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.

💡 Research Summary

The paper addresses a long‑standing puzzle in high‑energy astrophysics: the origin of the characteristic break observed in the X‑ray power spectral density (PSD) of accreting black holes, from super‑massive active galactic nuclei (AGN) down to stellar‑mass black hole binaries. Empirically, the break timescale (T_{\rm B}) follows a tight scaling relation with black‑hole mass and accretion rate, (T_{\rm B}\propto M_{\rm BH}^{2.1}\dot M^{-0.98}). Existing theoretical explanations have invoked a variety of dynamical timescales (viscous, thermal, propagation, electron‑proton coupling), but each requires model‑specific assumptions and often fails to reproduce the observed exponents without fine‑tuning.

The authors propose a fundamentally different viewpoint: the break is set by the cooling time of the hot electrons that produce the hard X‑ray continuum through inverse‑Compton scattering (Comptonisation). In the standard picture, soft UV/optical photons from a geometrically thin, optically thick accretion disc are up‑scattered by a corona of electrons with temperatures of order 100 keV. The energy loss rate of an electron in this radiation field is \