Context. The gas- and dust dissipation processes in disks around young stars remain uncertain despite numerous studies. At the distance of ~99–116 pc, HD 141569A is one of the nearest HerbigAe stars that is surrounded by a tenuous disk, probably in transition between a massive primordial disk and a debris disk. Atomic and molecular gases have been found in the structured 5-Myr old HD 141569A disk, making HD 141569A the perfect object within which to directly study the gaseous atomic and molecular component.\ud Aims. We wish to constrain the gas and dust mass in the disk around HD 141569A.\ud Methods. We observed the fine-structure lines of O I at 63 and 145 μm and the C ii line at 157 μm with the PACS instrument onboard the Herschel Space Telescope as part of the open-time large program GASPS. We complemented the atomic line observations with archival Spitzer spectroscopic and photometric continuum data, a ground-based VLT-VISIR image at 8.6 μm, and ^(12)CO fundamental ro-vibrational and pure rotational J = 3–2 observations. We simultaneously modeled the continuum emission and the line fluxes with the Monte Carlo radiative transfer code MCFOST and the thermo-chemical code ProDiMo to derive the disk gas- and dust properties assuming no dust settling.\ud Results. The models suggest that the oxygen lines are emitted from the inner disk around HD 141569A, whereas the [C ii] line emission is more extended. The CO submillimeter flux is emitted mostly by the outer disk. Simultaneous modeling of the photometric and line data using a realistic disk structure suggests a dust mass derived from grains with a radius smaller than 1 mm of ~2.1 × 10^(-7)M_⊙ and from grains with a radius of up to 1 cm of 4.9 × 10^(-6)M_⊙. We constrained the polycyclic aromatic hydrocarbons (PAH) mass to be between 2 × 10^(-11) and 1.4 × 10^(-10)M_⊙ assuming circumcircumcoronene (C_(150)H_(30)) as the representative PAH. The associated PAH abundance relative to hydrogen is lower than those found in the interstellar medium (3 × 10^(-7)) by two to three orders of magnitude. The disk around HD 141569A is less massive in gas (2.5 to 4.9 × 10^(-4)M_⊙ or 67 to 164 M_⊕) and has a flat opening angle (<10%).\ud Conclusions. We constrained simultaneously the silicate dust grain, PAH, and gas mass in a ~5-Myr old Herbig Ae disk. The disk-averaged gas-to-dust-mass is most likely around 100, which is the assumed value at the disk formation despite the uncertainties due to disagreements between the different gas tracers. If the disk was originally massive, the gas and the dust would have dissipated at the same rate
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