Physical properties of a very diffuse HI structure at high Galactic latitude

Aims.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. Methods.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. Results. 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 $(T \sim 2600~{\rm K}$). The WNM gas is mildly supersonic $(\langle M\rangle \sim1)$ and the unstable phase is definitely sub-sonic $(\langle M\rangle \sim0.3)$. 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 $(N_{\rm H}\sim 3\times 10^{19}$) which could have been formed by a convergent flow of WNM gas.