Evolution of the truncated disc and inner hot-flow of GX 339-4

Aims. We study the changes in geometry of the truncated disc and the inner hot-flow of GX 339-4 by analyzing the Power SpectralDensity (PSD) extracted from six XMM-Newton observations taken at the very end of an outburst. Methods. A theoretical model of the PSD of GX 339-4 in the 0.3-0.7 keV (thermal reverberation dominated) and 0.7-1.5 keV (disc continuum dominated) energy bands is developed. The model assumes the standard accretion disc to be truncated at a specific radius, inside of which are two distinct hot-flow zones: one spectrally soft and the other spectrally hard. The effects of disc-fluctuations and thermal reverberation are taken into account. Results. This model successfully produces the traditional bumpy PSD profiles and provides good fits to the GX 339-4 data. The truncation radius is found to increase from $r_{\rm trc}$ $\sim$ 10 to 55 $r_{\rm g}$ as the source luminosity decreases, strongly confirming that the truncation radius can be characterized as a function of luminosity. Keeping in mind the large uncertainty in previous measurements of the truncation radius, our values are larger than some obtained from spectroscopic analysis, but smaller than those implied from reverberation lag analysis. Furthermore, the size of two inner hot-flow zones which are spectrally hard and spectrally soft are also growing from $\sim$ 5 to 27 $r_{\rm g}$ and from $\sim$ 3 to 26 $r_{\rm g}$, respectively, as the flux decreases. We find that the radial range of inner hard zone is always larger than the range of the soft hot-flow zone, but by a comparatively small factor of $\sim$ 1.1-2.2