Multiwavelength campaign on Mrk 509: XV. Global modeling of the broad emission lines in the optical, UV, and X-ray bands

Aims. We model the broad emission lines present in the optical, UV, and X-ray spectra of Mrk 509, a bright type 1 Seyfert galaxy. The broad lines were simultaneously observed during a large multiwavelength campaign, using the XMM-Newton-OM for the optical lines, HST-COS for the UV lines, and XMM-Newton-RGS and Epic for the X-ray lines. We also used FUSE archival data for the broad lines observed in the far-ultraviolet. The goal is to find a physical connection among the lines measured at different wavelengths and to determine the size and the distance from the central source of the emitting gas components. Methods. We used the Locally Optimally emission Cloud (LOC) model which interprets the emissivity of the broad line region (BLR) as regulated by power law distributions of both gas density and distances from the central source. Results. We find that one LOC component cannot model all the lines simultaneously. In particular, we find that the X-ray and UV lines may likely originate in the more internal part of the AGN at radii in the range ~5 × 1014-3 × 1017 cm, while the optical lines and part of the UV lines may likely originate farther out at radii ~3 × 1017-3 × 1018 cm. These two gas components are parametrized by a radial distribution of the luminosities with a slope γ of ~1.15 and ~1.10, respectively, both of them covering at least 60% of the source. This simple parametrization points to a structured broad line region where the higher ionized emission comes from closer in, while the emission of the low-ionization lines is more concentrated in the outskirts of the broad line region.