SingLe: A F90-package devoted to Softened Gravity in gaseous discs

SofteningLength: Because Newton's law of Gravitation diverges as the relative separations |r'-r| tends to zero, it is common to add a positive constant λ also known as the "softening length", i.e. :

|r'-r|² ← |r'-r|² + λ².

SingLe determines the appropriate value of this Softening Length λ for a given disc local structure (thickness 2h and vertical stratification ρ), in the axially symmetric, flat disc limit, preserving at best the Newtonian character of the gravitational potential and associated forces. Mass density ρ(z) is assumed to be locally expandable in the z-direction according to:

ρ(z)= ρ0[1 + a1(z/h)2+...+aq (z/h)2q+...+aN (z/h)2 N].