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Title: Making maps of cosmic microwave background polarization for B-mode studies: the POLARBEAR example

Abstract

Analysis of cosmic microwave background (CMB) datasets typically requires some filtering of the raw time-ordered data. For instance, in the context of ground-based observations, filtering is frequently used to minimize the impact of low frequency noise, atmospheric contributions and/or scan synchronous signals on the resulting maps. In this paper, we have explicitly constructed a general filtering operator, which can unambiguously remove any set of unwanted modes in the data, and then amend the map-making procedure in order to incorporate and correct for it. We show that such an approach is mathematically equivalent to the solution of a problem in which the sky signal and unwanted modes are estimated simultaneously and the latter are marginalized over. We investigated the conditions under which this amended map-making procedure can render an unbiased estimate of the sky signal in realistic circumstances. We then discuss the potential implications of these observations on the choice of map-making and power spectrum estimation approaches in the context of B-mode polarization studies. Specifically, we have studied the effects of time-domain filtering on the noise correlation structure in the map domain, as well as impact it may haveon the performance of the popular pseudo-spectrum estimators. We conclude that although mapsmore » produced by the proposed estimators arguably provide the most faithful representation of the sky possible given the data, they may not straightforwardly lead to the best constraints on the power spectra of the underlying sky signal and special care may need to be taken to ensure this is the case. By contrast, simplified map-makers which do not explicitly correct for time-domain filtering, but leave it to subsequent steps in the data analysis, may perform equally well and be easier and faster to implement. We focused on polarization-sensitive measurements targeting the B-mode component of the CMB signal and apply the proposed methods to realistic simulations based on characteristics of an actual CMB polarization experiment, POLARBEAR. Finally, our analysis and conclusions are however more generally applicable.« less

Authors:
 [1];  [2];  [1];  [3];  [4];  [2];  [5];  [5];  [6];  [7];  [8];  [5];  [9];  [10];  [11];  [9];  [5];  [5];  [12];  [13] more »;  [14];  [5];  [10];  [15];  [9];  [5];  [16];  [10];  [6];  [6];  [17];  [18];  [10];  [5];  [10];  [10];  [10];  [10];  [2];  [19];  [7];  [10];  [10];  [20];  [1];  [5];  [21];  [10];  [5] « less
  1. Univ. of Paris Diderot, Paris (France)
  2. International School for Advanced Studies (SISSA), Trieste (Italy); National Inst. of Nuclear Physics (INFN), Trieste (Italy)
  3. Univ. of Sussex, Brighton (United Kingdom)
  4. Univ. of Wisconsin, Madison, WI (United States)
  5. Univ. of California, Berkeley, CA (United States)
  6. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)
  7. Dalhousie Univ., Halifax (Canada)
  8. Univ. of California, Berkeley, CA (United States); Univ. of Tokyo, Chiba (Japan)
  9. Imperial College, London (United Kingdom)
  10. Univ. of California, San Diego, CA (United States)
  11. Sorbone Univ. and Univ. of Paris, Paris (France)
  12. Harvard-Smithsonian Center for Astrophysics, Cambridge, MA (United States)
  13. High Energy Accelerator Research Organization (KEK), Tsukuba (Japan); Graduate University for Advanced Studies (SOKENDAI), Kanagawa (Japan)
  14. High Energy Accelerator Research Organization (KEK), Tsukuba (Japan); Graduate University for Advanced Studies (SOKENDAI), Kanagawa (Japan); Univ. of Tokyo (Japan)
  15. Academia Sinica, Taipei (Taiwan); High Energy Accelerator Research Organization (KEK), Tsukuba (Japan)
  16. Univ. of Tokyo (Japan)
  17. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  18. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  19. Univ. of Melbourne (Australia)
  20. California Inst. of Technology (CalTech), Pasadena, CA (United States)
  21. High Energy Accelerator Research Organization (KEK), Tsukuba (Japan)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1393212
Grant/Contract Number:
AC02-05CH11231
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Astronomy and Astrophysics
Additional Journal Information:
Journal Volume: 600; Journal ID: ISSN 0004-6361
Publisher:
EDP Sciences
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; cosmic background radiation; cosmology observations

Citation Formats

Poletti, Davide, Fabbian, Giulio, Le Jeune, Maude, Peloton, Julien, Arnold, Kam, Baccigalupi, Carlo, Barron, Darcy, Beckman, Shawn, Borrill, Julian, Chapman, Scott, Chinone, Yuji, Cukierman, Ari, Ducout, Anne, Elleflot, Tucker, Errard, Josquin, Feeney, Stephen, Goeckner-Wald, Neil, Groh, John, Hall, Grantland, Hasegawa, Masaya, Hazumi, Masashi, Hill, Charles, Howe, Logan, Inoue, Yuki, Jaffe, Andrew H., Jeong, Oliver, Katayama, Nobuhiko, Keating, Brian, Keskitalo, Reijo, Kisner, Theodore, Kusaka, Akito, Lee, Adrian T., Leon, David, Linder, Eric, Lowry, Lindsay, Matsuda, Frederick, Navaroli, Martin, Paar, Hans, Puglisi, Giuseppe, Reichardt, Christian L., Ross, Colin, Siritanasak, Praween, Stebor, Nathan, Steinbach, Bryan, Stompor, Radek, Suzuki, Aritoki, Tajima, Osamu, Teply, Grant, and Whitehorn, Nathan. Making maps of cosmic microwave background polarization for B-mode studies: the POLARBEAR example. United States: N. p., 2017. Web. doi:10.1051/0004-6361/201629467.
Poletti, Davide, Fabbian, Giulio, Le Jeune, Maude, Peloton, Julien, Arnold, Kam, Baccigalupi, Carlo, Barron, Darcy, Beckman, Shawn, Borrill, Julian, Chapman, Scott, Chinone, Yuji, Cukierman, Ari, Ducout, Anne, Elleflot, Tucker, Errard, Josquin, Feeney, Stephen, Goeckner-Wald, Neil, Groh, John, Hall, Grantland, Hasegawa, Masaya, Hazumi, Masashi, Hill, Charles, Howe, Logan, Inoue, Yuki, Jaffe, Andrew H., Jeong, Oliver, Katayama, Nobuhiko, Keating, Brian, Keskitalo, Reijo, Kisner, Theodore, Kusaka, Akito, Lee, Adrian T., Leon, David, Linder, Eric, Lowry, Lindsay, Matsuda, Frederick, Navaroli, Martin, Paar, Hans, Puglisi, Giuseppe, Reichardt, Christian L., Ross, Colin, Siritanasak, Praween, Stebor, Nathan, Steinbach, Bryan, Stompor, Radek, Suzuki, Aritoki, Tajima, Osamu, Teply, Grant, & Whitehorn, Nathan. Making maps of cosmic microwave background polarization for B-mode studies: the POLARBEAR example. United States. doi:10.1051/0004-6361/201629467.
Poletti, Davide, Fabbian, Giulio, Le Jeune, Maude, Peloton, Julien, Arnold, Kam, Baccigalupi, Carlo, Barron, Darcy, Beckman, Shawn, Borrill, Julian, Chapman, Scott, Chinone, Yuji, Cukierman, Ari, Ducout, Anne, Elleflot, Tucker, Errard, Josquin, Feeney, Stephen, Goeckner-Wald, Neil, Groh, John, Hall, Grantland, Hasegawa, Masaya, Hazumi, Masashi, Hill, Charles, Howe, Logan, Inoue, Yuki, Jaffe, Andrew H., Jeong, Oliver, Katayama, Nobuhiko, Keating, Brian, Keskitalo, Reijo, Kisner, Theodore, Kusaka, Akito, Lee, Adrian T., Leon, David, Linder, Eric, Lowry, Lindsay, Matsuda, Frederick, Navaroli, Martin, Paar, Hans, Puglisi, Giuseppe, Reichardt, Christian L., Ross, Colin, Siritanasak, Praween, Stebor, Nathan, Steinbach, Bryan, Stompor, Radek, Suzuki, Aritoki, Tajima, Osamu, Teply, Grant, and Whitehorn, Nathan. Thu . "Making maps of cosmic microwave background polarization for B-mode studies: the POLARBEAR example". United States. doi:10.1051/0004-6361/201629467. https://www.osti.gov/servlets/purl/1393212.
@article{osti_1393212,
title = {Making maps of cosmic microwave background polarization for B-mode studies: the POLARBEAR example},
author = {Poletti, Davide and Fabbian, Giulio and Le Jeune, Maude and Peloton, Julien and Arnold, Kam and Baccigalupi, Carlo and Barron, Darcy and Beckman, Shawn and Borrill, Julian and Chapman, Scott and Chinone, Yuji and Cukierman, Ari and Ducout, Anne and Elleflot, Tucker and Errard, Josquin and Feeney, Stephen and Goeckner-Wald, Neil and Groh, John and Hall, Grantland and Hasegawa, Masaya and Hazumi, Masashi and Hill, Charles and Howe, Logan and Inoue, Yuki and Jaffe, Andrew H. and Jeong, Oliver and Katayama, Nobuhiko and Keating, Brian and Keskitalo, Reijo and Kisner, Theodore and Kusaka, Akito and Lee, Adrian T. and Leon, David and Linder, Eric and Lowry, Lindsay and Matsuda, Frederick and Navaroli, Martin and Paar, Hans and Puglisi, Giuseppe and Reichardt, Christian L. and Ross, Colin and Siritanasak, Praween and Stebor, Nathan and Steinbach, Bryan and Stompor, Radek and Suzuki, Aritoki and Tajima, Osamu and Teply, Grant and Whitehorn, Nathan},
abstractNote = {Analysis of cosmic microwave background (CMB) datasets typically requires some filtering of the raw time-ordered data. For instance, in the context of ground-based observations, filtering is frequently used to minimize the impact of low frequency noise, atmospheric contributions and/or scan synchronous signals on the resulting maps. In this paper, we have explicitly constructed a general filtering operator, which can unambiguously remove any set of unwanted modes in the data, and then amend the map-making procedure in order to incorporate and correct for it. We show that such an approach is mathematically equivalent to the solution of a problem in which the sky signal and unwanted modes are estimated simultaneously and the latter are marginalized over. We investigated the conditions under which this amended map-making procedure can render an unbiased estimate of the sky signal in realistic circumstances. We then discuss the potential implications of these observations on the choice of map-making and power spectrum estimation approaches in the context of B-mode polarization studies. Specifically, we have studied the effects of time-domain filtering on the noise correlation structure in the map domain, as well as impact it may haveon the performance of the popular pseudo-spectrum estimators. We conclude that although maps produced by the proposed estimators arguably provide the most faithful representation of the sky possible given the data, they may not straightforwardly lead to the best constraints on the power spectra of the underlying sky signal and special care may need to be taken to ensure this is the case. By contrast, simplified map-makers which do not explicitly correct for time-domain filtering, but leave it to subsequent steps in the data analysis, may perform equally well and be easier and faster to implement. We focused on polarization-sensitive measurements targeting the B-mode component of the CMB signal and apply the proposed methods to realistic simulations based on characteristics of an actual CMB polarization experiment, POLARBEAR. Finally, our analysis and conclusions are however more generally applicable.},
doi = {10.1051/0004-6361/201629467},
journal = {Astronomy and Astrophysics},
number = ,
volume = 600,
place = {United States},
year = {Thu Mar 30 00:00:00 EDT 2017},
month = {Thu Mar 30 00:00:00 EDT 2017}
}

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  • We report a measurement of the B-mode polarization power spectrum in the cosmic microwave background (CMB) using the POLARBEAR experiment in Chile. The faint B-mode polarization signature carries information about the universe's entire history of gravitational structure formation, and the cosmic inflation that may have occurred in the very early universe. Our measurement covers the angular multipole range 500 < ℓ < 2100 and is based on observations of an effective sky area of 25 deg{sup 2} with 3.'5 resolution at 150 GHz. On these angular scales, gravitational lensing of the CMB by intervening structure in the universe is expectedmore » to be the dominant source of B-mode polarization. Including both systematic and statistical uncertainties, the hypothesis of no B-mode polarization power from gravitational lensing is rejected at 97.2% confidence. The band powers are consistent with the standard cosmological model. Fitting a single lensing amplitude parameter A{sub BB} to the measured band powers, A{sub BB}=1.12±0.61(stat){sub −0.12}{sup +0.04}(sys)±0.07(multi), where A{sub BB} = 1 is the fiducial WMAP-9 ΛCDM value. In this expression, 'stat' refers to the statistical uncertainty, 'sys' to the systematic uncertainty associated with possible biases from the instrument and astrophysical foregrounds, and 'multi' to the calibration uncertainties that have a multiplicative effect on the measured amplitude A{sub BB}.« less
  • SPTpol, POLARBEAR, and BICEP2 have recently measured the cosmic microwave background (CMB) B-mode polarization in various sky regions of several tens of square degrees and obtained BB power spectra in the multipole range 20-3000, detecting the components due to gravitational lensing and to inflationary gravitational waves. We analyze jointly the results of these three experiments and propose modifications to their analyses of the spectra to include in the model, in addition to the gravitational lensing and the inflationary gravitational wave components, and also the effects induced by the cosmic polarization rotation (CPR), if it exists within current upper limits. Althoughmore » in principle our analysis would also lead to new constraints on CPR, in practice these can only be given on its fluctuations (δα{sup 2}), since constraints on its mean angle are inhibited by the derotation which is applied by current CMB polarization experiments, in order to cope with the insufficient calibration of the polarization angle. The combined data fits from all three experiments (with 29% CPR-SPTpol correlation, depending on the theoretical model) gives the constraint (δα{sup 2}){sup 1/2} < 27.3 mrad (1.°56), with r = 0.194 ± 0.033. These results show that the present data are consistent with no CPR detection and the constraint on CPR fluctuation is about 1.°5. This method of constraining the CPR is new, is complementary to previous tests, which use the radio and optical/UV polarization of radio galaxies and the CMB E-mode polarization, and adds a new constraint for the sky areas observed by SPTpol, POLARBEAR, and BICEP2.« less
  • We develop an algorithm of separating the E and B modes of the cosmic microwave background (CMB) polarization from the noisy and discretized maps of Stokes parameters Q and U in a finite area. A key step of the algorithm is to take a wavelet-Galerkin discretization of the differential relation between the E, B and Q, U fields. This discretization allows derivative operator to be represented by a matrix, which is exactly diagonal in scale space, and narrowly banded in spatial space. We show that the effect of boundary can be eliminated by dropping a few discrete wavelet transform modes,more » located on or nearby the boundary. This method reveals that the derivative operators will cause large errors in the E and B power spectra on small scales if the Q and U maps contain Gaussian noise. It also reveals that if the Q and U maps are random, these fields lead to the mixing of E and B modes. Consequently, the B mode will be contaminated if the powers of E modes are much larger than that of B modes. Nevertheless, numerical tests show that the power spectra of both E and B on scales larger than the finest scale by a factor of 4 and higher can reasonably be recovered, even when the power ratio of E to B modes is as large as about 10{sup 2}, and the signal-to-noise ratio is equal to 10 and higher. This is because the Galerkin discretization is free of false correlations and keeps the contamination under control. As wavelet variables contain information of both spatial and scale spaces, the developed method is also effective to recover the spatial structures of the E and B mode fields.« less
  • Separation of the B component of a cosmic microwave background (CMB) polarization map from the much larger E component is an essential step in CMB polarimetry. For a map with incomplete sky coverage, this separation is necessarily hampered by the presence of ambiguous modes which could be either E or B modes. I present an efficient pixel-space algorithm for removing the ambiguous modes and separating the map into pure E and B components. The method, which works for arbitrary geometries, does not involve generating a complete basis of such modes and scales the cube of the number of pixels onmore » the boundary of the map.« less
  • We present a measurement of the B-mode polarization power spectrum (the BB spectrum) from 100more » $${\mathrm{deg}}^{2}$$ of sky observed with SPTpol, a polarization-sensitive receiver currently installed on the South Pole Telescope. The observations used in this work were taken during 2012 and early 2013 and include data in spectral bands centered at 95 and 150 GHz. We report the BB spectrum in five bins in multipole space, spanning the range $$300\leqslant {\ell }\leqslant 2300$$, and for three spectral combinations: 95 GHz × 95 GHz, 95 GHz × 150 GHz, and 150 GHz × 150 GHz. We subtract small (<0.5σ in units of statistical uncertainty) biases from these spectra and account for the uncertainty in those biases. The resulting power spectra are inconsistent with zero power but consistent with predictions for the BB spectrum arising from the gravitational lensing of E-mode polarization. If we assume no other source of BB power besides lensed B modes, we determine a preference for lensed B modes of 4.9σ. After marginalizing over tensor power and foregrounds, namely, polarized emission from galactic dust and extragalactic sources, this significance is 4.3σ. Fitting for a single parameter, $${A}_{\mathrm{lens}}$$, that multiplies the predicted lensed B-mode spectrum, and marginalizing over tensor power and foregrounds, we find $${A}_{\mathrm{lens}}=1.08\pm 0.26$$, indicating that our measured spectra are consistent with the signal expected from gravitational lensing. The data presented here provide the best measurement to date of the B-mode power spectrum on these angular scales.« less