Determination of the cosmic infrared background (CIB) at far infrared wavelengths using COBE/DIRBE data is limited by the accuracy to which foreground interplanetary and Galactic dust emission can be modeled and subtracted. Previous determinations of the far infrared CIB (e.g., Hauser et al. 1998) were based on the detection of residual isotropic emission in skymaps from which the emission from interplanetary dust and the neutral interstellar medium were removed. In this paper we use the Wisconsin H-alpha Mapper (WHAM) Northern Sky Survey as a tracer of the ionized medium to examine the effect of this foreground component on determination of the CIB. We decompose the DIRBE far infrared data for five high Galactic latitude regions into H I and H-alpha correlated components and a residual component. We find the H-alpha correlated component to be consistent with zero for each region, and we find that addition of an H-alpha correlated component in modeling the foreground emission has negligible effect on derived CIB results. Our CIB detections and 2 sigma upper limits are essentially the same as those derived by Hauser et al. and are given by nu I_nu (nW m-2 sr-1) < 75, < 32, 25 +- 8, and 13 +- 3 at 60, 100, 140, and 240 microns, respectively. Our residuals have not been subjected to a detailed anisotropy test, so our CIB results do not supersede those of Hauser et al. We derive upper limits on the 100 micron emissivity of the ionized medium that are typically about 40% of the 100 micron emissivity of the neutral atomic medium. This low value may be caused in part by a lower dust-to-gas mass ratio in the ionized medium than in the neutral medium, and in part by a shortcoming of using H-alpha intensity as a tracer of far infrared emission.
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