A physical model for the continuum variability and QPO in accreting black holes

The power spectra of black hole binaries have been well studied for decades, giving a detailed phenomenological picture of the variability properties and their correlation with the energy spectrum (spectral state) of the source. Here we take the truncated disc/hot inner flow picture which can describe the spectral changes, and show that propagating mass accretion rate fluctuations in the hot flow can match the broad band power spectral properties seen in black hole binaries, i.e. give approximately band limited noise between a low and high frequency break. The low frequency break marks the viscous timescale at the outer edge of the hot inner flow, which is the inner edge of the truncated disc. The model also predicts the Lense-Thirring precession timescale of the hot flow, as this is set by the surface density of the flow which is self consistently calculated from the propagating fluctuations. We show that this naturally gives the observed relation between the low frequency break and QPO frequency as the outer radius of the flow moves inwards, and that this model predicts many of the observed QPO properties such as correlation of coherence with frequency, and of the recently discovered correlation of frequency with flux on short timescales. We fit this total model of the variability to a sequence of 5 observed power spectra from the bright black hole binary XTE J1550-564 as the source transitioned from a low/hard to very high state. This is the first time that a power spectrum from a black hole binary has been fit with a physical model for the variability. The data are well fit if the inner radius of the flow remains constant, while the outer radius sweeps inwards from ~60-12 Rg. This range of radii agrees with models of the energy spectral evolution, giving the first self consistent description of the evolution of both the spectrum and variability of BHB.