The acceleration due to the NFW potential is: a = − − ∇ ∇ Φ Φ NFW ( r ) = G M vir ln ⁡ ⁡ ( 1 + c ) − − c / ( 1 + c ) r / ( r + R s ) − − ln ⁡ ⁡ ( 1 + r / R s ) r 3 r where r is the position vector and M vir = 4 π π 3 r vir 3 200 ρ ρ crit .