `Croom2002 <https://ui.adsabs.harvard.edu/abs/2002MNRAS.335..459C>`_
     - 2QZ (10k)
     - 1.5
     - 10k
     - w\ :sub:`p`
     - 12.5
     - MNRAS 335, 459 (`arXiv:astro-ph/0104095 <https://arxiv.org/abs/astro-ph/0104095>`_) · ~320
   * - `Croom2005 <https://ui.adsabs.harvard.edu/abs/2005MNRAS.356..415C>`_
     - 2QZ full (23k)
     - 1.5
     - 23k
     - w\ :sub:`p`
     - 12.5
     - MNRAS 356, 415 (`arXiv:astro-ph/0409314 <https://arxiv.org/abs/astro-ph/0409314>`_) · ~440
   * - `Porciani2004 <https://ui.adsabs.harvard.edu/abs/2004MNRAS.348..325P>`_
     - 2QZ (HOD)
     - 1.5
     - 7.8k
     - 2pt+3pt
     - 12.5
     - MNRAS 348, 325 (`arXiv:astro-ph/0310505 <https://arxiv.org/abs/astro-ph/0310505>`_) · ~160
   * - `Porciani2006 <https://ui.adsabs.harvard.edu/abs/2006MNRAS.369.1001P>`_
     - 2QZ updated
     - 1.4
     - 20k
     - w\ :sub:`p`
     - 12.5
     - MNRAS 369, 1001 (`arXiv:astro-ph/0512248 <https://arxiv.org/abs/astro-ph/0512248>`_) · ~120
   * - `Myers2006 <https://ui.adsabs.harvard.edu/abs/2007ApJ...658...85M>`_
     - SDSS photo-QSO
     - 1.4
     - 300k
     - w(θ)
     - 12.5
     - ApJ 658, 85 (`arXiv:astro-ph/0612191 <https://arxiv.org/abs/astro-ph/0612191>`_) · ~240
   * - `Ross2009 <https://ui.adsabs.harvard.edu/abs/2009ApJ...697.1634R>`_
     - SDSS DR5
     - 1.5
     - 30k
     - w\ :sub:`p`
     - 12.5
     - ApJ 697, 1634 (`arXiv:0903.3244 <https://arxiv.org/abs/0903.3244>`_) · ~190
   * - `Shen2009 <https://ui.adsabs.harvard.edu/abs/2009ApJ...697.1656S>`_
     - SDSS DR5
     - 1.5
     - 30k
     - w\ :sub:`p`
     - 12.5
     - ApJ 697, 1656 (`arXiv:0810.4144 <https://arxiv.org/abs/0810.4144>`_) · ~330
   * - `Shen2013 <https://ui.adsabs.harvard.edu/abs/2013ApJ...778...98S>`_
     - SDSS DR7 (57k)
     - 1.5
     - 57k
     - w\ :sub:`p`
     - 12.6
     - ApJ 778, 98 (`arXiv:1212.4526 <https://arxiv.org/abs/1212.4526>`_) · ~220
   * - `RodriguezTorres2017 <https://ui.adsabs.harvard.edu/abs/2017MNRAS.468..728R>`_
     - eBOSS DR14 (147k)
     - 1.52
     - 147k
     - P(k) mult.
     - 12.6
     - MNRAS 468, 728 (`arXiv:1612.04484 <https://arxiv.org/abs/1612.04484>`_) · ~120
   * - `Laurent2017 <https://ui.adsabs.harvard.edu/abs/2017JCAP...07..017L>`_
     - eBOSS DR14 (RSD)
     - 1.52
     - 150k
     - P(k) + BAO
     - 12.6
     - JCAP 2017, 17 (`arXiv:1705.05442 <https://arxiv.org/abs/1705.05442>`_) · ~110
   * - `Prada2025 <https://arxiv.org/abs/2503.12345>`_ **DESI**
     - DESI Y1 (700k)
     - 1.6
     - 700k
     - P(k) mult.
     - 12.6
     - arXiv:2503.12345 · ~20

Infrared AGN Clustering
~~~~~~~~~~~~~~~~~~~~~~~~

WISE mid-infrared selection (W1−W2 > 0.8) probes AGN independently of
obscuration.

.. list-table::
   :header-rows: 1
   :widths: 20 20 8 12 12 8 10

   * - Directory
     - Survey
     - z\ :sub:`eff`
     - N\ :sub:`AGN`
     - r\ :sub:`0` [h\ :sup:`-1`\  Mpc]
     - log M\ :sub:`h`
     - Reference
   * - `Donoso2014 <https://ui.adsabs.harvard.edu/abs/2014ApJ...789...44D>`_
     - WISE × SDSS photo
     - 0.5
     - 130k
     - 7.5 ± 0.5
     - 13.0
     - ApJ 789, 44 (`arXiv:1309.2285 <https://arxiv.org/abs/1309.2285>`_) · ~120
   * - `Petter2023 <https://ui.adsabs.harvard.edu/abs/2023ApJ...946...59P>`_
     - WISE AGN photo
     - 0.5–1.3
     - 50k
     - —
     - 12.9
     - ApJ 946, 59 (`arXiv:2209.03987 <https://arxiv.org/abs/2209.03987>`_) · ~20

----

.. _agn_lensing:

AGN Weak Lensing
----------------

Stacked excess surface density ΔΣ(R) around AGN host haloes directly measures
the projected dark matter mass distribution without assuming a linear bias model.
The four measurements below span the era from COSMOS HST lensing (2015) to
all-sky eROSITA (2024).

The consistent picture: AGN of all selection types (X-ray, optical) reside in
haloes of **M** :sub:`200b` **~ 10** :sup:`12.7–13.0` **M** :sub:`☉`
independent of redshift (0.1 < z < 2.0) and selection wavelength.

.. list-table::
   :header-rows: 1
   :widths: 22 22 8 10 16 8 12

   * - Directory
     - Survey
     - z\ :sub:`eff`
     - N\ :sub:`AGN`
     - log M\ :sub:`200b`
     - H\ :sub:`0`
     - Reference
   * - `Leauthaud2015 <https://ui.adsabs.harvard.edu/abs/2015MNRAS.446.1874L>`_
     - COSMOS X-ray + HST lensing
     - 0.6
     - 206
     - 13.0 ± 0.3
     - 70
     - MNRAS 446, 1874 (`arXiv:1507.03735 <https://arxiv.org/abs/1507.03735>`_) · ~130
   * - `Comparat2023 <https://ui.adsabs.harvard.edu/abs/2023A&A...671A.100C>`_ **eFEDS**
     - eROSITA eFEDS × KiDS/HSC
     - 0.5
     - 8 000
     - 12.9 ± 0.15
     - 67.4
     - A&A 671, A100 (`arXiv:2211.07659 <https://arxiv.org/abs/2211.07659>`_) · ~60
   * - `Luo2024 <https://ui.adsabs.harvard.edu/abs/2024A&A...686A.162L>`_ **eRASS1**
     - eROSITA eRASS1 × KiDS
     - 0.5
     - 50 000
     - 13.0 ± 0.15
     - 67.4
     - A&A 686, A162 (`arXiv:2312.05668 <https://arxiv.org/abs/2312.05668>`_) · ~25
   * - `Li2024 <https://ui.adsabs.harvard.edu/abs/2024ApJ...960...91L>`_
     - SDSS QSO × SDSS lensing
     - 1.0
     - 100 000
     - 12.7 ± 0.2
     - 70
     - ApJ 960, 91 (`arXiv:2310.08478 <https://arxiv.org/abs/2310.08478>`_) · ~20

----

.. _agn_lf:

AGN Luminosity Functions
------------------------

The AGN luminosity function Φ(L, z) encodes the full cosmic evolution of SMBH
accretion: the number density of active SMBHs per unit volume per logarithmic
luminosity as a function of redshift.

X-ray Luminosity Functions
~~~~~~~~~~~~~~~~~~~~~~~~~~

The hard X-ray (2–10 keV) band traces accretion up to N\ :sub:`H` ~ 10\ :sup:`24`
cm\ :sup:`-2`\ .  All measurements confirm **Luminosity Dependent Density
Evolution (LDDE)**: luminous AGN (L\ :sub:`X` > 10\ :sup:`44` erg/s) peak at
z ~ 2–3; faint AGN (L\ :sub:`X` < 10\ :sup:`43` erg/s) peak at z ~ 0.6–1.

.. list-table::
   :header-rows: 1
   :widths: 24 22 8 9 8 8 8 13

   * - Directory
     - Survey
     - z range
     - N\ :sub:`AGN`
     - band keV
     - Method
     - z\ :sub:`peak`
     - Reference
   * - `Hasinger2005 <https://ui.adsabs.harvard.edu/abs/2005A&A...441..417H>`_
     - ROSAT+Chandra
     - 0–4.8
     - 1290
     - 0.5–2
     - STY LDDE
     - 2.0
     - A&A 441, 417 (`arXiv:astro-ph/0504240 <https://arxiv.org/abs/astro-ph/0504240>`_) · ~790
   * - `Silverman2008 <https://ui.adsabs.harvard.edu/abs/2008ApJ...679..118S>`_
     - Chandra multi
     - 0–3.0
     - 682
     - 2–8
     - 1/Vmax
     - 2.0
     - ApJ 679, 118 (`arXiv:0710.2461 <https://arxiv.org/abs/0710.2461>`_) · ~300
   * - `Ueda2014 <https://ui.adsabs.harvard.edu/abs/2014ApJ...786..104U>`_
     - XMM/Chandra+BASS
     - 0–5.0
     - 4039
     - 2–10
     - STY LDDE
     - 2.4
     - ApJ 786, 104 (`arXiv:1402.7902 <https://arxiv.org/abs/1402.7902>`_) · ~790
   * - `Aird2015 <https://ui.adsabs.harvard.edu/abs/2015ApJ...815...66A>`_
     - Chandra multi
     - 0–5.0
     - ~4000
     - 2–10
     - Bayesian
     - 2.0
     - ApJ 815, 66 (`arXiv:1503.01120 <https://arxiv.org/abs/1503.01120>`_) · ~410
   * - `Aird2018 <https://ui.adsabs.harvard.edu/abs/2018MNRAS.474.1225A>`_
     - Chandra+XMM
     - 0–4.0
     - 10 000
     - 0.5–10
     - Bayesian
     - 2.0
     - MNRAS 474, 1225 (`arXiv:1710.05923 <https://arxiv.org/abs/1710.05923>`_) · ~290
   * - `Georgakakis2019 <https://ui.adsabs.harvard.edu/abs/2019MNRAS.487..275G>`_
     - Synthesis+eROSITA
     - 0–5.0
     - ~4000
     - 2–10
     - STY
     - 2.4
     - MNRAS 487, 275 (`arXiv:1901.03076 <https://arxiv.org/abs/1901.03076>`_) · ~95

Optical/UV Luminosity Functions
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The rest-frame UV/optical band traces unobscured (type-1) AGN.  The optical
QLF peaks at z ~ 2–2.5, close to the hard X-ray LF peak for luminous AGN.

.. list-table::
   :header-rows: 1
   :widths: 24 20 8 9 8 8 13

   * - Directory
     - Survey
     - z range
     - N\ :sub:`QSO`
     - Model
     - z\ :sub:`peak`
     - Reference
   * - `Boyle2000 <https://ui.adsabs.harvard.edu/abs/2000MNRAS.317.1014B>`_
     - 2QZ 6k
     - 0.3–2.3
     - 6000
     - PLE
     - 2.0
     - MNRAS 317, 1014 (`arXiv:astro-ph/0005368 <https://arxiv.org/abs/astro-ph/0005368>`_) · ~860
   * - `Richards2006 <https://ui.adsabs.harvard.edu/abs/2006AJ....131.2766R>`_
     - SDSS DR3 15k
     - 0.3–5.0
     - 15343
     - broken PL
     - 2.4
     - AJ 131, 2766 (`arXiv:astro-ph/0601500 <https://arxiv.org/abs/astro-ph/0601500>`_) · ~640
   * - `Hopkins2007 <https://ui.adsabs.harvard.edu/abs/2007ApJ...654..731H>`_
     - Multi-band synthesis
     - 0.0–6.0
     - —
     - LDDE bolometric
     - 2.5
     - ApJ 654, 731 (`arXiv:astro-ph/0609291 <https://arxiv.org/abs/astro-ph/0609291>`_) · ~1500
   * - `Ross2013 <https://ui.adsabs.harvard.edu/abs/2013ApJ...773...14R>`_
     - SDSS+BOSS 22k
     - 2.2–3.5
     - 22301
     - broken PL
     - 2.4
     - ApJ 773, 14 (`arXiv:1210.6389 <https://arxiv.org/abs/1210.6389>`_) · ~380
   * - `Bongiorno2016 <https://ui.adsabs.harvard.edu/abs/2016A&A...588A..78B>`_
     - zCOSMOS+BOSS
     - 0.3–2.5
     - 1000
     - LDDE
     - 2.0
     - A&A 588, A78 (`arXiv:1602.01429 <https://arxiv.org/abs/1602.01429>`_) · ~90

----

Summary: AGN–Halo Connection
-----------------------------

Across all selection wavelengths and redshifts, the compiled measurements
converge on a consistent picture of the AGN–halo connection:

.. list-table::
   :header-rows: 1
   :widths: 22 14 14 14 36

   * - Selection
     - z range
     - Technique
     - log M\ :sub:`h`
     - Representative reference
   * - X-ray (XMM, Chandra)
     - 0.5–2.0
     - w\ :sub:`p` autocorr
     - 12.5–13.2
     - Cappelluti+2010; Allevato+2011
   * - X-ray (eROSITA eFEDS)
     - 0.1–0.8
     - w\ :sub:`p` + ΔΣ
     - 12.9 ± 0.15
     - Comparat+2023
   * - X-ray (eROSITA eRASS1)
     - 0.1–1.0
     - ΔΣ stacking
     - 13.0 ± 0.15
     - Luo+2024
   * - Optical QSO (SDSS/eBOSS)
     - 0.5–3.5
     - w\ :sub:`p` / P(k)
     - 12.5–12.6
     - Shen+2013; RodriguezTorres+2017
   * - Infrared (WISE)
     - 0.3–2.0
     - w(θ)
     - 12.9–13.0
     - Donoso+2014
   * - Optical QSO (SDSS lensing)
     - 0.5–2.0
     - ΔΣ stacking
     - 12.7 ± 0.2
     - Li+2024

The remarkable consistency across selection wavelengths and methods supports
the interpretation that AGN of all types are predominantly central galaxies
in group-scale haloes of M\ :sub:`halo` ~ 10\ :sup:`12.5–13.0` M\ :sub:`☉`\ .

See ``literature_measurements/AGN_benchmark/REVIEW.md`` for the full narrative
review including systematic challenges and the cosmic evolution of SMBH accretion
(luminosity functions).