Compressed sensing reconstruction of a string signal from interferometric observations of the cosmic microwave background

We propose an algorithm for the reconstruction of the signal induced by cosmic strings in the cosmic microwave background (CMB), from radio-interferometric data at arcminute resolution. Radio interferometry provides incomplete and noisy Fourier measurements of the string signal, which exhibits sparse or compressible magnitude of the gradient due to the Kaiser-Stebbins effect. In this context, the versatile framework of compressed sensing naturally applies for solving the corresponding inverse problem. Our algorithm notably takes advantage of a model of the prior statistical distribution of the signal fitted on the basis of realistic simulations. Enhanced performance relative to the standard CLEAN algorithm is demonstrated by simulated observations under noise conditions including primary and secondary CMB anisotropie

Implications for compressed sensing of a new sampling theorem on the sphere

A sampling theorem on the sphere has been developed recently, requiring half as many samples as alternative equiangular sampling theorems on the sphere. A reduction by a factor of two in the number of samples required to represent a band-limited signal on the sphere exactly has important implications for compressed sensing, both in terms of the dimensionality and sparsity of signals. We illustrate the impact of this property with an inpainting problem on the sphere, where we show the superior reconstruction performance when adopting the new sampling theorem compared to the alternative.Comment: 1 page, 2 figures, Signal Processing with Adaptive Sparse Structured Representations (SPARS) 201

Sparse image reconstruction on the sphere: implications of a new sampling theorem

We study the impact of sampling theorems on the fidelity of sparse image reconstruction on the sphere. We discuss how a reduction in the number of samples required to represent all information content of a band-limited signal acts to improve the fidelity of sparse image reconstruction, through both the dimensionality and sparsity of signals. To demonstrate this result we consider a simple inpainting problem on the sphere and consider images sparse in the magnitude of their gradient. We develop a framework for total variation (TV) inpainting on the sphere, including fast methods to render the inpainting problem computationally feasible at high-resolution. Recently a new sampling theorem on the sphere was developed, reducing the required number of samples by a factor of two for equiangular sampling schemes. Through numerical simulations we verify the enhanced fidelity of sparse image reconstruction due to the more efficient sampling of the sphere provided by the new sampling theorem.Comment: 11 pages, 5 figure

Spread spectrum for imaging techniques in radio interferometry

We consider the probe of astrophysical signals through radio interferometers with a small field of view and baselines with a non-negligible and constant component in the pointing direction. In this context, the visibilities measured essentially identify with a noisy and incomplete Fourier coverage of the product of the planar signals with a linear chirp modulation. In light of the recent theory of compressed sensing and in the perspective of defining the best possible imaging techniques for sparse signals, we analyse the related spread spectrum phenomenon and suggest its universality relative to the sparsity dictionary. Our results rely both on theoretical considerations related to the mutual coherence between the sparsity and sensing dictionaries and on numerical simulation

Compressed sensing imaging techniques for radio interferometry

Radio interferometry probes astrophysical signals through incomplete and noisy Fourier measurements. The theory of compressed sensing demonstrates that such measurements may actually suffice for accurate reconstruction of sparse or compressible signals. We propose new generic imaging techniques based on convex optimization for global minimization problems defined in this context. The versatility of the framework notably allows introduction of specific prior information on the signals, which offers the possibility of significant improvements of reconstruction relative to the standard local matching pursuit algorithm CLEAN used in radio astronomy. We illustrate the potential of the approach by studying reconstruction performances on simulations of two different kinds of signals observed with very generic interferometric configurations. The first kind is an intensity field of compact astrophysical objects. The second kind is the imprint of cosmic strings in the temperature field of the cosmic microwave background radiation, of particular interest for cosmolog

Interpretive Authenticity: Performances, Versions, and Ontology

Julian Dodd defends the view that, in musical work-performance practice, interpretive authenticity is a more fundamental value than score compliance authenticity. According to him, compliance with a work’s score can be sacrificed in cases where it conflicts with interpretative authenticity. Stephen Davies and Andrew Kania reject this view, arguing that, if a performer intentionally departs from a work’s score, she is not properly instantiating that work and hence not producing an authentic performance of it. I argue that this objection fails. A detailed analysis of work-performance practice reveals, first, that the normative scope of interpretive authenticity encompasses the practice of composing musical versions and that, second, when performers sacrifice score compliance to maximize interpretive authenticity, they are performing the target work by means of performing a version of it. By means of the nested types theory, I then show how performances produced in this way can be properly formed instances, and hence authentic performances, of their target work.13515

The distribution of two-dimensional eccentricity of Sunyaev-Zeldovich Effect and X-ray surface brightness profiles

With the triaxial density profile of dark matter halos and the corresponding equilibrium gas distribution, we derive two-dimensional Sunyaev-Zeldovich (SZ) effect and X-ray surface brightness profiles for clusters of galaxies. It is found that the contour map of these observables can be well approximated by a series of concentric ellipses with scale-dependent eccentricities. The statistical distribution of their eccentricities (or equivalently axial ratios) is analyzed by taking into account the orientation of clusters with respect to the line of sight and the distribution of the axial ratios and the concentration parameters of dark matter halos. For clusters of mass $10^{13}h^{-1}{M}_{\odot}$ at redshift $z=0$, the axial ratio is peaked at $\eta \sim 0.9$ for both SZ and X-ray profiles. For larger clusters, the deviation from circular distributions is more apparent, with $\eta$ peaked at $\eta \sim 0.85$ for $M=10^{15}h^{-1}{M}_{\odot}$. To be more close to observations, we further study the axial-ratio distribution for mass-limited cluster samples with the number distribution of clusters at different redshifts described by a modified Press-Schechter model. For a mass limit of value $M_{lim}=10^{14}h^{-1}{M}_{\odot}$, the average axial ratio is $\sim 0.84$ with a tail extended to $\eta \sim 0.6$. With fast advance of high quality imaging observations of both SZ effect and X-ray emissions, our analyses provide a useful way to probe cluster halo profiles and therefore to test theoretical halo-formation models.Comment: 28 pages, 6 figures. Accepted for publication in the Astrophysical Journa

Limits on decaying dark energy density models from the CMB temperature-redshift relation

The nature of the dark energy is still a mystery and several models have been proposed to explain it. Here we consider a phenomenological model for dark energy decay into photons and particles as proposed by Lima (J. Lima, Phys. Rev. D 54, 2571 (1996)). He studied the thermodynamic aspects of decaying dark energy models in particular in the case of a continuous photon creation and/or disruption. Following his approach, we derive a temperature redshift relation for the CMB which depends on the effective equation of state $w_{eff}$ and on the "adiabatic index" $\gamma$. Comparing our relation with the data on the CMB temperature as a function of the redshift obtained from Sunyaev-Zel'dovich observations and at higher redshift from quasar absorption line spectra, we find $w_{eff}=-0.97 \pm 0.034$, adopting for the adiabatic index $\gamma=4/3$, in good agreement with current estimates and still compatible with $w_{eff}=-1$, implying that the dark energy content being constant in time.Comment: 8 pages, 1 figur

Low-Mass Star Formation, Triggered by Supernova in Primordial Clouds

The evolution of a gas shell, swept by the supernova remnant of a massive first generation star, is studied with H_2 and HD chemistry taken into account. When a first-generation star explodes as a supernova, H_2 and HD molecules are formed in the swept gas shell and effectively cool the gas shell to temperatures of 32 K - 154 K. If the supernova remnant can sweep to gather the ambient gas, the gas shell comes to be dominated by its self-gravity, and hence, is expected to fragment. Our result shows that for a reasonable range of temperatures (200 K - 1000 K) of interstellar gas, the formation of second-generation stars can be triggered by a single supernova or hypernova.Comment: 38pages, 10 figures, The Astrophysical Journal, accepted 8 Dec. 200

The first spectral line surveys searching for signals from the Dark Ages

Our aim is to observationally investigate the cosmic Dark Ages in order to constrain star and structure formation models, as well as the chemical evolution in the early Universe. Spectral lines from atoms and molecules in primordial perturbations at high redshifts can give information about the conditions in the early universe before and during the formation of the first stars in addition to the epoch of reionisation. The lines may arise from moving primordial perturbations before the formation of the first stars (resonant scattering lines), or could be thermal absorption or emission lines at lower redshifts. The difficulties in these searches are that the source redshift and evolutionary state, as well as molecular species and transition are unknown, which implies that an observed line can fall within a wide range of frequencies. The lines are also expected to be very weak. Observations from space have the advantages of stability and the lack of atmospheric features which is important in such observations. We have therefore, as a first step in our searches, used the Odin satellite to perform two sets of spectral line surveys towards several positions. The first survey covered the band 547-578 GHz towards two positions, and the second one covered the bands 542.0-547.5 GHz and 486.5-492.0 GHz towards six positions selected to test different sizes of the primordial clouds. Two deep searches centred at 543.250 and 543.100 GHz with 1 GHz bandwidth were also performed towards one position. The two lowest rotational transitions of H2 will be redshifted to these frequencies from z~20-30, which is the predicted epoch of the first star formation. No lines are detected at an rms level of 14-90 and 5-35 mK for the two surveys, respectively, and 2-7 mK in the deep searches with a channel spacing of 1-16 MHz. The broad bandwidth covered allows a wide range of redshifts to be explored for a number of atomic and molecular species and transitions. From the theoretical side, our sensitivity analysis show that the largest possible amplitudes of the resonant lines are about 1 mK at frequencies <200 GHz, and a few micro K around 500-600 GHz, assuming optically thick lines and no beam-dilution. However, if existing, thermal absorption lines have the potential to be orders of magnitude stronger than the resonant lines. We make a simple estimation of the sizes and masses of the primordial perturbations at their turn-around epochs, which previously has been identified as the most favourable epoch for a detection. This work may be considered as an important pilot study for our forthcoming observations with the Herschel Space Observatory.Comment: 15 pages, 9 figures, 3 on-line pages. Accepted for publication in Astronomy & Astrophysics 8 March 2010