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It is commonly believed that accretion discs are truncated and their innerregions are described by advection dominated accretion flows (ADAFs) in thehard spectral state of black hole X-ray binaries. However, the increasingoccurrence of a relativistically blurred Fe K$\alpha$ line together with a hardcontinuum points to the existence of a thin disc located near the innermoststable circular orbit (ISCO). Assuming the accretion in the hard state is viaan ADAF extending to near 100 Schwarzschild radii, which is supplied by eithera stellar wind from a companion star or resulting from an evaporated disc, westudy the possible condensation of the hot gas during its accretion towards theblack hole. It is found that a small fraction of the ADAF condenses into a colddisc as a consequence of efficient radiative cooling at small distances,forming a disc-corona configuration near the ISCO. This takes place for lowaccretion rates corresponding to luminosities ranging from $\sim 10^{-3}$ to afew per cent of the Eddington luminosity. The coexistence of the weak innerdisc and the dominant hot accretion flow provides a natural explanation of thebroad K$\alpha$ line in the hard state. Detailed computations demonstrate thatsuch accretion flows produce a hard X-ray spectrum accompanied by a weak disccomponent with a negative correlation between the 2-10 keV photon index and theEddington ratio. The predicted spectrum of Cygnus X-1 and the correlationbetween the photon index and the Eddington ratio are in good agreement withobservations.

Accretion flows in the hard state of black hole X-ray binaries: the effect of hot gas condensation