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1.
Several recent papers have studied lensing of the CMB by large-scale structures, which probes the projected matter distribution from z=103 to z0. This interest is motivated in part by upcoming high resolution, high sensitivity CMB experiments, such as APEX/SZ, ACT, SPT or Planck, which should be sensitive to lensing. In this paper, we examine the reconstruction of the large-scale dark matter distribution from lensed CMB temperature anisotropies. We go beyond previous work in using numerical simulations to include higher order, non-Gaussian effects and find that the convergence and its power spectrum are biased, with the bias increasing with the angular resolution. We also study the contamination by the kinetic Sunyaev–Zel'dovich signal, which is spectrally indistinguishable from lensed CMB anisotropies, and find that it leads to an overestimate of the convergence. We finish by estimating the sensitivity of the previously cited experiments and find that all of them could detect the lensing effect, but would be biased at around the 10% level.  相似文献   

2.
We present ray tracing simulations combined with sets of large N -body simulations. Experiments were performed to explore, for the first time, the statistical properties of fluctuations in angular separation of nearby light-ray pairs (the so-called lensing excursion angle) induced by weak lensing by large-scale structures. We found that the probability distribution function (PDF) of the lensing excursion angles is not simply Gaussian, but has an exponential tail. It is found, however, that the tail, or more generally the non-Gaussian nature of the PDF has no significant impact on the weak lensing of the cosmic microwave background (CMB). Moreover, we found that the variance in the lensing excursion angles predicted by the power spectrum approach is in good agreement with our numerical results. These results demonstrate the validity of using the power spectrum approach to compute lensing effects on the CMB.  相似文献   

3.
The Sunyaev–Zel'dovich (SZ) effect and the Faraday rotation from haloes are examined over a wide mass range, including gas condensation and magnetic field evolution. Contributions to the cosmic microwave background (CMB) angular power spectrum are evaluated for galaxy clusters, galaxy groups and galaxies. Smaller mass haloes are found to play a more important role than massive haloes for the B -mode polarization associated with the SZ CMB anisotropies. The B modes from the Faraday rotation dominate the secondary B modes caused by gravitational lensing at  ℓ > 3000  . Measurement of B -mode polarization in combination with the SZ power spectrum can potentially provide important constraints on intracluster magnetic field and gas evolution at early epochs.  相似文献   

4.
We use the large cosmological Millennium Simulation (MS) to construct the first all-sky maps of the lensing potential and the angle, aiming at gravitational lensing of the cosmic microwave background (CMB), with the goal of properly including small-scale non-linearities and non-Gaussianity. Exploiting the Born approximation, we implement a map-making procedure based on direct ray tracing through the gravitational potential of the MS. We stack the simulation box in redshift shells up to z ∼ 11, producing continuous all-sky maps with arcmin angular resolution. A randomization scheme avoids the repetition of structures along the line of sight, and structures larger than the MS box size are added to supply the missing contribution of large-scale (LS) structures to the lensing signal. The angular power spectra of the projected lensing potential and the deflection-angle modulus agree quite well with semi-analytic estimates on scales down to a few arcmin, while we find a slight excess of power on small scales, which we interpret as being due to non-linear clustering in the MS. Our map-making procedure, combined with the LS adding technique, is ideally suited for studying lensing of CMB anisotropies, for analysing cross-correlations with foreground structures, or other secondary CMB anisotropies such as the Rees–Sciama effect.  相似文献   

5.
We investigate the weak gravitational lensing effect that is due to the large-scale structure of the universe on two-point correlations of local maxima (hot spots) in the two-dimensional sky map of the cosmic microwave background (CMB) anisotropy. According to the Gaussian random statistics, as most inflationary scenarios predict, the hot spots are discretely distributed, with some characteristic angular separations on the last scattering surface that are due to oscillations of the CMB angular power spectrum. The weak lensing then causes pairs of hot spots, which are separated with the characteristic scale, to be observed with various separations. We found that the lensing fairly smooths out the oscillatory features of the two-point correlation function of hot spots. This indicates that the hot spot correlations can be a new statistical tool for measuring the shape and normalization of the power spectrum of matter fluctuations from the lensing signatures.  相似文献   

6.
We study the limits of accuracy for weak lensing maps of dark matter using diffuse 21-cm radiation from the pre-reionization epoch using simulations. We improve on previous 'optimal' quadratic lensing estimators by using shear and convergence instead of deflection angles. This is a generalization of the deflection estimator, and is more optimal for non-Gaussian sources. The cross-power spectrum of shear and convergence is an unbiased estimator of lensing power spectrum which does not require knowledge of the source four-point function. We find that non-Gaussianity provides a limit to the accuracy of weak lensing reconstruction, even if instrumental noise is reduced to zero. The best reconstruction result is equivalent to Gaussian sources with effective independent cell of side length  2.0  h −1 Mpc  . Using a source full map from z = 10 to 20, this limiting sensitivity allows mapping of dark matter at a signal-to-noise ratio greater than 1 out to l ≲ 6000, which is better than any other proposed technique for large-area weak lensing mapping.  相似文献   

7.
Using large numbers of simulations of the microwave sky, incorporating the cosmic microwave background (CMB) and the Sunyaev–Zel'dovich (SZ) effect due to clusters, we investigate the statistics of the power spectrum at microwave frequencies between spherical multipoles of 1000 and 10 000. From these virtual sky maps, we find that the spectrum of the SZ effect has a larger standard deviation by a factor of 3 than would be expected from purely Gaussian realizations, and has a distribution that is significantly skewed towards higher values, especially when small map sizes are used. The standard deviation is also increased by around 10 per cent compared to the trispectrum calculation due to the clustering of galaxy clusters. We also consider the effects of including residual point sources and uncertainties in the gas physics. This has implications for the excess power measured in the CMB power spectrum by the Cosmic Background Imager (CBI) and Berkeley–Illinois–Maryland Association (BIMA) experiments. Our results indicate that the observed excess could be explained using a lower value of σ8 than previously suggested, however the effect is not enough to match  σ8= 0.825  . The uncertainties in the gas physics could also play a substantial role. We have made our maps of the SZ effect available online.  相似文献   

8.
The weak lensing power spectrum carries cosmological information via its dependence on the growth of structure and on geometric factors. Since much of the cosmological information comes from scales affected by non-linear clustering, measurements of the lensing power spectrum can be degraded by non-Gaussian covariances. Recently, there have been conflicting studies about the level of this degradation. We use the halo model to estimate it and include new contributions related to the finite size of lensing surveys, following Rimes and Hamilton's study of three-dimensional simulations. We find that non-Gaussian correlations between different multipoles can degrade the cumulative signal-to-noise ratio (S/N) for the power spectrum amplitude by up to a factor of 2 (or 5 for a worst-case model that exceeds current N -body simulation predictions). However, using an eight-parameter Fisher analysis, we find that the marginalized errors on individual parameters are degraded by less than 10 per cent (or 20 per cent for the worst-case model). The smaller degradation in parameter accuracy is primarily because: individual parameters in a high-dimensional parameter space are degraded much less than the volume of the full Fisher ellipsoid; lensing involves projections along the line of sight, which reduce the non-Gaussian effect; some of the cosmological information comes from geometric factors which are not degraded at all. We contrast our findings with those of Lee and Pen who suggested a much larger degradation in information content. Finally, our results give a useful guide for exploring survey design by giving the cosmological information returns for varying survey area, depth and the level of some systematic errors.  相似文献   

9.
In this paper, I investigate a local effect of polarization of the Cosmic Microwave Background (CMB) in clusters of galaxies, induced by the Thomson scattering of an anisotropic radiation. A local anisotropy of the CMB is produced by some scattering and gravitational effects, as, for instance, the Sunyaev Zel‘dovich effect, the Doppler shift due to the cluster motion and the gravitational lensing. The resulting anisotropy ΔI/I depends on the physical properties of the clusters, in particular on their emissivity in the X band on their size, on their gravitational potential and on the peculiar conditions characterizing the gas they contain. By solving the Boltzmann radiative transfer equation in presence of such anisotropies I calculate the average polarization at the centre of some clusters, namelyA2218, A576 and A2163, whose properties are quite well known. I prove that the gravitational effects due to the contraction or to the expansion have some importance, particularly for high density structures; moreover, the peculiar motion of the cluster, considered as a gravitational lens, influences the propagation of the CMB photons by introducing a particular angular dependence in the gravitational anisotropy and in the scattering integrals. Thus, the gravitational and the scattering effects overally produce an appreciable local average polarization of the CMB, may be observable through a careful polarization measurements towards the centres of the galaxy clusters. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

10.
《New Astronomy》2003,8(6):565-573
We discuss fluctuations in the cosmic microwave background (CMB) polarization due to scattering from reionized gas at low redshifts. Polarization is produced by re-scattering of the primordial temperature anisotropy quadrupole and of the kinematic quadrupole that arises from gas motion transverse to the line of sight. We show that both effects produce equal E- and B-parity polarization, and are, in general, several orders of magnitude below the dominant polarization contributions at the last scattering surface to E-modes or the gravitational-lensing contribution to B-modes at intermediate redshifts. These effects are also several orders of magnitude below the B polarization due to lensing even after subtraction with higher-order correlations, and are thus too small to constitute a background for searches for the polarization signature of inflationary gravitational waves.  相似文献   

11.
The brightness temperature fluctuations in the 21-cm background related to the neutral hydrogen distribution provide a probe of the physics related to the era of reionization, when the intergalactic medium changed from being completely neutral to partially ionized. We formulate statistics of 21-cm brightness temperature anisotropies in terms of the angular power spectrum, the bispectrum, and the trispectrum. Using the trispectrum, we estimate the covariance related to the power spectrum measurements and show that correlations resulting from non-Gaussianities are below a per cent, at most. While all-sky observations of the 21-cm background at arcminute-scale resolution can be used to measure the bispectrum with a cumulative signal-to-noise ratio of the order of a few tens, in the presence of foregrounds and instrumental noise related to first-generation interferometers, the measurement is unlikely to be feasible. For most purposes, non-Gaussianities in 21-cm fluctuations can be ignored and the distribution can be described with Gaussian statistics. Because 21-cm fluctuations are significantly contaminated by foregrounds, such as galactic synchrotron or low-frequency radio point sources, the lack of significant non-Gaussianity in the signal suggests that any significant detection of non-Gaussianity could be the result of foregrounds. Similarly, in addition to the frequency information that is now proposed to separate 21-cm fluctuations from foregrounds, if the non-Gaussian structure of foregrounds is known a priori, this additional information could potentially be used to reduce the confusion further.  相似文献   

12.
Since the strength of weak gravitational lensing is proportional to the mass along the line of sight, it might be possible to use lensing data to find the masses of individual dark matter clusters. Unfortunately, the effect on the lensing field of other matter along the line of sight is substantial. We investigate to what extent we can correct for these projection effects if we have additional information about the most massive halos along the line of sight from deep optical data. We do this by calculating the contributions of these line-of-sight halos to the lensing field and then subtracting off this effect. Three different approaches are used to calculate these contributions: the first approach uses the exact mass distribution of the line-of-sight halos, the second assumes the masses are known and uses the NFW model and the third approach uses richness as an estimator for mass and then also assumes the NFW model. We find that, whichever approach we take, unless we know the masses and positions of line-of-sight halos down to a very low mass, we can only correct for a small part of the line-of-sight projection. We conclude that if we try to use lensing data to find individual cluster masses, there is an error of about 15–20% due to line-of-sight projection that cannot be corrected for.  相似文献   

13.
We have constructed the first all-sky cosmic microwave background (CMB) temperature and polarization lensed maps based on a high-resolution cosmological N -body simulation, the Millennium Simulation (MS). We have exploited the lensing potential map obtained using a previously developed map-making procedure which integrates along the line-of-sight the MS dark matter distribution by stacking and randomizing the simulation boxes up to   z = 127  , and which semi-analytically supplies the large-scale power in the angular lensing potential that is not correctly sampled by the N -body simulation. The lensed sky has been obtained by properly modifying the latest version of the LensPix code to account for the MS structures. We have also produced all-sky lensed maps of the so-called  ψ E   and  ψ B   potentials, which are directly related to the electric and magnetic types of polarization. The angular power spectra of the simulated lensed temperature and polarization maps agree well with semi-analytic estimates up to   l ≤ 2500  , while on smaller scales we find a slight excess of power which we interpret as being due to non-linear clustering in the MS. We also observe how non-linear lensing power in the polarized CMB is transferred to large angular scales by suitably misaligned modes in the CMB and the lensing potential. This work is relevant in view of the future CMB probes, as a way to analyse the lensed sky and disentangle the contribution from primordial gravitational waves.  相似文献   

14.
As the quality of the available galaxy cluster data improves, the models fitted to these data might be expected to become increasingly complex. Here we present the Bayesian approach to the problem of cluster data modelling: starting from simple, physically motivated parametrized functions to describe the cluster's gas density, gravitational potential and temperature, we explore the high-dimensional parameter spaces with a Markov-Chain Monte Carlo sampler, and compute the Bayesian evidence in order to make probabilistic statements about the models tested. In this way sufficiently good data will enable the models to be distinguished, enhancing our astrophysical understanding; in any case the models may be marginalized over in the correct way when estimating global, perhaps cosmological, parameters. In this work we apply this methodology to two sets of simulated interferometric Sunyaev–Zel'dovich effect and gravitational weak lensing data, corresponding to current and next-generation telescopes. We calculate the expected precision on the measurement of the cluster gas fraction from such experiments, and investigate the effect of the primordial cosmic microwave background (CMB) fluctuations on their accuracy. We find that data from instruments such as the Arcminute Microkelvin Imager (AMI), when combined with wide-field ground-based weak lensing data, should allow both cluster model selection and estimation of gas fractions to a precision of better than 30 per cent for a given cluster.  相似文献   

15.
The various measurements of the linear matter density perturbation amplitude obtained from the observations of the cosmic microwave background (CMB) anisotropy, weak gravitational lensing, galaxy cluster mass function, matter power spectrum, and redshift space distortions are compared. The Planck data on the CMB temperature anisotropy spectrum at high multipoles, ? > 1000 (where the effect of gravitational lensing is most significant), are shown to give a measurement of the matter density perturbation amplitude that contradicts all other measurements of this quantity from both Planck CMB anisotropy data and other data at a significance level of about 3.7σ. Thus, at present these data should not be combined together for the calculations of constraints on cosmological parameters. Except for the Planck data on the CMB temperature anisotropy spectrum at high multipoles, all the remaining measurements of the density perturbation amplitude agree well between themselves and give the following constraints: σ8 = 0.792± 0.006 on the linear matter density perturbation amplitude, Ωm = 0.287± 0.007 on the matter density parameter, and H0 = 69.4 ± 0.6 km s?1 Mpc?1 on the Hubble constant. Various constraints on the sum of neutrino masses and the number of neutrino flavors can be obtained by additionally taking into account the data on baryon acoustic oscillations and (or) direct Hubble constant measurements in the local Universe.  相似文献   

16.
One of the main obstacles for extracting the Cosmic Microwave Background (CMB) from mm/submm observations is the pollution from the main Galactic components: synchrotron, free‐free and thermal dust emission. The feasibility of using simple neural networks to extract CMB has been demonstrated on both temperature and polarization data obtained by the WMAP satellite. The main goal of this paper is to demonstrate the feasibility of neural networks for extracting the CMB signal from the Planck polarization data with high precision. Both auto‐correlation and cross‐correlation power spectra within a mask covering about 63 % of the sky have been used together with a “high pass filter” in order to minimize the influence of the remaining systematic errors in the Planck Q and U maps. Using the Planck 2015 released polarization maps, a BB power spectrum have been extracted by Multilayer Perceptron neural networks. This spectrum contains a bright feature with signal to noise ratios 4.5 within 200 ≪ l ≪ 250. The spectrum is significantly brighter than the BICEP2 2015 spectrum, with a spectral behaviour quite different from the “canonical” models (weak lensing plus B‐modes spectra with different tensor to scalar ratios). The feasibility of the neural network to remove the residual systematics from the available Planck polarization data to a high level has been demonstrated. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

17.
We study the contribution of a stochastic background (SB) of primordial magnetic fields (PMFs) on the anisotropies in temperature and polarization of the cosmic microwave background (CMB) radiation. A SB of PMF modelled as a fully inhomogeneous component induces non-Gaussian scalar, vector and tensor metric linear perturbations. We give the exact expressions for the Fourier spectra of the relevant energy–momentum components of such a SB, given a power-law dependence parametrized by a spectral index   nB   for the magnetic field power spectrum cut at a damping scale k D. For all the values of   nB   considered here, the contribution to the CMB temperature pattern by such a SB is dominated by the scalar contribution and then by the vector one at higher multipoles. We also give an analytic estimate of the scalar contribution to the CMB temperature pattern.  相似文献   

18.
Destriping methods for constructing maps of the cosmic microwave background (CMB) anisotropies have been investigated extensively in the literature. However, their error properties have been studied in less detail. Here we present an analysis of the effects of destriping errors on CMB power spectrum estimates for Planck -like scanning strategies. Analytic formulae are derived for certain simple scanning geometries that can be rescaled to account for different detector noise. Assuming Planck -like low-frequency noise, the noise power spectrum is accurately white at high multipoles  (ℓ≳ 50)  . Destriping errors, though dominant at lower multipoles, are small in comparison to the cosmic variance. These results show that simple destriping map-making methods should be perfectly adequate for the analysis of Planck data and support the arguments given in an earlier paper in favour of applying a fast hybrid power spectrum estimator to CMB data with realistic '1/ f ' noise.  相似文献   

19.
The identification of non-Gaussian signatures in cosmic microwave background (CMB) temperature maps is one of the main cosmological challenges today. We propose and investigate alternative methods to analyse CMB maps. Using the technique of constrained randomization, we construct surrogate maps which mimic both the power spectrum and the amplitude distribution of simulated CMB maps containing non-Gaussian signals. Analysing the maps with weighted scaling indices and Minkowski functionals yields in both cases statistically significant identification of the primordial non-Gaussianities. We demonstrate that the method is very robust with respect to noise. We also show that Minkowski functionals are able to account for non-linearities at higher noise level when applied in combination with surrogates than when only applied to noise added CMB maps and phase randomized versions of them, which only reproduce the power spectrum.  相似文献   

20.
The angular cross-correlation between two galaxy samples separated in redshift is shown to be a useful measure of weak lensing by large-scale structure. Angular correlations in faint galaxies arise as a result of spatial clustering of the galaxies as well as gravitational lensing by dark matter along the line of sight. The lensing contribution to the two-point autocorrelation function is typically small compared with the gravitational clustering. However, the cross-correlation between two galaxy samples is almost unaffected by gravitational clustering provided that their redshift distributions do not overlap. The cross-correlation is then induced by magnification bias resulting from lensing by large-scale structure. We compute the expected amplitude of the cross-correlation for popular theoretical models of structure formation. For two populations with mean redshifts of ≃0.3 and 1, we find a cross-correlation signal of ≃1 per cent on arcmin scales and ≃3 per cent on scales of a few arcsec. The dependence on the cosmological parameters Ω and Λ, the dark matter power spectrum and the bias factor of the foreground galaxy population is explored.  相似文献   

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