Article

# Principal Component Analysis of Weak Lensing Surveys

University of Bonn, Bonn, North Rhine-Westphalia, Germany

Astronomy and Astrophysics (Impact Factor: 4.38). 11/2005; 452(1). DOI: 10.1051/0004-6361:20054586 Source: arXiv

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**ABSTRACT:**We review progress in understanding dark matter by astrophysics, and particularly via the effect of gravitational lensing. Evidence from many different directions now all imply that five sixths of the material content of the universe is in this mysterious form, separate from and beyond the ordinary "baryonic" particles in the standard model of particle physics. Dark matter appears not to interact via the electromagnetic force, and therefore neither emits nor reflects light. However, it definitely does interact via gravity, and has played the most important role in shaping the Universe on large scales. The most successful technique with which to investigate it has so far been the effect of gravitational lensing. The curvature of space-time near any gravitating mass (including dark matter) deflects passing rays of light - observably shifting, distorting and magnifying the images of background galaxies. Measurements of such effects currently provide constraints on the mean density of dark matter, and its density relative to baryonic matter; the size and mass of individual dark matter particles; and its cross section under various fundamental forces. Comment: 48 page Rep Prog Phys review. Matches published version. - [Show abstract] [Hide abstract]

**ABSTRACT:**Using a semi-analytical model developed by Choudhury & Ferrara we study the observational constraints on reionization via a principal component analysis (PCA). Assuming that reionization at z > 6 is primarily driven by stellar sources, we decompose the unknown function Nion(z), representing the number of photons in the intergalactic medium per baryon in collapsed objects, into its principal components and constrain the latter using the photoionization rate, ΓPI, obtained from Lyα forest Gunn–Peterson optical depth, the 7 yr Wilkinson Microwave Anisotropy Probe (WMAP7) electron scattering optical depth τel and the redshift distribution of Lyman-limit systems dNLL/dz at z∼ 3.5. The main findings of our analysis are as follows. (i) It is sufficient to model Nion(z) over the redshift range 2 < z < 14 using five parameters to extract the maximum information contained within the data. (ii) All quantities related to reionization can be severely constrained for z < 6 because of a large number of data points whereas constraints at z > 6 are relatively loose. (iii) The weak constraints on Nion(z) at z > 6 do not allow to disentangle different feedback models with present data. There is a clear indication that Nion(z) must increase at z > 6, thus ruling out reionization by a single stellar population with non-evolving initial mass function, and/or star-forming efficiency, and/or photon escape fraction. The data allow for non-monotonic Nion(z) which may contain sharp features around z∼ 7. (iv) The PCA implies that reionization must be 99 per cent completed between 5.8 < z < 10.3 (95 per cent confidence level) and is expected to be 50 per cent complete at z≈ 9.5–12. With future data sets, like those obtained by Planck, the z > 6 constraints will be significantly improved.