Abstract
We present the first linear polarization measurements from the 2015 long-duration balloon flight of
Spider
, which is an experiment that is designed to map the polarization of the cosmic ...microwave background (CMB) on degree angular scales. The results from these measurements include maps and angular power spectra from observations of 4.8% of the sky at 95 and 150 GHz, along with the results of internal consistency tests on these data. While the polarized CMB anisotropy from primordial density perturbations is the dominant signal in this region of sky, Galactic dust emission is also detected with high significance. Galactic synchrotron emission is found to be negligible in the
Spider
bands. We employ two independent foreground-removal techniques to explore the sensitivity of the cosmological result to the assumptions made by each. The primary method uses a dust template derived from
Planck
data to subtract the Galactic dust signal. A second approach, which constitutes a joint analysis of
Spider
and
Planck
data in the harmonic domain, assumes a modified-blackbody model for the spectral energy distribution of the dust with no constraint on its spatial morphology. Using a likelihood that jointly samples the template amplitude and
r
parameter space, we derive 95% upper limits on the primordial tensor-to-scalar ratio from Feldman–Cousins and Bayesian constructions, finding
r
< 0.11 and
r
< 0.19, respectively. Roughly half the uncertainty in
r
derives from noise associated with the template subtraction. New data at 280 GHz from
Spider
’s second flight will complement the
Planck
polarization maps, providing powerful measurements of the polarized Galactic dust emission.
BEYONDPLANCK Svalheim, T. L.; Zonca, A.; Andersen, K. J. ...
Astronomy and astrophysics (Berlin),
07/2023, Letnik:
675
Journal Article
Recenzirano
Odprti dostop
We discuss the treatment of bandpass and beam leakage corrections in the Bayesian B
EYOND
P
LANCK
cosmic microwave background (CMB) analysis pipeline as applied to the
Planck
LFI measurements. As a ...preparatory step, we first applied three corrections to the nominal LFI bandpass profiles, including the removal of a known systematic effect in the ground measuring equipment at 61 GHz, along with a smoothing of standing wave ripples and edge regularization. The main net impact of these modifications is an overall shift in the 70 GHz bandpass of +0.6 GHz. We argue that any analysis of LFI data products, either from
Planck
or B
EYOND
P
LANCK
, should use these new bandpasses. In addition, we fit a single free bandpass parameter for each radiometer of the form Δ
i
= Δ
0
+
δ
i
, where Δ
0
represents an absolute frequency shift per frequency band and
δ
i
is a relative shift per detector. The absolute correction is only fitted at 30 GHz, with a full
χ
2
-based likelihood, resulting in a correction of Δ
30
= 0.24 ± 0.03 GHz. The relative corrections were fitted using a spurious map approach that is fundamentally similar to the method pioneered by the WMAP team, but excluding the introduction of many additional degrees of freedom. All the bandpass parameters were sampled using a standard Metropolis sampler within the main B
EYOND
P
LANCK
Gibbs chain and the bandpass uncertainties were thus propagated to all other data products in the analysis. In summary, we find that our bandpass model significantly reduces leakage effects. For beam leakage corrections, we adopted the official
Planck
LFI beam estimates without any additional degrees of freedom and we only marginalized over the underlying sky model. We note that this is the first time that leakage from beam mismatch has been included for
Planck
LFI maps.
BEYONDPLANCK Svalheim, T. L.; Andersen, K. J.; Aurlien, R. ...
Astronomy and astrophysics (Berlin),
06/2023, Letnik:
675
Journal Article
Recenzirano
Odprti dostop
Using the
Planck
Low Frequency Instrument (LFI) and WMAP data within the global Bayesian B
EYOND
P
LANCK
framework, we constrained the polarized foreground emission between 30 and 70 GHz. We ...combined, for the first time, full-resolution
Planck
LFI time-ordered data with low-resolution WMAP sky maps at 33, 40, and 61 GHz. The spectral parameters were fit with a likelihood defined at the native resolution of each frequency channel. This analysis represents the first implementation of true multi-resolution component separation applied to CMB observations for both amplitude and spectral energy distribution (SED) parameters. For the synchrotron emission, we approximated the SED as a power-law in frequency and we find that the low signal-to-noise ratio of the current data strongly limits the number of free parameters that can be robustly constrained. We partitioned the sky into four large disjoint regions (High Latitude; Galactic Spur; Galactic Plane; and Galactic Center), each associated with its own power-law index. We find that the High Latitude region is prior-dominated, while the Galactic Center region is contaminated by residual instrumental systematics. The two remaining regions appear to be signal-dominated, and for these we derive spectral indices of
β
s
Spur
= −3.17 ± 0.06 and β
s
Plane
= −3.03 ± 0.07, which is in good agreement with previous results. For the thermal dust emission, we assumed a modified blackbody model and we fit a single power-law index across the full sky. We find
β
d
= 1.64 ± 0.03, which is slightly steeper than the value reported in
Planck
HFI data, but still statistically consistent at the 2
σ
confidence level.
We present the first application of the C
OSMOGLOBE
analysis framework by analyzing nine-year WMAP time-ordered observations that uses similar machinery to that of B
EYOND
P
LANCK
for the
Planck
Low ...Frequency Instrument (LFI). We analyzed only the
Q
-band (41 GHz) data and report on the low-level analysis process based on uncalibrated time-ordered data to calibrated maps. Most of the existing B
EYOND
P
LANCK
pipeline may be reused for 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 WMAP team. Producing a single WMAP
Q
1-band sample requires 22 CPU-hrs, which is slightly more than the cost of a
Planck
44 GHz sample of 17 CPU-hrs; this demonstrates that a full end-to-end Bayesian processing of the WMAP data is computationally feasible. In general, our recovered maps are very similar to the maps released by the WMAP team, although with two notable differences. In terms of temperature, we find a ∼2 μK quadrupole difference that most likely is caused by different gain modeling, while in polarization we find a distinct 2.5 μK signal that has been previously referred to as poorly measured modes by the WMAP team. In the C
OSMOGLOBE
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 modeling these poorly measured modes within the assumed parametric model by using
Planck
information to break the sky-synchronous degeneracies inherent in the WMAP scanning strategy.
BEYONDPLANCK Gjerløw, E.; Ihle, H. T.; Galeotta, S. ...
Astronomy and astrophysics (Berlin),
06/2023, Letnik:
675
Journal Article
Recenzirano
Odprti dostop
We present a Bayesian calibration algorithm for cosmic microwave background (CMB) observations as implemented within the global end-to-end B
EYOND
P
LANCK
framework and applied to the
Planck
Low ...Frequency Instrument (LFI) data. Following the most recent
Planck
analysis, we decomposed the full time-dependent gain into a sum of three nearly orthogonal components: one absolute calibration term, common to all detectors, one time-independent term that can vary between detectors, and one time-dependent component that was allowed to vary between one-hour pointing periods. Each term was then sampled conditionally on all other parameters in the global signal model through Gibbs sampling. The absolute calibration is sampled using only the orbital dipole as a reference source, while the two relative gain components were sampled using the full sky signal, including the orbital and Solar CMB dipoles, CMB fluctuations, and foreground contributions. We discuss various aspects of the data that influence gain estimation, including the dipole-polarization quadrupole degeneracy and processing masks. Comparing our solution to previous pipelines, we find good agreement in general, with relative deviations of −0.67% (−0.84%) for 30 GHz, 0.12% (−0.04%) for 44 GHz and −0.03% (−0.64%) for 70 GHz, compared to
Planck
PR4 and
Planck
2018, respectively. We note that the B
EYOND
P
LANCK
calibration was performed globally, which results in better inter-frequency consistency than previous estimates. Additionally, WMAP observations were used actively in the B
EYOND
P
LANCK
analysis, which both breaks internal degeneracies in the
Planck
data set and results in an overall better agreement with WMAP. Finally, we used a Wiener filtering approach to smoothing the gain estimates. We show that this method avoids artifacts in the correlated noise maps as a result of oversmoothing the gain solution, which is difficult to avoid with methods like boxcar smoothing, as Wiener filtering by construction maintains a balance between data fidelity and prior knowledge. Although our presentation and algorithm are currently oriented toward LFI processing, the general procedure is fully generalizable to other experiments, as long as the Solar dipole signal is available to be used for calibration.
BEYONDPLANCK Herman, D.; Hensley, B.; Andersen, K. J. ...
Astronomy and astrophysics (Berlin),
07/2023, Letnik:
675
Journal Article
Recenzirano
Odprti dostop
We constrained the level of polarized anomalous microwave emission (AME) on large angular scales using
Planck
Low-Frequency Instrument (LFI) and WMAP polarization data within a Bayesian cosmic ...microwave background (CMB) analysis framework. We modeled synchrotron emission with a power-law spectral energy distribution, as well as the sum of AME and thermal dust emission through linear regression with the
Planck
High-Frequency Instrument (HFI) 353 GHz data. This template-based dust emission model allowed us to constrain the level of polarized AME while making minimal assumptions on its frequency dependence. We neglected CMB fluctuations, but show through simulations that these fluctuations have a minor impact on the results. We find that the resulting AME polarization fraction confidence limit is sensitive to the polarized synchrotron spectral index prior. In addition, for prior means
β
s
< −3.1 we find an upper limit of
p
AME
max
≲ 0.6% (95% confidence). In contrast, for means
β
s
= −3.0, we find a nominal detection of
p
AME
= 2.5 ± 1.0% (95% confidence). These data are thus not strong enough to simultaneously and robustly constrain both polarized synchrotron emission and AME, and our main result is therefore a constraint on the AME polarization fraction explicitly as a function of
β
s
. Combining the current
Planck
and WMAP observations with measurements from high-sensitivity low-frequency experiments such as C-BASS and QUIJOTE will be critical to improve these limits further.
We constrained the level of polarized anomalous microwave emission (AME) on large angular scales using Planck Low-Frequency Instrument (LFI) and WMAP polarization data within a Bayesian cosmic ...microwave background (CMB) analysis framework. We modeled synchrotron emission with a power-law spectral energy distribution, as well as the sum of AME and thermal dust emission through linear regression with the Planck High-Frequency Instrument (HFI) 353 GHz data. This template-based dust emission model allowed us to constrain the level of polarized AME while making minimal assumptions on its frequency dependence. We neglected CMB fluctuations, but show through simulations that these fluctuations have a minor impact on the results. We find that the resulting AME polarization fraction confidence limit is sensitive to the polarized synchrotron spectral index prior. In addition, for prior means βs < −3.1 we find an upper limit of pAMEmax ≲ 0.6% (95% confidence). In contrast, for means βs = −3.0, we find a nominal detection of pAME = 2.5 ± 1.0% (95% confidence). These data are thus not strong enough to simultaneously and robustly constrain both polarized synchrotron emission and AME, and our main result is therefore a constraint on the AME polarization fraction explicitly as a function of βs. Combining the current Planck and WMAP observations with measurements from high-sensitivity low-frequency experiments such as C-BASS and QUIJOTE will be critical to improve these limits further.
BEYONDPLANCK Colombo, L. P. L.; Eskilt, J. R.; Paradiso, S. ...
Astronomy and astrophysics (Berlin),
06/2023, Letnik:
675
Journal Article
Recenzirano
Odprti dostop
We present posterior sample-based cosmic microwave background (CMB) constraints from
Planck
LFI and WMAP observations as derived through global end-to-end Bayesian processing within the B
EYOND
P
...LANCK
framework. We first used these samples to study correlations between CMB, foreground, and instrumental parameters. We identified a particularly strong degeneracy between CMB temperature fluctuations and free-free emission on intermediate angular scales (400 ≲
ℓ
≲ 600), mitigated through model reduction, masking, and resampling. We compared our posterior-based CMB results with previous
Planck
products and found a generally good agreement, however, with notably higher noise due to our exclusion of
Planck
HFI data. We found a best-fit CMB dipole amplitude of 3362.7 ± 1.4 μK, which is in excellent agreement with previous
Planck
results. The quoted dipole uncertainty is derived directly from the sampled posterior distribution and does not involve any ad hoc contributions for
Planck
instrumental systematic effects. Similarly, we find a temperature quadrupole amplitude of $ \sigma^{TT}_2=229\pm97\,\muup{\rm K}^2 $ , which is in good agreement with previous results in terms of the amplitude, but the uncertainty is one order of magnitude greater than the naive diagonal Fisher uncertainty. Concurrently, we find less evidence of a possible alignment between the quadrupole and octopole than previously reported, due to a much larger scatter in the individual quadrupole coefficients that is caused both by marginalizing over a more complete set of systematic effects – as well as by requiring a more conservative analysis mask to mitigate the free-free degeneracy. For higher multipoles, we find that the angular temperature power spectrum is generally in good agreement with both
Planck
and WMAP. At the same time, we note that this is the first time that the sample-based, asymptotically exact Blackwell-Rao estimator has been successfully established for multipoles up to
ℓ
≤ 600. It now accounts for the majority of the cosmologically important information. Overall, this analysis demonstrates the unique capabilities of the Bayesian approach with respect to end-to-end systematic uncertainty propagation and we believe it can and should play an important role in the analysis of future CMB experiments. Cosmological parameter constraints are presented in a companion paper.
BEYONDPLANCK Herman, D; Watson, R A; Andersen, K J ...
Astronomy & astrophysics,
07/2023, Letnik:
675
Journal Article
Recenzirano
Odprti dostop
We describe the correction procedure for Analog-to-Digital Converter (ADC) differential non-linearities (DNL) adopted in the Bayesian end-to-end BEYONDPLANCK analysis framework. This method is nearly ...identical to that developed for the official Planck Low Frequency Instrument (LFI) Data Processing Center (DPC) analysis, and relies on the binned rms noise profile of each detector data stream. However, rather than building the correction profile directly from the raw rms profile, we first fit a Gaussian to each significant ADC-induced rms decrement, and then derive the corresponding correction model from this smooth model. The main advantage of this approach is that only samples which are significantly affected by ADC DNLs are corrected, as opposed to the DPC approach in which the correction is applied to all samples, filtering out signals not associated with ADC DNLs. The new corrections are only applied to data for which there is a clear detection of the non-linearities, and for which they perform at least comparably with the DPC corrections. Out of a total of 88 LFI data streams (sky and reference load for each of the 44 detectors) we apply the new minimal ADC corrections in 25 cases, and maintain the DPC corrections in 8 cases. All these corrections are applied to 44 or 70 GHz channels, while, as in previous analyses, none of the 30 GHz ADCs show significant evidence of non-linearity. By comparing the BEYONDPLANCK and DPC ADC correction methods, we estimate that the residual ADC uncertainty is about two orders of magnitude below the total noise of both the 44 and 70 GHz channels, and their impact on current cosmological parameter estimation is small. However, we also show that non-idealities in the ADC corrections can generate sharp stripes in the final frequency maps, and these could be important for future joint analyses with the Planck High Frequency Instrument (HFI), Wilkinson Microwave Anisotropy Probe (WMAP), or other datasets. We therefore conclude that, although the existing corrections are adequate for LFI-based cosmological parameter analysis, further work on LFI ADC corrections is still warranted.
BEYONDPLANCK Andersen, K J; Aurlien, R; Banerji, R ...
Astronomy & astrophysics,
07/2023, Letnik:
675
Journal Article
Recenzirano
Odprti dostop
We describe the BEYONDPLANCK project in terms of our motivation, methodology, and main products, and provide a guide to a set of companion papers that describe each result in more detail. Building ...directly on experience from ESA’s Planck mission, we implemented a complete end-to-end Bayesian analysis framework for the Planck Low Frequency Instrument (LFI) observations. The primary product is a full joint posterior distribution P(ω ∣ d), where ω represents the set of all free instrumental (gain, correlated noise, bandpass, etc.), astrophysical (synchrotron, free-free, thermal dust emission, etc.), and cosmological (cosmic microwave background – CMB – map, power spectrum, etc.) parameters. Some notable advantages of this approach compared to a traditional pipeline procedure are seamless end-to-end propagation of uncertainties; accurate modeling of both astrophysical and instrumental effects in the most natural basis for each uncertain quantity; optimized computational costs with little or no need for intermediate human interaction between various analysis steps; and a complete overview of the entire analysis process within one single framework. As a practical demonstration of this framework, we focus in particular on low-ℓ CMB polarization reconstruction with Planck LFI. In this process, we identify several important new effects that have not been accounted for in previous pipelines, including gain over-smoothing and time-variable and non-1/f correlated noise in the 30 and 44 GHz channels. Modeling and mitigating both previously known and newly discovered systematic effects, we find that all results are consistent with the ΛCDM model, and we constrained the reionization optical depth to τ = 0.066 ± 0.013, with a low-resolution CMB-based χ2 probability to exceed of 32%. This uncertainty is about 30% larger than the official pipelines, arising from taking a more complete instrumental model into account. The marginal CMB solar dipole amplitude is 3362.7 ± 1.4 μK, where the error bar was derived directly from the posterior distribution without the need of any ad hoc instrumental corrections. We are currently not aware of any significant unmodeled systematic effects remaining in the Planck LFI data, and, for the first time, the 44 GHz channel is fully exploited in the current analysis. We argue that this framework can play a central role in the analysis of many current and future high-sensitivity CMB experiments, including LiteBIRD, and it will serve as the computational foundation of the emerging community-wide COSMOGLOBE effort, which aims to combine state-of-the-art radio, microwave, and submillimeter data sets into one global astrophysical model.
