A System of Interaction and Structure

This paper introduces a logical system, called BV, which extends multiplicative linear logic by a non-commutative self-dual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved therein. It becomes very natural in a new formalism, called the calculus of structures, which is the main contribution of this work. Structures are formulae submitted to certain equational laws typical of sequents. The calculus of structures is obtained by generalising the sequent calculus in such a way that a new top-down symmetry of derivations is observed, and it employs inference rules that rewrite inside structures at any depth. These properties, in addition to allow the design of BV, yield a modular proof of cut elimination.Comment: This is the authoritative version of the article, with readable pictures, in colour, also available at . (The published version contains errors introduced by the editorial processing.) Web site for Deep Inference and the Calculus of Structures at <http://alessio.guglielmi.name/res/cos

Model-Independent Reionization Observables in the CMB

We represent the reionization history of the universe as a free function in redshift and study the potential for its extraction from CMB polarization spectra. From a principal component analysis, we show that the ionization history information is contained in 5 modes, resembling low-order Fourier modes in redshift space. The amplitude of these modes represent a compact description of the observable properties of reionization in the CMB, easily predicted given a model for the ionization fraction. Measurement of these modes can ultimately constrain the total optical depth, or equivalently the initial amplitude of fluctuations to the 1% level regardless of the true model for reionization.Comment: 4 pages, 5 figures, submitted to PRD (rapid communications

The power-law behaviours of angular spectra of polarized Galactic synchrotron

We study the angular power spectra of polarized Galactic synchrotron in the range 10<l<800, at several frequencies between 0.4 and 2.7 GHz and at several Galactic latitudes up to near the North Galactic Pole. Electric- and magnetic-parity polarization spectra are found to have slopes around alpha _{E,B} = 1.4 - 1.5 in the Parkes and Effelsberg Galactic-Plane surveys, but strong local fluctuations of alpha_{E,B} are found at | b | ~ 10 degree from the 1.4 GHz Effelsberg survey. The C_{PIl} spectrum, which is insensitive to the polarization direction, is somewhat steeper, being alpha_{PI} = 1.6 - 1.8 for the same surveys. The low-resolution multifrequency survey of Brouw and Spoelstra (1976) shows some flattening of the spectra below 1 GHz, more intense for C_{E,Bl} than for C_{PIl}. In no case we find evidence for really steep spectra. The extrapolation to the cosmological window shows that at 90 GHz the detection of E-mode harmonics in the cosmic background radiation should not be disturbed by synchrotron, even around l~10 for a reionization optical depth tau _{ri}>~0.05.Comment: 20 pages, 9 figures, accepted to New Astronom

An iterative destriping technique for diffuse background polarization data

We describe a simple but effective iterative procedure specifically designed to destripe Q and U Stokes parameter data as those collected by the SPOrt experiment onboard the International Space Station (ISS). The method is general enough to be useful for other experiments, both in polarization and total intensity. The only requirement for the algorithm to work properly is that the receiver knee frequency must be lower than the signal modulation frequency, corresponding in our case to the ISS orbit period. Detailed performances of the technique are presented in the context of the SPOrt experiment, both in terms of added rms noise and residual correlated noise.Comment: Accepted for publication by A&A (8 pages, 6 figures

1.4 GHz polarimetric observations of the two fields imaged by the DASI experiment

We present results of polarization observations at 1.4 GHz of the two fields imaged by the DASI experiment ($\alpha = 23^{\rm h} 30^{\rm m}$, $\delta = -55^{\circ}$ and $\alpha = 00^{\rm h} 30^{\rm m}$, $\delta = -55^{\circ}$, respectively). Data were taken with the Australia Telescope Compact Array with 3.4 arcmin resolution and $\sim 0.18$ mJy beam$^{-1}$ sensitivity. The emission is dominated by point sources and we do not find evidence for diffuse synchrotron radiation even after source subtraction. This allows to estimate an upper limit of the diffuse polarized emission. The extrapolation to 30 GHz suggests that the synchrotron radiation is lower than the polarized signal measured by the DASI experiment by at least 2 orders of magnitude. This further supports the conclusions drawn by the DASI team itself about the negligible Galactic foreground contamination in their data set, improving by a factor $\sim 5$ the upper limit estimated by Leitch et al. (2005). The dominant point source emission allows us to estimate the contamination of the CMB by extragalactic foregrounds. We computed the power spectrum of their contribution and its extrapolation to 30 GHz provides a framework where the CMB signal should dominate. However, our results do not match the conclusions of the DASI team about the negligibility of point source contamination, suggesting to take into account a source subtraction from the DASI data.Comment: 7 pages, six figures, submitted to MNRA

A polarized synchrotron template for CMBP experiments after WMAP data

We build template maps for the polarized Galactic--synchrotron emission on large angular scales (FWHM =~7$^\circ$), in the 20-90 GHz microwave range, by using WMAP data. The method, presented in a recent work, requires a synchrotron total intensity survey and the {\it polarization horizon} to model the polarized intensity and a starlight polarization map to model polarization angles. The basic template is obtained directly at 23 GHz with about 94% sky--coverage by using the synchrotron map released by the WMAP team. Extrapolations to 32, 60 and 90 GHz are performed by computing a synchrotron spectral index map, which strongly reduces previous uncertainties in passing from low (1.4 GHz) to microwave frequencies. Differing from low frequency data, none of our templates presents relevant structures out of the Galactic Plane. Our map at 90 GHz suggests that the synchrotron emission at high Galactic latitudes is low enough to allow a robust detection of the $E$--mode component of the cosmological signal on large--scale, even in models with low--reionization ($\tau = 0.05$). Detection of the weaker $B$--mode on the largest scales ($\ell < 10$) might be jeopardized unless the value $\tau = 0.17$ found by WMAP is confirmed, and $T/S > 0.1$. For lower levels of the gravitational--wave background the $B$--mode seems to be accessible only at the $\ell \sim 100$ peak and in selected low--synchrotron emission areas.Comment: 13 pages, 14 figures, accepted for pubblications by MNRAS. For a version with full resolution color figures see http://sp0rt.bo.iasf.cnr.it:8080/Docs/Public/papers.ph

High Galactic latitude polarized emission at 1.4 GHz and implications for cosmic microwave background observations

We analyse the polarized emission at 1.4 GHz in a 3x3 deg^2 area at high Galactic latitude (b ~ -40deg). The region, centred in (RA=5h, Dec=-49deg), was observed with the Australia Telescope Compact Array radio-interferometer, whose 3-30 arcmin angular sensitivity range allows the study of scales appropriate for CMB Polarization (CMBP) investigations. The angular behavior of the diffuse emission is analysed through the E- and B-mode power spectra. These follow a power law $C^X_l \propto l^{\beta_X}$ with slopes \beta_E = -1.97 \pm 0.08 and \beta_B = -1.98 \pm 0.07. The emission is found to be about a factor 25 fainter than in Galactic plane regions. The comparison of the power spectra with other surveys indicates that this area is intermediate between strong and negligible Faraday rotation effects. A similar conclusion can be reached by analysing both the frequency and Galactic latitude behaviors of the diffuse Galactic emission of the 408-1411 MHz Leiden survey data. We present an analysis of the Faraday rotation effects on the polarized power spectra, and find that the observed power spectra can be enhanced by a transfer of power from large to small angular scales. The extrapolation of the spectra to 32 and 90GHz of the CMB window suggests that Galactic synchrotron emission leaves the CMBP E-mode uncontaminated at 32GHz. The level of the contamination at 90GHz is expected to be more than 4 orders of magnitude below the CMBP spectrum. Extrapolating to the relevant angular scales, this region also appears adequate for investigation of the CMBP B-modes for models with tensor/scalar fluctuation power ratio T/S>0.01. We also identify polarized point sources in the field, providing a 9 object list which is complete down to the polarized flux limit of S^p_lim = 2 mJy.Comment: 13 pages, 11 figures, accepted for publication in MNRA

Cosmological Reionization Around the First Stars: Monte Carlo Radiative Transfer

We study the evolution of ionization fronts around the first proto-galaxies by using high resolution numerical cosmological (Lambda+CDM model) simulations and Monte Carlo radiative transfer methods. We present the numerical scheme in detail and show the results of test runs from which we conclude that the scheme is both fast and accurate. As an example of interesting cosmological application, we study the reionization produced by a stellar source of total mass M=2 10^8 M_\odot turning on at z=12, located at a node of the cosmic web. The study includes a Spectral Energy Distribution of a zero-metallicity stellar population, and two Initial Mass Functions (Salpeter/Larson). The expansion of the I-front is followed as it breaks out from the galaxy and it is channeled by the filaments into the voids, assuming, in a 2D representation, a characteristic butterfly shape. The ionization evolution is very well tracked by our scheme, as realized by the correct treatment of the channeling and shadowing effects due to overdensities. We confirm previous claims that both the shape of the IMF and the ionizing power metallicity dependence are important to correctly determine the reionization of the universe.Comment: 8 pages, 8 figures. Revised version, accepted for publication by MNRA

Cosmic Microwave Background Polarization and reionization: constraining models with a double reionization

Neutral hydrogen around high-z QSO and an optical depth tau ~ 0.17 can be reconciled if reionization is more complex than a single transition at z ~ 6-8. Tracing its details could shed a new light on the first sources of radiation. Here we discuss how far such details can be inspected through planned experiments on CMB large-scale anisotropy and polarization, by simulating an actual data analysis. By considering a set of double reionization histories of Cen (2003) type, a relevant class of models not yet considered by previous works, we confirm that large angle experiments rival high resolution ones in reconstructing the reionization history. We also confirm that reionization histories, studied with the prior of a single and sharp reionization, yield a biased tau, showing that this bias is generic. We further find a monotonic trend in the bias for the models that we consider, and propose an explanation of the trend, as well as the overall bias. We also show that in long-lived experiments such a trend can be used to discriminate between single and double reionization patterns.Comment: 8 pages, 11 figures. Substantial rewriting, replaced with accepted version. To be published in A&

Foregrounds for observations of the cosmological 21 cm line: I. First Westerbork measurements of Galactic emission at 150 MHz in a low latitude field

We present the first results from a series of observations conducted with the Westerbork telescope in the 140--160 MHz range with a 2 arcmin resolution aimed at characterizing the properties of the foregrounds for epoch of reionization experiments. For the first time we have detected fluctuations in the Galactic diffuse emission on scales greater than 13 arcmin at 150 MHz, in the low Galactic latitude area known as Fan region. Those fluctuations have an $rms$ of 14 K. The total intensity power spectrum shows a power--law behaviour down to $\ell \sim 900$ with slope $\beta^I_\ell = -2.2 \pm 0.3$. The detection of diffuse emission at smaller angular scales is limited by residual point sources. We measured an $rms$ confusion noise of $\sim$3 mJy beam$^{-1}$. Diffuse polarized emission was also detected for the first time at this frequency. The polarized signal shows complex structure both spatially and along the line of sight. The polarization power spectrum shows a power--law behaviour down to $\ell \sim 2700$ with slope $\beta^P_\ell = -1.65 \pm 0.15$. The $rms$ of polarization fluctuations is 7.2 K on 4 arcmin scales. By extrapolating the measured spectrum of total intensity emission, we find a contamination on the cosmological signal of $\delta T= \sqrt{\ell (\ell+1) C^I_\ell / 2\pi} \sim 5.7$ K on 5 arcmin scales and a corresponding $rms$ value of $\sim$18.3 K at the same angular scale. The level of the polarization power spectrum is $\delta T \sim 3.3$ K on 5 arcmin scales. Given its exceptionally bright polarized signal, the Fan region is likely to represent an upper limit on the sky brightness at moderate and high Galactic latitude.Comment: Minor corrections made to match the final version printed on A&A. A version with high resolution figures is available at http://www.astro.rug.nl/~bernardi/FAN/fan.pd