We review and compare two different CMB dipole estimators discussed in the literature, and assess their performances through Monte Carlo simulations. The first method amounts to simple template ...regression with partial sky data, while the second method is an optimal Wiener filter (or Gibbs sampling) implementation. The main difference between the two methods is that the latter approach takes into account correlations with higher-order CMB temperature fluctuations that arise from non-orthogonal spherical harmonics on an incomplete sky, which for recent CMB data sets (such as Planck) is the dominant source of uncertainty. For an accepted sky fraction of 81% and an angular CMB power spectrum corresponding to the best-fit Planck 2018 \(\Lambda\)CDM model, we find that the uncertainty on the recovered dipole amplitude is about six times smaller for the Wiener filter approach than for the template approach, corresponding to 0.5 and 3\(~\mu\)K, respectively. Similar relative differences are found for the corresponding directional parameters and other sky fractions. We note that the Wiener filter algorithm is generally applicable to any dipole estimation problem on an incomplete sky, as long as a statistical and computationally tractable model is available for the unmasked higher-order fluctuations. The methodology described in this paper forms the numerical basis for the most recent determination of the CMB solar dipole from Planck, as summarized by arXiv:2007.04997.
A methodology to provide the polarization angle requirements for different sets of detectors, at a given frequency of a CMB polarization experiment, is presented. The uncertainties in the ...polarization angle of each detector set are related to a given bias on the tensor-to-scalar ratio \(r\) parameter. The approach is grounded in using a linear combination of the detector sets to obtain the CMB polarization signal. In addition, assuming that the uncertainties on the polarization angle are in the small angle limit (lower than a few degrees), it is possible to derive analytic expressions to establish the requirements. The methodology also accounts for possible correlations among detectors, that may originate from the optics, wafers, etc. The approach is applied to the LiteBIRD space mission. We show that, for the most restrictive case (i.e., full correlation of the polarization angle systematics among detector sets), the requirements on the polarization angle uncertainties are of around 1 arcmin at the most sensitive frequency bands (i.e., \(\approx 150\) GHz) and of few tens of arcmin at the lowest (i.e., \(\approx 40\) GHz) and highest (i.e., \(\approx 400\) GHz) observational bands. Conversely, for the least restrictive case (i.e., no correlation of the polarization angle systematics among detector sets), the requirements are \(\approx 5\) times less restrictive than for the previous scenario. At the global and the telescope levels, polarization angle knowledge of a few arcmins is sufficient for correlated global systematic errors and can be relaxed by a factor of two for fully uncorrelated errors in detector polarization angle. The reported uncertainty levels are needed in order to have the bias on \(r\) due to systematics below the limit established by the LiteBIRD collaboration.
We present a Gibbs sampling solution to the map-making problem for CMB measurements, building on existing destriping methodology. Gibbs sampling breaks the computationally heavy destriping problem ...into two separate steps; noise filtering and map binning. Considered as two separate steps, both are computationally much cheaper than solving the combined problem. This provides a huge performance benefit as compared to traditional methods, and allows us for the first time to bring the destriping baseline length to a single sample. We apply the Gibbs procedure to simulated Planck 30 GHz data. We find that gaps in the time-ordered data are handled efficiently by filling them with simulated noise as part of the Gibbs process. The Gibbs procedure yields a chain of map samples, from which we may compute the posterior mean as a best-estimate map. The variation in the chain provides information on the correlated residual noise, without need to construct a full noise covariance matrix. However, if only a single maximum-likelihood frequency map estimate is required, we find that traditional conjugate gradient solvers converge much faster than a Gibbs sampler in terms of total number of iterations. The conceptual advantages of the Gibbs sampling approach lies in statistically well-defined error propagation and systematic error correction, and this methodology forms the conceptual basis for the map-making algorithm employed in the BeyondPlanck framework, which implements the first end-to-end Bayesian analysis pipeline for CMB observations.
The Probe of Inflation and Cosmic Origins (PICO) is a proposed probe-scale space mission consisting of an imaging polarimeter operating in frequency bands between 20 and 800 GHz. We describe the ...science achievable by PICO, which has sensitivity equivalent to more than 3300 Planck missions, the technical implementation, the schedule and cost.
We estimate the spectral index, beta, of polarized synchrotron emission as observed in the 9 yr WMAP sky maps using two methods, linear regression ("T-T plot") and maximum likelihood. We partition ...the sky into 24 disjoint sky regions, and evaluate the spectral index for all polarization angles between 0 deg and 85 deg in steps of 5. Averaging over polarization angles, we derive a mean spectral index of beta_all-sky=-2.99+-0.01 in the frequency range of 23-33 GHz. We find that the synchrotron spectral index steepens by 0.14 from low to high Galactic latitudes, in agreement with previous studies, with mean spectral indices of beta_plane=-2.98+-0.01 and beta_high-lat=-3.12+-0.04. In addition, we find a significant longitudinal variation along the Galactic plane with a steeper spectral index toward the Galactic center and anticenter than toward the Galactic spiral arms. This can be well modeled by an offset sinusoidal, beta(l)=-2.85+0.17sin(2l-90). Finally, we study synchrotron emission in the BICEP2 field, in an attempt to understand whether the claimed detection of large-scale B-mode polarization could be explained in terms of synchrotron contamination. Adopting a spectral index of beta=-3.12, typical for high Galactic latitudes, we find that the most likely bias corresponds to about 2% of the reported signal (r=0.003). The flattest index allowed by the data in this region is beta=-2.5, and under the assumption of a straight power-law frequency spectrum, we find that synchrotron emission can account for at most 20% of the reported BICEP2 signal.
We present the first application of the Cosmoglobe analysis framework by analyzing 9-year \(\mathit{WMAP}\) time-ordered observations using similar machinery as BeyondPlanck utilizes for ...\(\mathit{Planck}\) LFI. We analyze only the \(\mathit Q\)-band (41 GHz) data and report on the low-level analysis process from uncalibrated time-ordered data to calibrated maps. Most of the existing BeyondPlanck pipeline may be reused for \(\mathit{WMAP}\) analysis with minimal changes to the existing codebase. The main modification is the implementation of the same preconditioned biconjugate gradient mapmaker used by the \(\mathit{WMAP}\) team. Producing a single \(\mathit{WMAP}\) \(\mathit Q\)1-band sample requires 22 CPU-hrs, which is slightly more than the cost of a \(\mathit{Planck}\) 44 GHz sample of 17 CPU-hrs; this demonstrates that full end-to-end Bayesian processing of the \(\mathit{WMAP}\) data is computationally feasible. In general, our recovered maps are very similar to the maps released by the \(\mathit{WMAP}\) team, although with two notable differences. In temperature we find a \(\sim2\,\mathrm{\mu K}\) quadrupole difference that most likely is caused by different gain modeling, while in polarization we find a distinct \(2.5\,\mathrm{\mu K}\) signal that has been previously called poorly-measured modes by the \(\mathit{WMAP}\) team. In the Cosmoglobe processing, this pattern arises from temperature-to-polarization leakage from the coupling between the CMB Solar dipole, transmission imbalance, and sidelobes. No traces of this pattern are found in either the frequency map or TOD residual map, suggesting that the current processing has succeeded in modelling these poorly measured modes within the assumed parametric model by using \(\mathit{Planck}\) information to break the sky-synchronous degeneracies inherent in the \(\mathit{WMAP}\) scanning strategy.
Inflation is the leading theory of the first instant of the universe. Inflation, which postulates that the universe underwent a period of rapid expansion an instant after its birth, provides ...convincing explanation for cosmological observations. Recent advancements in detector technology have opened opportunities to explore primordial gravitational waves generated by the inflation through B-mode (divergent-free) polarization pattern embedded in the Cosmic Microwave Background anisotropies. If detected, these signals would provide strong evidence for inflation, point to the correct model for inflation, and open a window to physics at ultra-high energies. LiteBIRD is a satellite mission with a goal of detecting degree-and-larger-angular-scale B-mode polarization. LiteBIRD will observe at the second Lagrange point with a 400 mm diameter telescope and 2,622 detectors. It will survey the entire sky with 15 frequency bands from 40 to 400 GHz to measure and subtract foregrounds. The U.S. LiteBIRD team is proposing to deliver sub-Kelvin instruments that include detectors and readout electronics. A lenslet-coupled sinuous antenna array will cover low-frequency bands (40 GHz to 235 GHz) with four frequency arrangements of trichroic pixels. An orthomode-transducer-coupled corrugated horn array will cover high-frequency bands (280 GHz to 402 GHz) with three types of single frequency detectors. The detectors will be made with Transition Edge Sensor (TES) bolometers cooled to a 100 milli-Kelvin base temperature by an adiabatic demagnetization refrigerator.The TES bolometers will be read out using digital frequency multiplexing with Superconducting QUantum Interference Device (SQUID) amplifiers. Up to 78 bolometers will be multiplexed with a single SQUID amplidier. We report on the sub-Kelvin instrument design and ongoing developments for the LiteBIRD mission.
We demonstrate that, for the baseline design of the CORE satellite mission, the polarized foregrounds can be controlled at the level required to allow the detection of the primordial cosmic microwave ...background (CMB) \(B\)-mode polarization with the desired accuracy at both reionization and recombination scales, for tensor-to-scalar ratio values of \({r\gtrsim 5\times 10^{-3}}\). We consider detailed sky simulations based on state-of-the-art CMB observations that consist of CMB polarization with \(\tau=0.055\) and tensor-to-scalar values ranging from \(r=10^{-2}\) to \(10^{-3}\), Galactic synchrotron, and thermal dust polarization with variable spectral indices over the sky, polarized anomalous microwave emission, polarized infrared and radio sources, and gravitational lensing effects. Using both parametric and blind approaches, we perform full component separation and likelihood analysis of the simulations, allowing us to quantify both uncertainties and biases on the reconstructed primordial \(B\)-modes. Under the assumption of perfect control of lensing effects, CORE would measure an unbiased estimate of \(r=\left(5 \pm 0.4\right)\times 10^{-3}\) after foreground cleaning. In the presence of both gravitational lensing effects and astrophysical foregrounds, the significance of the detection is lowered, with CORE achieving a \(4\sigma\)-measurement of \(r=5\times 10^{-3}\) after foreground cleaning and \(60\)% delensing. For lower tensor-to-scalar ratios (\(r=10^{-3}\)) the overall uncertainty on \(r\) is dominated by foreground residuals, not by the 40% residual of lensing cosmic variance. Moreover, the residual contribution of unprocessed polarized point-sources can be the dominant foreground contamination to primordial B-modes at this \(r\) level, even on relatively large angular scales, \(\ell \sim 50\). Finally, we report two sources of potential bias for the detection of the primordial \(B\)-modes.abridged
We describe a simple but efficient method for deriving a consistent set of monopole and dipole corrections for multi-frequency sky map data sets, allowing robust parametric component separation with ...the same data set. The computational core of this method is linear regression between pairs of frequency maps, often called "T-T plots". Individual contributions from monopole and dipole terms are determined by performing the regression locally in patches on the sky, while the degeneracy between different frequencies is lifted when ever the dominant foreground component exhibits a significant spatial spectral index variation. Based on this method, we present two different, but each internally consistent, sets of monopole and dipole coefficients for the 9-year WMAP, Planck 2013, SFD 100 um, Haslam 408 MHz and Reich & Reich 1420 MHz maps. The two sets have been derived with different analysis assumptions and data selection, and provides an estimate of residual systematic uncertainties. In general, our values are in good agreement with previously published results. Among the most notable results are a relative dipole between the WMAP and Planck experiments of 10-15 uK (depending on frequency), an estimate of the 408 MHz map monopole of 8.9 +- 1.3 K, and a non-zero dipole in the 1420 MHz map of $0.15 +- 0.03 K pointing towards Galactic coordinates (l,b) = (308,-36) +- 14 degrees. These values represent the sum of any instrumental and data processing offsets, as well as any Galactic or extra-Galactic component that is spectrally uniform over the full sky.
We present polarization observations of two Galactic plane fields centered on Galactic coordinates (l,b)=(0 deg,0 deg) and (329 deg, 0 deg) at Q- (43 GHz) and W-band (95 GHz), covering between 301 ...and 539 square degrees depending on frequency and field. These measurements were made with the QUIET instrument between 2008 October and 2010 December, and include a total of 1263 hours of observations. The resulting maps represent the deepest large-area Galactic polarization observations published to date at the relevant frequencies with instrumental rms noise varying between 1.8 and 2.8 uK deg, 2.3-6 times deeper than corresponding WMAP and Planck maps. The angular resolution is 27.3' and 12.8' FWHM at Q- and W-band, respectively. We find excellent agreement between the QUIET and WMAP maps over the entire fields, and no compelling evidence for significant residual instrumental systematic errors in either experiment, whereas the Planck 44 GHz map deviates from these in a manner consistent with reported systematic uncertainties for this channel. We combine QUIET and WMAP data to compute inverse-variance-weighted average maps, effectively retaining small angular scales from QUIET and large angular scales from WMAP. From these combined maps, we derive constraints on several important astrophysical quantities, including a robust detection of polarized synchrotron spectral index steepening of ~0.2 off the plane, as well as the Faraday rotation measure toward the Galactic center (RM=-4000 +/- 200 rad m^-2), all of which are consistent with previously published results. Both the raw QUIET and the co-added QUIET+WMAP maps are made publicly available together with all necessary ancillary information.
