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