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Register a new userRevised estimates of CMB $B$-mode polarization induced by patchy reionization
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The search for primordial gravitational waves through the $B$-mode polarization pattern in the CMB is one of the major goals of current and future CMB experiments. Besides foregrounds, a potential hurdle in this search is the anisotropic secondary $B$-mode polarization generated by the scattering of CMB photons off free electrons produced during patchy cosmological reionization. Robust predictions of these secondary anisotropies are challenging because of uncertainties in the reionization history. In this paper, we revise estimates of the reionization-induced $B$-mode signal by incorporating recent advances in the understanding of reionization through observations of the Lyman-$alpha$ forest. To derive these $B$-mode estimates, we use high-dynamic-range radiative transfer simulations of reionization that are calibrated to the Ly$alpha$ data. These simulations are also consistent with a variety of other high-redshift observations. We find that around multipoles $ellapprox 100$, reionization induces $B$-mode power with $ell(ell+1)C_ell^{BB}/2piapprox 4times 10^{-6},mu$K$^2$. This secondary signal is thus at the level of the primordial signal with the tensor-to-scalar ratio $r<10^{-4}$, and can increase by a factor of $sim 50$ if reionization is sourced by highly clustered sources residing in haloes with mass of $sim 10^{11}$ M$_odot$. Our findings suggest that the contribution of patchy reionization to the search for primordial gravitational waves is unlikely to be a concern for currently planned CMB experiments.
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B-modes in CMB polarization from patchy reionization arise from two effects: generation of polarization from scattering of quadrupole moments by reionization bubbles, and fluctuations in the screening of E-modes from recombination. The scattering contribution has been studied previously, but the screening contribution has not yet been calculated. We show that on scales smaller than the acoustic scale (l>300), the B-mode power from screening is larger than the B-mode power from scattering. The ratio approaches a constant ~2.5 below the damping scale (l>2000). On degree scales relevant for gravitational waves (l<100), screening B-modes have a white noise tail and are subdominant to the scattering effect. These results are robust to uncertainties in the modeling of patchy reionization.
Inhomogeneous reionization gives rise to angular fluctuations in the Cosmic Microwave Background (CMB) optical depth tau(n) to the last scattering surface, correlating different spherical harmonic modes and imprinting characteristic non-Gaussianity on CMB maps. Recently the minimum variance quadratic estimator has been derived using this mode-coupling signal, and found that the optical depth fluctuations could be detected with (S/N)^2 ~ 100 in futuristic experiments like CMBPol. We first demonstrate that the non-Gaussian signal from gravitational lensing of CMB is the dominant source of contamination for reconstructing inhomogeneous reionization signals, even with 98% of its contribution removed by delensing. We then construct unbiased estimators that simultaneously reconstruct inhomogeneous reionization signals tau(n) and gravitational lensing potential phi(n). We apply our new unbiased estimators to future CMB experiment to assess the detectability of inhomogeneous reionization signals. With more physically motivated simulations of inhomogenuous reionizations that predict an order of magnitude smaller optical depth power spectrum than previous studies, we show that a CMBPol-like experiment could achieve a marginal detection of inhomogeneous reionization,(S/N)^2 ~ O(1) with this quadratic estimator to ~O(10) with the analogous maximum likelihood estimator.
We present constraints on the patchy reionization by measuring the trispectrum of the Planck 2015 cosmic microwave background (CMB) temperature anisotropies. The patchy reionization leads to anisotropies in the CMB optical depth, and the statistics of the observed CMB anisotropies is altered. We estimate the trispectrum of the CMB temperature anisotropies to constrain spatial variation of the optical depth. We show that the measured trispectrum is consistent with that from the standard lensed CMB simulation at $2sigma$. While no evidence of the patchy reionization is found in the Planck 2015 temperature trispectrum, the CMB constraint on the patchy reionization is significantly improved from previous works. Assuming the analytic bubble-halo model of Wang and Hu (2006), the constraint obtained in this work rules out the typical bubble size at the ionization fraction of $sim0.5$ as $Rgtrsim 10$ Mpc. Further, our constraint implies that large-scale $B$-modes from the patchy reionization are not a significant contamination in detecting the primordial gravitational waves of $rgtrsim0.001$ if the $B$ mode induced by the patchy reionization is described by Dvorkin et al. (2009). The CMB trispectrum data starts to provide meaningful constraints on the patchy reionization.
We present a demonstration of delensing the observed cosmic microwave background (CMB) B-mode polarization anisotropy. This process of reducing the gravitational-lensing generated B-mode component will become increasingly important for improving searches for the B modes produced by primordial gravitational waves. In this work, we delens B-mode maps constructed from multi-frequency SPTpol observations of a 90 deg$^2$ patch of sky by subtracting a B-mode template constructed from two inputs: SPTpol E-mode maps and a lensing potential map estimated from the $textit{Herschel}$ $500,mu m$ map of the CIB. We find that our delensing procedure reduces the measured B-mode power spectrum by 28% in the multipole range $300 < ell < 2300$; this is shown to be consistent with expectations from theory and simulations and to be robust against systematics. The null hypothesis of no delensing is rejected at $6.9 sigma$. Furthermore, we build and use a suite of realistic simulations to study the general properties of the delensing process and find that the delensing efficiency achieved in this work is limited primarily by the noise in the lensing potential map. We demonstrate the importance of including realistic experimental non-idealities in the delensing forecasts used to inform instrument and survey-strategy planning of upcoming lower-noise experiments, such as CMB-S4.
The Epoch of Reionization (EoR) depends on the complex astrophysics governing the birth and evolution of the first galaxies and structures in the intergalactic medium. EoR models rely on cosmic microwave background (CMB) observations, and in particular the large-scale E-mode polarization power spectra (EE PS), to help constrain their highly uncertain parameters. However, rather than directly forward-modelling the EE PS, most EoR models are constrained using a summary statistic -- the Thompson scattering optical depth, $tau_e$. Compressing CMB observations to $tau_e$ requires adopting a basis set for the EoR history. The common choice is the unphysical, redshift-symmetric hyperbolic tangent (Tanh) function, which differs in shape from physical EoR models based on hierarchical structure formation. Combining public EoR and CMB codes, 21cmFAST and CLASS, here we quantify how inference using the $tau_e$ summary statistic impacts the resulting constraints on galaxy properties and EoR histories. Using the last Planck 2018 data release, we show that the marginalized constraints on the EoR history are more sensitive to the choice of the basis set (Tanh vs physical model) than to the CMB likelihood statistic ($tau_e$ vs PS). For example, EoR histories implied by the growth of structure show a small tail of partial reionization extending to higher redshifts. However, biases in inference using $tau_e$ are negligible for the Planck 2018 data. Using EoR constraints from high-redshift observations including the quasar dark fraction, galaxy UV luminosity functions and CMB EE PS, our physical model recovers $tau_e=0.0569^{+0.0081}_{-0.0066}$.
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