  Black hole accretion flows show rapid X-ray variability. The Power Spectral
Density (PSD) of this is typically fit by a phenomenological model of multiple
Lorentzians for both the broad band noise and Quasi-Periodic Oscillations
(QPOs). Our previous paper (Ingram & Done 2011) developed the first physical
model for the PSD and fit this to observational data. This was based on the
same truncated disc/hot inner flow geometry which can explain the correlated
properties of the energy spectra. This assumes that the broad band noise is
from propagating fluctuations in mass accretion rate within the hot flow, while
the QPO is produced by global Lense-Thirring precession of the same hot flow.
  Here we develop this model, making some significant improvements. Firstly we
specify that the viscous frequency (equivalently, surface density) in the hot
flow has the same form as that measured from numerical simulations of
precessing, tilted accretion flows. Secondly, we refine the statistical
techniques which we use to fit the model to the data. We re-analyse the PSD
from the 1998 rise to outburst of XTE J1550-564 with our new model in order to
assess the impact of these changes. We find that the derived outer radii of the
hot flow (set by the inner radius of the truncated disc) are rather similar,
changing from ~68-13 Rg throughout the outburst rise. However, the more
physical assumptions of our new model also allow us to constrain the scale
height of the flow. This decreases as the outer radius of the flow decreases,
as expected from the spectral evolution. The spectrum steepens in response to
the increased cooling as the as the truncation radius sweeps in, so gas
pressure support for the flow decreases.
  The new model, propfluc, is publically available within the xspec spectral
fitting package.
