First detection of the warm ionised medium dust emission - Implication forthe cosmic far-infrared background

We present a new analysis of the far-IR emission at high Galactic latitude based on COBE and HI data. A decomposition of the Far-IR emission over the HI, H+ and H-2 Galactic gas components and the Cosmic Far InfraRed Backgrou nd (CFIRB) is described. For the first time the far-TR emission of dust associated with the Warm Ion ised Medium (WIM) is evidenced. This component determined on about: 25% of the sky is detected at a 10 sigma level in the [200, 350] mu m band. The be st representation of the WIM dust spectrum is obtained for a temperature of 29.1 K and an emissivity law tau/N-H(+) = 3.8 +/- 0.8 10(-26) (lambda/250 mu m)(-1) cm(2). With a spectral index equal to 2, the emissivity law becom es tau/N-H(+) = 1.0 +/- 0.210(-25) (lambda/250 mu m)(-2) cm(2), with a temp erature of 20 K, which is significantly higher than the temperature of dust associated with KI gas. The Variation in the dust spectrum from the HI to the WIM component can be explained by only changing the upper cutoff of the Big Grain size distribution from 0.1 mu m to 30 nm. The detection of IR emission of dust in the WIM significantly decreases the intensity of the CFIRB, especially around 200 mu m which corresponds to th e peak of energy.