The main goal of this analysis is to present a new method to estimate the
physical properties of diffuse cloud of atomic hydrogen observed at high
Galactic latitude. This method, based on a comparison of the observations with
fractional Brownian motion simulations, uses the statistical properties of the
integrated emission, centroid velocity and line width to constrain the physical
properties of the 3D density and velocity fields, as well as the average
temperature of HI. We applied this method to interpret 21 cm observations
obtained with the Green Bank Telescope of a very diffuse HI cloud at high
Galactic latitude located in Firback North 1. We first show that the
observations cannot be reproduced solely by highly-turbulent CNM type gas and
that there is a significant contribution of thermal broadening to the line
width observed. To reproduce the profiles one needs to invoke two components
with different average temperature and filling factor. We established that, in
this very diffuse part of the ISM, 2/3 of the column density is made of WNM and
1/3 of thermally unstable gas (T ~2600 K). The WNM gas is mildly supersonic
(~1) and the unstable phase is definitely sub-sonic (~0.3). The density
contrast (i.e., the standard deviation relative to the mean of density
distribution) of both components is close to 0.8. The filling factor of the WNM
is 10 times higher that of the unstable gas, which has a density structure
closer to what would be expected for CNM gas. This field contains a signature
of CNM type gas at a very low level (N_H ~ 3 x 10^19) which could have been
formed by a convergent flow of WNM gas.Comment: 13 pages, 12 figures, accepted for publication in A&