HI filaments are cold and associated with dark molecular gas. HI4PI based estimates of the local diffuse CO-dark H2 distribution

Context. There are significant amounts of H-2 in the Milky Way. Due to its symmetry H-2 does not radiate at radio frequencies. CO is thought to be a tracer for H-2; however, CO is formed at significantly higher opacities than H-2. Thus, toward high Galactic latitudes significant amounts of H-2 are hidden and are called CO-dark. Aims. We demonstrate that the dust-to-gas ratio is a tool for identifying locations and column densities of CO-dark H-2. Methods. We adopt the hypothesis of a constant E(B-V)/N-H ratio, independent of phase transitions from HI to H-2. We investigate the Doppler temperatures T-D, from a Gaussian decomposition of HI4PI data, to study temperature dependences of E(B-V)/N-HI. Results. The E(B-V)/N-HI ratio in the cold HI gas phase is high in comparison to the warmer phase. We consider this as evidence that cold HI gas toward high Galactic latitudes is associated with H-2. Beyond CO-bright regions, for T-D <= 1165 K we find a correlation (N-HI + 2N(H2))/N-HI proportional to - log T-D. In combination with a factor X-CO = 4.0 x 10(20) cm(-2) (K km s(-1))(-1) this yields N-H/E(B-V) similar to 5.1 to 6.7 x 10(21) cm(-2) mag(-1) for the full sky, which is compatible with X-ray scattering and UV absorption line observations. Conclusions. Cold HI with T-D <= 1165 K contains on average 46% CO-dark H-2. Prominent filaments have T-D <= 220 K and typical excitation temperatures T-ex similar to 50 K. With a molecular gas fraction of >= 61% they are dominated dynamically by H-2.