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Determining the gas density and temperature structures of protoplanetarydisks is a fundamental task to constrain planet formation theories. This is achallenging procedure and most determinations are based on model-dependentassumptions. We attempt a direct determination of the radial and verticaltemperature structure of the Flying Saucer disk, thanks to its favorableinclination of 90 degrees. We present a method based on the tomographic studyof an edge-on disk. Using ALMA, we observe at 0.5$"$ resolution the FlyingSaucer in CO J=2-1 and CS J=5-4. This edge-on disk appears in silhouetteagainst the CO J=2-1 emission from background molecular clouds in $\rho$ Oph.The combination of velocity gradients due to the Keplerian rotation of the diskand intensity variations in the CO background as a function of velocity providea direct measure of the gas temperature as a function of radius and heightabove the disk mid-plane. The overall thermal structure is consistent withmodel predictions, with a cold ($< 15-12 $~K), CO-depleted mid-plane, and awarmer disk atmosphere. However, we find evidence for CO gas along themid-plane beyond a radius of about 200\,au, coincident with a change of grainproperties. Such a behavior is expected in case of efficient rise of UVpenetration re-heating the disk and thus allowing CO thermal desorption orfavoring direct CO photo-desorption. CO is also detected up to 3-4 scaleheights while CS is confined around 1 scale height above the mid-plane. Thelimits of the method due to finite spatial and spectral resolutions are alsodiscussed. This method appears to be very promising to determine the gasstructure of planet-forming disks, provided that the molecular data have anangular resolution which is high enough, of the order of $0.3 - 0.1"$ at thedistance of the nearest star forming regions.

The Flying Saucer: Tomography of the thermal and density gas structure of an edge-on protoplanetary disk