H I 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 H2 in the Milky Way. Due to its symmetry H2 does not radiate at radio frequencies. CO is thought to be a tracer for H2 ; however, CO is formed at significantly higher opacities than H2 . Thus, toward high Galactic latitudes significant amounts of H2 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 H2 .Methods. We adopt the hypothesis of a constant E (B −V )∕N H ratio, independent of phase transitions from H I to H2 . 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 H I gas phase is high in comparison to the warmer phase. We consider this as evidence that cold H I gas toward high Galactic latitudes is associated with H2 . Beyond CO–bright regions, for T D ≤ 1165 K we find a correlation (N HI + 2N H2 )∕N HI ∝−logT D . In combination with a factor X CO = 4.0 × 1020 cm−2 (K km s−1 )−1 this yields N H ∕E (B −V ) ~ 5.1 to 6.7 × 1021  cm−2  mag−1 for the full sky, which is compatible with X-ray scattering and UV absorption line observations.Conclusions. Cold H I with T D ≤ 1165 K contains on average 46% CO–dark H2 . Prominent filaments have T D ≤ 220 K and typical excitation temperatures T ex ~ 50 K. With a molecular gas fraction of ≥61% they are dominated dynamically by H2 .