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In this article, we extend previous studies based on CMB spherical harmonic phases (SHP) to examine the validity of the hypothesis that the temperature field of the CMB is consistent with a Gaussian random field (GRF). The null hypothesis is that the corresponding CMB SHP are independent and identically distributed in terms of a uniform distribution in the interval [0, 2$\pi$] \citep{1986ApJ...304...15B,2013rossmanith}. We devise a new model-independent method where we use ordered and non-parametric Rao's statistic, based on sample arc-lengths to comprehensively test uniformity and independence of SHP. We performed our analysis on the scales limited by spherical harmonic modes $\le$ 128, to restrict ourselves to signal-dominated regions. To find the non-uniform or dependent sets of SHP, we calculate the statistic for the data and 10000 Monte Carlo simulated uniformly random sets of SHP and use 0.05 and 0.001 $\alpha$ levels to distinguish between statistically significant and highly significant detections. We first establish the performance of our method using simulated Gaussian, non-Gaussian CMB temperature maps, along with observed non-Gaussian 100 and 143 GHz Planck channel maps. We find that our method performs efficiently and accurately in detecting phase correlations generated in all of the non-Gaussian simulations and observed foreground contaminated 100 and 143 GHz Planck channel temperature maps. We apply our method on the Planck satellite mission's final released CMB temperature anisotropy maps- COMMANDER, SMICA, NILC, and SEVEM along with WMAP 9 year released ILC map. We report that SHP corresponding to some of the $m$-modes is non-uniform, some of the $\ell$ mode SHP and neighboring mode pair SHP are correlated in cleaned CMB maps. The detection of non-uniformity or correlation in the SHP indicates the presence of non-Gaussian signals in the foreground minimized CMB maps., Comment: 42 pages, 23 figures, 6 tables

We report an improved technique for diffuse foreground minimization from Cosmic Microwave Background (CMB) maps using a new multi-phase iterative internal-linear-combination (ILC) approach in harmonic space. The new procedure consists of two phases. In phase 1, a diffuse foreground cleaned map is obtained by performing a usual ILC operation in the harmonic space in a single iteration over the desired portion of the sky. In phase 2, we obtain the final foreground cleaned map using an iterative ILC approach also in the harmonic space, however, now, during each iteration of foreground minimization, some of the regions of the sky that are not being cleaned in the current iteration, are replaced by the corresponding cleaned portions of the phase 1 cleaned map. The new ILC method nullifies a foreground leakage signal that is otherwise inevitably present in the old and usual harmonic space iterative ILC method. The new method is flexible to handle input frequency maps, irrespective of whether or not they initially have the same instrumental and pixel resolution, by bringing them to a common and maximum possible beam and pixel resolution at the beginning of the analysis. This dramatically reduces data redundancy and hence memory usage and computational cost. During the ILC weight calculation it avoids any need to deconvolve partial sky spherical harmonic coefficients by the beam and pixel window functions, which in strict mathematical sense, is not well-defined for azimuthally symmetric window functions. Using WMAP 9-year and Planck-2015 published frequency maps we obtain a pair of foreground cleaned CMB maps and CMB angular power spectrum. Our power spectrum match well with Planck-2015 results, with some difference. Finally, we show that the weights for ILC foreground minimization have an intrinsic characteristic that it tends to produce a statistically isotropic CMB map as well., Comment: 17 pages, 17 figures