Despite past panchromatic observations of the innermost part of the Milky Way , the overall structure of the Galactic Centre ( GC ) remains enigmatic in terms of geometry .
In this paper , we aim to show how polarimetry can probe the three-dimensional position of the molecular material in the central \sim 100 pc of the GC .
We investigate a model where the central supermassive black hole Sgr A ^ { * } is radiatively coupled to a fragmented circumnuclear disc ( CND ) , an elliptical twisted ring representative of the central molecular zone ( CMZ ) , and the two main , bright molecular clouds Sgr B2 and Sgr C. 8 – 35 keV integrated polarization mapping reveals that Sgr B2 and Sgr C , situated at the two sides of the CMZ , present the highest polarization degrees ( 66.5 and 47.8 per cent respectively ) , both associated with a polarization position angle \psi = 90 ^ { \circ } ( normal to the scattering plane ) .
The CND shows a lower polarization degree , 1.0 per cent with \psi = -20.5 ^ { \circ } , tracing the inclination of the CND with respect to the Galactic plane .
The CMZ polarization is spatially variable .
We also consider a range of spatial locations for Sgr A ^ { * } and the reprocessing media , and investigate how the modeled three-dimensional geometry influences the resulting GC polarization .
The two reflection nebulae are found to always produce high polarization degrees ( \gg 10 per cent ) .
We show that a 500 ks observation with a broadband polarimeter could constrain the location and the morphology of the scattering material with respect to the emitting source , revealing the past activity of Sgr A ^ { * } .