Absorption Measure Distribution in Mrk 509

In this paper we model the observed absorption measure distribution (AMD) in Mrk 509, which spans three orders of magnitude in ionization level with a single-zone absorber in pressure equilibrium. AMD is usually constructed from observations of narrow absorption lines in radio-quiet active galaxies with warm absorbers. We study the properties of the warm absorber in Mrk~509 using recently published broad-band spectral energy distribution observed with different instruments. This spectrum is an input in radiative transfer computations with full photoionisation treatment using {\sc titan} code. We show that the simplest way to fully reproduce the shape of AMD is to assume that the warm absorber is a single zone under constant total pressure. With this assumption we found theoretical AMD which matches the observed one determined on the basis of 600 ks RGS XMM-Newton spectrum of Mrk~509. The softness of the source spectrum and the important role of the free-free emission breaks the usual degeneracy in the ionization state calculations, and the explicit dependence of the depths of AMD dips on density open a new path to density diagnostic for the warm absorber. In Mrk 509 the implied density is of the order of $10^8$ cm$^{-3}$.