Thermal and turbulent properties of the Warm Neutral Medium in the solar neighborhood

20 pages, 14 figures, 3 tables. Accepted for publication in ApJInternational audienceThe transition from the diffuse warm neutral medium (WNM) to the dense cold neutral medium (CNM) is what set the initial conditions to the formation of molecular clouds. The properties of the turbulent cascade in the WNM, essential to describe this radiative condensation process, have remained elusive in part due to the difficulty to map out the structure and kinematics of each H I thermal phases. Here we present an analysis of a 21 cm hyper-spectral data cube from the GHIGLS HI survey where the contribution of the WNM is extracted using ROHSA, a Gaussian decomposition tool that includes spatial regularization. The distance and volume of the WNM emission is estimated using 3D dust extinction map information. The thermal and turbulent contributions to the Doppler line width of the WNM were disentangled using two techniques, one based on the statistical properties of the column density and centroid velocity fields, and another on the relative motions of CNM structures as a probe of turbulent motions. We found that the volume of WNM sampled here, located at the outer edge of the Local Bubble, shows thermal properties in accordance with expected values for heating and cooling processes typical of the Solar neighbourhood. The WNM has the properties of sub/trans-sonic turbulence, with a turbulent Mach number at the largest scale probed here (l = 130 pc) of Ms = 0.87 +- 0.15, a density contrast of 0.6 +- 0.2, and velocity and density power spectra compatible with k-11/3. The low Mach number of the WNM provides dynamical conditions that allows the condensation mode of thermal instability (TI) to grow freely and form CNM structures, as predicted by theory