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The X-ray polarization properties of the reflection nebulae in the Galacticcenter inform us about the direction of the illuminating source (through thepolarization angle) and the cloud position along the line of sight (through thepolarization degree). However, the detected polarization degree is expected tobe lowered because the polarized emission of the clouds is mixed with theunpolarized diffuse emission that permeates the Galactic center region. In areal observation, also the morphological smearing of the source due to thepoint spread function and the unpolarized instrumental background contribute indiluting the polarization degree. So far, these effects have never beenincluded in the estimation of the dilution. We evaluate the detectability ofthe X-ray polarization predicted for the MC2, Bridge-B2, G0.11-0.11, Sgr B2,Sgr C1, Sgr C2, and Sgr C3 molecular clouds with modern X-ray imagingpolarimeters such as the Imaging X-ray Polarimetry Explorer (IXPE) and theEnhanced X-ray Timing and Polarimetry mission (eXTP). We perform realisticsimulations of X-ray polarimetric observations considering (with the aid ofChandra maps and spectra) the spatial, spectral, and polarization properties ofall the diffuse emission and background components in each region of interest.We find that in the 4.0-8.0 keV band, where the emission of the molecularclouds outshines the other components, the dilution of the polarization degree,including the contribution due to the morphological smearing of the source,ranges between $\sim$19\% and $\sim$55\%. We conclude that for some distancevalues reported in the literature, the diluted polarization degree ofG0.11-0.11, Sgr B2, Bridge-B2, Bridge-E, Sgr C1, and Sgr C3 may be detectablein a 2 Ms long IXPE observations. The enhanced capabilities of eXTP may allowdetecting the 4.0-8.0 keV of all the targets considered here.

Prospects for IXPE and eXTP polarimetric archaeology of the reflection nebulae in the Galactic center