Equation Walkthrough

Step through the derivation of C(ρ) interactively. Each step adds one piece to the equation and explains why it's there.

Step 1 of 6

Step 1: Start with density

ρ — the local mass/energy density

Everything begins with density. In a galaxy, ρ is the baryon density profile. In chemistry, it's the number density of particles. The same starting point everywhere.

Density is the universal input to the coherence function.

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Full Equation

C(ρ) = tanh(γ · log(ρ/ρcrit + 1))
The Coherence Function

Related Concepts

Parameter DerivationsFirst-principles origin of every parameterThe Coherence FunctionC(ρ) = tanh(γ log(ρ/ρ_crit + 1))