§ Interactive

Populate halos with galaxies.

Move the three knobs on the right. Galaxies appear and cluster; the correlation function below updates in real time.

dark-matter halo central galaxy satellite
50 Mpc/h
scroll · drag · dbl-click to reset

Halo Occupation Distribution

⟨N_cen⟩ = ½[1 + erf((log M_h − log M_min) / σ)]  ·  ⟨N_sat⟩ = ⟨N_cen⟩ · ((M_h − M_cut) / M_1)^α

log Mmin central threshold 11.5
Only halos above this mass host a central galaxy. Raise it → galaxies disappear from small halos.
log M1 one-satellite scale 13.0
Halo mass at which a central hosts, on average, one satellite. Lower it → satellites bloom.
α satellite slope 1.00
Slope of ⟨N_sat⟩(M_h). Higher α → satellite numbers rise steeply with halo mass.
N galaxies—
Satellite frac.—
Galaxy bias—
⟨N_cen⟩—
⟨N_sat⟩—
M_eff—

Two-point correlation function ξ(r)

model 1-halo 2-halo reference