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Register a new userA CMB Gibbs sampler for localized secondary anisotropies
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As well as primary fluctuations, CMB temperature maps contain a wealth of additional information in the form of secondary anisotropies. Secondary effects that can be identified with individual objects, such as the thermal and kinetic Sunyaev-Zeldovich (SZ) effects due to galaxy clusters, are difficult to unambiguously disentangle from foreground contamination and the primary CMB however. We develop a Bayesian formalism for rigorously characterising anisotropies that are localised on the sky, taking the TSZ and KSZ effects as an example. Using a Gibbs sampling scheme, we are able to efficiently sample from the joint posterior distribution for a multi-component model of the sky with many thousands of correlated physical parameters. The posterior can then be exactly marginalised to estimate properties of the secondary anisotropies, fully taking into account degeneracies with the other signals in the CMB map. We show that this method is computationally tractable using a simple implementation based on the existing Commander component separation code, and also discuss how other types of secondary anisotropy can be accommodated within our framework.
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Spatially fluctuating primordial magnetic fields (PMFs) inhomogeneously reheat the Universe when they dissipate deep inside the horizon before recombination. Such an energy injection turns into an additional photon temperature perturbation. We investigate secondary cosmic microwave background (CMB) temperature anisotropies originated from this mechanism, which we call {it inhomogeneous magnetic reheating}. We find that it can bring us information about non-linear coupling between PMFs and primordial curvature perturbations parametrized by $b_{rm NL}$, which should be important for probing the generation mechanism of PMFs. In fact, by using current CMB observations, we obtain an upper bound on the non-linear parameter as $log (b_{rm NL} (B_{lambda}/{rm nG})^2) lesssim {-36.5n_{B} - 94.0}$ with $B_{lambda}$ and $n_{rm B}$ being a magnetic field amplitude smoothed over $lambda=1; {rm Mpc}$ scale and a spectral index of the PMF power spectrum, respectively. Our constraints are far stronger than a previous forecast based on the future CMB spectral distortion anisotropy measurements because inhomogeneous magnetic reheating covers a much wider range of scales, i.e., $1; {rm Mpc}^{-1} lesssim klesssim 10^{15}; {rm Mpc}^{-1}$.
In this article, we derive a novel non-reversible, continuous-time Markov chain Monte Carlo (MCMC) sampler, called Coordinate Sampler, based on a piecewise deterministic Markov process (PDMP), which can be seen as a variant of the Zigzag sampler. In addition to proving a theoretical validation for this new sampling algorithm, we show that the Markov chain it induces exhibits geometrical ergodicity convergence, for distributions whose tails decay at least as fast as an exponential distribution and at most as fast as a Gaussian distribution. Several numerical examples highlight that our coordinate sampler is more efficient than the Zigzag sampler, in terms of effective sample size.
We study the propagation of a specific class of instrumental systematics to the reconstruction of the B-mode power spectrum of the cosmic microwave background (CMB). We focus on non-idealities of the half-wave plate (HWP), a polarization modulator that will be deployed by future CMB experiments, such as the phase-A satellite mission LiteBIRD. More in details, we study the effects of non-ideal HWP properties, such as transmittance, phase shift and cross-polarization. To this purpose, we develop a simple, yet stand-alone end-to-end simulation pipeline adapted to LiteBIRD. Through the latter, we analyze the effects of a possible mismatch between the measured frequency profiles of HWP properties (used in the mapmaking stage of the pipeline) and the actual profiles (used in the sky-scanning step). We simulate single-frequency, CMB-only observations to emphasize the effects of non-idealities on the BB power spectrum. We also consider multi-frequency observations to account for the frequency dependence of HWP properties and the contribution of foreground emission. We quantify the systematics effects in terms of a bias $Delta r$ on the tensor-to-scalar ratio $r$ with respect to the ideal case of no-systematics. We derive the accuracy requirements on the measurements of HWP properties by requiring $Delta r < 10^{-5}$ (1% of the expected LiteBIRD sensitivity on $r$). The analysis is introduced by a detailed presentation of the mathematical formalism employed in this work, including the use of the Jones and Mueller matrix representations.
Magnetized plasmas within halos of galaxies leave their footprint on the polarized anisotropies of the cosmic microwave background. The two dominant effects for astrophysical halos are Faraday rotation generating rotation of the plane of linear polarization, and Faraday conversion inducing a leakage from linear polarization to circular polarization. We revisit these sources of secondary anisotropies by computing the angular power spectra of the Faraday rotation angle and of the Faraday conversion rate by the large scale structures. To this end, we use the halo model and we pay special attention to the impact of magnetic field projections. Assuming magnetic fields of halos to be uncorrelated, we found a vanishing 2-halo term, and angular power spectra peaking at multipoles $ellsim10^4$. The Faraday rotation angle is dominated by the contribution of thermal electrons. For the Faraday conversion rate, we found that both thermal electrons and relativistic, non-thermal electrons contribute equally in the most optimistic case for the density and Lorentz factor of relativistic electrons, while in more pessimistic cases the thermal electrons give the dominant contribution. Assuming the magnetic field to be independent of the halo mass, the angular power spectra for both effects roughly scale with the amplitude of matter perturbations as $simsigma_8^3$, and with a very mild dependence with the density of cold dark matter. Introducing a dependence of the magnetic field strength with the halo mass leads to an increase of the scaling with the amplitude of matter fluctuations, up to $simsigma_8^{9.5}$ for Faraday rotation and $simsigma_8^{15}$ for Faraday conversion for a magnetic field strength scaling linearly with the halo mass.
In many fields, researchers are interested in discovering features with substantial effect on the response from a large number of features and controlling the proportion of false discoveries. By incorporating the knockoff procedure in the Bayesian framework, we develop the Bayesian knockoff filter (BKF) for selecting features that have important effect on the response. In contrast to the fixed knockoff variables in the frequentist procedures, we allow the knockoff variables to be continuously updated in the Markov chain Monte Carlo. Based on the posterior samples and elaborated greedy selection procedures, our method can distinguish the truly important features as well as controlling the Bayesian false discovery rate at a desirable level. Numerical experiments on both synthetic and real data demonstrate the advantages of our method over existing knockoff methods and Bayesian variable selection approaches, i.e., the BKF possesses higher power and yields a lower false discovery rate.
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