  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.
