Rotational Brownian motion (astronomy) that the rotation axis of the binary is oriented at angle θ at time "t". The evolution equation for "F" is formula_17 If <Δξ>, "a", ρ and σ are constant in time, this becomes formula_18 where μ = cos θ and τ is the time in units of the relaxation time "t", where formula_19 The solution to this equation states that the expectation value of μ decays with time as formula_20 Hence, "t" is the time constant for the binary's orientation to be randomized by torques from field stars. Rotational Brownian motion was first discussed in the context of binary
Rotational Brownian motion (astronomy) slingshot. It can be shown that the rms change in the binary's orientation, from the time the binary forms until the two black holes collide, is roughly formula_21 In a real galaxy, the two black holes would eventually coalesce due to emission of gravitational waves. The spin axis of the coalesced hole will be aligned with the angular momentum axis of the orbit of the pre-existing binary. Hence, a mechanism like rotational Brownian motion that affects the orbits of binary black holes can also affect the distribution of black hole spins. This may explain in part why the spin axes