C. B. Netterfield

University of Toronto, Toronto, Ontario, Canada

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Publications (264)684.75 Total impact

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    ABSTRACT: We present results from an analysis of all data taken by the BICEP2 and Keck Array cosmic microwave background (CMB) polarization experiments up to and including the 2014 observing season. This includes the first Keck Array observations at 95 GHz. The maps reach a depth of 50 nK deg in Stokes Q and U in the 150 GHz band and 127 nK deg in the 95 GHz band. We take auto- and cross-spectra between these maps and publicly available maps from WMAP and Planck at frequencies from 23 to 353 GHz. An excess over lensed ΛCDM is detected at modest significance in the 95×150 BB spectrum, and is consistent with the dust contribution expected from our previous work. No significant evidence for synchrotron emission is found in spectra such as 23×95, or for correlation between the dust and synchrotron sky patterns in spectra such as 23×353. We take the likelihood of all the spectra for a multicomponent model including lensed ΛCDM, dust, synchrotron, and a possible contribution from inflationary gravitational waves (as parametrized by the tensor-to-scalar ratio r) using priors on the frequency spectral behaviors of dust and synchrotron emission from previous analyses of WMAP and Planck data in other regions of the sky. This analysis yields an upper limit r_{0.05}<0.09 at 95% confidence, which is robust to variations explored in analysis and priors. Combining these B-mode results with the (more model-dependent) constraints from Planck analysis of CMB temperature plus baryon acoustic oscillations and other data yields a combined limit r_{0.05}<0.07 at 95% confidence. These are the strongest constraints to date on inflationary gravitational waves.
    No preview · Article · Jan 2016 · Physical Review Letters
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    ABSTRACT: BICEP3 is a $550~mm$ aperture telescope with cold, on-axis, refractive optics designed to observe at the $95~GHz$ band from the South Pole. It is the newest member of the BICEP/Keck family of inflationary probes specifically designed to measure the polarization of the cosmic microwave background (CMB) at degree-angular scales. BICEP3 is designed to house 1280 dual-polarization pixels, which, when fully-populated, totals to $\sim$9$\times$ the number of pixels in a single Keck $95~GHz$ receiver, thus further advancing the BICEP/Keck program's $95~GHz$ mapping speed. BICEP3 was deployed during the austral summer of 2014-2015 with 9 detector tiles, to be increased to its full capacity of 20 in the second season. After instrument characterization measurements were taken, CMB observation commenced in April 2015. Together with multi-frequency observation data from Planck, BICEP2, and the Keck Array, BICEP3 is projected to set upper limits on the tensor-to-scalar ratio to $r$ $\lesssim 0.03$ at $95\%$ C.L..
    Full-text · Article · Dec 2015 · Journal of Low Temperature Physics
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    ABSTRACT: The lensing-induced $B$-mode signal is a valuable probe of the dark matter distribution integrated back to the last-scattering surface, with a broad kernel that peaks at $z\simeq2$. It also constitutes an important contaminant for the extraction of the primary CMB $B$-modes from inflation. Combining all-sky coverage and high resolution and sensitivity, Planck provides accurate nearly all-sky measurements of both the polarization $E$-mode signal and the integrated mass distribution via the reconstruction of the CMB gravitational lensing. By combining these two data products, we have produced an all-sky template map of the secondary CMB $B$-modes using a real-space algorithm that minimizes the impact of sky masks. The cross-correlation of this template with an observed (primordial and secondary) $B$-mode map can be used to measure the lensing $B$-mode power spectrum at all angular scales. In particular when cross-correlating with the $B$-mode contribution directly derived from the Planck polarization maps, we obtain lensing-induced $B$-mode power spectrum measurements at a significance of $12\,\sigma$, which are in agreement with the theoretical expectation derived from the \Planck\ best-fit $\Lambda$CDM model. This unique nearly all-sky secondary $B$-mode template, which includes the lensing-induced information from intermediate to small ($10\lesssim \ell\lesssim 1000$) angular scales, is delivered as part of the Planck 2015 public data release. It will be particularly useful for experiments searching for primordial $B$-modes, such as BICEP2/Keck Array or LiteBIRD, since it will enable an estimate to be made of the secondary (i.e., lensing) contribution to the measured total CMB $B$-modes.
    Full-text · Article · Dec 2015
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    ABSTRACT: In a companion paper, we have reported a >5σ detection of degree scale B-mode polarization at 150 GHz by the Bicep2 experiment. Here we provide a detailed study of potential instrumental systematic contamination to that measurement. We focus extensively on spurious polarization that can potentially arise from beam imperfections. We present a heuristic classification of beam imperfections according to their symmetries and uniformities, and discuss how resulting contamination adds or cancels in maps that combine observations made at multiple orientations of the telescope about its boresight axis. We introduce a technique, which we call "deprojection," for filtering the leading order beam-induced contamination from time-ordered data, and show that it reduces power in Bicep2's actual and null-test BB spectra consistent with predictions using high signal-to-noise beam shape measurements. We detail the simulation pipeline that we use to directly simulate instrumental systematics and the calibration data used as input to that pipeline. Finally, we present the constraints on BB contamination from individual sources of potential systematics. We find that systematics contribute BB power that is a factor of ∼10× below Bicep2's three-year statistical uncertainty, and negligible compared to the observed BB signal. The contribution to the best-fit tensor/scalar ratio is at a level equivalent to r = (3-6) ×10-3. © 2015. The American Astronomical Society. All rights reserved.
    No preview · Article · Nov 2015 · The Astrophysical Journal
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    ABSTRACT: We present results from an analysis of all data taken by the BICEP2 & Keck Array CMB polarization experiments up to and including that taken during the 2014 observing season. This includes the first Keck Array observations at 95 GHz. The maps reach a depth of 50 nK deg in Stokes $Q$ and $U$ in the 150 GHz band and 127 nK deg in the 95 GHz band. We take auto- and cross-spectra between these maps and publicly available maps from WMAP and Planck at frequencies from 23 GHz to 353 GHz. An excess over lensed-LCDM is detected at modest significance in the 95x150 $BB$ spectrum, and is consistent with the dust contribution expected from our previous work. No significant evidence for synchrotron emission is found in spectra such as 23x95, or for dust/sync correlation in spectra such as 23x353. We take the likelihood of all the spectra for a multi-component model including lensed-LCDM, dust, synchrotron and a possible contribution from inflationary gravitational waves (as parametrized by the tensor-to-scalar ratio $r$), using priors on the frequency spectral behaviors of dust and synchrotron emission from previous analyses of WMAP and Planck data in other regions of the sky. This analysis yields an upper limit $r_{0.05}<0.09$ at 95% confidence, which is robust to variations explored in analysis and priors. Combining these $B$-mode results with the (more model-dependent) constraints from Planck analysis of CMB temperature and other evidence yields a combined limit $r_{0.05}<0.07$. These are the strongest constraints to date on inflationary gravitational waves.
    Full-text · Article · Oct 2015
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    ABSTRACT: We describe the cryogenic half-wave plate rotation mechanisms built for and used in Spider, a polarization-sensitive balloon-borne telescope array that observed the Cosmic Microwave Background at 95 GHz and 150 GHz during a stratospheric balloon flight from Antarctica in January 2015. The mechanisms operate at liquid helium temperature in flight. A three-point contact design keeps the mechanical bearings relatively small but allows for a large (305 mm) diameter clear aperture. A worm gear driven by a cryogenic stepper motor allows for precise positioning and prevents undesired rotation when the motors are depowered. A custom-built optical encoder system monitors the bearing angle to an absolute accuracy of 0.1 degrees. The system performed well in Spider during its successful 16 day flight.
    Preview · Article · Oct 2015 · Review of Scientific Instruments
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    ABSTRACT: We present the 8th Full Focal Plane simulation set (FFP8), deployed in support of the Planck 2015 results. FFP8 consists of 10 fiducial mission realizations reduced to 18144 maps, together with the most massive suite of Monte Carlo realizations of instrument noise and CMB ever generated, comprising $10^4$ mission realizations reduced to about $10^6$ maps. The resulting maps incorporate the dominant instrumental, scanning, and data analysis effects; remaining subdominant effects will be included in future updates. Generated at a cost of some 25 million CPU-hours spread across multiple high-performance-computing (HPC) platforms, FFP8 is used for the validation and verification of analysis algorithms, as well as their implementations, and for removing biases from and quantifying uncertainties in the results of analyses of the real data.
    Full-text · Article · Sep 2015
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    ABSTRACT: We present results for Vela C obtained during the 2012 flight of the Balloon-borne Large Aperture Submillimeter Telescope for Polarimetry (BLASTPol). We mapped polarized intensity across almost the entire extent of this giant molecular cloud, in bands centered at 250, 350, and 500 {\mu}m. In this initial paper, we show our 500 {\mu}m data smoothed to a resolution of 2.5 arcminutes (approximately 0.5 pc). We show that the mean level of the fractional polarization p and most of its spatial variations can be accounted for using an empirical three-parameter power-law fit, p = p_0 N^(-0.4) S^(-0.6), where N is the hydrogen column density and S is the polarization-angle dispersion on 0.5 pc scales. The decrease of p with increasing S is expected because changes in the magnetic field direction within the cloud volume sampled by each measurement will lead to cancellation of polarization signals. The decrease of p with increasing N might be caused by the same effect, if magnetic field disorder increases for high column density sightlines. Alternatively, the intrinsic polarization efficiency of the dust grain population might be lower for material along higher density sightlines. We find no significant correlation between N and S. Comparison of observed submillimeter polarization maps with synthetic polarization maps derived from numerical simulations provides a promising method for testing star formation theories. Realistic simulations should allow for the possibility of variable intrinsic polarization efficiency. The measured levels of correlation among p, N, and S provide points of comparison between observations and simulations.
    No preview · Article · Sep 2015
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    ABSTRACT: We update the all-sky Planck catalogue of 1227 clusters and cluster candidates (PSZ1) published in March 2013, derived from detections of the Sunyaev-Zeldovich (SZ) effect using the first 15.5 months of Planck satellite observations. As an addendum, we deliver an updated version of the PSZ1 catalogue, reporting the further confirmation of 86 Planck-discovered clusters. In total, the PSZ1 now contains 947 confirmed clusters, of which 214 were confirmed as newly discovered clusters through follow-up observations undertaken by the Planck Collaboration. The updated PSZ1 contains redshifts for 913 systems, of which 736 (similar to 80.6%) are spectroscopic, and associated mass estimates derived from the Y-z mass proxy. We also provide a new SZ quality flag for the remaining 280 candidates. This flag was derived from a novel artificial neural-network classification of the SZ signal. Based on this assessment, the purity of the updated PSZ1 catalogue is estimated to be 94%. In this release, we provide the full updated catalogue and an additional readme file with further information on the Planck SZ detections.
    Full-text · Article · Sep 2015
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    ABSTRACT: The Second Planck Catalogue of Compact Sources is a catalogue of sources detected in single-frequency maps from the full duration of the Planck mission and supersedes previous versions of the Planck compact source catalogues. It consists of compact sources, both Galactic and extragalactic, detected over the entire sky. Compact sources detected in the lower frequency channels are assigned to the PCCS2, while at higher frequencies they are assigned to one of two sub-catalogues, the PCCS2 or PCCS2E, depending on their location on the sky. The first of these catalogues covers most of the sky and allows the user to produce subsamples at higher reliabilities than the target 80% integral reliability of the catalogue. The PCCS2E contains sources detected in sky regions where the diffuse emission makes it difficult to quantify the reliability of the detections. Both the PCCS2 and PCCS2E include polarization measurements, in the form of polarized flux densities, or upper limits, and orientation angles for all seven polarization-sensitive Planck channels. The improved data-processing of the full-mission maps and their reduced noise levels allow us to increase the number of objects in the catalogue, improving its completeness for the target 80 % reliability as compared with the previous versions, the PCCS and ERCSC catalogues.
    Full-text · Article · Jul 2015
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    ABSTRACT: We describe the SPIDER flight cryostat, which is designed to cool six millimeter-wavelength telescopes during an Antarctic long-duration balloon flight. The cryostat, one of the largest to have flown on a stratospheric payload, uses liquid helium-4 to deliver cooling power to stages at 4.2 and 1.6 K. Stainless steel capillaries facilitate a high flow impedance connection between the main liquid helium tank and a smaller superfluid tank, allowing the latter to operate at 1.6 K as long as there is liquid in the 4.2 K main tank. Each telescope houses a closed cycle helium-3 adsorption refrigerator that further cools the focal planes down to 300 mK. Liquid helium vapor from the main tank is routed through heat exchangers that cool radiation shields, providing negative thermal feedback. The system performed successfully during a 17 day flight in the 2014-2015 Antarctic summer. The cryostat had a total hold time of 16.8 days, with 15.9 days occurring during flight.
    Preview · Article · Jun 2015 · Cryogenics
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    ABSTRACT: (abridged) We discuss the Galactic foreground emission between 20 and 100GHz based on observations by Planck/WMAP. The Commander component-separation tool has been used to separate the various astrophysical processes in total intensity. Comparison with RRL templates verifies the recovery of the free-free emission along the Galactic plane. Comparison of the high-latitude Halpha emission with our free-free map shows residuals that correlate with dust optical depth, consistent with a fraction (~30%) of Halpha having been scattered by high-latitude dust. We highlight a number of diffuse spinning dust morphological features at high latitude. There is substantial spatial variation in the spinning dust spectrum, with the emission peak ranging from below 20GHz to more than 50GHz. There is a strong tendency for the spinning dust component near many prominent HII regions to have a higher peak frequency, suggesting that this increase in peak frequency is associated with dust in the photodissociation regions around the nebulae. The emissivity of spinning dust in these diffuse regions is of the same order as previous detections in the literature. Over the entire sky, the commander solution finds more anomalous microwave emission than the WMAP component maps, at the expense of synchrotron and free-free emission. This can be explained by the difficulty in separating multiple broadband components with a limited number of frequency maps. Future surveys (5-20GHz), will greatly improve the separation by constraining the synchrotron spectrum. We combine Planck/WMAP data to make the highest S/N ratio maps yet of the intensity of the all-sky polarized synchrotron emission at frequencies above a few GHz. Most of the high-latitude polarized emission is associated with distinct large-scale loops and spurs, and we re-discuss their structure...
    Full-text · Article · Jun 2015
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    ABSTRACT: We present a description of the pipeline used to calibrate the Planck Low Frequency Instrument (LFI) timelines into thermodynamic temperatures for the Planck 2015 data release, covering 4 years of uninterrupted operations. As in the 2013 data release, our calibrator is provided by the spin-synchronous modulation of the CMB dipole, exploiting both the orbital and solar components. Our 2015 LFI analysis provides an independent Solar dipole estimate in excellent agreement with that of HFI and within $1\sigma$ (0.3 % in amplitude) of the WMAP value. This 0.3 % shift in the peak-to-peak dipole temperature from WMAP and a global overhaul of the iterative calibration code increases the overall level of the LFI maps by 0.45 % (30 GHz), 0.64 % (44 GHz), and 0.82 % (70 GHz) in temperature with respect to the 2013 Planck data release, thus reducing the discrepancy with the power spectrum measured by WMAP. We estimate that the LFI calibration uncertainty is at the level of 0.20 % for the 70 GHz map, 0.26 % for the 44 GHz map, and 0.35 % for the 30 GHz map. We provide a detailed description of the impact of all the changes implemented in the calibration since the previous data release.
    Full-text · Article · May 2015
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    ABSTRACT: We present foreground-reduced CMB maps derived from the full Planck data set in both temperature and polarization. Compared to the corresponding Planck 2013 temperature sky maps, the total data volume is larger by a factor of 3.2 for frequencies between 30 and 70 GHz, and by 1.9 for frequencies between 100 and 857 GHz. In addition, systematic errors in the forms of temperature-to-polarization leakage, analogue-to-digital conversion uncertainties, and very long time constant errors have been dramatically reduced, to the extent that the cosmological polarization signal may now be robustly recovered on angular scales $\ell\gtrsim40$. On the very largest scales, instrumental systematic residuals are still non-negligible compared to the expected cosmological signal, and modes with $\ell < 20$ are accordingly suppressed in the current polarization maps by high-pass filtering. As in 2013, four different CMB component separation algorithms are applied to these observations, providing a measure of stability with respect to algorithmic and modelling choices. The resulting polarization maps have rms instrumental noise ranging between 0.21 and 0.27$\,\mu\textrm{K}$ averaged over 55 arcmin pixels, and between 4.5 and 6.1$\,\mu\textrm{K}$ averaged over 3.4 arcmin pixels. The cosmological parameters derived from the analysis of temperature power spectra are in agreement at the $1\sigma$ level with the Planck 2015 likelihood. Unresolved mismatches between the noise properties of the data and simulations prevent a satisfactory description of the higher-order statistical properties of the polarization maps. Thus, the primary applications of these polarization maps are those that do not require massive simulations for accurate estimation of uncertainties, for instance estimation of cross-spectra and cross-correlations, or stacking analyses.
    Full-text · Article · Feb 2015
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    ABSTRACT: Within ten nearby (d < 450 pc) Gould Belt molecular clouds we evaluate statistically the relative orientation between the magnetic field projected on the plane of sky, inferred from the polarized thermal emission of Galactic dust observed by Planck at 353 GHz, and the gas column density structures, quantified by the gradient of the column density, $N_H$. The relative orientation is evaluated pixel by pixel and analyzed in bins of column density using the novel statistical tool Histogram of Relative Orientations. Within most clouds we find that the relative orientation changes progressively with increasing $N_H$ from preferentially parallel or no preferred orientation to preferentially perpendicular. In simulations of magnetohydrodynamic turbulence in molecular clouds this trend in relative orientation is a signature of Alfv\'enic or sub-Alfv\'enic turbulence, implying that the magnetic field is significant for the gas dynamics at the scales probed by Planck. We compare the deduced magnetic field strength with estimates we obtain from other methods and discuss the implications of the Planck observations for the general picture of molecular cloud formation and evolution.
    Full-text · Article · Feb 2015
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    ABSTRACT: We present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be $n_\mathrm{s} = 0.968 \pm 0.006$ and tightly constrain its scale dependence to $d n_s/d \ln k =-0.003 \pm 0.007$ when combined with the Planck lensing likelihood. When the high-$\ell$ polarization data is included, the results are consistent and uncertainties are reduced. The upper bound on the tensor-to-scalar ratio is $r_{0.002} < 0.11$ (95% CL), consistent with the B-mode polarization constraint $r< 0.12$ (95% CL) obtained from a joint BICEP2/Keck Array and Planck analysis. These results imply that $V(\phi) \propto \phi^2$ and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as $R^2$ inflation. Three independent methods reconstructing the primordial power spectrum are investigated. The Planck data are consistent with adiabatic primordial perturbations. We investigate inflationary models producing an anisotropic modulation of the primordial curvature power spectrum as well as generalized models of inflation not governed by a scalar field with a canonical kinetic term. The 2015 results are consistent with the 2013 analysis based on the nominal mission data.
    Full-text · Article · Feb 2015
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    ABSTRACT: We present the all-sky Planck catalogue of Sunyaev-Zeldovich (SZ) sources detected from the 29 month full-mission data. The catalogue (PSZ2) is the largest SZ-selected sample of galaxy clusters yet produced and the deepest all-sky catalogue of galaxy clusters. It contains 1653 detections, of which 1203 are confirmed clusters with identified counterparts in external data-sets, and is the first SZ-selected cluster survey containing > 103 confirmed clusters. We present a detailed analysis of the survey selection function in terms of its completeness and statistical reliability, placing a lower limit of 83% on the purity. Using simulations, we find that the Y5R500 estimates are robust to pressure-profile variation and beam systematics, but accurate conversion to Y500 requires. the use of prior information on the cluster extent. We describe the multi-wavelength search for counterparts in ancillary data, which makes use of radio, microwave, infra-red, optical and X-ray data-sets, and which places emphasis on the robustness of the counterpart match. We discuss the physical properties of the new sample and identify a population of low-redshift X-ray under- luminous clusters revealed by SZ selection. These objects appear in optical and SZ surveys with consistent properties for their mass, but are almost absent from ROSAT X-ray selected samples.
    Full-text · Article · Feb 2015
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    ABSTRACT: We predict and investigate four types of imprint of a stochastic background of primordial magnetic fields (PMFs) on the cosmic microwave background (CMB) anisotropies: the impact of PMFs on the CMB spectra; the effect on CMB polarization induced by Faraday rotation; magnetically-induced non-Gaussianities; and the magnetically-induced breaking of statistical isotropy. Overall, Planck data constrain the amplitude of PMFs to less than a few nanogauss. In particular, individual limits coming from the analysis of the CMB angular power spectra, using the Planck likelihood, are $B_{1\,\mathrm{Mpc}}< 4.4$ nG (where $B_{1\,\mathrm{Mpc}}$ is the comoving field amplitude at a scale of 1 Mpc) at 95% confidence level, assuming zero helicity, and $B_{1\,\mathrm{Mpc}}< 5.6$ nG when we consider a maximally helical field. For nearly scale-invariant PMFs we obtain $B_{1\,\mathrm{Mpc}}<2.1$ nG and $B_{1\,\mathrm{Mpc}}<0.7$ nG if the impact of PMFs on the ionization history of the Universe is included in the analysis. From the analysis of magnetically-induced non-Gaussianity we obtain three different values, corresponding to three applied methods, all below 5 nG. The constraint from the magnetically-induced passive-tensor bispectrum is $B_{1\,\mathrm{Mpc}}< 2.8$ nG. A search for preferred directions in the magnetically-induced passive bispectrum yields $B_{1\,\mathrm{Mpc}}< 4.5$ nG, whereas the the compensated-scalar bispectrum gives $B_{1\,\mathrm{Mpc}}< 3$ nG. The analysis of the Faraday rotation of CMB polarization by PMFs uses the Planck power spectra in $EE$ and $BB$ at 70 GHz and gives $B_{1\,\mathrm{Mpc}}< 1380$ nG. In our final analysis, we consider the harmonic-space correlations produced by Alfv\'en waves, finding no significant evidence for the presence of these waves. Together, these results comprise a comprehensive set of constraints on possible PMFs with Planck data.
    Full-text · Article · Feb 2015
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    ABSTRACT: We present the most significant measurement of the cosmic microwave background (CMB) lensing potential to date (at a level of 40 sigma), using temperature and polarization data from the Planck 2015 full-mission release. Using a polarization-only estimator we detect lensing at a significance of 5 sigma. We cross-check the accuracy of our measurement using the wide frequency coverage and complementarity of the temperature and polarization measurements. Public products based on this measurement include an estimate of the lensing potential over approximately 70% of the sky, an estimate of the lensing potential power spectrum in bandpowers for the multipole range 40<L<400 and an associated likelihood for cosmological parameter constraints. We find good agreement between our measurement of the lensing potential power spectrum and that found in the best-fitting LCDM model based on the Planck temperature and polarization power spectra. Using the lensing likelihood alone we obtain a percent-level measurement of the parameter combination Sigma_8 Omega_m^{0.25} = 0.591+-0.021. We combine our determination of the lensing potential with the E-mode polarization also measured by Planck to generate an estimate of the lensing B-mode. We show that this lensing B-mode estimate is correlated with the B-modes observed directly by Planck at the expected level and with a statistical significance of 10 sigma, confirming Planck's sensitivity to this known sky signal. We also correlate our lensing potential estimate with the large-scale temperature anisotropies, detecting a cross-correlation at the 3 sigma level, as expected due to dark energy in the concordance LCDM model.
    Full-text · Article · Feb 2015
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    ABSTRACT: This paper describes the mapmaking procedure applied to Planck LFI (Low Frequency Instrument) data. The mapmaking step takes as input the calibrated timelines and pointing information. The main products are sky maps of $I,Q$, and $U$ Stokes components. For the first time, we present polarization maps at LFI frequencies. The mapmaking algorithm is based on a destriping technique, enhanced with a noise prior. The Galactic region is masked to reduce errors arising from bandpass mismatch and high signal gradients. We apply horn-uniform radiometer weights to reduce effects of beam shape mismatch. The algorithm is the same as used for the 2013 release, apart from small changes in parameter settings. We validate the procedure through simulations. Special emphasis is put on the control of systematics, which is particularly important for accurate polarization analysis. We also produce low-resolution versions of the maps, and corresponding noise covariance matrices. These serve as input in later analysis steps and parameter estimation. The noise covariance matrices are validated through noise Monte Carlo simulations. The residual noise in the map products is characterized through analysis of half-ring maps, noise covariance matrices, and simulations.
    Full-text · Article · Feb 2015

Publication Stats

12k Citations
684.75 Total Impact Points

Institutions

  • 1970-2015
    • University of Toronto
      • • Department of Physics
      • • Department of Astronomy and Astrophysics
      • • Canadian Institute for Theoretical Astrophysics
      Toronto, Ontario, Canada
  • 2010
    • Cardiff University
      • School of Physics and Astronomy
      Cardiff, WLS, United Kingdom
  • 2008
    • Università degli Studi di Roma "La Sapienza"
      • Department of Physics
      Roma, Latium, Italy
  • 2000
    • Centra Health
      Lynchburg, Virginia, United States
  • 1999
    • California Institute of Technology
      • Department of Physics
      Pasadena, California, United States
  • 1995-1998
    • Princeton University
      • Department of Physics
      Princeton, New Jersey, United States