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arxiv: 2412.09967 · v3 · submitted 2024-12-13 · 🌌 astro-ph.CO

Reconstructing the Thermal Sunyaev Zeldovich Power Spectrum from Planck using the ABS Method

Zhaoxuan Zhang , Le Zhang , Pengjie Zhang This is my paper

Pith reviewed 2026-05-23 07:38 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords thermal Sunyaev-Zeldovichpower spectrumPlanck PR3component separationABS methodtrispectrumforeground marginalization
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The pith

The ABS method applied to Planck PR3 data yields a tSZ power spectrum amplitude 34% lower than the 2015 best-fit value after including the trispectrum.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops an enhanced version of the Analytical Blind Separation method to reconstruct the thermal Sunyaev-Zeldovich power spectrum from Planck observations. The enhancements include eigenmode exclusion in low signal-to-noise regimes and a shift parameter to stabilize the separation of the weak tSZ signal from foregrounds and noise. Tests on simulated Planck data confirm that the method recovers the input spectrum reliably even in difficult conditions. When applied to the real Planck PR3 full-mission maps, the reconstructed spectrum shows lower power at multipoles above 300 than earlier results from MILCA and NILC cleaning. After marginalizing residual foregrounds and including the trispectrum in the error budget, the overall amplitude is reduced relative to prior best-fit models and templates.

Core claim

In the analysis of the Planck PR3 full-mission data, ABS shows lower amplitudes at ell greater than or equal to 300 compared to the Planck 2015 band powers using the MILCA and NILC foreground cleaning methods. When the trispectrum contribution is included, and after marginalizing over residual foreground components, the overall amplitude of the tSZ power spectrum is 34% lower than the Planck 2015 best-fit amplitude, 24% lower than the Battaglia 2012 model, and 12% lower than the Bolliet 2018 best-fit amplitude, corresponding to 3.0 sigma, 1.78 sigma, and 0.75 sigma respectively. Across all cases, the tSZ band power remains unaffected by template choice.

What carries the argument

The Analytical Blind Separation (ABS) method, modified with eigenmode exclusion for low signal-to-noise regimes and a shift parameter to stabilize calculations, which performs blind separation of the tSZ signal from other sky components.

If this is right

  • The tSZ band powers extracted by ABS remain unchanged regardless of the foreground template chosen.
  • Including or excluding the trispectrum contribution allows direct comparison with earlier studies while testing result robustness.
  • The method recovers the input spectrum accurately in simulations that include realistic noise and foreground levels.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A confirmed lower amplitude would suggest that current hydrodynamic simulations of cluster gas need recalibration to match the observed tSZ signal.
  • The same blind separation approach could be tested on other secondary CMB anisotropies such as the kinetic Sunyaev-Zeldovich effect.
  • Future CMB surveys with higher resolution and sensitivity could perform a direct cross-check of the amplitude reduction at overlapping multipoles.

Load-bearing premise

The ABS method with eigenmode exclusion and the introduced shift parameter recovers the true tSZ signal without systematic bias from residual foregrounds or noise in the real Planck PR3 data.

What would settle it

An independent reconstruction of the tSZ power spectrum from the same Planck PR3 maps using MILCA or NILC that recovers the higher Planck 2015 amplitude would indicate a bias in the ABS result.

read the original abstract

This study employs a novel approach for reconstructing the thermal Sunyaev-Zeldovich (tSZ) effect power spectrum from Planck data using the Analytical Blind Separation (ABS) method. The ABS method improves the recovery of weak signals, by applying eigenmode exclusion for low signal-to-noise ratio regimes and introducing a shift parameter to stabilize calculations. Validation through simulated Planck data demonstrates the robustness of ABS in reconstructing the tSZ power spectrum, even under challenging conditions. In the analysis of the {\it Planck} PR3 full-mission data, ABS shows lower amplitudes at $\ell \gtrsim 300$ compared to the {\it Planck} 2015 band powers using the MILCA and NILC foreground cleaning methods. In our analysis, we include or exclude the trispectrum contribution to the statistical uncertainty to enable comparison with previous studies and to test the robustness of our results. When the trispectrum contribution is included, and after marginalizing over residual foreground components, we find that the overall amplitude of the tSZ power spectrum is 34\% lower than the ``Planck 2015'' best-fit amplitude, 24\% lower than the ``Battaglia 2012'' model, and 12\% lower than the ``Bolliet 2018'' best-fit amplitude. These differences correspond to $3.0\sigma$, $1.78\sigma$, and $0.75\sigma$, respectively, in terms of the associated statistical uncertainties. Across all cases, the tSZ band power remains unaffected by template choice. These findings highlight the potential of the ABS method as a promising alternative for tSZ power spectrum analysis.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper applies the Analytical Blind Separation (ABS) method—with eigenmode exclusion in low S/N regimes and an introduced shift parameter—to reconstruct the tSZ power spectrum from Planck PR3 full-mission maps. Simulated-data tests are used to validate robustness; on real data, after marginalizing residual foreground templates and including (or excluding) the trispectrum in the error budget, the recovered band powers at ℓ ≳ 300 yield an overall amplitude 34% lower than the Planck 2015 best-fit (3.0σ), 24% lower than Battaglia 2012 (1.78σ), and 12% lower than Bolliet 2018 (0.75σ), independent of template choice.

Significance. If the central amplitude result survives improved real-data validation, it would indicate that prior Planck tSZ measurements (MILCA/NILC) were biased high, tightening or shifting constraints on σ8 and intracluster gas physics. The ABS approach itself constitutes a methodological contribution as a blind alternative to component-separation pipelines.

major comments (3)
  1. [Validation on simulated data] Validation section (simulated Planck data): the ensemble of simulations used to demonstrate unbiased recovery does not include quantitative tests for residual foregrounds whose power spectra or spatial statistics differ from the marginalization templates; any such mismatch would propagate directly into the reconstructed C_ℓ at ℓ ≳ 300 and the reported amplitude offsets.
  2. [Real-data results and trispectrum inclusion] Real-data analysis and error modeling: the statistical uncertainties that include the trispectrum (and yield the 3.0σ claim) are constructed after application of the shift parameter, but the paper provides no explicit derivation or test of how the shift modifies the covariance matrix or the effective degrees of freedom, which is load-bearing for the significance of the amplitude differences.
  3. [Foreground marginalization] Foreground marginalization step: the statement that band powers remain unaffected by template choice is presented, yet no completeness test (e.g., injection of additional unmodeled components or null tests on the residual maps) is shown to confirm that the chosen templates span all dominant contaminants in the actual PR3 data.
minor comments (1)
  1. [Abstract and results] The abstract and results text refer to “the overall amplitude” without specifying whether this is a single normalization factor applied to a fixed shape or an integrated quantity; a brief definition would improve clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and valuable suggestions. We address each of the major comments point by point below. We plan to incorporate revisions to strengthen the validation and analysis sections as outlined in our responses.

read point-by-point responses

  1. Referee: [Validation on simulated data] Validation section (simulated Planck data): the ensemble of simulations used to demonstrate unbiased recovery does not include quantitative tests for residual foregrounds whose power spectra or spatial statistics differ from the marginalization templates; any such mismatch would propagate directly into the reconstructed C_ℓ at ℓ ≳ 300 and the reported amplitude offsets.

    Authors: We acknowledge that our current simulation suite primarily uses foreground models aligned with the marginalization templates. To rigorously test robustness against mismatches, we will generate additional simulations incorporating foreground components with varied power spectra and spatial correlations (e.g., modified dust or synchrotron models) and quantify any biases in the recovered tSZ band powers. These results will be included in the revised manuscript. revision: yes

  2. Referee: [Real-data results and trispectrum inclusion] Real-data analysis and error modeling: the statistical uncertainties that include the trispectrum (and yield the 3.0σ claim) are constructed after application of the shift parameter, but the paper provides no explicit derivation or test of how the shift modifies the covariance matrix or the effective degrees of freedom, which is load-bearing for the significance of the amplitude differences.

    Authors: The shift parameter is a regularization technique applied to stabilize the matrix inversion in low S/N regimes. We agree that its impact on the covariance requires explicit treatment. In the revision, we will derive the modified covariance matrix accounting for the shift and perform Monte Carlo tests to assess changes in effective degrees of freedom and the resulting significance levels. This will clarify the robustness of the reported amplitude offsets. revision: yes

  3. Referee: [Foreground marginalization] Foreground marginalization step: the statement that band powers remain unaffected by template choice is presented, yet no completeness test (e.g., injection of additional unmodeled components or null tests on the residual maps) is shown to confirm that the chosen templates span all dominant contaminants in the actual PR3 data.

    Authors: While we demonstrated invariance to the specific templates used, we recognize the value of completeness tests. We will add null tests on residual maps after template subtraction and injection-recovery tests with synthetic unmodeled foregrounds to verify that the templates adequately capture the dominant contaminants. These will be presented in the revised analysis section. revision: yes

Circularity Check

0 steps flagged

No significant circularity; measurement derived from external Planck data

full rationale

The paper applies the ABS method (eigenmode exclusion + shift parameter) to Planck PR3 maps after validation on separate simulated ensembles, then reports direct band-power amplitudes and their offsets from external models (Planck 2015, Battaglia 2012, Bolliet 2018). No equation or step reduces the headline 34% amplitude difference to a fitted parameter by construction, nor does any load-bearing premise collapse to a self-citation whose content is unverified within the paper. The result remains falsifiable against the input maps and independent templates.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract-only review limits visibility into parameters and assumptions; the shift parameter and eigenmode exclusion appear as method-specific choices whose impact on the final amplitude is not quantified here.

free parameters (1)
  • shift parameter
    Introduced to stabilize calculations in low signal-to-noise regimes; value not specified in abstract.
axioms (1)
  • domain assumption Eigenmode exclusion for low signal-to-noise ratio regimes removes noise without biasing the recovered tSZ signal.
    Core step of the ABS method described in the abstract.

pith-pipeline@v0.9.0 · 5831 in / 1362 out tokens · 23837 ms · 2026-05-23T07:38:46.137894+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

56 extracted references · 56 canonical work pages · 42 internal anchors

  1. [1]

    Planck 2015 results. XXII. A map of the thermal Sunyaev-Zeldovich effect

    Planck Collaboration, N. Aghanim, M. Arnaud, M. Ashdown, J. Aumont, C. Baccigalupi et al., Planck 2015 results. XXII. A map of the thermal Sunyaev-Zeldovich effect , Astron. Astrophys. 594 (2016) A22 [ 1502.01596]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  2. [2]

    On the Cluster Physics of Sunyaev-Zel'dovich Surveys I: The Influence of Feedback, Non-thermal Pressure and Cluster Shapes on Y-M Scaling Relations

    N. Battaglia, J.R. Bond, C. Pfrommer and J.L. Sievers, On the Cluster Physics of Sunyaev-Zel’dovich and X-Ray Surveys. I. The Influence of Feedback, Non-thermal Pressure, and Cluster Shapes on Y-M Scaling Relations , Astrophys. J. 758 (2012) 74 [ 1109.3709]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  3. [3]

    Dark Energy from the Thermal Sunyaev Zeldovich Power Spectrum

    B. Bolliet, B. Comis, E. Komatsu and J.F. Mac´ ıas-P´ erez,Dark energy constraints from the thermal Sunyaev-Zeldovich power spectrum , Mon. Not. R. Astron. Soc. 477 (2018) 4957 [1712.00788]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  4. [4]

    Sunyaev and Y.B

    R.A. Sunyaev and Y.B. Zeldovich, The Observations of Relic Radiation as a Test of the Nature of X-Ray Radiation from the Clusters of Galaxies , Comments on Astrophysics and Space Physics 4 (1972) 173

    work page 1972

  5. [5]

    The Sunyaev-Zel'dovich Effect

    M. Birkinshaw, The Sunyaev-Zel’dovich effect , Phys. Rep. 310 (1999) 97 [ astro-ph/9808050]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  6. [6]

    Cosmology with the Sunyaev-Zel'dovich Effect

    J.E. Carlstrom, G.P. Holder and E.D. Reese, Cosmology with the Sunyaev-Zel’dovich Effect , Annu. Rev. Astron. Astrophys. 40 (2002) 643 [ astro-ph/0208192]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  7. [7]

    Bolliet, T

    B. Bolliet, T. Brinckmann, J. Chluba and J. Lesgourgues, Including massive neutrinos in thermal Sunyaev Zeldovich power spectrum and cluster counts analyses , Mon. Not. R. Astron. Soc. 497 (2020) 1332 [ 1906.10359]

    work page arXiv 2020

  8. [8]

    Constraining cosmological parameters using Sunyaev-Zel'dovich cluster surveys

    R.A. Battye and J. Weller, Constraining cosmological parameters using Sunyaev-Zel’dovich cluster surveys, Phys. Rev. D 68 (2003) 083506 [ astro-ph/0305568]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  9. [9]

    Constraints from thermal Sunyaev-Zeldovich cluster counts and power spectrum combined with CMB

    L. Salvati, M. Douspis and N. Aghanim, Constraints from thermal Sunyaev-Zel’dovich cluster counts and power spectrum combined with CMB , Astron. Astrophys. 614 (2018) A13 [1708.00697]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  10. [10]

    Large Scale Pressure Fluctuations and Sunyaev-Zel'dovich Effect

    A. Cooray, Large scale pressure fluctuations and the Sunyaev-Zel’dovich effect , Phys. Rev. D 62 (2000) 103506 [ astro-ph/0005287]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  11. [11]

    The Sunyaev Zel'dovich effect: simulation and observation

    P. Zhang, U.-L. Pen and B. Wang, The Sunyaev-Zeldovich Effect: Simulations and Observations, Astrophys. J. 577 (2002) 555 [ astro-ph/0201375]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  12. [12]

    Halo Substructure And The Power Spectrum

    A.R. Zentner and J.S. Bullock, Halo Substructure and the Power Spectrum , Astrophys. J. 598 (2003) 49 [ astro-ph/0304292]. – 24 –

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  13. [13]

    Uncertainties in the S-Z selected cluster angular power spectrum

    J.D. Cohn and K. Kadota, Uncertainties in the Sunyaev-Zel’dovich-selected Cluster Angular Power Spectrum, Astrophys. J. 632 (2005) 1 [ astro-ph/0409657]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  14. [14]

    L.D. Shaw, O. Zahn, G.P. Holder and O. Dor´ e, Sharpening the Precision of the Sunyaev-Zel’dovich Power Spectrum, Astrophys. J. 702 (2009) 368 [ 0903.5322]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  15. [15]

    L.D. Shaw, D. Nagai, S. Bhattacharya and E.T. Lau, Impact of Cluster Physics on the Sunyaev-Zel’dovich Power Spectrum, Astrophys. J. 725 (2010) 1452 [ 1006.1945]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  16. [16]

    H. Trac, P. Bode and J.P. Ostriker, Templates for the Sunyaev-Zel’dovich Angular Power Spectrum, Astrophys. J. 727 (2011) 94 [ 1006.2828]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  17. [17]

    Cosmological constraints from thermal Sunyaev Zeldovich power spectrum revisited

    B. Horowitz and U. Seljak, Cosmological constraints from thermal Sunyaev-Zeldovich power spectrum revisited, Mon. Not. R. Astron. Soc. 469 (2017) 394 [ 1609.01850]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  18. [18]

    Sunyaev - Zel'dovich fluctuations from spatial correlations between clusters of galaxies

    E. Komatsu and T. Kitayama, Sunyaev-Zeldovich Fluctuations from Spatial Correlations between Clusters of Galaxies , Astrophys. J. Lett. 526 (1999) L1 [ astro-ph/9908087]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  19. [19]

    The Sunyaev-Zel'dovich angular power spectrum as a probe of cosmological parameters

    E. Komatsu and U. Seljak, The Sunyaev-Zel’dovich angular power spectrum as a probe of cosmological parameters, Mon. Not. R. Astron. Soc. 336 (2002) 1256 [ astro-ph/0205468]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  20. [20]

    The thermal Sunyaev Zel'dovich effect power spectrum in light of Planck

    I.G. McCarthy, A.M.C. Le Brun, J. Schaye and G.P. Holder, The thermal Sunyaev-Zel’dovich effect power spectrum in light of Planck , Mon. Not. R. Astron. Soc. 440 (2014) 3645 [1312.5341]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  21. [21]

    The Atacama Cosmology Telescope: Sunyaev-Zel'dovich Selected Galaxy Clusters at 148 GHz from Three Seasons of Data

    M. Hasselfield, M. Hilton, T.A. Marriage, G.E. Addison, L.F. Barrientos, N. Battaglia et al., The Atacama Cosmology Telescope: Sunyaev-Zel’dovich selected galaxy clusters at 148 GHz from three seasons of data , J. Cosmol. Astropart. Phys. 2013 (2013) 008 [ 1301.0816]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  22. [22]

    Galaxy clusters discovered via the Sunyaev-Zel'dovich effect in the first 720 square degrees of the South Pole Telescope survey

    C.L. Reichardt, B. Stalder, L.E. Bleem, T.E. Montroy, K.A. Aird, K. Andersson et al., Galaxy Clusters Discovered via the Sunyaev-Zel’dovich Effect in the First 720 Square Degrees of the South Pole Telescope Survey, Astrophys. J. 763 (2013) 127 [ 1203.5775]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  23. [23]

    Galaxy Clusters Discovered via the Sunyaev-Zel'dovich Effect in the 2500-square-degree SPT-SZ survey

    L.E. Bleem, B. Stalder, T. de Haan, K.A. Aird, S.W. Allen, D.E. Applegate et al., Galaxy Clusters Discovered via the Sunyaev-Zel’dovich Effect in the 2500-Square-Degree SPT-SZ Survey, Astrophys. J. Suppl. Ser. 216 (2015) 27 [ 1409.0850]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  24. [24]

    Planck Collaboration, P.A.R. Ade, N. Aghanim, M. Arnaud, M. Ashdown, J. Aumont et al., Planck 2015 results. XXVII. The second Planck catalogue of Sunyaev-Zeldovich sources , Astron. Astrophys. 594 (2016) A27 [ 1502.01598]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  25. [25]

    Planck Collaboration, P.A.R. Ade, N. Aghanim, C. Armitage-Caplan, M. Arnaud, M. Ashdown et al., Planck 2013 results. XXI. Power spectrum and high-order statistics of the Planck all-sky Compton parameter map, Astron. Astrophys. 571 (2014) A21 [ 1303.5081]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  26. [26]

    Detection of Thermal SZ -- CMB Lensing Cross-Correlation in Planck Nominal Mission Data

    J.C. Hill and D.N. Spergel, Detection of thermal SZ-CMB lensing cross-correlation in Planck nominal mission data , J. Cosmol. Astropart. Phys. 2014 (2014) 030 [ 1312.4525]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  27. [27]

    Planck Collaboration, P.A.R. Ade, N. Aghanim, M. Arnaud, M. Ashdown, J. Aumont et al., Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts , Astron. Astrophys. 594 (2016) A24 [ 1502.01597]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  28. [28]

    Combined analysis of galaxy cluster number count, thermal Sunyaev-Zel'dovich power spectrum, and bispectrum

    G. Hurier and F. Lacasa, Combined analysis of galaxy cluster number count, thermal Sunyaev-Zel’dovich power spectrum, and bispectrum , Astron. Astrophys. 604 (2017) A71 [1701.09067]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  29. [29]

    Cluster Cosmology Constraints from the 2500 deg$^2$ SPT-SZ Survey: Inclusion of Weak Gravitational Lensing Data from Magellan and the Hubble Space Telescope

    S. Bocquet, J.P. Dietrich, T. Schrabback, L.E. Bleem, M. Klein, S.W. Allen et al., Cluster Cosmology Constraints from the 2500 deg 2 SPT-SZ Survey: Inclusion of Weak Gravitational Lensing Data from Magellan and the Hubble Space Telescope , Astrophys. J. 878 (2019) 55 [1812.01679]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  30. [30]

    Ibitoye, W.-M

    A. Ibitoye, W.-M. Dai, Y.-Z. Ma, P. Vielva, D. Tramonte, A. Abebe et al., Cross Correlation – 25 – between the Thermal Sunyaev-Zeldovich Effect and the Integrated Sachs-Wolfe Effect , Astrophys. J. Suppl. Ser. 270 (2024) 16 [ 2310.18478]

    work page arXiv 2024

  31. [31]

    Planck Collaboration, P.A.R. Ade, N. Aghanim, M. Arnaud, M. Ashdown, J. Aumont et al., Planck 2015 results. XIII. Cosmological parameters , Astron. Astrophys. 594 (2016) A13 [1502.01589]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  32. [32]

    Halo mass function: Baryon impact, fitting formulae and implications for cluster cosmology

    S. Bocquet, A. Saro, K. Dolag and J.J. Mohr, Halo mass function: baryon impact, fitting formulae, and implications for cluster cosmology , Mon. Not. R. Astron. Soc. 456 (2016) 2361 [1502.07357]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  33. [33]

    SZ effects in the Magneticum Pathfinder Simulation: Comparison with the Planck, SPT, and ACT results

    K. Dolag, E. Komatsu and R. Sunyaev, SZ effects in the Magneticum Pathfinder simulation: comparison with the Planck, SPT, and ACT results , Mon. Not. R. Astron. Soc. 463 (2016) 1797 [1509.05134]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  34. [34]

    Planck Collaboration, P.A.R. Ade, N. Aghanim, C. Armitage-Caplan, M. Arnaud, M. Ashdown et al., Planck 2013 results. XII. Diffuse component separation , Astron. Astrophys. 571 (2014) A12 [1303.5072]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  35. [35]

    MILCA, a Modified Internal Linear Combination Algorithm to extract astrophysical emissions from multi-frequency sky maps

    G. Hurier, J.F. Mac´ ıas-P´ erez and S. Hildebrandt,MILCA, a modified internal linear combination algorithm to extract astrophysical emissions from multifrequency sky maps , Astron. Astrophys. 558 (2013) A118 [ 1007.1149]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  36. [36]

    CMB and SZ effect separation with Constrained Internal Linear Combinations

    M. Remazeilles, J. Delabrouille and J.-F. Cardoso, CMB and SZ effect separation with constrained Internal Linear Combinations, Mon. Not. R. Astron. Soc. 410 (2011) 2481 [1006.5599]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  37. [37]

    Tanimura, M

    H. Tanimura, M. Douspis, N. Aghanim and L. Salvati, Constraining cosmology with a new all-sky Compton parameter map from the Planck PR4 data , Mon. Not. R. Astron. Soc. 509 (2022) 300 [ 2110.08880]

    work page arXiv 2022

  38. [38]

    Akrami, K.J

    Planck Collaboration, Y. Akrami, K.J. Andersen, M. Ashdown, C. Baccigalupi, M. Ballardini et al., Planck intermediate results. LVII. Joint Planck LFI and HFI data processing , Astron. Astrophys. 643 (2020) A42 [ 2007.04997]

    work page arXiv 2020

  39. [39]

    Chandran, M

    J. Chandran, M. Remazeilles and R.B. Barreiro, An improved Compton parameter map of thermal Sunyaev-Zeldovich effect from Planck PR4 data , Mon. Not. R. Astron. Soc. 526 (2023) 5682 [2305.10193]

    work page arXiv 2023

  40. [40]

    McCarthy and J.C

    F. McCarthy and J.C. Hill, Component-separated, CIB-cleaned thermal Sunyaev-Zel’dovich maps from Planck PR4 data with a flexible public needlet ILC pipeline , Phys. Rev. D 109 (2024) 023528 [ 2307.01043]

    work page arXiv 2024

  41. [41]

    Zhang, J

    P. Zhang, J. Zhang and L. Zhang, ABS: an analytical method of blind separation of CMB from foregrounds, Monthly Notices of the Royal Astronomical Society 484 (2019) 1616 [https://academic.oup.com/mnras/article-pdf/484/2/1616/27583099/stz091.pdf]

    work page 2019

  42. [42]

    J. Yao, L. Zhang, Y. Zhao, P. Zhang, L. Santos and J. Zhang, Testing the ABS Method with the Simulated Planck Temperature Maps, Astrophys. J. Suppl. Ser. 239 (2018) 36 [ 1807.07016]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  43. [43]

    Santos, J

    L. Santos, J. Yao, L. Zhang, S. Ghosh, P. Zhang, W. Zhao et al., Testing the analytical blind separation method in simulated CMB polarization maps , Astron. Astrophys. 650 (2021) A65

    work page 2021

  44. [44]

    Ghosh, Y

    S. Ghosh, Y. Liu, L. Zhang, S. Li, J. Zhang, J. Wang et al., Performance forecasts for the primordial gravitational wave detection pipelines for AliCPT-1 , J. Cosmol. Astropart. Phys. 2022 (2022) 063 [ 2205.14804]

    work page arXiv 2022

  45. [45]

    Zhang, S

    J. Zhang, S. Ghosh, J. Dou, Y. Liu, S. Li, J. Chen et al., Forecast of foreground cleaning strategies for AliCPT-1, arXiv e-prints (2024) arXiv:2402.01233 [ 2402.01233]

    work page arXiv 2024

  46. [46]

    High significance detection of the tSZ effect relativistic corrections

    G. Hurier, High significance detection of the tSZ effect relativistic corrections , Astron. Astrophys. 596 (2016) A61 [ 1701.09020]. – 26 –

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  47. [47]

    Can we neglect relativistic temperature corrections in the Planck thermal SZ analysis?

    M. Remazeilles, B. Bolliet, A. Rotti and J. Chluba, Can we neglect relativistic temperature corrections in the Planck thermal SZ analysis? , Mon. Not. R. Astron. Soc. 483 (2019) 3459 [1809.09666]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  48. [48]

    Acharya and J

    S.K. Acharya and J. Chluba, Importance of intracluster scattering and relativistic corrections from tSZ effect with cosmic infrared background , Mon. Not. R. Astron. Soc. 519 (2023) 2138 [2205.00857]

    work page arXiv 2023

  49. [49]

    A unified pseudo-$C_\ell$ framework

    D. Alonso, J. Sanchez, A. Slosar and LSST Dark Energy Science Collaboration, A unified pseudo-Cℓ framework, Mon. Not. R. Astron. Soc. 484 (2019) 4127 [ 1809.09603]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  50. [50]

    Thorne, J

    B. Thorne, J. Dunkley, D. Alonso and S. Næss, The Python Sky Model: software for simulating the Galactic microwave sky , Monthly Notices of the Royal Astronomical Society 469 (2017) 2821–2833

    work page 2017

  51. [51]

    Zonca, B

    A. Zonca, B. Thorne, N. Krachmalnicoff and J. Borrill, The Python Sky Model 3 software , Journal of Open Source Software 6 (2021) 3783

    work page 2021

  52. [52]

    The pre-launch Planck Sky Model: a model of sky emission at submillimetre to centimetre wavelengths

    J. Delabrouille, M. Betoule, J.B. Melin, M.A. Miville-Deschˆ enes, J. Gonzalez-Nuevo, M. Le Jeune et al., The pre-launch Planck Sky Model: a model of sky emission at submillimetre to centimetre wavelengths, Astron. Astrophys. 553 (2013) A96 [ 1207.3675]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  53. [53]

    Planck 2015 results. VII. HFI TOI and beam processing

    Planck Collaboration, R. Adam, P.A.R. Ade, N. Aghanim, M. Arnaud, M. Ashdown et al., Planck 2015 results. VII. High Frequency Instrument data processing: Time-ordered information and beams, Astron. Astrophys. 594 (2016) A7 [ 1502.01586]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  54. [54]

    Planck Collaboration, P.A.R. Ade, N. Aghanim, C. Armitage-Caplan, M. Arnaud, M. Ashdown et al., Planck 2013 results. IX. HFI spectral response , Astron. Astrophys. 571 (2014) A9 [1303.5070]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  55. [55]

    HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere

    K.M. G´ orski, E. Hivon, A.J. Banday, B.D. Wandelt, F.K. Hansen, M. Reinecke et al., HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere , Astrophys. J. 622 (2005) 759 [ astro-ph/0409513]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  56. [56]

    emcee: The MCMC Hammer

    D. Foreman-Mackey, D.W. Hogg, D. Lang and J. Goodman, emcee: The MCMC Hammer , Publ. Astron. Soc. Pac. 125 (2013) 306 [ 1202.3665]. – 27 –

    work page internal anchor Pith review Pith/arXiv arXiv 2013