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X-ray variability of active galactic nuclei (AGN) and black hole binaries canbe analysed by means of the power spectral density (PSD). The break observed inthe power spectrum defines a characteristic variability timescale of theaccreting system. The empirical variability scaling that relates characteristictimescale, black hole mass, and accretion rate ($T_B \proptoM_{BH}^{2.1}/\dot{M}^{0.98}$) extends from supermassive black holes in AGN downto stellar-mass black holes in binary systems. We suggest that the PSD breaktimescale is associated with the cooling timescale of electrons in theComptonisation process at the origin of the observed hard X-ray emission. Weobtain that the Compton cooling timescale directly leads to the observationalscaling and naturally reproduces the functional dependence on black hole massand accretion rate ($t_C \propto M_{BH}^{2}/\dot{M}$). This result simplyarises from general properties of the emission mechanism and is independent ofthe details of any specific accretion model.

The physical origin of the X-ray power spectral density break timescale in accreting black holes