First detection of the WIM dust emission. Implication for the 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 Background (CFIRB) is described. For the first time the far-IR emission of dust associated with the Warm Ionised Medium (WIM) is evidenced. This component determined on about 25% of the sky is detected at a 10 sigma level in the [200, 350]micron band. The best representation of the WIM dust spectrum is obtained for a temperature of 29.1 K and an emissivity law $tau/N_H+=3.8 \pm 0.8 10^{-26} (\lambda/250\mic)^{-1} cm^2$. With a spectral index equal to 2, the emissivity law becomes $\tau/N_H^+= 1.0 \pm 0.2 10^{-25} (\lambda/250\mic)^{-2} cm^2$, with a temperature of 20 K, which is significantly higher than the temperature of dust associated with HI 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 micron to 30 nm. The detection of IR emission of dust in the WIM significantly decreases the intensity of the CFIRB, especially around 200 micron which corresponds to the peak of energy.