The two-point correlation function of the galaxy distribution is a key cosmological observable that allows us to constrain the dynamical and geometrical state of our Universe. To measure the ...correlation function we need to know both the galaxy positions and the expected galaxy density field. The expected field is commonly specified using a Monte-Carlo sampling of the volume covered by the survey and, to minimize additional sampling errors, this random catalog has to be much larger than the data catalog. Correlation function estimators compare data–data pair counts to data–random and random–random pair counts, where random–random pairs usually dominate the computational cost. Future redshift surveys will deliver spectroscopic catalogs of tens of millions of galaxies. Given the large number of random objects required to guarantee sub-percent accuracy, it is of paramount importance to improve the efficiency of the algorithm without degrading its precision. We show both analytically and numerically that splitting the random catalog into a number of subcatalogs of the same size as the data catalog when calculating random–random pairs and excluding pairs across different subcatalogs provides the optimal error at fixed computational cost. For a random catalog fifty times larger than the data catalog, this reduces the computation time by a factor of more than ten without affecting estimator variance or bias.
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 Brilenkov, M.; Fornazier, K. S. F.; Hergt, L. T. ...
Astronomy and astrophysics (Berlin),
07/2023, Letnik:
675
Journal Article
Recenzirano
Odprti dostop
End-to-end simulations play a key role in the analysis of any high-sensitivity cosmic microwave background (CMB) experiment, providing high-fidelity systematic error propagation capabilities that are ...unmatched by any other means. In this paper, we address an important issue regarding such simulations, namely, how to define the inputs in terms of sky model and instrument parameters. These may either be taken as a constrained realization derived from the data or as a random realization independent from the data. We refer to these as posterior and prior simulations, respectively. We show that the two options lead to significantly different correlation structures, as prior simulations (contrary to posterior simulations) effectively include cosmic variance, but they exclude realization-specific correlations from non-linear degeneracies. Consequently, they quantify fundamentally different types of uncertainties. We argue that as a result, they also have different and complementary scientific uses, even if this dichotomy is not absolute. In particular, posterior simulations are in general more convenient for parameter estimation studies, while prior simulations are generally more convenient for model testing. Before B
EYOND
P
LANCK
, most pipelines used a mix of constrained and random inputs and applied the same hybrid simulations for all applications, even though the statistical justification for this is not always evident. B
EYOND
P
LANCK
represents the first end-to-end CMB simulation framework that is able to generate both types of simulations and these new capabilities have brought this topic to the forefront. The B
EYOND
P
LANCK
posterior simulations and their uses are described extensively in a suite of companion papers. In this work, we consider one important applications of the corresponding prior simulations, namely, code validation. Specifically, we generated a set of one-year LFI 30 GHz prior simulations with known inputs and we used these to validate the core low-level B
EYOND
P
LANCK
algorithms dealing with gain estimation, correlated noise estimation, and mapmaking.
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.
The BeyondPlanck and Cosmoglobe collaborations have implemented the first integrated Bayesian end-to-end analysis pipeline for CMB experiments. The primary long-term motivation for this work is to ...develop a common analysis platform that supports efficient global joint analysis of complementary radio, microwave, and sub-millimeter experiments. A strict prerequisite for this to succeed is broad participation from the CMB community, and two foundational aspects of the program are therefore reproducibility and Open Science. In this paper, we discuss our efforts toward this aim. We also discuss measures toward facilitating easy code and data distribution, community-based code documentation, user-friendly compilation procedures, etc. This work represents the first publicly released end-to-end CMB analysis pipeline that includes raw data, source code, parameter files, and documentation. We argue that such a complete pipeline release should be a requirement for all major future and publicly-funded CMB experiments, noting that a full public release significantly increases data longevity by ensuring that the data quality can be improved whenever better processing techniques, complementary datasets, or more computing power become available, and thereby also taxpayers’ value for money; providing only raw data and final products is not sufficient to guarantee full reproducibility in the future.
Planck 2018 results Aghanim, N.; Akrami, Y.; Aumont, J. ...
Astronomy and astrophysics (Berlin),
09/2020, Letnik:
641
Journal Article
Recenzirano
Odprti dostop
We present measurements of the cosmic microwave background (CMB) lensing potential using the final
Planck
2018 temperature and polarization data. Using polarization maps filtered to account for the ...noise anisotropy, we increase the significance of the detection of lensing in the polarization maps from 5
σ
to 9
σ
. Combined with temperature, lensing is detected at 40
σ
. We present an extensive set of tests of the robustness of the lensing-potential power spectrum, and construct a minimum-variance estimator likelihood over lensing multipoles 8 ≤
L
≤ 400 (extending the range to lower
L
compared to 2015), which we use to constrain cosmological parameters. We find good consistency between lensing constraints and the results from the
Planck
CMB power spectra within the ΛCDM model. Combined with baryon density and other weak priors, the lensing analysis alone constrains
σ
8
Ω
m
0.25
= 0.589 ± 0.020 (1
σ
errors). Also combining with baryon acoustic oscillation data, we find tight individual parameter constraints,
σ
8
= 0.811 ± 0.019,
H
0
= 67.9
−1.3
+1.2
km s
−1
Mpc
−1
, and Ω
m
= 0.303
−0.018
+0.016
. Combining with
Planck
CMB power spectrum data, we measure
σ
8
to better than 1% precision, finding
σ
8
= 0.811 ± 0.006. CMB lensing reconstruction data are complementary to galaxy lensing data at lower redshift, having a different degeneracy direction in
σ
8
− Ω
m
space; we find consistency with the lensing results from the Dark Energy Survey, and give combined lensing-only parameter constraints that are tighter than joint results using galaxy clustering. Using the
Planck
cosmic infrared background (CIB) maps as an additional tracer of high-redshift matter, we make a combined
Planck
-only estimate of the lensing potential over 60% of the sky with considerably more small-scale signal. We additionally demonstrate delensing of the
Planck
power spectra using the joint and individual lensing potential estimates, detecting a maximum removal of 40% of the lensing-induced power in all spectra. The improvement in the sharpening of the acoustic peaks by including both CIB and the quadratic lensing reconstruction is detected at high significance.
Planck 2018 results Aghanim, N.; Akrami, Y.; Aumont, J. ...
Astronomy and astrophysics (Berlin),
09/2020, Letnik:
641
Journal Article
Recenzirano
Odprti dostop
We describe the legacy
Planck
cosmic microwave background (CMB) likelihoods derived from the 2018 data release. The overall approach is similar in spirit to the one retained for the 2013 and 2015 ...data release, with a hybrid method using different approximations at low (
ℓ
< 30) and high (
ℓ
≥ 30) multipoles, implementing several methodological and data-analysis refinements compared to previous releases. With more realistic simulations, and better correction and modelling of systematic effects, we can now make full use of the CMB polarization observed in the High Frequency Instrument (HFI) channels. The low-multipole
EE
cross-spectra from the 100 GHz and 143 GHz data give a constraint on the ΛCDM reionization optical-depth parameter
τ
to better than 15% (in combination with the
TT
low-
ℓ
data and the high-
ℓ
temperature and polarization data), tightening constraints on all parameters with posterior distributions correlated with
τ
. We also update the weaker constraint on
τ
from the joint TEB likelihood using the Low Frequency Instrument (LFI) channels, which was used in 2015 as part of our baseline analysis. At higher multipoles, the CMB temperature spectrum and likelihood are very similar to previous releases. A better model of the temperature-to-polarization leakage and corrections for the effective calibrations of the polarization channels (i.e., the polarization efficiencies) allow us to make full use of polarization spectra, improving the ΛCDM constraints on the parameters
θ
MC
,
ω
c
,
ω
b
, and
H
0
by more than 30%, and n
s
by more than 20% compared to TT-only constraints. Extensive tests on the robustness of the modelling of the polarization data demonstrate good consistency, with some residual modelling uncertainties. At high multipoles, we are now limited mainly by the accuracy of the polarization efficiency modelling. Using our various tests, simulations, and comparison between different high-multipole likelihood implementations, we estimate the consistency of the results to be better than the 0.5
σ
level on the ΛCDM parameters, as well as classical single-parameter extensions for the joint likelihood (to be compared to the 0.3
σ
levels we achieved in 2015 for the temperature data alone on ΛCDM only). Minor curiosities already present in the previous releases remain, such as the differences between the best-fit ΛCDM parameters for the
ℓ
< 800 and
ℓ
> 800 ranges of the power spectrum, or the preference for more smoothing of the power-spectrum peaks than predicted in ΛCDM fits. These are shown to be driven by the temperature power spectrum and are not significantly modified by the inclusion of the polarization data. Overall, the legacy
Planck
CMB likelihoods provide a robust tool for constraining the cosmological model and represent a reference for future CMB observations.
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