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:
AGN Clustering — projected autocorrelation wp(rp) and cross-correlation with galaxies, plus redshift-space power spectrum multipoles for optical QSOs.
AGN Weak Lensing — excess surface density ΔΣ(R) around AGN host haloes from stacked weak lensing.
AGN Luminosity Functions — 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.
AGN Clustering
Two-point correlation function measurements of AGN spatial distribution probe the large-scale halo bias bAGN and, through HOD modelling, the typical host halo mass Mhalo and duty cycle fduty.
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 halo ~ 10 12.5–13.0 M ☉ — 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.
Directory |
Survey |
zeff |
NAGN |
r0 [h-1 Mpc] |
log Mh |
H0 |
Reference |
|---|---|---|---|---|---|---|---|
XMM-CDFS |
1.0 |
538 |
10.3 ± 0.7 |
13.5 |
70 |
A&A 494, 33 (arXiv:0903.1106) · ~310 |
|
XMM-COSMOS |
1.2 |
593 |
8.7 ± 0.5 |
13.2 |
70 |
ApJ 716, 348 (arXiv:0910.5716) · ~190 |
|
Chandra AEGIS |
0.65 |
1325 |
7.4 ± 0.9 |
12.9 |
70 |
ApJ 741, 15 (arXiv:1010.0786) · ~85 |
|
XMM-COSMOS (HOD) |
1.2 |
593 |
8.65 ± 0.5 |
13.2 |
70 |
ApJ 736, 99 (arXiv:1107.5000) · ~220 |
|
Chandra multi-field |
0.8 |
1466 |
7.9 ± 0.9 |
13.0 |
70 |
MNRAS 428, 1382 (arXiv:1212.4399) · ~100 |
|
Chandra COSMOS Legacy |
0.5 |
1760 |
6.5 ± 0.5 |
12.7 |
70 |
ApJ 858, 82 (arXiv:1803.09386) · ~95 |
|
XMM-COSMOS soft |
1.2 |
1366 |
6.1 ± 1.2 |
12.5 |
70 |
A&A 629, A14 (arXiv:1903.01568) · ~30 |
|
Chandra COSMOS Legacy |
1.2 |
1472 |
6.9 ± 0.5 |
12.8 |
70 |
ApJ 879, 23 (arXiv:1905.05782) · ~40 |
|
Comparat2023 eFEDS |
eROSITA eFEDS (140 deg²) |
0.5 |
8 000 |
7.1 ± 0.5 |
12.9 |
67.4 |
A&A 673, A125 (arXiv:2306.11053) · ~50 |
X-ray × Galaxy Cross-Correlation
Six cross-correlation measurements using galaxy catalogues as dense tracers.
Directory |
Survey |
zeff |
NAGN |
bAGN |
log Mh |
Reference |
|---|---|---|---|---|---|---|
ROSAT × SDSS DR6 |
0.15 |
1552 |
1.28 ± 0.09 |
13.1 |
ApJ 713, 558 (arXiv:1001.2782) · ~180 |
|
ROSAT/XMM × SDSS DR7 |
0.25 |
3000 |
1.1–1.5 |
12.7–13.3 |
ApJ 815, L17 (arXiv:1501.00041) · ~110 |
|
ROSAT+BASS × SDSS DR12 |
0.12 |
4200 |
1.35 ± 0.07 |
13.1 |
MNRAS 474, 1773 (arXiv:1805.03671) · ~65 |
|
Krumpe2023 eFEDS |
eROSITA eFEDS × SDSS DR16 |
0.4 |
22 020 |
1.9 ± 0.1 |
13.0 |
A&A 669, A32 (arXiv:2212.06476) · ~35 |
PRIMUS/DEEP2 |
0.6 |
3200 |
1.7 ± 0.2 |
12.8 |
ApJ 821, 55 (arXiv:1604.02381) · ~55 |
|
XMM-XXL × SDSS |
0.5 |
1200 |
— |
13.0 |
MNRAS 490, 5077 (arXiv:1906.07547) · ~30 |
Optical QSO Clustering
Eleven measurements from 2QZ (2002) to DESI Y1 (2025).
Directory |
Survey |
zeff |
NQSO |
Statistic |
log Mh |
Reference |
|---|---|---|---|---|---|---|
2QZ (10k) |
1.5 |
10k |
wp |
12.5 |
MNRAS 335, 459 (arXiv:astro-ph/0104095) · ~320 |
|
2QZ full (23k) |
1.5 |
23k |
wp |
12.5 |
MNRAS 356, 415 (arXiv:astro-ph/0409314) · ~440 |
|
2QZ (HOD) |
1.5 |
7.8k |
2pt+3pt |
12.5 |
MNRAS 348, 325 (arXiv:astro-ph/0310505) · ~160 |
|
2QZ updated |
1.4 |
20k |
wp |
12.5 |
MNRAS 369, 1001 (arXiv:astro-ph/0512248) · ~120 |
|
SDSS photo-QSO |
1.4 |
300k |
w(θ) |
12.5 |
ApJ 658, 85 (arXiv:astro-ph/0612191) · ~240 |
|
SDSS DR5 |
1.5 |
30k |
wp |
12.5 |
ApJ 697, 1634 (arXiv:0903.3244) · ~190 |
|
SDSS DR5 |
1.5 |
30k |
wp |
12.5 |
ApJ 697, 1656 (arXiv:0810.4144) · ~330 |
|
SDSS DR7 (57k) |
1.5 |
57k |
wp |
12.6 |
ApJ 778, 98 (arXiv:1212.4526) · ~220 |
|
eBOSS DR14 (147k) |
1.52 |
147k |
P(k) mult. |
12.6 |
MNRAS 468, 728 (arXiv:1612.04484) · ~120 |
|
eBOSS DR14 (RSD) |
1.52 |
150k |
P(k) + BAO |
12.6 |
JCAP 2017, 17 (arXiv:1705.05442) · ~110 |
|
Prada2025 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.
Directory |
Survey |
zeff |
NAGN |
r0 [h-1 Mpc] |
log Mh |
Reference |
|---|---|---|---|---|---|---|
WISE × SDSS photo |
0.5 |
130k |
7.5 ± 0.5 |
13.0 |
ApJ 789, 44 (arXiv:1309.2285) · ~120 |
|
WISE AGN photo |
0.5–1.3 |
50k |
— |
12.9 |
ApJ 946, 59 (arXiv:2209.03987) · ~20 |
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 200b ~ 10 12.7–13.0 M ☉ independent of redshift (0.1 < z < 2.0) and selection wavelength.
Directory |
Survey |
zeff |
NAGN |
log M200b |
H0 |
Reference |
|---|---|---|---|---|---|---|
COSMOS X-ray + HST lensing |
0.6 |
206 |
13.0 ± 0.3 |
70 |
MNRAS 446, 1874 (arXiv:1507.03735) · ~130 |
|
Comparat2023 eFEDS |
eROSITA eFEDS × KiDS/HSC |
0.5 |
8 000 |
12.9 ± 0.15 |
67.4 |
A&A 671, A100 (arXiv:2211.07659) · ~60 |
Luo2024 eRASS1 |
eROSITA eRASS1 × KiDS |
0.5 |
50 000 |
13.0 ± 0.15 |
67.4 |
A&A 686, A162 (arXiv:2312.05668) · ~25 |
SDSS QSO × SDSS lensing |
1.0 |
100 000 |
12.7 ± 0.2 |
70 |
ApJ 960, 91 (arXiv:2310.08478) · ~20 |
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 NH ~ 1024 cm-2. All measurements confirm Luminosity Dependent Density Evolution (LDDE): luminous AGN (LX > 1044 erg/s) peak at z ~ 2–3; faint AGN (LX < 1043 erg/s) peak at z ~ 0.6–1.
Directory |
Survey |
z range |
NAGN |
band keV |
Method |
zpeak |
Reference |
|---|---|---|---|---|---|---|---|
ROSAT+Chandra |
0–4.8 |
1290 |
0.5–2 |
STY LDDE |
2.0 |
A&A 441, 417 (arXiv:astro-ph/0504240) · ~790 |
|
Chandra multi |
0–3.0 |
682 |
2–8 |
1/Vmax |
2.0 |
ApJ 679, 118 (arXiv:0710.2461) · ~300 |
|
XMM/Chandra+BASS |
0–5.0 |
4039 |
2–10 |
STY LDDE |
2.4 |
ApJ 786, 104 (arXiv:1402.7902) · ~790 |
|
Chandra multi |
0–5.0 |
~4000 |
2–10 |
Bayesian |
2.0 |
ApJ 815, 66 (arXiv:1503.01120) · ~410 |
|
Chandra+XMM |
0–4.0 |
10 000 |
0.5–10 |
Bayesian |
2.0 |
MNRAS 474, 1225 (arXiv:1710.05923) · ~290 |
|
Synthesis+eROSITA |
0–5.0 |
~4000 |
2–10 |
STY |
2.4 |
MNRAS 487, 275 (arXiv: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.
Directory |
Survey |
z range |
NQSO |
Model |
zpeak |
Reference |
|---|---|---|---|---|---|---|
2QZ 6k |
0.3–2.3 |
6000 |
PLE |
2.0 |
MNRAS 317, 1014 (arXiv:astro-ph/0005368) · ~860 |
|
SDSS DR3 15k |
0.3–5.0 |
15343 |
broken PL |
2.4 |
AJ 131, 2766 (arXiv:astro-ph/0601500) · ~640 |
|
Multi-band synthesis |
0.0–6.0 |
— |
LDDE bolometric |
2.5 |
ApJ 654, 731 (arXiv:astro-ph/0609291) · ~1500 |
|
SDSS+BOSS 22k |
2.2–3.5 |
22301 |
broken PL |
2.4 |
ApJ 773, 14 (arXiv:1210.6389) · ~380 |
|
zCOSMOS+BOSS |
0.3–2.5 |
1000 |
LDDE |
2.0 |
A&A 588, A78 (arXiv: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:
Selection |
z range |
Technique |
log Mh |
Representative reference |
|---|---|---|---|---|
X-ray (XMM, Chandra) |
0.5–2.0 |
wp autocorr |
12.5–13.2 |
Cappelluti+2010; Allevato+2011 |
X-ray (eROSITA eFEDS) |
0.1–0.8 |
wp + 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 |
wp / 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 Mhalo ~ 1012.5–13.0 M☉.
See literature_measurements/AGN_benchmark/REVIEW.md for the full narrative
review including systematic challenges and the cosmic evolution of SMBH accretion
(luminosity functions).