Exponentialdisk

An exponential disk is a model describing the stellar distribution in the disk component of a spiral or lenticular galaxy. In this model, the surface brightness and the stellar mass surface density decline approximately exponentially with distance from the galactic center.

The radial light profile is commonly written as I(R) = I0 exp(-R/h), where I(R) is the surface brightness at radius R and h is the scale length. A related three-dimensional density can be approximated as ρ(R, z) ≈ ρ0 exp(-R/h) exp(-|z|/hz), with hz the vertical scale height. Exponential disks are often observed to extend over a wide radial range, though real disks may show breaks at large radii.

Observationally, many disk galaxies exhibit this exponential behavior, including the Milky Way and Andromeda. A historic guideline, Freeman’s law, noted a relatively constant central surface brightness in the B-band for disk galaxies, though modern surveys reveal substantial variation. Typical scale lengths for spiral disks range from about 1 to 5 kiloparsecs, with the Milky Way’s disk often quoted around 2–3 kpc.

Disks can show deviations from a single exponential, producing break profiles. Type I disks follow a single exponential; Type II (down-bending) and Type III (up-bending) disks feature changes in slope at certain radii. Exponential disks remain a widely used approximation in galactic studies, informing models of formation, evolution, rotation curves, and mass distribution.