Statistically anisotropic Gaussian simulations of the CMB temperature field

Although theoretically expected to be statistically isotropic (SI), the observed cosmic microwave background (CMB) temperature and polarization field would exhibit SI violation due to various inevitable effects like weak lensing, Doppler boost and practical limitations of observations like noncircular beam masking, etc. However the presence of any SI violation beyond these effects may lead to a discovery of inherent cosmic SI violation in the CMB temperature and polarization field. Recently, Planck presented strong evidence of SI violation as a dipolar power asymmetry of the CMB temperature field in two hemispheres. Statistical studies of SI violation effect require non SI (nSI) Gaussian realizations of the CMB temperature field. The nSI Gaussian temperature field leads to nonzero off-diagonal terms in the spherical harmonics (SH) space covariance matrix encoded in the coefficients of the bipolar spherical harmonics (BipoSH) representation. We discuss an effective numerical algorithm, code for nonisotropic Gaussian sky (CoNIGS) to generate nSI realizations of the Gaussian CMB temperature field of Planck like resolution with specific cases of SI violation. Realizations of nSI CMB temperature field are obtained for nonzero quadrupolar (L = 2) BipoSH measurements by WMAP, dipolar asymmetry (resembles L = 1 BipoSH coefficients) with a scale dependent modulation field as measured by Planck and for Doppler-boosted CMB temperature field which also leads to L = 1 BipoSH spectra. Our method, CoNIGS can incorporate any kind of SI violation and can produce nSI realizations efficiently