# Toy highly decorrelated dust model

July 3 2017, Clem Pryke

This post follows on from Checking dust decorrelation in models d1/d4/d7 and hipdt. Planck Intermediate Paper L arxiv/1606.07335 (PIPL) suggests that there may be significant decorrelation of the dust pattern. The Van Syngel paper arxiv/1611.02577 gives in appendix B an analytical result for the scaling of decorrelation with frequency separation in the case where it arises from spatially varying spectral index - this is exp(log^2(nu1/nu2)). Section 6.1 of the same paper also provides a method to generate Gaussian random skies across a series of frequencies which have any desired set of auto and cross spectra. Noting that Fig2 of PIPL suggests decorrelation which increases perhaps linearly with increasing ell we can construct a toy model model using these ingredients which has one free parameter - the ratio of the 217x353 cross spectrum to the gmean of 217x217 and 353x353 at ell=80. For low neutral hydrogen column densities PIPL Fig2 and Eqn6 show correlation ratios as low as 0.85. The following plot is analogous to those in the previous posting but for the first realization of this new model: