All-Sky Observational Evidence for An Inverse Correlation Between Dust Temperature and Emissivity Spectral Index

We show that a one-component variable-emissivity-spectral-index model (the free- model) provides more physically motivated estimates of dust temperature at the Galactic polar caps than one- or two-component fixed-emissivity-spectral-index models (fixed- models) for interstellar dust thermal emission at far-infrared and millimeter wavelengths. For the comparison we have fit all-sky one-component dust models with fixed or variable emissivity spectral index to a new and improved version of the 210-channel dust spectra from the COBE-FIRAS, the 100-240 micrometer maps from the COBE-DIRBE and the 94 GHz dust map from the WMAP. The best model, the free-alpha model, is well constrained by data at 60-3000 GHz over 86 per cent of the total sky area. It predicts dust temperature (T(sub dust)) to be 13.7-22.7 (plus or minus 1.3) K, the emissivity spectral index (alpha) to be 1.2-3.1 (plus or minus 0.3) and the optical depth (tau) to range 0.6-46 x 10(exp -5) with a 23 per cent uncertainty. Using these estimates, we present all-sky evidence for an inverse correlation between the emissivity spectral index and dust temperature, which fits the relation alpha = 1/(delta + omega (raised dot) T(sub dust) with delta = -.0.510 plus or minus 0.011 and omega = 0.059 plus or minus 0.001. This best model will be useful to cosmic microwave background experiments for removing foreground dust contamination and it can serve as an all-sky extended-frequency reference for future higher resolution dust models.