Effect of noncircularity of experimental beam on CMB parameter estimation

Abstract

Abstract. Measurement of Cosmic Microwave Background (CMB) anisotropies has been playing a lead role in precision cosmology by providing some of the tightest constrains on cosmological models and parameters. However, precision can only be meaningful when all major systematic effects are taken into account. Non-circular beams in CMB experiments can cause large systematic deviation in the angular power spectrum, not only by modifying the measurement at a given multipole, but also introducing coupling between different multipoles through a deterministic bias matrix. Here we add a mechanism for emulating the effect of a full bias matrix to the Planck likelihood code through the parameter estimation code SCoPE. We show that if the angular power spectrum was measured with a non-circular beam, the assumption of circular Gaussian beam or considering only the diagonal part of the bias matrix can lead to huge error in parameter estimation. We demonstrate that, at least for elliptical Gaussian beams, use of scalar beam window functions obtained via Monte Carlo simulations starting from a fiducial spectrum, as implemented in Planck analyses for example, leads to only few percent of sigma deviation of the best-fit parameters. However, we notice more significant differences in the posterior distributions for some of the parameters, which would in turn lead to incorrect errorbars. These differences can be reduced, so that the errorbars match within few percent, by adding an iterative reanalysis step, where the beam window function would be recomputed using the best-fit spectrum estimated in the first step.

Pixel space convolution for cosmic microwave background experiments

“…For instance, the effect of symmetrical beams with smooth profiles can be analytically accounted for when computing the power spectra of CMB maps (see [17]). The impact of other related systematic effects, like beam mismatch, has also been described in the literature (see [5,16,23]). When the beam has more complex features, like sidelobes, numerical methods must be used instead.…”

Leakage of power from dipole to higher multipoles due to non-symmetric beam shape of the CMB missions

“…At this point it can be noted that if the centroid of the beam i. is taken as the pointing direction of the beam then the amount of power leakage becomes almost negligible for the WMAP beams. Though considering a separate line of sight can introduce other complex features in the observed sky-map as shown in [15][16][17], which can only be understood through proper simulations.…”

“…Therefore, the contribution of this effect contaminates the resultant map, generated by this inadequate data analysis technique. The effects of non-symmetric beam are discussed by different authors [14][15][16][17][18][19][20][21]. However, this particular effect has not been studied in any previous literature.…”

Estimating statistical isotropy violation in CMB due to non-circular beam and complex scan in minutes

“…The effect of NC beam on angular power spectrum of CMB has been studied in literature and the non-trivial impact on high precision cosmological inferences has been appreciated but not satisfactorily resolved, particularly, within the available computational resources. A significant body of literature attempting to deal with NC beam effect on the angular power spectrum exists, e.g., [1][2][3][4][5][6][7][8][9][10][11]. However, current and upcoming CMB experiments also hold the promise to observationally constrain the underlying, often implicit, SI assumption (closely linked to the so called, 'cosmological principle'), which implies rotational invariance of the n-point correlation function.…”

“…The effect of non-circular (NC) beam on angular power spectrum of CMB has been studied in literature and the non-trivial impact on high precision cosmological inferences has been appreciated but not satisfactorily resolved, particularly, within the available computational resources. A significant body of literature attempting to deal with NC beam effect on the angular power spectrum exists, e.g., [1][2][3][4][5][6][7][8][9][10][11]. However, current and upcoming CMB…”