Dark Flow: Anomalous Bulk Motion of Galaxy Clusters

Inject a Dark Flow

Bulk flow speed 400 km/s

Peculiar-velocity noise σ 300 km/s

Cluster sample size 150

Show peculiar velocity only (subtract Hubble flow)

Recovered Bulk Flow

Measured speed

0 km/s

Angular offset

0.0°

Direction (θ, φ) vs injected flow

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How it works

Each cluster i sits at comoving position r_i and, besides the isotropic Hubble expansion, carries a peculiar velocity — motion relative to the smooth expanding background:

v_total(r_i) = H0·r_i  +  v_pec(i)
v_pec(i)     = V_flow  +  n_i,   n_i ~ N(0, σ²) per axis

V_flow is a single coherent vector shared by every cluster (the hypothesised "dark flow"); n_i is independent per-cluster noise from ordinary local gravitational tugs. A real bulk-flow survey never sees V_flow directly — only the noisy sum. It recovers the coherent part by vector-averaging many clusters' peculiar velocities:

V_est = (1/N) Σ v_pec(i)      Var(V_est) ≈ σ² / N

Averaging cancels the random n_i component (it shrinks as 1/√N) while the shared V_flow survives untouched — exactly the statistical argument used in real cluster-velocity "dark flow" studies. Raise σ and the estimate gets noisy and drifts off-axis; raise N and it locks back onto the injected direction.

Bulk flow speed — magnitude of the injected coherent vector V_flow.
Peculiar-velocity noise σ — per-axis random dispersion added to each cluster.
Sample size — number of clusters averaged; larger N suppresses noise.
Resample — draws a fresh random cluster field with the same statistics.
Show peculiar velocity only — toggles the drawn arrows between the full 3D velocity (dominated by outward Hubble flow) and the small residual peculiar component that actually carries the dark-flow signal.

Galaxy clusters Cluster velocity vector Injected dark-flow direction Recovered estimate

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