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Abstract

Context. Edge-on disks offer a unique opportunity to directly examine their vertical structure, providing valuable insights into planet formation processes. We investigate the dust properties, as well as the CO and HCO$^+$ gas properties, in the edge-on disk surrounding the T Tauri star 2MASS J04202144+281349 (SSTTau042021). Aims. We estimate the radial and vertical temperature and density profile for the gas and the dust. Methods. We use ALMA archival data of CO isotopologues and continuum emission at 2, 1.3 and 0.9 mm together with new NOEMA HCO$^+$ 3-2 observations. We retrieve the gas and dust disk properties using the tomographic method and the \textsc{DiskFit} model. Results. The vertical CO emission appears very extended, partly tracing the H$_2$ wind observed by JWST. C$^{18}$O, $^{13}$CO and HCO$^+$ emission characterize the bulk of the molecular layer. The dust and gas have a mid-plane temperatures of $\sim 7-11$ K. The temperature of the molecular layer (derived from $^{13}$CO and HCO$^+$) is on the order of 16 K. HCO$^+$ 3-2 being thermalized, we derive a lower limit for the H$_2$ volume density of $\sim 3 \times 10^6$ cm$^{-3}$ at radius 100-200 au between 1 and 2 scale heights. The atmosphere temperature of the CO gas is of the order $\sim$ 31 K at a radius of 100 au. We directly observe CO and HCO$^+$ gas onto the mid-plane beyond the dust outer radius ($\ge 300$ au). The (gas+dust) disk mass estimated up to a radius of 300 au is on the order of $4.6 \times 10^{-2} \mathrm{M}_\odot$. Conclusions. Thanks to the favorable disk inclination, we present the first quantitative evidence for vertical molecular stratification with direct observation of CO and HCO$^+$ gas along the mid-plane. We estimate the temperature profile with temperature of 7-11 K near the mid-plane, and 15-20 K in the dense part of the molecular layer up to $\sim$ 35 K above.