Multiwavelength campaign on Mrk 509 XII. Broad band spectral analysis

(Abridged) The simultaneous UV to X-rays/gamma rays data obtained during the multi-wavelength XMM/INTEGRAL campaign on the Seyfert 1 Mrk 509 are used in this paper and tested against physically motivated broad band models. Each observation has been fitted with a realistic thermal comptonisation model for the continuum emission. Prompted by the correlation between the UV and soft X-ray flux, we use a thermal comptonisation component for the soft X-ray excess. The UV to X-rays/gamma-rays emission of Mrk 509 can be well fitted by these components. The presence of a relatively hard high-energy spectrum points to the existence of a hot (kT~100 keV), optically-thin (tau~0.5) corona producing the primary continuum. On the contrary, the soft X-ray component requires a warm (kT~1 keV), optically-thick (tau~15) plasma. Estimates of the amplification ratio for this warm plasma support a configuration close to the "theoretical" configuration of a slab corona above a passive disk. An interesting consequence is the weak luminosity-dependence of its emission, a possible explanation of the roughly constant spectral shape of the soft X-ray excess seen in AGNs. The temperature (~ 3 eV) and flux of the soft-photon field entering and cooling the warm plasma suggests that it covers the accretion disk down to a transition radius $R_{tr}$ of 10-20 $R_g$. This plasma could be the warm upper layer of the accretion disk. On the contrary the hot corona has a more photon-starved geometry. The high temperature ($\sim$ 100 eV) of the soft-photon field entering and cooling it favors a localization of the hot corona in the inner flow. This soft-photon field could be part of the comptonised emission produced by the warm plasma. In this framework, the change in the geometry (i.e. $R_{tr}$) could explain most of the observed flux and spectral variability.