Publications (11)51.07 Total impact
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ABSTRACT: We study various measures of weaklensing distortions in future surveys, taking into account the noise arising from the finite survey size and the intrinsic ellipticity of galaxies. We also consider a realistic redshift distribution of the sources, as expected for the SNAP mission. We focus on the loworder moments and the full distribution function (PDF) of the aperture mass Map and of the smoothed shear component γis. We also propose new unbiased estimators for loworder cumulants which have less scatter than the usual estimators of nonGaussianity based on the moments themselves. Then, using an analytical model which has already been seen to provide a good description of weak gravitational lensing through a comparison with numerical simulations, we study the statistical measures that can be extracted from future surveys such as the SNAP experiment. We recover the fact that at small angular scales (1 < θs < 10 arcmin) the variance can be extracted with an accuracy of a few per cent. NonGaussianity can also be measured from the skewness of the aperture mass (at a 10 per cent level), while the shear kurtosis is more noisy and cannot be easily measured beyond 6 arcmin. On the other hand, we find that the PDF of the estimator associated with the aperture mass can be distinguished both from the Gaussian and the Edgeworth expansion and could provide useful constraints, while this appears to be difficult to realize with the shear component. Finally, we investigate various survey strategies and the possibility of performing a redshift binning of the sample.  [Show abstract] [Hide abstract]
ABSTRACT: We describe the predictions for the smoothed weak lensing shear, γs, and aperture mass,Map, of two simple analytical models of the density field: the minimal tree model and the stellar model. Both models give identical results for the statistics of the three‐dimensional density contrast smoothed over spherical cells and only differ by the detailed angular dependence of the many‐body density correlations. We have shown in previous work that they also yield almost identical results for the probability distribution function (PDF) of the smoothed convergence, κs. We find that the two models give rather close results for both the shear and the positive tail of the aperture mass. However, we note that at small angular scales (θs≲ 2 arcmin) the tail of the PDF, , for negative Map shows a strong variation between the two models, and the stellar model actually breaks down for θs≲ 0.4 arcmin and Map < 0. This shows that the statistics of the aperture mass provides a very precise probe of the detailed structure of the density field, as it is sensitive to both the amplitude and the detailed angular behaviour of the many‐body correlations. On the other hand, the minimal tree model shows good agreement with numerical simulations over all the scales and redshifts of interest, while both models provide a good description of the PDF, , of the smoothed shear components. Therefore, the shear and the aperture mass provide robust and complementary tools to measure the cosmological parameters as well as the detailed statistical properties of the density field. 
Article: From linear to nonlinear scales: Analytical and numerical predictions for weaklensing convergence
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ABSTRACT: Weak lensing convergence can be used directly to map and probe the dark mass distribution in the universe. Building on earlier studies, we recall how the statistics of the convergence field are related to the statistics of the underlying mass distribution, in particular to the manybody density correlations. We describe two modelindependent approximations which provide two simple methods to compute the probability distribution function, pdf, of the convergence. We apply one of these to the case where the density field can be described by a lognormal pdf. Next, we discuss two hierarchical models for the highorder correlations which allow one to perform exact calculations and evaluate the previous approximations in such specific cases. Finally, we apply these methods to a very simple model for the evolution of the density field from linear to highly nonlinear scales. Comparisons with the results obtained from numerical simulations, obtained from a number of different realizations, show excellent agreement with our theoretical predictions. We have probed various angular scales in the numerical work and considered sources at 14 different redshifts in each of two different cosmological scenarios, an open cosmology and a flat cosmology with nonzero cosmological constant. Our simulation technique employs computations of the full 3d shear matrices along the line of sight from the source redshift to the observer and is complementary to more popular raytracing algorithms. Our results therefore provide a valuable crosscheck for such complementary simulation techniques, as well as for our simple analytical model, from the linear to the highly nonlinear regime. Comment: 20 pages, final version published in MNRAS  [Show abstract] [Hide abstract]
ABSTRACT: Weak gravitational lensing surveys are rapidly becoming important tools to probe directly the mass density fluctuations in the Universe and its background dynamics. Earlier studies have shown that it is possible to model the statistics of the convergence field on small angular scales by suitably modelling the statistics of the underlying density field in the highly nonlinear regime. We extend such methods to model the complete probability distribution function of the shear as a function of smoothing angle. Our model relies on a simple hierarchical Ansatz for the behaviour of the higherorder correlations in the density field. We compare our predictions with the results of numerical simulations and find excellent agreement for different cosmological scenarios. Our method provides a new way to study the evolution of nonGaussianity in gravitational clustering and should help to break the degeneracies in parameter estimation based on analysis of the power spectrum alone.  [Show abstract] [Hide abstract]
ABSTRACT: We present new results on the gravitational lensing shear and magnification power spectra obtained from numerical simulations of a flat cosmology with a cosmological constant. These results are of considerable interest since both the shear and the magnification are observables. We find that the power spectrum in the convergence behaves as expected, but the magnification develops a shotnoise spectrum due to the effects of discrete, massive clusters and symptomatic of moderate lensing beyond the weaklensing regime. We find that this behaviour can be suppressed by ‘clipping’ of the largest projected clusters. Our results are compared with predictions from a halomodelinspired functional fit for the nonlinear evolution of the matter field and show excellent agreement. We also study the higherorder moments of the convergence field and find a new scaling relationship with redshift. In particular, the statistic S3 is found to vary as z−2.00±0.08s (where zs is the source redshift) for the cosmology studied, which makes corrections for different median redshifts in different observational surveys particularly simple to apply.  [Show abstract] [Hide abstract]
ABSTRACT: The weak lensing shear signal has been measured numerically in Nbody simulations at 14 different redshifts (zs= 0.1 to 3.6) and on angular scales of θ= 2 to 32 arcmin. In addition, the data have been validated by analytical computations for an identical cosmology, with density parameter Ωm= 0.3 and vacuum energy density parameter λ0= 0.7. This paper reports on the scale and redshift dependence of the shear variance, 〈γ2〉, which may be described by a simple formula of the form 〈γ2〉 (θ, zs) =a(θ) zsb(θ). The redshift dependence for source redshifts up to 1.6 is found to be close to zs2, which is a stronger dependence than earlier analytical predictions (〈γ2〉∝zs1.52), although, at higher redshifts, the zs dependence of the shear variance is clearly less steep. The strong redshift dependence further emphasizes the need to know the precise redshift distribution for the galaxy sources in any given survey, so that they can be allocated to redshift bins accordingly, and the cosmic shear signal correctly interpreted. Equations are also given for the variance in the reduced shear, which is a more directly measurable quantity observationally.  [Show abstract] [Hide abstract]
ABSTRACT: Significant adjustments to the values of the cosmological parameters estimated from highredshift Type Ia supernovae data are reported, almost an order of magnitude greater than previously found. They arise from the effects of weak gravitational lensing on observations of highredshift sources. The lensing statistics used have been obtained from computations of the threedimensional shear in a range of cosmological Nbody simulations, from which it is estimated that cosmologies with an underlying deceleration parameter may be interpreted as having q0=−0.55 (appropriate to the currently popular cosmology with density parameter ΩM=0.3 and vacuum energy density parameter ΩΛ=0.7). In addition, the standard deviation expected from weak lensing for the peak magnitudes of Type Ia supernovae at redshifts of z=1 is expected to be approximately 0.078 mag, and 0.185 mag at redshift z=2. This latter value is greater than the accepted intrinsic dispersion of 0.17 mag. Consequently, the effects of weak lensing in observations of highredshift sources must be taken properly into account.  [Show abstract] [Hide abstract]
ABSTRACT: We present the results of weak gravitational lensing statistics in four different cosmological Nbody simulations. The data have been generated using an algorithm for the threedimensional shear, which makes use of a variable softening facility for the Nbody particle masses, and enables a physical interpretation for the largescale structure to be made. Working in three dimensions also allows the correct use of the appropriate angular diameter distances. Our results are presented on the basis of the filledbeam approximation in view of the variable particle softening scheme in our algorithm. The importance of the smoothness of matter in the Universe for the weak lensing results is discussed in some detail. The lowdensity cosmology with a cosmological constant appears to give the broadest distributions for all the statistics computed for sources at high redshifts. In particular, the range in magnification values for this cosmology has implications for the determination of the cosmological parameters from highredshift type Ia supernovae. The possibility of determining the density parameter from the nonGaussianity in the probability distribution for the convergence is discussed.  [Show abstract] [Hide abstract]
ABSTRACT: The effects of differences between the local and global values of the Hubble parameter on the cosmologies consistent with studies of highredshift Type Ia supernov\ae are discussed. It is found that with a local Hubble parameter around 10 per cent higher than the global value then open cosmological models (such as $\Omega_{M} = 0.3, \Omega_{\Lambda}=0$) are prefered and if the local value is around 20 per cent higher then standard cosmological models ($\Omega_{M} = 1, \Omega_{\Lambda}=0$) can be recovered. Even in the case where the Hubble parameter ratio is 1, low $\Omega_M$ open cosmologies with $\Omega_{\Lambda} = 0$ are not rejected at the 95 per cent confidence level.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the effects of weak gravitational lensing in the standard Cold Dark Matter cosmology, using an algorithm which evaluates the shear in three dimensions. The algorithm has the advantage of variable softening for the particles, and our method allows the appropriate angular diameter distances to be applied to every evaluation location within each threedimensional simulation box. We investigate the importance of shear in the distanceredshift relation, and find it to be very small. We also establish clearly defined values for the smoothness parameter in the relation, finding its value to be at least 0.88 at all redshifts in our simulations. From our results, obtained by linking the simulation boxes back to source redshifts of 4, we are able to observe the formation of structure in terms of the computed shear, and also note that the major contributions to the shear come from a very broad range of redshifts. We show the probability distributions for the magnification, source ellipticity and convergence, and also describe the relationships amongst these quantities for a range of source redshifts. We find a broad range of magnifications and ellipticities; for sources at a redshift of 4, 97{1/2}% of all lines of sight show magnifications up to 1.3 and ellipticities up to 0.195. There is clear evidence that the magnification is not linear in the convergence, as might be expected for weak lensing, but contains contributions from higher order terms in both the convergence and the shear. Comment: 14 pages, LaTeX, 15 figures included  [Show abstract] [Hide abstract]
ABSTRACT: We have developed a new threedimensional algorithm, based on the standard P$^3$M method, for computing deflections due to weak gravitational lensing. We compare the results of this method with those of the twodimensional planar approach, and rigorously outline the conditions under which the two approaches are equivalent. Our new algorithm uses a Fast Fourier Transform convolution method for speed, and has a variable softening feature to provide a realistic interpretation of the largescale structure in a simulation. The output values of the code are compared with those from the Ewald summation method, which we describe and develop in detail. With an optimal choice of the high frequency filtering in the Fourier convolution, the maximum errors, when using only a single particle, are about 7 per cent, with an rms error less than 2 per cent. For ensembles of particles, used in typical $N$body simulations, the rms errors are typically 0.3 per cent. We describe how the output from the algorithm can be used to generate distributions of magnification, source ellipticity, shear and convergence for largescale structure. Comment: 22 pages, latex, 11 figures
Publication Stats
194  Citations  
51.07  Total Impact Points  
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Institutions

19982004

University of Sussex
 Astronomy Centre
Brighton, England, United Kingdom
