Galaxy Merger: Dynamical Friction Sinking

Satellite Galaxy

Satellite mass ratio M_sat/M_host 0.010

Coulomb logarithm lnΛ 3.0

Initial orbital radius r_i 8.0

Simulation speed 1.0×

Live State

Orbit decaying — satellite still bound.

Orbital radius r

8.00

Orbital speed v

1.00

Elapsed time t

0.00

Predicted t_df

—

How it works

A small satellite galaxy orbiting inside a larger host's dark-matter halo drags a gravitational "wake" of background particles behind it. That wake pulls back on the satellite — a braking force called dynamical friction, first derived by Chandrasekhar (1943):

F_df = -4πG² M_sat² ρ(r) lnΛ / v³ · v_vec

Here ρ(r) is the local background density, v is the satellite's orbital speed, and lnΛ (the Coulomb logarithm) accounts for the range of gravitational encounters. For a singular isothermal sphere halo with flat rotation speed v_c, the density is ρ(r) = v_c² / (4πG r²), so the drag acceleration on the satellite simplifies to:

a_df = -(G M_sat v_c² lnΛ) / (r² v³) · v_vec

Combined with the host's own (inward, centripetal) gravity, this drag steadily removes orbital angular momentum, so the satellite spirals inward instead of orbiting forever. The standard order-of-magnitude sinking timescale (Binney & Tremaine) is:

t_df ≈ (1.17 / lnΛ) · (r_i² v_c) / (G M_sat)

Satellite mass ratio — heavier satellites raise a bigger wake and sink faster (t_df ∝ 1/M_sat).
Coulomb logarithm — larger lnΛ (bigger host, smaller satellite) also speeds up the sink.
Initial radius — sinking time grows as r_i², so satellites starting further out take much longer to merge.
This is exactly how the Milky Way is currently swallowing the Sagittarius and Large Magellanic Cloud dwarf galaxies, and how galaxy clusters build up their central giant ellipticals over cosmic time — distinct from a fast, head-on tidal-tail collision between two comparable-mass galaxies.

Satellite galaxy Decaying orbit trail Host halo core

⭐ Merger completeSatellite absorbed into the host — relaunch to try new parameters.

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