Map-making in small field modulated CMB polarisation experiments: approximating the maximum-likelihood method

Map-making presents a significant computational challenge to the next generation of kilopixel CMB polarisation experiments. Years worth of time ordered data (TOD) from thousands of detectors will need to be compressed into maps of the T, Q and U Stokes parameters. Fundamental to the science goal of these experiments, the observation of B-modes, is the ability to control noise and systematics. In this paper, we consider an alternative to the maximum-likelihood method, called destriping, where the noise is modelled as a set of discrete offset functions and then subtracted from the time-stream. We compare our destriping code (Descart: the DEStriping CARTographer) to a full maximum-likelihood map-maker, applying them to 200 Monte-Carlo simulations of time-ordered data from a ground based, partial-sky polarisation modulation experiment. In these simulations, the noise is dominated by either detector or atmospheric 1/f noise. Using prior information of the power spectrum of this noise, we produce destriped maps of T, Q and U which are negligibly different from optimal. The method does not filter the signal or bias the E or B-mode power spectra. Depending on the length of the destriping baseline, the method delivers between 5 and 22 times improvement in computation time over the maximum-likelihood algorithm. We find that, for the specific case of single detector maps, it is essential to destripe the atmospheric 1/f in order to detect B-modes, even though the Q and U signals are modulated by a half-wave plate spinning at 5-Hz.Comment: 18 pages, 17 figures, MNRAS accepted v2: content added (inc: table 2), typos correcte

SANEPIC: A Map-Making Method for Timestream Data From Large Arrays

We describe a map-making method which we have developed for the Balloon-borne Large Aperture Submillimeter Telescope (BLAST) experiment, but which should have general application to data from other submillimeter arrays. Our method uses a Maximum Likelihood based approach, with several approximations, which allows images to be constructed using large amounts of data with fairly modest computer memory and processing requirements. This new approach, Signal And Noise Estimation Procedure Including Correlations (SANEPIC), builds upon several previous methods, but focuses specifically on the regime where there is a large number of detectors sampling the same map of the sky, and explicitly allowing for the the possibility of strong correlations between the detector timestreams. We provide real and simulated examples of how well this method performs compared with more simplistic map-makers based on filtering. We discuss two separate implementations of SANEPIC: a brute-force approach, in which the inverse pixel-pixel covariance matrix is computed; and an iterative approach, which is much more efficient for large maps. SANEPIC has been successfully used to produce maps using data from the 2005 BLAST flight.Comment: 27 Pages, 15 figures; Submitted to the Astrophysical Journal; related results available at http://blastexperiment.info/ [the BLAST Webpage

Fast and precise map-making for massively multi-detector CMB experiments

Future cosmic microwave background (CMB) polarisation experiments aim to measure an unprecedentedly small signal - the primordial gravity wave component of the polarisation field B-mode. To achieve this, they will analyse huge datasets, involving years worth of time-ordered data (TOD) from massively multi-detector focal planes. This creates the need for fast and precise methods to complement the M-L approach in analysis pipelines. In this paper, we investigate fast map-making methods as applied to long duration, massively multi-detector, ground-based experiments, in the context of the search for B-modes. We focus on two alternative map-making approaches: destriping and TOD filtering, comparing their performance on simulated multi-detector polarisation data. We have written an optimised, parallel destriping code, the DEStriping CARTographer DESCART, that is generalised for massive focal planes, including the potential effect of cross-correlated TOD 1/f noise. We also determine the scaling of computing time for destriping as applied to a simulated full-season data-set for a realistic experiment. We find that destriping can out-perform filtering in estimating both the large-scale E and B-mode angular power spectra. In particular, filtering can produce significant spurious B-mode power via EB mixing. Whilst this can be removed, it contributes to the variance of B-mode bandpower estimates at scales near the primordial B-mode peak. For the experimental configuration we simulate, this has an effect on the possible detection significance for primordial B-modes. Destriping is a viable alternative fast method to the full M-L approach that does not cause the problems associated with filtering, and is flexible enough to fit into both M-L and Monte-Carlo pseudo-Cl pipelines.Comment: 16 pages, 14 figures. MNRAS accepted. Typos corrected and computing time/memory requirement orders-of-magnitude numbers in section 4 replaced by precise number

Planck 2015 results. XX. Constraints on inflation

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 s = 0.968 ± 0.006 and tightly constrain its scale dependence to dn s /dlnk = −0.003 ± 0.007 when combined with the Planck lensing likelihood. When the high-ℓ 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(ϕ)∝ϕ 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

All-sky convolution for polarimetry experiments

We discuss all-sky convolution of the instrument beam with the sky signal in polarimetry experiments, such as the Planck mission which will map the temperature anisotropy and polarization of the cosmic microwave background (CMB). To account properly for stray light (from e.g. the galaxy, sun, and planets) in the far side-lobes of such an experiment, it is necessary to perform the beam convolution over the full sky. We discuss this process in multipole space for an arbitrary beam response, fully including the effects of beam asymmetry and cross-polarization. The form of the convolution in multipole space is such that the Wandelt-Gorski fast technique for all-sky convolution of scalar signals (e.g. temperature) can be applied with little modification. We further show that for the special case of a pure co-polarized, axisymmetric beam the effect of the convolution can be described by spin-weighted window functions. In the limits of a small angle beam and large Legendre multipoles, the spin-weight 2 window function for the linear polarization reduces to the usual scalar window function used in previous analyses of beam effects in CMB polarimetry experiments. While we focus on the example of polarimetry experiments in the context of CMB studies, we emphasise that the formalism we develop is applicable to anisotropic filtering of arbitrary tensor fields on the sphere.Comment: 8 pages, 1 figure; Minor changes to match version accepted by Phys. Rev.

QUIJOTE scientific results-I. Measurements of the intensity and polarisation of the anomalous microwave emission in the Perseus molecular complex

et al.In this paper, we present Q-U-I JOint Tenerife Experiment (QUIJOTE) 10–20 GHz observations (194 h in total over ≈250 deg2) in intensity and polarisation of G159.6-18.5, one of the most widely studied regions harbouring anomalous microwave emission (AME). By combining with other publicly available intensity data, we achieve the most precise spectrum of the AME measured to date in an individual region, with 13 independent data points between 10 and 50 GHz being dominated by this emission. The four QUIJOTE data points provide the first independent confirmation of the downturn of the AME spectrum at low frequencies, initially unveiled by the COSMOlogical Structures On Medium Angular Scales experiment in this region. Our polarisation maps, which have an angular resolution of ≈1° and a sensitivity of ≈ 25 μK beam−1, are consistent with zero polarisation. We obtain upper limits on the polarisation fraction of Π < 6.3 and <2.8 per cent (95 per cent C.L.), respectively, at 12 and 18 GHz (ΠAME < 10.1 and <3.4 per cent with respect to the residual AME intensity), a frequency range where no AME polarisation observations have been reported to date. The combination of these constraints with those from other experiments confirm that all the magnetic dust models based on single-domain grains, and most of those considering randomly oriented magnetic inclusions, predict higher polarisation levels than is observed towards regions with AME. Also, neither of the two considered models of electric dipole emission seems to be compatible with all the observations together. More stringent constraints of the AME polarisation at 10–40 GHz are necessary to disentangle between different models, to which future QUIJOTE data will contribute.This work has been partially funded by the Spanish Ministry of Economy and Competitiveness (MINECO) under the projects AYA2007-68058-C03-01, AYA2010-21766-C03-02, AYA2012-39475-C02-01 and the Consolider-Ingenio project CSD2010-00064 (EPI: Exploring the Physics of Inflation). CD acknowledges support from an ERC Starting (Consolidator) Grant (no. 307209), SH from an STFC-funded studentship, and CHLC from the DIULS (Research Directorship of the University of La Serena).Peer Reviewe

The QUIJOTE experiment: project overview and first results

QUIJOTE (Q-U-I JOint TEnerife) is a new polarimeter aimed to characterize the polarization of the Cosmic Microwave Background and other Galactic and extragalactic signals at medium and large angular scales in the frequency range 10-40 GHz. The multi-frequency (10-20~GHz) instrument, mounted on the first QUIJOTE telescope, saw first light on November 2012 from the Teide Observatory (2400~m a.s.l). During 2014 the second telescope has been installed at this observatory. A second instrument at 30~GHz will be ready for commissioning at this telescope during summer 2015, and a third additional instrument at 40~GHz is now being developed. These instruments will have nominal sensitivities to detect the B-mode polarization due to the primordial gravitational-wave component if the tensor-to-scalar ratio is larger than r=0.05.Comment: To appear in "Highlights of Spanish Astrophysics VIII", Proceedings of the XI Scientific Meeting of the Spanish Astronomical Society, Teruel, Spain (2014