ALPACA: a new semi-analytical model for metal absorption lines emerging from clumpy galactic environments

We present a new semi-analytical formalism for modelling metal absorption lines that emerge from a clumpy galactic environment, ALPACA. We predict the "down-the-barrel" (DTB) metal absorption line profiles and the equivalent width (EW) of absorption at different impact parameters (b) as a function of the clump properties, including clump kinematics, clump volume filling factor, clump number density profile, and clump ion column densities. With ALPACA, we jointly model the stacked DTB C II lambda 1334 spectrum of a sample of z similar to 3 Lyman break galaxies and the EW versus b profile of a sample of z similar to 2 star-forming galaxy-galaxy pairs. ALPACA successfully reproduced two data sets simultaneously, and the best fit prefers a low clump volume filling factor (similar to 3 x 10(-3)). The radial velocities of the clumps are a superposition of a rapidly accelerated outflow with a maximum velocity of similar to 400kms(-1) and a velocity dispersion of sigma similar to 120kms(-1). The joint modelling reveals a physical scenario where the absorption observed at a particular velocity is contributed by the clumps distributed over a fairly broad range of radii. We also find that the commonly adopted Sobolev approximation is at best only applicable within a narrow range of radii where the clumps are undergoing rapid acceleration in a non-volume-filling clumpy medium. Lastly, we find that the clump radial velocity profile may not be fully constrained by the joint modelling and spatially resolved Ly alpha emission modelling may help break the degeneracy.