scalelength

Scale length, or scalelength, is a characteristic length that describes how a quantity changes with distance in a system. When a variable decreases approximately exponentially with distance, its scale length is the distance over which the quantity falls by a factor of e. In many disciplines, scale length serves as a convenient, dimensionful parameter that allows comparison across systems and the nondimensionalization of equations.

In astronomy, scale length is commonly used for disk galaxies: the surface brightness I(r) ≈ I0 exp(-r/h), where h is the radial scale length. It also appears in models of stellar and gas density. The scale length quantifies how quickly the disk fades with radius and relates to total luminosity and mass.

In physics and materials science, scale lengths appear in diffusion, heat conduction, and screening problems. For example, diffusion length L = sqrt(D t) characterizes how far carriers travel during time t; the Debye length in plasmas and electrolytes is a screening scale length. In biology and chemistry, reaction-diffusion systems and morphogen gradients have characteristic length scales that determine pattern formation and concentration profiles.

Estimating a scale length typically involves fitting data to exponential or other decay models, or computing a length scale from model parameters. The concept is widely used because it provides a simple, dimensionless way to compare different systems and to link local behavior to global properties.