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We study the conditions for the onset of Thermal Instability in the innermostregions of compact galactic nuclei, where the properties of the interstellarenvironment are governed by the interplay of quasi-spherical accretion onto asupermassive black hole (SMBH) and the heating/cooling processes of gas in adense nuclear star cluster. Stellar winds are the source of material forradiatively inefficient (quasi-spherical, non-magnetised) inflow/outflow ontothe central SMBH, where a stagnation point develops within the Bondi typeaccretion. We study the local thermal equilibrium to determine the parameterspace which allows cold and hot phases in mutual contact to co-exist. Weinclude the effects of mechanical heating by stellar winds and radiativecooling/heating by the ambient field of the dense star cluster. We consider twoexamples: the Nuclear Star Cluster (NSC) in the Milky Way central region(including the gaseous Mini-spiral of Sgr~A*), and the Ultra-Compact Dwarfgalaxy M60-UCD1. We find that the two systems behave in different ways becausethey are placed in different areas of parameter space in the instabilitydiagram: gas temperature vs. dynamical ionization parameter. In the case ofSgr~A*, stellar heating prevents the spontaneous formation of cold clouds. Theplasma from stellar winds joins the hot X-ray emitting phase and forms anoutflow. In M60-UCD1 our model predicts spontaneous formation of cold clouds inthe inner part of the galaxy. These cold clouds may survive since the coolingtimescale is shorter than the inflow/outflow timescale.

Multi-phase environment of compact galactic nuclei: the role of the Nuclear Star Cluster