C. Dickinson

Towards a free-free template for CMB foregrounds

A full-sky template map of the Galactic free-free foreground emission component is increasingly important for high sensitivity CMB experiments. We use the recently published Hα data of both the northern and southern skies as the basis for such a template. The first step is to correct the Hα maps for dust absorption using the 100 � m dust maps of Schlegel, Finkbeiner & Davis (1998). We show that for a range of longitudes, the Galactic latitude distribution of absorption suggests that it is 33 per cent of the full extragalactic absorption. A reliable absorption-corrected Hα map can be produced for � 95 per cent of the sky; the area for which a template cannot be recovered is the Galactic plane area |b| < 5 ◦ , l = 260 ◦ 0 ◦ 160 ◦ and some isolated dense dust clouds at intermediate latitudes. The second step is to convert the dust-corrected Hα data into a predicted radio surface brightness. The free-free emission formula is revised to give an accurate expression (1 per cent) for the radio emission covering the frequency range 100 MHz to 100 GHz and the electron temperature range 3000 to 20000 K. The main uncertainty when applying this expression is the variation of electron temperature across the sky. The emission formula is verified in several extended Hii regions using data in the range 408 to 2326 MHz. A full-sky free-free template map is presented at 30 GHz; the scaling to other frequencies is given. The Haslam et al. all-sky 408 MHz map of the sky can be corrected for this free-free component, which amounts to a � 6 per cent correction at intermediate and high latitudes, to provide a pure synchrotron all-sky template. The implications for CMB experiments are discussed.

Component separation methods for the PLANCK mission

Context. The PLANCK satellite will map the full sky at nine frequencies from 30 to 857 GHz. The CMB intensity and polarization that are its prime targets are contaminated by foreground emission. Aims. The goal of this paper is to compare proposed methods for separating CMB from foregrounds based on their different spectral and spatial characteristics, and to separate the foregrounds into “components” with different physical origins (Galactic synchrotron, free-free and dust emissions; extra-galactic and far-IR point sources; Sunyaev-Zeldovich effect, etc.) Methods. A component separation challenge has been organised, based on a set of realistically complex simulations of sky emission. Several methods including those based on internal template subtraction, maximum entropy method, parametric method, spatial and harmonic cross correlation methods, and independent component analysis have been tested. Results. Different methods proved to be effective in cleaning the CMB maps of foreground contamination, in reconstructing maps of diffuse Galactic emissions, and in detecting point sources and thermal Sunyaev-Zeldovich signals. The power spectrum of the residuals is, on the largest scales, four orders of magnitude lower than the input Galaxy power spectrum at the foreground minimum. The CMB power spectrum was accurately recovered up to the sixth acoustic peak. The point source detection limit reaches 100 mJy, and about 2300 clusters are detected via the thermal SZ effect on two thirds of the sky. We have found that no single method performs best for all scientific objectives. Conclusions. We foresee that the final component separation pipeline for PLANCK will involve a combination of methods and iterations between processing steps targeted at different objectives such as diffuse component separation, spectral estimation, and compact source extraction.

Polarization Observations with the Cosmic Background Imager

Polarization observations of the cosmic microwave background with the Cosmic Background Imager from September 2002 to May 2004 provide a significant detection of the E-mode polarization and reveal an angular power spectrum of polarized emission showing peaks and valleys that are shifted in phase by half a cycle relative to those of the total intensity spectrum. This key agreement between the phase of the observed polarization spectrum and that predicted on the basis of the total intensity spectrum provides support for the standard model of cosmology, in which dark matter and dark energy are the dominant constituents, the geometry is close to flat, and primordial density fluctuations are predominantly adiabatic with a matter power spectrum commensurate with inflationary cosmological models.

Joint Bayesian Component Separation and CMB Power Spectrum Estimation

We describe and implement an exact, flexible, and computationally efficient algorithm for joint component separation and CMB power spectrum estimation, building on a Gibbs sampling framework. Two essential new features are (1) conditional sampling of foreground spectral parameters and (2) joint sampling of all amplitude-type degrees of freedom (e.g., CMB, foreground pixel amplitudes, and global template amplitudes) given spectral parameters. Given a parametric model of the foreground signals, we estimate efficiently and accurately the exact joint foreground-CMB posterior distribution and, therefore, all marginal distributions such as the CMB power spectrum or foreground spectral index posteriors. The main limitation of the current implementation is the requirement of identical beam responses at all frequencies, which restricts the analysis to the lowest resolution of a given experiment. We outline a future generalization to multiresolution observations. To verify the method, we analyze simple models and compare the results to analytical predictions. We then analyze a realistic simulation with properties similar to the 3 yr WMAP data, downgraded to a common resolution of 3? FWHM. The results from the actual 3 yr WMAP temperature analysis are presented in a companion Letter.

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

We present the Planck Sky Model (PSM), a parametric model for generating all-sky, few arcminute resolution maps of sky emission at submillimetre to centimetre wavelengths, in both intensity and polarisation. Several options are implemented to model the cosmic microwave background, Galactic diffuse emission (synchrotron, free-free, thermal and spinning dust, CO lines), Galactic HII regions, extragalactic radio sources, dusty galaxies, and thermal and kinetic Sunyaev-Zeldovich signals from clusters of galaxies. Each component is simulated by means of educated interpolations/extrapolations of data sets available at the time of the launch of the Planck mission, complemented by state-of-the-art models of the emission. Distinctive features of the simulations are spatially varying spectral properties of synchrotron and dust; different spectral parameters for each point source; modelling of the clustering properties of extragalactic sources and of the power spectrum of fluctuations in the cosmic infrared background. The PSM enables the production of random realisations of the sky emission, constrained to match observational data within their uncertainties. It is implemented in a software package that is regularly updated with incoming information from observations. The model is expected to serve as a useful tool for optimising planned microwave and sub-millimetre surveys and testing data processing and analysis pipelines. It is, in particular, used to develop and validate data analysis pipelines within the Planck collaboration. A version of the software that can be used for simulating the observations for a variety of experiments is made available on a dedicated website.

A refined model for spinning dust radiation

We present a comprehensive treatment of the spectrum of electric dipole emission from spinning dust grains, updating the commonly used model of Draine & Lazarian. Grain angular velocity distributions are computed using the Fokker–Planck equation; we revisit the drift and diffusion coefficients for the major torques on the grain, including collisions, grain-plasma interactions and infrared emission. We use updated grain optical properties and size distributions. The theoretical formalism is implemented in the companion code, spdust, which is publicly available. The effect of some environmental and grain parameters on the emissivity is shown and analysed.

IMPLICATIONS OF THE COSMIC BACKGROUND IMAGER POLARIZATION DATA

We present new measurements of the power spectra of the E mode of cosmic microwave background (CMB) polarization, the temperature T, the cross-correlation of E and T, and upper limits on the B mode from 2.5 yr of dedicated Cosmic Background Imager (CBI) observations. Both raw maps and optimal signal images in the (u, v)-plane and the sky plane show strong detections of the E mode (11.7 σ for the EE power spectrum overall) and no detection of the B mode. The power spectra are used to constrain parameters of the flat tilted adiabatic ΛCDM models: those determined from EE and TE bandpowers agree with those from TT, which is a powerful consistency check. There is little tolerance for shifting polarization peaks from the TT-forecast locations, as measured by the angular sound crossing scale θ = 100/l_s = 1.03 ± 0.02 from EE and TE; compare with 1.044 ± 0.005 with the TT data included. The scope for extra out-of-phase peaks from subdominant isocurvature modes is also curtailed. The EE and TE measurements of CBI, DASI, and BOOMERANG are mutually consistent and, taken together rather than singly, give enhanced leverage for these tests.

High-sensitivity measurements of the cosmic microwave background power spectrum with the extended Very Small Array

We present deep Ka-band (ν ≈ 33 GHz) observations of the cosmic microwave background (CMB) made with the extended Very Small Array (VSA). This configuration produces a naturally weighted synthesized FWHM beamwidth of ∼11 arcmin, which covers anrange of 300 to 1500. On these scales, foreground extragalactic sources can be a major source of contamination to the CMB anisotropy. This problem has been alleviated by identifying sources at 15 GHz with the Ryle Telescope and then monitoring these sources at 33 GHz using a single-baseline interferometer collocated with the VSA. Sources with flux densities20 mJy at 33 GHz are subtracted from the data. In addition, we calculate a statistical correction for the small residual contribution from weaker sources that are below the detection limit of the survey. The CMB power spectrum corrected for Galactic foregrounds and extragalactic point sources is presented. A totalrange of 150-1500 is achieved by combining the complete extended array data with earlier VSA data in a compact configuration. Our resolution of �� ≈ 60 allows the first three acoustic peaks to be clearly delineated. This is achieved by using mosaiced observations in seven regions covering a total area of 82 deg 2 . There is good agreement with the Wilkinson Microwave Anisotropy Probe (WMAP) data up to � = 700 where WMAP data run out of resolution. For highervalues out to � = 1500, the agreement in power spectrum amplitudes with other experiments is also very good despite differences in frequency and observing technique.

Cosmic microwave background component separation by parameter estimation

We propose a solution to the CMB component separation problem based on standard parameter estimation techniques. We assume a parametric spectral model for each signal component, and fit the corresponding parameters pixel by pixel in a two-stage process. First we fit for the full parameter set (e.g., component amplitudes and spectral indices) in low-resolution and high signal-to-noise ratio maps using MCMC, obtaining both best-fit values for each parameter, and the associated uncertainty. The goodness-of-fit is evaluated by a chi^2 statistic. Then we fix all non-linear parameters at their low-resolution best-fit values, and solve analytically for high-resolution component amplitude maps. This likelihood approach has many advantages: The fitted model may be chosen freely, and the method is therefore completely general; all assumptions are transparent; no restrictions on spatial variations of foreground properties are imposed; the results may be rigorously monitored by goodness-of-fit tests; and, most importantly, we obtain reliable error estimates on all estimated quantities. We apply the method to simulated Planck and six-year WMAP data based on realistic models, and show that separation at the muK level is indeed possible in these cases. We also outline how the foreground uncertainties may be rigorously propagated through to the CMB power spectrum and cosmological parameters using a Gibbs sampling technique.We propose a method for CMB component separation based on standard Bayesian parameter estimation techniques. We assume a parametric spectral model for each signal component and fit the corresponding parameters pixel by pixel in a two-stage process. First we fit for the full parameter set (e.g., component amplitudes and spectral indices) in low-resolution and high signal-to-noise ratio maps using MCMC, obtaining both best-fit values for each parameter and the associated uncertainty. The goodness of fit is approximated by a χ2 statistic. Then we fix all nonlinear parameters at their low-resolution best-fit values and solve analytically for high-resolution component amplitude maps. This likelihood approach has many advantages: the fitted model may be chosen freely, and the method is therefore completely general; all assumptions are transparent; no restrictions on spatial variations of foreground properties are imposed; the results may be monitored by goodness-of-fit tests; and, most importantly, we obtain reliable error estimates on all estimated quantities. We apply the method to simulated Planck satellite and 6 year WMAP data based on realistic models and show that separation at the microkelvin level is indeed possible in these cases. We also outline how the foreground uncertainties may be rigorously propagated through to the CMB power spectrum and cosmological parameters using a Gibbs sampling technique.

Morphological Analysis of the Centimeter-Wave Continuum in the Dark Cloud LDN 1622

The spectral energy distribution of the dark cloud LDN 1622, as measured by Finkbeiner using WMAP data, drops above 30 GHz and is suggestive of a Boltzmann cutoff in grain rotation frequencies, characteristic of spinning dust emission. LDN 1622 is conspicuous in the 31 GHz image we obtained with the Cosmic Background Imager, which is the first centimeter-wave resolved image of a dark cloud. The 31 GHz emission follows the emission traced by the four IRAS bands. The normalized cross-correlation of the 31 GHz image with the IRAS images is higher by 6.6 σ for the 12 and 25 μm bands than for the 60 and 100 μm bands: C12+25 = 0.76 ± 0.02, and C60+100 = 0.64 ± 0.01. The mid-IR-centimeter-wave correlation in LDN 1622 is evidence for very small grain (VSG) or continuum emission at 26-36 GHz from a hot molecular phase. In dark clouds and their photon-dominated regions (PDRs), the 12 and 25 μm emission is attributed to stochastic heating of the VSGs. The mid-IR and centimeter-wave dust emissions arise in a limb-brightened shell coincident with the PDR of LDN 1622, where the incident UV radiation from the Ori OB 1b association heats and charges the grains, as is required for spinning dust.