Constraints on Radiatively Inefficient Accretion History of Active Galactic Nuclei from Hard Cosmological X-ray Background

The transition of a standard thin disk to a radiatively inefficient accretion flow (RIAF) is expected to occur, when its accretion rate ṁ is lower than the critical value ṁcrit (ṁ = Ṁ/ṀEdd). The RIAF is very hot, and it radiates mostly in the hard X-ray band (& 100 keV). Assuming that the accretion disk in every bright active galactic nucleus (AGN) will finally undergo a RIAF phase while ṁ < ṁcrit, we calculate the contribution of the RIAFs in AGNs to the cosmological X-ray background of 10 − 1000 keV. We find that the timescale tRIAF of the RIAF accreting at ∼ ṁcrit should be shorter than ∼ 10−2tb if ṁcrit = 0.01, where tb is the lifetime of bright AGNs, i.e., ṁ declines from ṁcrit to a rate significantly lower than ṁcrit within tRIAF. The derived timescale tRIAF is affected by the parameters adopted in the model calculations, which is also discussed in this Letter. Subject headings: galaxies: active—quasars: general—accretion, accretion disks—black hole physics; X-rays: diffuse background