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Register a new userSystematic Effects in Interferometric Observations of the CMB Polarization
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The detection of the primordial $B$-mode spectrum of the polarized cosmic microwave background (CMB) signal may provide a probe of inflation. However, observation of such a faint signal requires excellent control of systematic errors. Interferometry proves to be a promising approach for overcoming such a challenge. In this paper we present a complete simulation pipeline of interferometric observations of CMB polarization, including systematic errors. We employ two different methods for obtaining the power spectra from mock data produced by simulated observations: the maximum likelihood method and the method of Gibbs sampling. We show that the results from both methods are consistent with each other, as well as, within a factor of 6, with analytical estimates. Several categories of systematic errors are considered: instrumental errors, consisting of antenna gain and antenna coupling errors, and beam errors, consisting of antenna pointing errors, beam cross-polarization and beam shape (and size) errors. In order to recover the tensor-to-scalar ratio, $r$, within a 10% tolerance level, which ensures the experiment is sensitive enough to detect the $B$-signal at $r=0.01$ in the multipole range $28 < ell < 384$, we find that, for a QUBIC-like experiment, Gaussian-distributed systematic errors must be controlled with precisions of $|g_{rms}| = 0.1$ for antenna gain, $|epsilon_{rms}| = 5 times 10^{-4}$ for antenna coupling, $delta_{rms} approx 0.7^circ$ for pointing, $zeta_{rms} approx 0.7^circ$ for beam shape, and $mu_{rms} = 5 times 10^{-4}$ for beam cross-polarization.
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We investigate the impact of instrumental systematic errors in interferometric measurements of the cosmic microwave background (CMB) temperature and polarization power spectra. We simulate interferometric CMB observations to generate mock visibilities and estimate power spectra using the statistically optimal maximum likelihood technique. We define a quadratic error measure to determine allowable levels of systematic error that do not induce power spectrum errors beyond a given tolerance. As an example, in this study we focus on differential pointing errors. The effects of other systematics can be simulated by this pipeline in a straightforward manner. We find that, in order to accurately recover the underlying B-modes for r=0.01 at 28<l<384, Gaussian-distributed pointing errors must be controlled to 0.7^circ rms for an interferometer with an antenna configuration similar to QUBIC, in agreement with analytical estimates. Only the statistical uncertainty for 28<l<88 would be changed at ~10% level. With the same instrumental configuration, we find the pointing errors would slightly bias the 2-sigma upper limit of the tensor-to-scalar ratio r by ~10%. We also show that the impact of pointing errors on the TB and EB measurements is negligibly small.
Heterodyne receivers register the sky signal on either a circular polarization basis (where it is split into left-hand and right-hand circular polarization) or a linear polarization basis (where it is split into horizontal and vertical linear polarization). We study the problem of interferometric observations performed with telescopes that observe on different polarization bases, hence producing visibilities that we call mixed basis (i.e., linear in one telescope and circular in the other). We present novel algorithms for the proper calibration and treatment of such interferometric observations and test our algorithms with both simulations and real data. The use of our algorithms will be important for the optimum calibration of forthcoming observations with the Atacama Large mm/submm Array (ALMA) in very-long-baseline interferometry (VLBI) mode. Our algorithms will also allow us to optimally calibrate future VLBI observations at very high data rates (i.e., wide bandwidths), where linear-polarization feeds will be preferable at some stations, to overcome the polarimetric limitations due to the use of quarter-wave plates.
We develop a systematic and unified approach to estimate all possible secondary (i.e. non-primordial) nonlinear effects to the cosmic microwave background (CMB) polarization, named curve-of-sight integration approach. In this approach, the Boltzmann equation for polarized photons is rewritten in a line-of-sight integral along an exact geodesic in the perturbed universe, rather than a geodesic in the background universe used in the linear-order CMB calculation. This approach resolves the difficulty to solve the Boltzmann hierarchy with the nonlinear gravitational effects in the photon free-streaming regime and thus unifies the standard remapping approach for CMB lensing into the direct approach solving the Boltzmann equation for the nonlinear collisional effects. In this paper, we derive formulae that: (i) include all the nonlinear effects; (ii) can treat extended sources such as the contributions after the reionization. It offers a solid framework to discuss possible systematics in the standard estimation of CMB lensing by the remapping approach. As an explicit demonstration, we estimate the secondary B-mode power spectrum induced by all foreground gravitational effects: lensing, redshift, time-delay, emission-angle, and polarization-rotation effects. We define these effects properly so that they do not have any overlap, also without overlooking any effect. Then, we show that these effects only give corrections of the order of 0.001-0.01% to the standard lensing-induced B-mode power spectrum in the concordance $Lambda$ cold dark matter model. Our result confirms the reliability of using the remapping approach in upcoming CMB experiments aiming to detect the primordial gravitational waves with the tensor-to-scalar ratio of $r sim 10^{-3}$.
We explore the hemispherical asymmetry predicted in cosmic microwave background polarization when there is an asymmetry in temperature anisotropies due to primordial perturbations. We consider the cases of asymmetries due to adiabatic and isocurvature modes, and tensor perturbations. We show that the asymmetry in the TE, EE and/or BB correlations can be substantially larger than those in the TT power spectrum in certain cases. The relative asymmetry in the different cross-correlations, as well as the angular scale dependence, can in principle distinguish between different origins for the asymmetry.
Future high-sensitivity measurements of the cosmic microwave background (CMB) anisotropies and energy spectrum will be limited by our understanding and modeling of foregrounds. Not only does more information need to be gathered and combined, but also novel approaches for the modeling of foregrounds, commensurate with the vast improvements in sensitivity, have to be explored. Here, we study the inevitable effects of spatial averaging on the spectral shapes of typical foreground components, introducing a moment approach, which naturally extends the list of foreground parameters that have to be determined through measurements or constrained by theoretical models. Foregrounds are thought of as a superposition of individual emitting volume elements along the line of sight and across the sky, which then are observed through an instrumental beam. The beam and line of sight averages are inevitable. Instead of assuming a specific model for the distributions of physical parameters, our method identifies natural new spectral shapes for each foreground component that can be used to extract parameter moments (e.g., mean, dispersion, cross-terms, etc.). The method is illustrated for the superposition of power-laws, free-free spectra, gray-body and modified blackbody spectra, but can be applied to more complicated fundamental spectral energy distributions. Here, we focus on intensity signals but the method can be extended to the case of polarized emission. The averaging process automatically produces scale-dependent spectral shapes and the moment method can be used to propagate the required information across scales in power spectrum estimates. The approach is not limited to applications to CMB foregrounds but could also be useful for the modeling of X-ray emission in clusters of galaxies.
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