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Astron. Astrophys. 321, 696-702 (1997)

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2. Dark clusters formation

Our scenario encompasses the one originally proposed by Fall and Rees (1985 ) for the origin of globular clusters and can be summarized as follows. After its initial collapse, the proto galaxy (PG) is expected to be shock heated to its virial temperature [FORMULA] K. Since overdense regions cool more rapidly than average, proto globular cluster (PGC) clouds form in pressure equilibrium with hot diffuse gas. Below [FORMULA] K, the main coolants are H2 molecules and the evolution of the PGC clouds will be different in the inner and outer part of the Galaxy, depending on the decreasing collision rate and ultraviolet (UV) fluxes as the galactocentric distance increases.

In the central region of the Galaxy the presence of an AGN and a first population of massive stars (which act as strong sources of UV radiation that dissociates the H2 molecules) heavily suppress the cooling and so the PGC clouds remain for a long time at temperature [FORMULA] K. Later on, when the UV flux decreases and after enough H2 has formed, the cloud temperature suddenly drops and the subsequent evolution leads to the formation of stars and ultimately to globular clusters of mass [FORMULA].

In the outer regions of the halo the UV flux is suppressed (due to the larger galactocentric distance), so that no substantial H2 depletion actually happens. On top of this, further H2 is produced via three-body reactions, thus dramatically increasing the cooling efficiency. In such a situation, a subsequent fragmentation of the primordial PGC clouds occurs into smaller clouds that remain optically thin until the minimum value of the Jeans mass [FORMULA] is attained, thus leading to the formation of MACHOs clumped into dark clusters. Moreover, since the conversion efficiency of the constituent gas could scarcely have been 100%, in the absence of strong stellar winds the gas remains gravitationally bound in the dark clusters in form of cold molecular clouds. The further possibility that a few percent of the initial gas remains in diffuse form inside dark clusters is not excluded, although its high virial temperature (which would make the gas observable) place stringent limits to its amount.

MACHOs inside dark clusters are detected via gravitational microlensing (possibly as clustered events), while the presence of molecular clouds with expected mass [FORMULA] in the range [FORMULA] and radius [FORMULA] (from the virial theorem) from [FORMULA] to [FORMULA] pc is difficult to prove due to both their very low temperature - close to that of the Cosmic Background Radiation (CBR) - and low optical depth.

Further details of this scenario can be founded elsewhere (De Paolis et al. 1996a ). In particular we also discussed several methods to test the above model and the existence of the halo molecular clouds. Here we remark only that dark clusters can form only at galactocentric distance larger than [FORMULA] kpc and that (due to the absence of an "imprinting" mass) we do not expect a characteristic mass for the dark clusters. Indeed, their mass [FORMULA] can vary in the range [FORMULA] and their radius [FORMULA] is expected to be between 1-10 pc. Obviously, the above discussion implicitly assumes that the dark clusters have survived until today in the galactic halo. The last issue is surely met if [FORMULA] is in the range [FORMULA], as follows from constraints on the evaporation time and close encounters between dark clusters (De Paolis et al. 1996b ).

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998