Columnintegrated

Columnintegrated refers to a quantity that has been obtained by integrating a local, three-dimensional property along a line of sight through a medium, producing a two-dimensional field defined on the plane of the sky. The idea is to collapse a spatial dimension by summing or integrating the quantity as one looks through the column of material between the observer and the far side.

Mathematically, if q(x, y, z) is a volumetric quantity, the columnintegrated (or column) quantity Q at a projected position (x, y) is often written as Q(x, y) = ∫ q(x, y, z) dz along the line of sight, though the integration path may be different depending on geometry. Common examples include column density N(x, y) = ∫ n(x, y, z) dz, column-integrated emissivity I_col(x, y) = ∫ j(x, y, z) dz, and column-integrated optical depth τ_col(x, y) = ∫ κ(x, y, z) ρ(x, y, z) dz.

Columnintegrated quantities are frequently directly related to observations, since many measurements partition light or material by sky position rather than by depth. They are widely used in astrophysics to map gas and dust, in atmospheric science to profile atmospheric constituents, and in plasma physics to characterize line-of-sight properties. A key limitation is that integrating along the line of sight hides the internal distribution, potentially masking structure along depth. The term is often written column-integrated or column-integrated, with the concatenated form columnintegrated appearing in variable names or software.