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(Abridged) Context. With the Herschel Space Observatory, lines of simplemolecules (C+, O, and CO) have been observed in the atmosphere ofprotoplanetary disks. When combined with ground-based [CI], all principle formsof carbon can be studied. The absence of neutral carbon [CI], which ispredicted by models to be strong, can then be interpreted together with [CII]and carbon monoxide.  Aims. We study the gas temperature, excitation, and chemical abundance of thesimple carbon-bearing species by the method of chemical-physical modeling. Weexplore the sensitivity of the lines to the entering parameters and constrainthe region from which the line radiation emerges.  Methods. Numerical models of the radiative transfer are used together with achemical network simulation and a calculation of the gas energetics to obtainthe gas temperature. We present our new model, which is based on our previousmodels but includes several improvements.  Results. A model of the disk around the Herbig Be star HD 100546 is able toreproduce the CO ladder together with the atomic fine-structure lines of [OI]and either [CI] or [CII]. We find that the high-J lines of CO can only bereproduced by a warm atmosphere with Tgas>>Tdust. The high-J CO observable withPACS are dominated from regions within some tens of AU.  Conclusions. Only a warm atmosphere with Tgas>>Tdust can reproduce the COladder. The CO ladder together with [O I] and the upper limit to [CI] can bereproduced by models with a high gas/dust ratio and a low abundance of volatilecarbon. These models however produce too small amounts of [CII]. Models with alow gas/dust ratio and more volatile carbon also reproduce CO and [OI], are incloser agreement with observations of [CII], but overproduce [CI]. Due to theuncertain origin of the [CII] emission, we prefer the high gas/dust ratiomodels, indicating a low abundance of volatile carbon.

The warm gas atmosphere of the HD 100546 disk seen by Herschel (Evidence of a gas-rich, carbon-poor atmosphere?)