Herschel water maps towards the vicinity of the black hole Sgr A*

Aims: We study the spatial distribution and kinematics of water emission in a ~64 pc$^2$ region of the Galactic Center (GC) around Sgr A*. We also analyze the water excitation to derive the physical conditions and water abundances in the CND and the `quiescent clouds'. Methods: We presented the integrated intensity maps of the ortho 1$_{10}-1_{01}$, and para 2$_{02}-1_{11}$ and 1$_{11}-0_{00}$ water transitions observed with the HIFI instrument on board Herschel. To study the water excitation we used ground state ortho and para H$_2^{18}$O transitions. In our study, we also used SPIRE continuum measurements of the CND. Using a non-LTE radiative transfer code, the water line profiles and dust continuum were modeled. We also used a rotating ring model to reproduce the CND kinematics represented by the PV diagram. Results: We identify the water emission arising from the CND, the Western Streamer, and the 20 and 50 km s$^{-1}$ clouds. The ortho water maps show absorption structures in the range of [-220,10] km s$^{-1}$. The PV diagram shows that the 2$_{02}-1_{11}$ H$_2$O emission traces the CND. We derive high X$_{H_2O}$ of $\sim$(0.1-1.3)$\times$10$^{-5}$, V$_t$ of 14-23 km s$^{-1}$ and T$_d$ of 15-45 K for the CND, and the lower X$_{\rm H_2O}$ of 4$\times$10$^{-8}$ and V$_t$ of 9 km s$^{-1}$ for the 20 km s$^{-1}$ cloud. Collisional excitation and dust effects are responsible for the water excitation in the southwest lobe of the CND and the 20 km s$^{-1}$ cloud, whereas only collisions can account for the water excitation in the northeast lobe of the CND. We propose that the water vapor in the CND is caused by grain sputtering by shocks of 10-20 km s$^{-1}$, with some contribution of high temperature and cosmic-ray chemistries plus a PDR chemistry. The low X$_{\rm H_2O}$ derived for the 20 km s$^{-1}$ cloud could be partially a consequence of the water freeze-out on grains.