The three dimensional skeleton: tracing the filamentary structure of the universe

Understand

The skeleton formalism aims at extracting and quantifying the filamentary structure of the universe is generalized to 3D density fields; a numerical method for computating a local approximation of the skeleton is presented and validated here on Gaussian random fields.

• This method manages to trace well the filamentary structure in 3D fields such as given by numerical simulations of the dark matter distribution on large scales and is insensitive to monotonic biasing.
• Two of its characteristics, namely its length and differential length, are analyzed for Gaussian random fields.
• Its differential length per unit normalized density contrast scales like the PDF of the underlying density contrast times the total length times a quadratic Edgeworth correction involving the square of the spectral parameter.