BEYONDPLANCK Galloway, M.; Andersen, K. J.; Aurlien, R. ...
Astronomy and astrophysics (Berlin),
06/2023, Letnik:
675
Journal Article
Recenzirano
Odprti dostop
We describe the computational infrastructure for end-to-end Bayesian cosmic microwave background (CMB) analysis implemented by the BeyondPlanck Collaboration. The code is called
Commander3
. It ...provides a statistically consistent framework for global analysis of CMB and microwave observations and may be useful for a wide range of legacy, current, and future experiments. The paper has three main goals. Firstly, we provide a high-level overview of the existing code base, aiming to guide readers who wish to extend and adapt the code according to their own needs or re-implement it from scratch in a different programming language. Secondly, we discuss some critical computational challenges that arise within any global CMB analysis framework, for instance in-memory compression of time-ordered data, fast Fourier transform optimization, and parallelization and load-balancing. Thirdly, we quantify the CPU and RAM requirements for the current B
EYOND
P
LANCK
analysis, finding that a total of 1.5 TB of RAM is required for efficient analysis and that the total cost of a full Gibbs sample for LFI is 170 CPU-hrs, including both low-level processing and high-level component separation, which is well within the capabilities of current low-cost computing facilities. The existing code base is made publicly available under a GNU General Public Library (GPL) license.
BEYONDPLANCK Andersen, K. J.; Herman, D.; Aurlien, R. ...
Astronomy and astrophysics (Berlin),
06/2023, Letnik:
675
Journal Article
Recenzirano
Odprti dostop
We present the intensity foreground algorithms and model employed within the B
EYOND
P
LANCK
analysis framework. The B
EYOND
P
LANCK
analysis is aimed at integrating component separation and ...instrumental parameter sampling within a global framework, leading to complete end-to-end error propagation in the
Planck
Low Frequency Instrument (LFI) data analysis. Given the scope of the B
EYOND
P
LANCK
analysis, a limited set of data is included in the component separation process, leading to foreground parameter degeneracies. In order to properly constrain the Galactic foreground parameters, we improve upon the previous
Commander
component separation implementation by adding a suite of algorithmic techniques. These algorithms are designed to improve the stability and computational efficiency for weakly constrained posterior distributions. These are: (1) joint foreground spectral parameter and amplitude sampling, building on ideas from M
IRAMARE
; (2) component-based monopole determination; (3) joint spectral parameter and monopole sampling; and (4) application of informative spatial priors for component amplitude maps. We find that the only spectral parameter with a significant signal-to-noise ratio using the current B
EYOND
P
LANCK
data set is the peak frequency of the anomalous microwave emission component, for which we find
ν
p
= 25.3 ± 0.5 GHz; all others must be constrained through external priors. Future works will be aimed at integrating many more data sets into this analysis, both map and time-ordered based, thereby gradually eliminating the currently observed degeneracies in a controlled manner with respect to both instrumental systematic effects and astrophysical degeneracies. When this happens, the simple LFI-oriented data model employed in the current work will need to be generalized to account for both a richer astrophysical model and additional instrumental effects. This work will be organized within the Open Science-based C
OSMOGLOBE
community effort.
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.
BEYONDPLANCK Basyrov, A.; Suur-Uski, A.-S.; Colombo, L. P. L. ...
Astronomy and astrophysics (Berlin),
06/2023, Letnik:
675
Journal Article
Recenzirano
Odprti dostop
We present
Planck
Low Frequency Instrument (LFI) frequency sky maps derived within the B
EYOND
P
LANCK
framework. This framework draws samples from a global posterior distribution that includes ...instrumental, astrophysical, and cosmological parameters, and the main product is an entire ensemble of frequency sky map samples, each of which corresponds to one possible realization of the various modeled instrumental systematic corrections, including correlated noise, time-variable gain, as well as far sidelobe and bandpass corrections. This ensemble allows for computationally convenient end-to-end propagation of low-level instrumental uncertainties into higher-level science products, including astrophysical component maps, angular power spectra, and cosmological parameters. We show that the two dominant sources of LFI instrumental systematic uncertainties are correlated noise and gain fluctuations, and the products presented here support – for the first time – full Bayesian error propagation for these effects at full angular resolution. We compared our posterior mean maps with traditional frequency maps delivered by the Planck Collaboration, and find generally good agreement. The most important quality improvement is due to significantly lower calibration uncertainties in the new processing, as we find a fractional absolute calibration uncertainty at 70 GHz of Δ
g
0
/
g
0
= 5 × 10
−5
, which is nominally 40 times smaller than that reported by
Planck
2018. However, we also note that the original
Planck
2018 estimate has a nontrivial statistical interpretation, and this further illustrates the advantage of the new framework in terms of producing self-consistent and well-defined error estimates of all involved quantities without the need of ad hoc uncertainty contributions. We describe how low-resolution data products, including dense pixel-pixel covariance matrices, may be produced from the posterior samples directly, without the need for computationally expensive analytic calculations or simulations. We conclude that posterior-based frequency map sampling provides unique capabilities in terms of low-level systematics modeling and error propagation, and may play an important role for future Cosmic Microwave Background (CMB)
B
-mode experiments aiming at nanokelvin precision.
BEYONDPLANCK Paradiso, S.; Colombo, L. P. L.; Andersen, K. J. ...
Astronomy and astrophysics (Berlin),
06/2023, Letnik:
675
Journal Article
Recenzirano
Odprti dostop
We present cosmological parameter constraints estimated using the Bayesian B
EYOND
P
LANCK
analysis framework. This method supports seamless end-to-end error propagation from raw time-ordered data ...onto final cosmological parameters. As a first demonstration of the method, we analyzed time-ordered
Planck
LFI observations, combined with selected external data (WMAP 33–61 GHz,
Planck
HFI DR4 353 and 857 GHz, and Haslam 408 MHz) in the form of pixelized maps that are used to break critical astrophysical degeneracies. Overall, all the results are generally in good agreement with previously reported values from
Planck
2018 and WMAP, with the largest relative difference for any parameter amounting about 1
σ
when considering only temperature multipoles between 30 ≤
ℓ
≤ 600. In cases where there are differences, we note that the B
EYOND
P
LANCK
results are generally slightly closer to the high-
ℓ
HFI-dominated
Planck
2018 results than previous analyses, suggesting slightly less tension between low and high multipoles. Using low-
ℓ
polarization information from LFI and WMAP, we find a best-fit value of
τ
= 0.066 ± 0.013, which is higher than the low value of
τ
= 0.052 ± 0.008 derived from
Planck
2018 and slightly lower than the value of 0.069 ± 0.011 derived from the joint analysis of official LFI and WMAP products. Most importantly, however, we find that the uncertainty derived in the B
EYOND
P
LANCK
processing is about 30 % greater than when analyzing the official products, after taking into account the different sky coverage. We argue that this uncertainty is due to a marginalization over a more complete model of instrumental and astrophysical parameters, which results in more reliable and more rigorously defined uncertainties. We find that about 2000 Monte Carlo samples are required to achieve a robust convergence for a low-resolution cosmic microwave background (CMB) covariance matrix with 225 independent modes, and producing these samples takes about eight weeks on a modest computing cluster with 256 cores.
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 Andersen, K. J.; Aurlien, R.; Banerji, R. ...
Astronomy and astrophysics (Berlin),
06/2023, Letnik:
675
Journal Article
Recenzirano
Odprti dostop
We describe the B
EYOND
P
LANCK
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
χ
2
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 C
OSMOGLOBE
effort, which aims to combine state-of-the-art radio, microwave, and submillimeter data sets into one global astrophysical model.
BEYONDPLANCK Galloway, M.; Reinecke, M.; Andersen, K. J. ...
Astronomy and astrophysics (Berlin),
06/2023, Letnik:
675
Journal Article
Recenzirano
Odprti dostop
We introduce a new formulation of the
Conviqt
convolution algorithm in terms of spin harmonics, and apply this to the problem of sidelobe correction for B
EYOND
P
LANCK
, the first end-to-end ...Bayesian Gibbs sampling framework for CMB analysis. We compare our implementation to the previous
Planck
LevelS implementation, and find good agreement between the two codes in terms of accuracy, but with a speed-up reaching a factor of 3–10, depending on the frequency bandlimits,
l
max
and
m
max
. The new algorithm is significantly simpler to implement and maintain, since all low-level calculations are handled through an external spherical harmonic transform library. We find that our mean sidelobe estimates for
Planck
LFI are in good agreement with previous efforts. Additionally, we present novel sidelobe rms maps that quantify the uncertainty in the sidelobe corrections due to variations in the sky model.
BEYONDPLANCK Ihle, H. T.; Bersanelli, M.; Franceschet, C. ...
Astronomy and astrophysics (Berlin),
06/2023, Letnik:
675
Journal Article
Recenzirano
Odprti dostop
We present a Bayesian method for estimating instrumental noise parameters and propagating noise uncertainties within the global B
EYOND
P
LANCK
Gibbs sampling framework, which we applied to
Planck
...Low Frequency Instrument (LFI) time-ordered data. Following previous works in the literature, we initially adopted a 1/
f
model for the noise power spectral density (PSD), but we found the need for an additional lognormal component in the noise model in the 30 and 44 GHz bands. We implemented an optimal Wiener-filter (or constrained realization) gap-filling procedure to account for masked data. We then used this procedure to both estimate the gapless correlated noise in the time-domain,
n
corr
, and to sample the noise PSD parameters,
ξ
n
= {
σ
0
,
f
knee
,
α
,
A
p
}. In contrast to previous
Planck
analyses, we assumed piecewise stationary noise only within each pointing period (PID), and not throughout the full mission, but we adopted the LFI Data Processing Center results as priors on
α
and
f
knee
. We generally found best-fit correlated noise parameters that are mostly consistent with previous results, with a few notable exceptions. However, a detailed inspection of the time-dependent results has revealed many important findings. First and foremost, we find strong evidence for statistically significant temporal variations in all noise PSD parameters, many of which are directly correlated with satellite housekeeping data. Second, while the simple 1/
f
model appears to be an excellent fit for the LFI 70 GHz channel, there is evidence for additional correlated noise that is not described by a 1/
f
model in the 30 and 44 GHz channels, including within the primary science frequency range of 0.1–1 Hz. In general, most 30 and 44 GHz channels exhibit deviations from 1/
f
at the 2–3
σ
level in each one-hour pointing period, motivating the addition of the lognormal noise component for these bands. For certain periods of time, we also find evidence of strong common mode noise fluctuations across the entire focal plane. Overall, we conclude that a simple 1/
f
profile is not adequate for obtaining a full characterization of the
Planck
LFI noise, even when fitted hour-by-hour, and a more general model is required. These findings have important implications for large-scale CMB polarization reconstruction with the
Planck
LFI data and the current work is a first attempt at understanding and mitigating these issues.
