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Register a new userA hybrid approach to CMB lensing reconstruction on all-sky intensity maps
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Added by
Stephane Plaszczynski
Publication date
2012
fields
Physics
and research's language is
English
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Based on realistic simulations, we propose an hybrid method to reconstruct the lensing potential power spectrum, directly on PLANCK-like CMB frequency maps. It implies using a large galactic mask and dealing with a strong inhomogeneous noise. For l < 100, we show that a full-sky inpainting method, already described in a previous work, still allows a minimal variance reconstruction, with a bias that must be accounted for by a Monte-Carlo method, but that does not couple to the deflection field. For l>100 we develop a method based on tiling the cut-sky with local 10x10 degrees overlapping tangent planes (referred to in the following as patches). It requires to solve various issues concerning their size/position, non-periodic boundaries and irregularly sampled data after the sphere-to-plane projection. We show how the leading noise term of the quadratic lensing estimator applied onto an apodized patch can still be taken directly from the data. To not loose spatial accuracy, we developed a tool that allows the fast determination of the complex Fourier series coefficients from a bi-dimensional irregularly sampled dataset, without performing an interpolation. We show that the multi-patch approach allows the lensing power spectrum reconstruction with a very small bias, thanks to avoiding the galactic mask and lowering the noise inhomogeneities, while still having almost a minimal variance. The data quality can be assessed at each stage and simple bi-dimensional spectra build, which allows the control of local systematic errors.
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Detailed measurements of the CMB lensing signal are an important scientific goal of ongoing ground-based CMB polarization experiments, which are mapping the CMB at high resolution over small patches of the sky. In this work we simulate CMB polarization lensing reconstruction for the $EE$ and $EB$ quadratic estimators with current-generation noise levels and resolution, and show that without boundary effects the known and expected zeroth and first order $N^{(0)}$ and $N^{(1)}$ biases provide an adequate model for non-signal contributions to the lensing power spectrum estimators. Small sky areas present a number of additional challenges for polarization lensing reconstruction, including leakage of $E$ modes into $B$ modes. We show how simple windowed estimators using filtered pure-$B$ modes can greatly reduce the mask-induced mean-field lensing signal and reduce variance in the estimators. This provides a simple method (used with recent observations) that gives an alternative to more optimal but expensive inverse-variance filtering.
We discuss the effects of inhomogeneous sky-coverage on CMB lens reconstruction, focusing on application to the recently launched Planck satellite. We discuss the mean-field which is induced by noise inhomogeneities, as well as three approaches to lens reconstruction in this context: an optimal maximum-likelihood approach which is computationally expensive to evaluate, and two suboptimal approaches which are less intensive. The first of these is only sub-optimal at the five per-cent level for Planck, and the second prevents biasing due to uncertainties in the noise model.
Gravitational lensing of the CMB is a valuable cosmological signal that correlates to tracers of large-scale structure and acts as a important source of confusion for primordial $B$-mode polarization. State-of-the-art lensing reconstruction analyses use quadratic estimators, which are easily applicable to data. However, these estimators are known to be suboptimal, in particular for polarization, and large improvements are expected to be possible for high signal-to-noise polarization experiments. We develop a method and numerical code, $rm{LensIt}$, that is able to find efficiently the most probable lensing map, introducing no significant approximations to the lensed CMB likelihood, and applicable to beamed and masked data with inhomogeneous noise. It works by iteratively reconstructing the primordial unlensed CMB using a deflection estimate and its inverse, and removing residual lensing from these maps with quadratic estimator techniques. Roughly linear computational cost is maintained due to fast convergence of iterative searches, combined with the local nature of lensing. The method achieves the maximal improvement in signal to noise expected from analytical considerations on the unmasked parts of the sky. Delensing with this optimal map leads to forecast tensor-to-scalar ratio parameter errors improved by a factor $simeq 2 $ compared to the quadratic estimator in a CMB stage IV configuration.
We explore the reconstruction of the gravitational lensing field of the cosmic microwave background in real space showing that very little statistical information is lost when estimators of short range on the celestial sphere are used in place of the customary estimators in harmonic space, which are nonlocal and in principle require a simultaneous analysis of the entire sky without any cuts or excisions. Because virtually all the information relevant to lensing reconstruction lies on angular scales close to the resolution scale of the sky map, the gravitational lensing dilatation and shear fields (which unlike the deflection field or lensing potential are directly related to the observations in a local manner) may be reconstructed by means of quadratic combinations involving only very closely separated pixels. Even though harmonic space provides a more natural context for understanding lensing reconstruction theoretically, the real space methods developed here have the virtue of being faster to implement and are likely to prove useful for analyzing realistic maps containing a galactic cut and possibly numerous small excisions to exclude point sources that cannot be reliably subtracted.
Cosmic microwave background (CMB) lensing is an integrated effect whose kernel is greater than half the peak value in the range $1<z<5$. Measuring this effect offers a powerful tool to probe the large-scale structure of the Universe at high redshifts. With the increasing precision of ongoing CMB surveys, other statistics than the lensing power spectrum, in particular the lensing bi-spectrum, will be measured at high statistical significance. This will provide ways to improve the constraints on cosmological models and lift degeneracies. Following on an earlier paper, we test analytical predictions of the CMB lensing bi-spectrum against full-sky lensing simulations, and discuss their validity and limitation in detail. The tree-level prediction of perturbation theory agrees with the simulation only up to $ellsim 200$, but the one-loop order allows capturing the simulation results up to $ellsim 600$. We also show that analytical predictions based on fitting formulas for the matter bi-spectrum agree reasonably well with simulation results, although the precision of the agreement depends on the configurations and scales considered. For instance, the agreement is at the $10%$-level for the equilateral configuration at multipoles up to $ellsim2000$, but the difference in the squeezed limit raises to more than a factor of two at $ellsim2000$. This discrepancy appears to come from limitations in the fitting formula of the matter bi-spectrum. We also find that the analytical prediction for the post-Born correction to the bi-spectrum is in good agreement with the simulation. We conclude by discussing the bi-spectrum prediction in some theories of modified gravity.
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