The pros and cons of the inversion method approach to derive 3D dust emission properties of the ISM: the Hi-GAL field centred on (l,b)=(30^(circ),0^(circ))

Herschel FIR continuum data obtained as part of the Hi-GAL survey have been used, together with the GLIMPSE 8 $\mu$m and MIPSGAL 24 $\mu$m data, to attempt the first 3D-decomposition of dust emission associated with atomic, molecular and ionized gas at 15 arcmin angular resolution. Our initial test case is a 2$\times$2 square degrees region centred on (l,b)=(30$^{\circ}$,0$^{\circ}$), a direction that encompasses the origin point of the Scutum-Crux Arm at the tip of the Galactic Bar. Coupling the IR maps with velocity maps specific for different gas phases (HI 21cm, $^{12}$CO and $^{13}$CO, and RRLs), we estimate the properties of dust blended with each of the gas components and at different Galactocentric distances along the LOS. A statistical Pearson's coefficients analysis is used to study the correlation between the column densities and the intensity of the IR emission. This analysis provides evidence that the 2$\times$2 square degree field under consideration is characterized by the presence of a gas component not accounted for by the standard tracers, possibly associated with warm H$_{2}$ and cold HI. We demonstrate that the IR radiation in the range 8 $\mu$m $<$ $\lambda$ $<$ 500 $\mu$m is systematically dominated by emission originating within the Scutum-Crux Arm. By applying an inversion method, we recover the dust emissivities associated with atomic, molecular and ionized gas. Using the DustEM model we obtain an indication for PAHs depletion in the diffuse ionized gas. However, the main goal of this work is to discuss the impact of the missing column density associated with the dark gas component on the accurate evaluation of the dust properties, and to shed light on the limitations of the inversion method approach when this is applied to a small section of the Galactic Plane and when the working resolution allows sufficient de-blending of the gas components along the LOS.