This study aims to probe the thermodynamic properties of the hot intragroup medium (IGM) plasma in the core regions of the NGC 4636 galaxy group by detailed measurements of several emission lines and their relative intensities. We analyzed deep XMM-Newton Reflection Grating Spectrometer (RGS) data in five adjacent spectral regions in the central parts of the NGC 4636 galaxy group. We examined the suppression of the Fe xvii resonance line (15.01 {AA}) as compared to the forbidden lines of the same ion (17.05 {AA} and 17.10 {AA}). The presence and radial dependence of the cooling flow was investigated through spectral modeling. In addition, a parallel analysis with deep Chandra Advances CCD Imaging Spectrometer (ACIS) data was conducted to gain additional information about the thermodynamical properties of the IGM. We find that the plasma at the group center to the north shows efficient Fe xvii ion resonant scattering, wheras no resonant scattering was detected at the south side. The regions featuring resonant scattering coincide with those embodying large amounts of cool ($kTlesssim0.4$ keV) gas phases, and the spectral imprints of cooling gas with a total mass deposition rate of $sim0.8$ M$_{odot}$ yr$^{-1}$ within the examined region of $2.4^{prime}times 5.0^{prime}$. We interpret the results as possible evidence of asymmetric turbulence distribution in the NGC 4636 IGM: Turbulence dominates the gas dynamics to the south, while collective gas motions characterize the dynamics to the north. X-ray images show imprints of energetic AGN at both sides, yet we find evidence of turbulence heating at the south and gas cooling at the north of the core. We infer that the observed asymmetry may be the result of the specific observation angle to the source, or arise from the turbulence driven by core sloshing at south side.
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