Prospects of 3D mapping of the Galactic Centre clouds with X-ray
  polarimetry
  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 ~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 = 90deg
(normal to the scattering plane). The CND shows a lower polarization degree,
1.0 per cent with psi = -20.5deg, 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 (>> 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*.
