Journal articles: 'Tomographic Weak Lensing'

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Munshi, D., T. Namikawa, T. D. Kitching, J. D. McEwen, and F. R. Bouchet. "Weak lensing skew-spectrum." Monthly Notices of the Royal Astronomical Society 498, no. 4 (September 14, 2020): 6057–68. http://dx.doi.org/10.1093/mnras/staa2769.

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ABSTRACT We introduce the skew-spectrum statistic for weak lensing convergence κ maps and test it against state-of-the-art high-resolution all-sky numerical simulations. We perform the analysis as a function of source redshift and smoothing angular scale for individual tomographic bins. We also analyse the cross-correlation between different tomographic bins. We compare the numerical results to fitting-functions used to model the bispectrum of the underlying density field as a function of redshift and scale. We derive a closed form expression for the skew-spectrum for gravity-induced secondary non-Gaussianity. We also compute the skew-spectrum for the projected κ inferred from cosmic microwave background (CMB) studies. As opposed to the low redshift case, we find the post-Born corrections to be important in the modelling of the skew-spectrum for such studies. We show how the presence of a mask and noise can be incorporated in the estimation of a skew-spectrum.

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Sipp, Marvin, Björn Malte Schäfer, and Robert Reischke. "Optimizing tomography for weak gravitational lensing surveys." Monthly Notices of the Royal Astronomical Society 501, no. 1 (November 30, 2020): 683–92. http://dx.doi.org/10.1093/mnras/staa3710.

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ABSTRACT The subject of this paper is optimization of weak lensing tomography: we carry out numerical minimization of a measure of total statistical error as a function of the redshifts of the tomographic bin edges by means of a Nelder–Mead algorithm in order to optimize the sensitivity of weak lensing with respect to different optimization targets. Working under the assumption of a Gaussian likelihood for the parameters of a w0wa CDM (cold dark matter) model and using euclid’s conservative survey specifications, we compare an equipopulated, equidistant, and optimized bin setting and find that in general the equipopulated setting is very close to the optimal one, while an equidistant setting is far from optimal and also suffers from the ad hoc choice of a maximum redshift. More importantly, we find that nearly saturated information content can be gained using already few tomographic bins. This is crucial for photometric redshift surveys with large redshift errors. We consider a large range of targets for the optimization process that can be computed from the parameter covariance (or equivalently, from the Fisher matrix), extend these studies to information entropy measures such as the Kullback–Leibler divergence and conclude that in many cases equipopulated binning yields results close to the optimum, which we support by analytical arguments.

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Benjamin, Jonathan, Ludovic Van Waerbeke, Catherine Heymans, Martin Kilbinger, Thomas Erben, Hendrik Hildebrandt, Henk Hoekstra, et al. "CFHTLenS tomographic weak lensing: quantifying accurate redshift distributions." Monthly Notices of the Royal Astronomical Society 431, no. 2 (March 9, 2013): 1547–64. http://dx.doi.org/10.1093/mnras/stt276.

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Munshi, D., R. Takahashi, and J. D. McEwen. "On weak lensing response functions." Journal of Cosmology and Astroparticle Physics 2022, no. 10 (October 1, 2022): 022. http://dx.doi.org/10.1088/1475-7516/2022/10/022.

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Abstract We introduce the response function approach to model the weak lensing statistics in the context of separate universe formalism. Numerical results for the RFs are presented for various semi-analytical models that includes perturbative modelling and variants of halo models. These results extend the recent studies of the Integrated Bispectrum and Trispectrum to arbitrary order. We find that due to the line-of-sight projection effects, the expressions for RFs are not identical to the squeezed correlation functions of the same order. We compute the RFs in three-dimensions using the spherical Fourier-Bessel formalism which provides a natural framework for incorporating photometric redshifts, and relate these expressions to tomographic and projected statistics. We generalise the concept of k-cut power spectrum to k-cut response functions. In addition to response functions, we also define their counterparts in real space, since they are easier to estimate from surveys with low sky-coverage and non-trivial survey boundaries.

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Coulton, William R., Jia Liu, Mathew S. Madhavacheril, Vanessa Böhm, and David N. Spergel. "Constraining neutrino mass with the tomographic weak lensing bispectrum." Journal of Cosmology and Astroparticle Physics 2019, no. 05 (May 24, 2019): 043. http://dx.doi.org/10.1088/1475-7516/2019/05/043.

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Myles, J., A. Alarcon, A. Amon, C. Sánchez, S. Everett, J. DeRose, J. McCullough, et al. "Dark Energy Survey Year 3 results: redshift calibration of the weak lensing source galaxies." Monthly Notices of the Royal Astronomical Society 505, no. 3 (May 27, 2021): 4249–77. http://dx.doi.org/10.1093/mnras/stab1515.

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ABSTRACT Determining the distribution of redshifts of galaxies observed by wide-field photometric experiments like the Dark Energy Survey (DES) is an essential component to mapping the matter density field with gravitational lensing. In this work we describe the methods used to assign individual weak lensing source galaxies from the DES Year 3 Weak Lensing Source Catalogue to four tomographic bins and to estimate the redshift distributions in these bins. As the first application of these methods to data, we validate that the assumptions made apply to the DES Y3 weak lensing source galaxies and develop a full treatment of systematic uncertainties. Our method consists of combining information from three independent likelihood functions: self-organizing map p(z) (sompz), a method for constraining redshifts from galaxy photometry; clustering redshifts (WZ), constraints on redshifts from cross-correlations of galaxy density functions; and shear ratios (SRs), which provide constraints on redshifts from the ratios of the galaxy-shear correlation functions at small scales. Finally, we describe how these independent probes are combined to yield an ensemble of redshift distributions encapsulating our full uncertainty. We calibrate redshifts with combined effective uncertainties of σ〈z〉 ∼ 0.01 on the mean redshift in each tomographic bin.

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Hildebrandt, H., M. Viola, C. Heymans, S. Joudaki, K. Kuijken, C. Blake, T. Erben, et al. "KiDS-450: cosmological parameter constraints from tomographic weak gravitational lensing." Monthly Notices of the Royal Astronomical Society 465, no. 2 (November 2, 2016): 1454–98. http://dx.doi.org/10.1093/mnras/stw2805.

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Munshi, D., T. Namikawa, J. D. McEwen, T. D. Kitching, and F. R. Bouchet. "Morphology of weak lensing convergence maps." Monthly Notices of the Royal Astronomical Society 507, no. 1 (July 22, 2021): 1421–33. http://dx.doi.org/10.1093/mnras/stab2101.

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ABSTRACT We study the morphology of convergence maps by perturbatively reconstructing their Minkowski functionals (MFs). We present a systematic study using a set of three generalized skew spectra as a function of source redshift and smoothing angular scale. These spectra denote the leading-order corrections to the Gaussian MFs in the quasi-linear regime. They can also be used as independent statistics to probe the bispectrum. Using an approach based on pseudo-Sℓs, we show how these spectra will allow the reconstruction of MFs in the presence of an arbitrary mask and inhomogeneous noise in an unbiased way. Our theoretical predictions are based on a recently introduced fitting function to the bispectrum. We compare our results against state-of-the-art numerical simulations and find an excellent agreement. The reconstruction can be carried out in a controlled manner as a function of angular harmonics ℓ and source redshift zs, which allows for a greater handle on any possible sources of non-Gaussianity. Our method has the advantage of estimating the topology of convergence maps directly using shear data. We also study weak lensing convergence maps inferred from cosmic microwave background observations, and we find that, though less significant at low redshift, the post-Born corrections play an important role in any modelling of the non-Gaussianity of convergence maps at higher redshift. We also study the cross-correlations of estimates from different tomographic bins.

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Tugendhat, Tim M., Robert Reischke, and Björn Malte Schäfer. "Statistical separation of weak gravitational lensing and intrinsic ellipticities based on galaxy colour information." Monthly Notices of the Royal Astronomical Society 494, no. 2 (March 6, 2020): 2969–81. http://dx.doi.org/10.1093/mnras/staa641.

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ABSTRACT Intrinsic alignments of galaxies are recognized as one of the most important systematic in weak lensing surveys on small angular scales. In this paper, we investigate ellipticity correlation functions that are measured separately on elliptical and spiral galaxies, for which we assume the generic alignment mechanisms based on tidal shearing and tidal torquing, respectively. Including morphological information allows to find linear combinations of measured ellipticity correlation functions that suppress the gravitational lensing signal completely or which show a strongly boosted gravitational lensing signal relative to intrinsic alignments. Specifically, we find that (i) intrinsic alignment spectra can be measured in a model-independent way at a significance of Σ ≃ 60 with a wide-angle tomographic survey such as Euclid’s, (ii) the underlying intrinsic alignment model parameters can be determined at per cent-level precision, (iii) this measurement is not impeded by misclassifying galaxies and assuming a wrong alignment model, (iv) parameter estimation from a cleaned weak lensing spectrum is possible with almost no bias, and (v) the misclassification would not strongly impact parameter estimation from the boosted weak lensing spectrum.

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Casarini, L., S. A. Bonometto, S. Borgani, K. Dolag, G. Murante, M. Mezzetti, L. Tornatore, and G. La Vacca. "Tomographic weak-lensing shear spectra from largeN-body and hydrodynamical simulations." Astronomy & Astrophysics 542 (June 2012): A126. http://dx.doi.org/10.1051/0004-6361/201118617.

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Rizzato, Matteo, Karim Benabed, Francis Bernardeau, and Fabien Lacasa. "Tomographic weak lensing bispectrum: a thorough analysis towards the next generation of galaxy surveys." Monthly Notices of the Royal Astronomical Society 490, no. 4 (October 12, 2019): 4688–714. http://dx.doi.org/10.1093/mnras/stz2862.

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ABSTRACT We address key points for an efficient implementation of likelihood codes for modern weak lensing large-scale structure surveys. Specifically, we focus on the joint weak lensing convergence power spectrum–bispectrum probe and we tackle the numerical challenges required by a realistic analysis. Under the assumption of (multivariate) Gaussian likelihoods, we have developed a high performance code that allows highly parallelized prediction of the binned tomographic observables and of their joint non-Gaussian covariance matrix accounting for terms up to the six-point correlation function and supersample effects. This performance allows us to qualitatively address several interesting scientific questions. We find that the bispectrum provides an improvement in terms of signal-to-noise ratio (S/N) of about 10 per cent on top of the power spectrum, making it a non-negligible source of information for future surveys. Furthermore, we are capable to test the impact of theoretical uncertainties in the halo model used to build our observables; with presently allowed variations we conclude that the impact is negligible on the S/N. Finally, we consider data compression possibilities to optimize future analyses of the weak lensing bispectrum. We find that, ignoring systematics, five equipopulated redshift bins are enough to recover the information content of a Euclid-like survey, with negligible improvement when increasing to 10 bins. We also explore principal component analysis and dependence on the triangle shapes as ways to reduce the numerical complexity of the problem.

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Porqueres, Natalia, Alan Heavens, Daniel Mortlock, and Guilhem Lavaux. "Lifting weak lensing degeneracies with a field-based likelihood." Monthly Notices of the Royal Astronomical Society 509, no. 3 (November 10, 2021): 3194–202. http://dx.doi.org/10.1093/mnras/stab3234.

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ABSTRACT We present a field-based approach to the analysis of cosmic shear data to infer jointly cosmological parameters and the dark matter distribution. This forward modelling approach samples the cosmological parameters and the initial matter fluctuations, using a physical gravity model to link the primordial fluctuations to the non-linear matter distribution. Cosmological parameters are sampled and updated consistently through the forward model, varying (1) the initial matter power spectrum, (2) the geometry through the distance-redshift relationship, and (3) the growth of structure and light-cone effects. Our approach extracts more information from the data than methods based on two-point statistics. We find that this field-based approach lifts the strong degeneracy between the cosmological matter density, Ωm, and the fluctuation amplitude, σ8, providing tight constraints on these parameters from weak lensing data alone. In the simulated four-bin tomographic experiment we consider, the field-based likelihood yields marginal uncertainties on σ8 and Ωm that are, respectively, a factor of 3 and 5 smaller than those from a two-point power spectrum analysis applied to the same underlying data.

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Huang, Hung-Jin, Tim Eifler, Rachel Mandelbaum, and Scott Dodelson. "Modelling baryonic physics in future weak lensing surveys." Monthly Notices of the Royal Astronomical Society 488, no. 2 (June 21, 2019): 1652–78. http://dx.doi.org/10.1093/mnras/stz1714.

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Abstract Modifications of the matter power spectrum due to baryonic physics are one of the major theoretical uncertainties in cosmological weak lensing measurements. Developing robust mitigation schemes for this source of systematic uncertainty increases the robustness of cosmological constraints, and may increase their precision if they enable the use of information from smaller scales. Here we explore the performance of two mitigation schemes for baryonic effects in weak lensing cosmic shear: the principal component analysis (PCA) method and the halo-model approach in hmcode. We construct mock tomographic shear power spectra from four hydrodynamical simulations, and run simulated likelihood analyses with cosmolike assuming LSST-like survey statistics. With an angular scale cut of ℓmax < 2000, both methods successfully remove the biases in cosmological parameters due to the various baryonic physics scenarios, with the PCA method causing less degradation in the parameter constraints than hmcode. For a more aggressive ℓmax = 5000, the PCA method performs well for all but one baryonic physics scenario, requiring additional training simulations to account for the extreme baryonic physics scenario of Illustris; hmcode exhibits tensions in the 2D posterior distributions of cosmological parameters due to lack of freedom in describing the power spectrum for $k \gt 10\ h^{-1}\, \mathrm{Mpc}$. We investigate variants of the PCA method and improve the bias mitigation through PCA by accounting for the noise properties in the data via Cholesky decomposition of the covariance matrix. Our improved PCA method allows us to retain more statistical constraining power while effectively mitigating baryonic uncertainties even for a broad range of baryonic physics scenarios.

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Mootoovaloo, Arrykrishna, Alan F. Heavens, Andrew H. Jaffe, and Florent Leclercq. "Parameter inference for weak lensing using Gaussian Processes and MOPED." Monthly Notices of the Royal Astronomical Society 497, no. 2 (July 17, 2020): 2213–26. http://dx.doi.org/10.1093/mnras/staa2102.

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ABSTRACT In this paper, we propose a Gaussian Process (GP) emulator for the calculation both of tomographic weak lensing band powers, and of coefficients of summary data massively compressed with the MOPED algorithm. In the former case cosmological parameter inference is accelerated by a factor of ∼10–30 compared with Boltzmann solver class applied to KiDS-450 weak lensing data. Much larger gains of order 103 will come with future data, and MOPED with GPs will be fast enough to permit the Limber approximation to be dropped, with acceleration in this case of ∼105. A potential advantage of GPs is that an error on the emulated function can be computed and this uncertainty incorporated into the likelihood. However, it is known that the GP error can be unreliable when applied to deterministic functions, and we find, using the Kullback–Leibler divergence between the emulator and class likelihoods, and from the uncertainties on the parameters, that agreement is better when the GP uncertainty is not used. In future, weak lensing surveys such as Euclid, and the Legacy Survey of Space and Time, will have up to ∼104 summary statistics, and inference will be correspondingly more challenging. However, since the speed of MOPED is determined not the number of summary data, but by the number of parameters, MOPED analysis scales almost perfectly, provided that a fast way to compute the theoretical MOPED coefficients is available. The GP provides such a fast mechanism.

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Köhlinger, F., M. Viola, B. Joachimi, H. Hoekstra, E. van Uitert, H. Hildebrandt, A. Choi, et al. "KiDS-450: the tomographic weak lensing power spectrum and constraints on cosmological parameters." Monthly Notices of the Royal Astronomical Society 471, no. 4 (July 19, 2017): 4412–35. http://dx.doi.org/10.1093/mnras/stx1820.

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Joudaki, S., H. Hildebrandt, D. Traykova, N. E. Chisari, C. Heymans, A. Kannawadi, K. Kuijken, et al. "KiDS+VIKING-450 and DES-Y1 combined: Cosmology with cosmic shear." Astronomy & Astrophysics 638 (May 29, 2020): L1. http://dx.doi.org/10.1051/0004-6361/201936154.

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We present a combined tomographic weak gravitational lensing analysis of the Kilo Degree Survey (KV450) and the Dark Energy Survey (DES-Y1). We homogenize the analysis of these two public cosmic shear datasets by adopting consistent priors and modeling of nonlinear scales, and determine new redshift distributions for DES-Y1 based on deep public spectroscopic surveys. Adopting these revised redshifts results in a 0.8σ reduction in the DES-inferred value for S8, which decreases to a 0.5σ reduction when including a systematic redshift calibration error model from mock DES data based on the MICE2 simulation. The combined KV450+DES-Y1 constraint on S8 = 0.762−0.024+0.025 is in tension with the Planck 2018 constraint from the cosmic microwave background at the level of 2.5σ. This result highlights the importance of developing methods to provide accurate redshift calibration for current and future weak-lensing surveys.

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Barthelemy, A., S. Codis, C. Uhlemann, F. Bernardeau, and R. Gavazzi. "A nulling strategy for modelling lensing convergence in cones with large deviation theory." Monthly Notices of the Royal Astronomical Society 492, no. 3 (January 9, 2020): 3420–39. http://dx.doi.org/10.1093/mnras/staa053.

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ABSTRACT The distribution of the cosmic convergence field is modelled using a large deviation principle where all non-Gaussian contributions are computed from first principles. The geometry of the past light-cone is accounted for by constructing the total weak-lensing signal from contributions of the matter density in thin disc slices. The prediction of this model is successfully tested against numerical simulation with ray-tracing, and found to be accurate within at least 5 per cent in the tails at redshift 1 and opening angle of 10 arcmin and even more so with increasing source redshift and opening angle. An accurate analytical approximation to the theory is also provided for practical implementation. The lensing kernel that mixes physical scales along the line of sight tends to reduce the domain of validity of this theoretical approach compared to the three-dimensional case of cosmic densities in spherical cells. This effect is shown to be avoidable if a nulling procedure is implemented in order to localize the lensing line-of-sight integrations in a tomographic analysis. Accuracy in the tails is thus achieved within a per cent for source redshifts between 0.5 and 1.5 and an opening angle of 10 arcmin. Applications to future weak-lensing surveys like Euclid and the specific issue of shape noise are discussed.

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Pyne, Susan, and Benjamin Joachimi. "Self-calibration of weak lensing systematic effects using combined two- and three-point statistics." Monthly Notices of the Royal Astronomical Society 503, no. 2 (February 12, 2021): 2300–2317. http://dx.doi.org/10.1093/mnras/stab413.

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ABSTRACT We investigate the prospects for using the weak lensing bispectrum alongside the power spectrum to control systematic uncertainties in a Euclid-like survey. Three systematic effects are considered: the intrinsic alignment of galaxies, uncertainties in the means of tomographic redshift distributions, and multiplicative bias in the measurement of the shear signal. We find that the bispectrum is very effective in mitigating these systematic errors. Varying all three systematics simultaneously, a joint power spectrum and bispectrum analysis reduces the area of credible regions for the cosmological parameters Ωm and σ8 by a factor of 90 and for the two parameters of a time-varying dark energy equation of state by a factor of almost 20, compared with the baseline approach of using the power spectrum alone and of imposing priors consistent with the accuracy requirements specified for Euclid. We also demonstrate that including the bispectrum self-calibrates all three systematic effects to the stringent levels required by the forthcoming generation of weak lensing surveys, thereby reducing the need for external calibration data.

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Yuan, Shuo, Chuzhong Pan, Xiangkun Liu, Qiao Wang, and Zuhui Fan. "Cosmological Studies from Tomographic Weak Lensing Peak Abundances and Impacts of Photo-z Errors." Astrophysical Journal 884, no. 2 (October 22, 2019): 164. http://dx.doi.org/10.3847/1538-4357/ab40a5.

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Simpson, Fergus, Catherine Heymans, David Parkinson, Chris Blake, Martin Kilbinger, Jonathan Benjamin, Thomas Erben, et al. "CFHTLenS: testing the laws of gravity with tomographic weak lensing and redshift-space distortions." Monthly Notices of the Royal Astronomical Society 429, no. 3 (December 21, 2012): 2249–63. http://dx.doi.org/10.1093/mnras/sts493.

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Heymans, Catherine, Emma Grocutt, Alan Heavens, Martin Kilbinger, Thomas D. Kitching, Fergus Simpson, Jonathan Benjamin, et al. "CFHTLenS tomographic weak lensing cosmological parameter constraints: Mitigating the impact of intrinsic galaxy alignments." Monthly Notices of the Royal Astronomical Society 432, no. 3 (May 9, 2013): 2433–53. http://dx.doi.org/10.1093/mnras/stt601.

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Upham, Robin E., Michael L. Brown, and Lee Whittaker. "Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys." Monthly Notices of the Royal Astronomical Society 503, no. 2 (February 24, 2021): 1999–2013. http://dx.doi.org/10.1093/mnras/stab522.

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ABSTRACT We investigate whether a Gaussian likelihood is sufficient to obtain accurate parameter constraints from a Euclid-like combined tomographic power spectrum analysis of weak lensing, galaxy clustering, and their cross-correlation. Testing its performance on the full sky against the Wishart distribution, which is the exact likelihood under the assumption of Gaussian fields, we find that the Gaussian likelihood returns accurate parameter constraints. This accuracy is robust to the choices made in the likelihood analysis, including the choice of fiducial cosmology, the range of scales included, and the random noise level. We extend our results to the cut sky by evaluating the additional non-Gaussianity of the joint cut-sky likelihood in both its marginal distributions and dependence structure. We find that the cut-sky likelihood is more non-Gaussian than the full-sky likelihood, but at a level insufficient to introduce significant inaccuracy into parameter constraints obtained using the Gaussian likelihood. Our results should not be affected by the assumption of Gaussian fields, as this approximation only becomes inaccurate on small scales, which in turn corresponds to the limit in which any non-Gaussianity of the likelihood becomes negligible. We nevertheless compare against N-body weak lensing simulations and find no evidence of significant additional non-Gaussianity in the likelihood. Our results indicate that a Gaussian likelihood will be sufficient for robust parameter constraints with power spectra from stage IV weak lensing surveys.

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Blake, Chris, Alexandra Amon, Marika Asgari, Maciej Bilicki, Andrej Dvornik, Thomas Erben, Benjamin Giblin, et al. "Testing gravity using galaxy-galaxy lensing and clustering amplitudes in KiDS-1000, BOSS, and 2dFLenS." Astronomy & Astrophysics 642 (October 2020): A158. http://dx.doi.org/10.1051/0004-6361/202038505.

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The physics of gravity on cosmological scales affects both the rate of assembly of large-scale structure and the gravitational lensing of background light through this cosmic web. By comparing the amplitude of these different observational signatures, we can construct tests that can distinguish general relativity from its potential modifications. We used the latest weak gravitational lensing dataset from the Kilo-Degree Survey, KiDS-1000, in conjunction with overlapping galaxy spectroscopic redshift surveys, BOSS and 2dFLenS, to perform the most precise existing amplitude-ratio test. We measured the associated EG statistic with 15 − 20% errors in five Δz = 0.1 tomographic redshift bins in the range 0.2 < z < 0.7 on projected scales up to 100 h−1 Mpc. The scale-independence and redshift-dependence of these measurements are consistent with the theoretical expectation of general relativity in a Universe with matter density Ωm = 0.27 ± 0.04. We demonstrate that our results are robust against different analysis choices, including schemes for correcting the effects of source photometric redshift errors, and we compare the performance of angular and projected galaxy-galaxy lensing statistics.

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Stafford, Sam G., Ian G. McCarthy, Juliana Kwan, Shaun T. Brown, Andreea S. Font, and Andrew Robertson. "Testing extensions to ΛCDM on small scales with forthcoming cosmic shear surveys." Monthly Notices of the Royal Astronomical Society 508, no. 2 (October 2, 2021): 2537–55. http://dx.doi.org/10.1093/mnras/stab2787.

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ABSTRACT We investigate the constraining power of forthcoming Stage-IV weak lensing surveys (Euclid, lsst, and NGRST) for extensions to the Lambda cold dark matter model on small scales, via their impact on the cosmic shear power spectrum. We use high-resolution cosmological simulations to calculate how warm dark matter (WDM), self-interacting dark matter (SIDM), and a running of the spectral index affect the non-linear matter power spectrum, P(k), as a function of scale and redshift. We evaluate the cosmological constraining power using synthetic weak lensing observations derived from these power spectra and that take into account the anticipated source densities, shape noise, and cosmic variance errors of upcoming surveys. We show that upcoming Stage-IV surveys will be able to place useful, independent constraints on both WDM models (ruling out models with a particle mass of ≲0.5 keV) and SIDM models (ruling out models with a velocity-independent cross-section of ≳10 cm2 g−1) through their effects on the small-scale cosmic shear power spectrum. Similarly, they will be able to strongly constrain cosmologies with a running spectral index. Finally, we explore the error associated with the cosmic shear cross-spectrum between tomographic bins, finding that it can be significantly affected by Poisson noise (the standard assumption is that the Poisson noise cancels between tomographic bins). We provide a new analytic form for the error on the cross-spectrum that accurately captures this effect.

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Dong, Fuyu, Pengjie Zhang, Le Zhang, Ji Yao, Zeyang Sun, Changbom Park, and Xiaohu Yang. "Detection of a Cross-correlation between Cosmic Microwave Background Lensing and Low-density Points." Astrophysical Journal 923, no. 2 (December 1, 2021): 153. http://dx.doi.org/10.3847/1538-4357/ac2d31.

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Abstract Low-density points (LDPs), obtained by removing high-density regions of observed galaxies, can trace the large-scale structures (LSSs) of the universe. In particular, it offers an intriguing opportunity to detect weak gravitational lensing from low-density regions. In this work, we investigate the tomographic cross-correlation between Planck cosmic microwave background (CMB) lensing maps and LDP-traced LSSs, where LDPs are constructed from the DR8 data release of the DESI legacy imaging survey, with about 106–107 galaxies. We find that, due to the large sky coverage (20,000 deg2) and large redshift depth (z ≤ 1.2), a significant detection (10σ–30σ) of the CMB lensing–LDP cross-correlation in all six redshift bins can be achieved, with a total significance of ∼53σ over ℓ ≤ 1024. Moreover, the measurements are in good agreement with a theoretical template constructed from our numerical simulation in the WMAP 9 yr ΛCDM cosmology. A scaling factor for the lensing amplitude A lens is constrained to A lens = 1 ± 0.12 for z < 0.2, A lens = 1.07 ± 0.07 for 0.2 < z < 0.4, and A lens = 1.07 ± 0.05 for 0.4 < z < 0.6, with the r-band absolute magnitude cut of −21.5 for LDP selection. A variety of tests have been performed to check the detection reliability against variations in LDP samples and galaxy magnitude cuts, masks, CMB lensing maps, multipole ℓ cuts, sky regions, and photo-z bias. We also perform a cross-correlation measurement between CMB lensing and galaxy number density, which is consistent with the CMB lensing–LDP cross-correlation. This work therefore further convincingly demonstrates that LDP is a competitive tracer of LSS.

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Buchs, R., C. Davis, D. Gruen, J. DeRose, A. Alarcon, G. M. Bernstein, C. Sánchez, et al. "Phenotypic redshifts with self-organizing maps: A novel method to characterize redshift distributions of source galaxies for weak lensing." Monthly Notices of the Royal Astronomical Society 489, no. 1 (August 9, 2019): 820–41. http://dx.doi.org/10.1093/mnras/stz2162.

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ABSTRACT Wide-field imaging surveys such as the Dark Energy Survey (DES) rely on coarse measurements of spectral energy distributions in a few filters to estimate the redshift distribution of source galaxies. In this regime, sample variance, shot noise, and selection effects limit the attainable accuracy of redshift calibration and thus of cosmological constraints. We present a new method to combine wide-field, few-filter measurements with catalogues from deep fields with additional filters and sufficiently low photometric noise to break degeneracies in photometric redshifts. The multiband deep field is used as an intermediary between wide-field observations and accurate redshifts, greatly reducing sample variance, shot noise, and selection effects. Our implementation of the method uses self-organizing maps to group galaxies into phenotypes based on their observed fluxes, and is tested using a mock DES catalogue created from N-body simulations. It yields a typical uncertainty on the mean redshift in each of five tomographic bins for an idealized simulation of the DES Year 3 weak-lensing tomographic analysis of σΔz = 0.007, which is a 60 per cent improvement compared to the Year 1 analysis. Although the implementation of the method is tailored to DES, its formalism can be applied to other large photometric surveys with a similar observing strategy.

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Harnois-Déraps, Joachim, Nicolas Martinet, and Robert Reischke. "Cosmic shear beyond 2-point statistics: Accounting for galaxy intrinsic alignment with projected tidal fields." Monthly Notices of the Royal Astronomical Society 509, no. 3 (November 11, 2021): 3868–88. http://dx.doi.org/10.1093/mnras/stab3222.

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ABSTRACT Developing analysis pipelines based on statistics beyond two-point functions is critical for extracting a maximal amount of cosmological information from current and upcoming weak lensing surveys. In this paper, we study the impact of the intrinsic alignment of galaxies (IA) on three promising probes measured from aperture mass maps – the lensing peaks, minima, and full PDF. Our 2D IA infusion method converts the light-cone-projected mass sheets into projected tidal tensors, which are then linearly coupled to an intrinsic ellipticity component with a strength controlled by the coupling parameter AIA. We validate our method with the γ-2PCFs statistics, recovering well the linear alignment model of Bridle & King in a full tomographic setting, and for different AIA values. We next use our method to infuse at the galaxy catalogue level a non-linear IA model that includes the density-weighting term introduced in Blazek et al., and compute the impact on the three aperture mass map statistics. We find that large $\mathcal {S}/\mathcal {N}$ peaks are maximally affected, with deviations reaching 30 per cent (10 per cent) for a Euclid-like (KiDS-like) survey. Modelling the signal in a wCDM cosmology universe with N-body simulations, we forecast the cosmological bias caused by unmodelled IA for 100 deg2 of Euclid-like data, finding very large offsets in w0 (5-10σstat), Ωm (4-6σstat), and $S_8 \equiv \sigma _8\sqrt{\Omega _{\rm m}/0.3}$ (∼3σstat). The method presented in this paper offers a compelling avenue to account for IA in beyond-two-point weak lensing statistics, with a flexibility comparable to that of current γ-2PCFs IA analytical models.

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Cordero, Juan P., Ian Harrison, Richard P. Rollins, G. M. Bernstein, S. L. Bridle, A. Alarcon, O. Alves, et al. "Dark Energy Survey Year 3 results: marginalization over redshift distribution uncertainties using ranking of discrete realizations." Monthly Notices of the Royal Astronomical Society 511, no. 2 (January 28, 2022): 2170–85. http://dx.doi.org/10.1093/mnras/stac147.

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ABSTRACT Cosmological information from weak lensing surveys is maximized by sorting source galaxies into tomographic redshift subsamples. Any uncertainties on these redshift distributions must be correctly propagated into the cosmological results. We present hyperrank, a new method for marginalizing over redshift distribution uncertainties, using discrete samples from the space of all possible redshift distributions, improving over simple parametrized models. In hyperrank, the set of proposed redshift distributions is ranked according to a small (between one and four) number of summary values, which are then sampled, along with other nuisance parameters and cosmological parameters in the Monte Carlo chain used for inference. This approach can be regarded as a general method for marginalizing over discrete realizations of data vector variation with nuisance parameters, which can consequently be sampled separately from the main parameters of interest, allowing for increased computational efficiency. We focus on the case of weak lensing cosmic shear analyses and demonstrate our method using simulations made for the Dark Energy Survey (DES). We show that the method can correctly and efficiently marginalize over a wide range of models for the redshift distribution uncertainty. Finally, we compare hyperrank to the common mean-shifting method of marginalizing over redshift uncertainty, validating that this simpler model is sufficient for use in the DES Year 3 cosmology results presented in companion papers.

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Martinet, Nicolas, Tiago Castro, Joachim Harnois-Déraps, Eric Jullo, Carlo Giocoli, and Klaus Dolag. "Impact of baryons in cosmic shear analyses with tomographic aperture mass statistics." Astronomy & Astrophysics 648 (April 2021): A115. http://dx.doi.org/10.1051/0004-6361/202040155.

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NonGaussian cosmic shear statistics based on weak-lensing aperture mass (Map) maps can outperform the classical shear two-point correlation function (γ-2PCF) in terms of cosmological constraining power. However, reaching the full potential of these new estimators requires accurate modeling of the physics of baryons as the extra nonGaussian information mostly resides at small scales. We present one such modeling based on the Magneticum hydrodynamical simulation for the KiDS-450 and DES-Y1 surveys and a Euclid-like survey. We compute the bias due to baryons on the lensing PDF and the distribution of peaks and voids in Map maps and propagate it to the cosmological forecasts on the structure growth parameter S8, the matter density parameter Ωm, and the dark energy equation of state w0 using the SLICS and cosmo-SLICS sets of dark-matter-only simulations. We report a negative bias of a few percent on S8 and Ωm and also measure a positive bias of the same level on w0 when including a tomographic decomposition. These biases reach ∼5% when combining Map statistics with the γ-2PCF as these estimators show similar dependency on the AGN feedback. We verify that these biases constitute a less than 1σ shift on the probed cosmological parameters for current cosmic shear surveys. However, baryons need to be accounted for at the percentage level for future Stage IV surveys and we propose to include the uncertainty on the AGN feedback amplitude by marginalizing over this parameter using multiple simulations such as those presented in this paper. Finally, we explore the possibility of mitigating the impact of baryons by filtering the Map map but find that this process would require suppressing the small-scale information to a point where the constraints would no longer be competitive.

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Tröster, Tilman, Alexander J. Mead, Catherine Heymans, Ziang Yan, David Alonso, Marika Asgari, Maciej Bilicki, et al. "Joint constraints on cosmology and the impact of baryon feedback: Combining KiDS-1000 lensing with the thermal Sunyaev–Zeldovich effect from Planck and ACT." Astronomy & Astrophysics 660 (April 2022): A27. http://dx.doi.org/10.1051/0004-6361/202142197.

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We conduct a pseudo-Cℓ analysis of the tomographic cross-correlation between 1000 deg2 of weak-lensing data from the Kilo-Degree Survey (KiDS-1000) and the thermal Sunyaev–Zeldovich (tSZ) effect measured by Planck and the Atacama Cosmology Telescope (ACT). Using HMX, a halo-model-based approach that consistently models the gas, star, and dark matter components, we are able to derive constraints on both cosmology and baryon feedback for the first time from these data, marginalising over redshift uncertainties, intrinsic alignment of galaxies, and contamination by the cosmic infrared background (CIB). We find our results to be insensitive to the CIB, while intrinsic alignment provides a small but significant contribution to the lensing–tSZ cross-correlation. The cosmological constraints are consistent with those of other low-redshift probes and prefer strong baryon feedback. The inferred amplitude of the lensing–tSZ cross-correlation signal, which scales as σ8(Ωm/0.3)0.2, is low by ∼2 σ compared to the primary cosmic microwave background constraints by Planck. The lensing–tSZ measurements are then combined with pseudo-Cℓ measurements of KiDS-1000 cosmic shear into a novel joint analysis, accounting for the full cross-covariance between the probes, providing tight cosmological constraints by breaking parameter degeneracies inherent to both probes. The joint analysis gives an improvement of 40% on the constraint of S8 = σ8Ωm/0.3 over cosmic shear alone, while providing constraints on baryon feedback consistent with hydrodynamical simulations, demonstrating the potential of such joint analyses with baryonic tracers such as the tSZ effect. We discuss remaining modelling challenges that need to be addressed if these baryonic probes are to be included in future precision-cosmology analyses.

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Samuroff, S., J. Blazek, M. A. Troxel, N. MacCrann, E. Krause, C. D. Leonard, J. Prat, et al. "Dark Energy Survey Year 1 results: constraints on intrinsic alignments and their colour dependence from galaxy clustering and weak lensing." Monthly Notices of the Royal Astronomical Society 489, no. 4 (August 16, 2019): 5453–82. http://dx.doi.org/10.1093/mnras/stz2197.

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Abstract We perform a joint analysis of intrinsic alignments and cosmology using tomographic weak lensing, galaxy clustering, and galaxy–galaxy lensing measurements from Year 1 (Y1) of the Dark Energy Survey. We define early- and late-type subsamples, which are found to pass a series of systematics tests, including for spurious photometric redshift error and point spread function correlations. We analyse these split data alongside the fiducial mixed Y1 sample using a range of intrinsic alignment models. In a fiducial non-linear alignment model analysis, assuming a flat Λ cold dark matter cosmology, we find a significant difference in intrinsic alignment amplitude, with early-type galaxies favouring $A_\mathrm{IA} = 2.38^{+0.32}_{-0.31}$ and late-type galaxies consistent with no intrinsic alignments at $0.05^{+0.10}_{-0.09}$. The analysis is repeated using a number of extended model spaces, including a physically motivated model that includes both tidal torquing and tidal alignment mechanisms. In multiprobe likelihood chains in which cosmology, intrinsic alignments in both galaxy samples and all other relevant systematics are varied simultaneously, we find the tidal alignment and tidal torquing parts of the intrinsic alignment signal have amplitudes $A_1 = 2.66 ^{+0.67}_{-0.66}$, $A_2=-2.94^{+1.94}_{-1.83}$, respectively, for early-type galaxies and $A_1 = 0.62 ^{+0.41}_{-0.41}$, $A_2 = -2.26^{+1.30}_{-1.16}$ for late-type galaxies. In the full (mixed) Y1 sample the best constraints are $A_1 = 0.70 ^{+0.41}_{-0.38}$, $A_2 = -1.36 ^{+1.08}_{-1.41}$. For all galaxy splits and IA models considered, we report cosmological parameter constraints consistent with the results of the main DES Y1 cosmic shear and multiprobe cosmology papers.

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Peel, Austin, Chieh-An Lin, François Lanusse, Adrienne Leonard, Jean-Luc Starck, and Martin Kilbinger. "Cosmological constraints with weak-lensing peak counts and second-order statistics in a large-field survey." Astronomy & Astrophysics 599 (March 2017): A79. http://dx.doi.org/10.1051/0004-6361/201629928.

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Peak statistics in weak-lensing maps access the non-Gaussian information contained in the large-scale distribution of matter in the Universe. They are therefore a promising complementary probe to two-point and higher-order statistics to constrain our cosmological models. Next-generation galaxy surveys, with their advanced optics and large areas, will measure the cosmic weak-lensing signal with unprecedented precision. To prepare for these anticipated data sets, we assess the constraining power of peak counts in a simulated Euclid-like survey on the cosmological parameters Ωm, σ8, and w0de. In particular, we study how Camelus, a fast stochastic model for predicting peaks, can be applied to such large surveys. The algorithm avoids the need for time-costly N-body simulations, and its stochastic approach provides full PDF information of observables. Considering peaks with a signal-to-noise ratio ≥ 1, we measure the abundance histogram in a mock shear catalogue of approximately 5000 deg2 using a multiscale mass-map filtering technique. We constrain the parameters of the mock survey using Camelus combined with approximate Bayesian computation, a robust likelihood-free inference algorithm. Peak statistics yield a tight but significantly biased constraint in the σ8–Ωm plane, as measured by the width ΔΣ8 of the 1σ contour. We find Σ8 = σ8(Ωm/ 0.27)α = 0.77-0.05+0.06 with α = 0.75 for a flat ΛCDM model. The strong bias indicates the need to better understand and control the model systematics before applying it to a real survey of this size or larger. We perform a calibration of the model and compare results to those from the two-point correlation functions ξ± measured on the same field. We calibrate the ξ± result as well, since its contours are also biased, although not as severely as for peaks. In this case, we find for peaks Σ8 = 0.76-0.03+0.02 with α = 0.65, while for the combined ξ+ and ξ− statistics the values are Σ8 = 0.76-0.01+0.02 and α = 0.70. We conclude that the constraining power can therefore be comparable between the two weak-lensing observables in large-field surveys. Furthermore, the tilt in the σ8–Ωm degeneracy direction for peaks with respect to that of ξ± suggests that a combined analysis would yield tighter constraints than either measure alone. As expected, w0de cannot be well constrained without a tomographic analysis, but its degeneracy directions with the other two varied parameters are still clear for both peaks and ξ±.

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Hildebrandt, H., J. L. van den Busch, A. H. Wright, C. Blake, B. Joachimi, K. Kuijken, T. Tröster, et al. "KiDS-1000 catalogue: Redshift distributions and their calibration." Astronomy & Astrophysics 647 (March 2021): A124. http://dx.doi.org/10.1051/0004-6361/202039018.

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We present redshift distribution estimates of galaxies selected from the fourth data release of the Kilo-Degree Survey over an area of ∼1000 deg2 (KiDS-1000). These redshift distributions represent one of the crucial ingredients for weak gravitational lensing measurements with the KiDS-1000 data. The primary estimate is based on deep spectroscopic reference catalogues that are re-weighted with the help of a self-organising map (SOM) to closely resemble the KiDS-1000 sources, split into five tomographic redshift bins in the photometric redshift range 0.1 < zB ≤ 1.2. Sources are selected such that they only occupy that volume of nine-dimensional magnitude-space that is also covered by the reference samples (‘gold’ selection). Residual biases in the mean redshifts determined from this calibration are estimated from mock catalogues to be ≲0.01 for all five bins with uncertainties of ∼0.01. This primary SOM estimate of the KiDS-1000 redshift distributions is complemented with an independent clustering redshift approach. After validation of the clustering-z on the same mock catalogues and a careful assessment of systematic errors, we find no significant bias of the SOM redshift distributions with respect to the clustering-z measurements. The SOM redshift distributions re-calibrated by the clustering-z represent an alternative calibration of the redshift distributions with only slightly larger uncertainties in the mean redshifts of ∼0.01 − 0.02 to be used in KiDS-1000 cosmological weak lensing analyses. As this includes the SOM uncertainty, clustering-z are shown to be fully competitive on KiDS-1000 data.

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Ilbert, O., S. de la Torre, N. Martinet, A. H. Wright, S. Paltani, C. Laigle, I. Davidzon, et al. "Euclid preparation." Astronomy & Astrophysics 647 (March 2021): A117. http://dx.doi.org/10.1051/0004-6361/202040237.

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The analysis of weak gravitational lensing in wide-field imaging surveys is considered to be a major cosmological probe of dark energy. Our capacity to constrain the dark energy equation of state relies on an accurate knowledge of the galaxy mean redshift ⟨z⟩. We investigate the possibility of measuring ⟨z⟩ with an accuracy better than 0.002 (1 + z) in ten tomographic bins spanning the redshift interval 0.2 < z < 2.2, the requirements for the cosmic shear analysis of Euclid. We implement a sufficiently realistic simulation in order to understand the advantages and complementarity, as well as the shortcomings, of two standard approaches: the direct calibration of ⟨z⟩ with a dedicated spectroscopic sample and the combination of the photometric redshift probability distribution functions (zPDFs) of individual galaxies. We base our study on the Horizon-AGN hydrodynamical simulation, which we analyse with a standard galaxy spectral energy distribution template-fitting code. Such a procedure produces photometric redshifts with realistic biases, precisions, and failure rates. We find that the current Euclid design for direct calibration is sufficiently robust to reach the requirement on the mean redshift, provided that the purity level of the spectroscopic sample is maintained at an extremely high level of > 99.8%. The zPDF approach can also be successful if the zPDF is de-biased using a spectroscopic training sample. This approach requires deep imaging data but is weakly sensitive to spectroscopic redshift failures in the training sample. We improve the de-biasing method and confirm our finding by applying it to real-world weak-lensing datasets (COSMOS and KiDS+VIKING-450).

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Hildebrandt, H., F. Köhlinger, J. L. van den Busch, B. Joachimi, C. Heymans, A. Kannawadi, A. H. Wright, et al. "KiDS+VIKING-450: Cosmic shear tomography with optical and infrared data." Astronomy & Astrophysics 633 (January 2020): A69. http://dx.doi.org/10.1051/0004-6361/201834878.

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We present a tomographic cosmic shear analysis of the Kilo-Degree Survey (KiDS) combined with the VISTA Kilo-Degree Infrared Galaxy Survey. This is the first time that a full optical to near-infrared data set has been used for a wide-field cosmological weak lensing experiment. This unprecedented data, spanning 450 deg2, allows us to significantly improve the estimation of photometric redshifts, such that we are able to include robustly higher-redshift sources for the lensing measurement, and – most importantly – to solidify our knowledge of the redshift distributions of the sources. Based on a flat ΛCDM model we find S8 ≡ σ8 Ωm/0.3 = 0.737+0.040−0.036 in a blind analysis from cosmic shear alone. The tension between KiDS cosmic shear and the Planck-Legacy CMB measurements remains in this systematically more robust analysis, with S8 differing by 2.3σ. This result is insensitive to changes in the priors on nuisance parameters for intrinsic alignment, baryon feedback, and neutrino mass. KiDS shear measurements are calibrated with a new, more realistic set of image simulations and no significant B-modes are detected in the survey, indicating that systematic errors are under control. When calibrating our redshift distributions by assuming the 30-band COSMOS-2015 photometric redshifts are correct (following the Dark Energy Survey and the Hyper Suprime-Cam Survey), we find the tension with Planck is alleviated. The robust determination of source redshift distributions remains one of the most challenging aspects for future cosmic shear surveys.

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Barthelemy, Alexandre, Sandrine Codis, and Francis Bernardeau. "Probability distribution function of the aperture mass field with large deviation theory." Monthly Notices of the Royal Astronomical Society 503, no. 4 (March 27, 2021): 5204–22. http://dx.doi.org/10.1093/mnras/stab818.

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ABSTRACT In the context of tomographic cosmic shear surveys, a theoretical model for the one-point statistics of the aperture mass (Map) is developed. This formalism is based on the application of the large deviation principle to the projected matter density field and more specifically to the angular aperture masses. The latter holds the advantage of being an observable that can be directly extracted from the observed shear field and to be, by construction, independent from the long wave modes. Furthermore, we show that, with the help of a nulling procedure based on the so-called BNT transform, it is possible to build observables that depend only on a finite range of redshifts making them also independent from the small-scale modes. This procedure makes predictions for the shape of the one-point probability distribution function of such an observable very accurate, comparable to what had been previously obtained for 3D observables. Comparisons with specific simulations reveal however inconsistent results showing that synthetic lensing maps were not accurate enough for such refined observables. It points to the need for more precise dedicated numerical developments whose performances could be benchmarked with such observables. We furthermore review the possible systematics that could affect such a formalism in future weak-lensing surveys like Euclid, notably the impact of shape noise as well as leading corrections coming from lend–lens couplings, geodesic deviation, reduced shear and magnification bias.

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Tanidis, Konstantinos, Stefano Camera, and David Parkinson. "Developing a unified pipeline for large-scale structure data analysis with angular power spectra – II. A case study for magnification bias and radio continuum surveys." Monthly Notices of the Royal Astronomical Society 491, no. 4 (December 4, 2019): 4869–83. http://dx.doi.org/10.1093/mnras/stz3394.

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ABSTRACT Following on our purpose of developing a unified pipeline for large-scale structure data analysis with angular power spectra, we now include the weak lensing effect of magnification bias on galaxy clustering in a publicly available, modular parameter estimation code. We thus forecast constraints on the parameters of the concordance cosmological model, dark energy, and modified gravity theories from galaxy clustering tomographic angular power spectra. We find that a correct modelling of magnification is crucial not to bias the parameter estimation, especially in the case of deep galaxy surveys. Our case study adopts specifications of the Evolutionary Map of the Universe, which is a full-sky, deep radio-continuum survey, expected to probe the Universe up to redshift z ∼ 6. We assume the Limber approximation, and include magnification bias on top of density fluctuations and redshift-space distortions. By restricting our analysis to the regime where the Limber approximation holds true, we significantly minimize the computational time needed, compared to that of the exact calculation. We also show that there is a trend for more biased parameter estimates from neglecting magnification when the redshift bins are very wide. We conclude that this result implies a strong dependence on the lensing contribution, which is an integrated effect and becomes dominant when wide redshift bins are considered. Finally, we note that instead of being considered a contaminant, magnification bias encodes important cosmological information, and its inclusion leads to an alleviation of its degeneracy between the galaxy bias and the amplitude normalization of the matter fluctuations.

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Gatti, M., G. Giannini, G. M. Bernstein, A. Alarcon, J. Myles, A. Amon, R. Cawthon, et al. "Dark Energy Survey Year 3 Results: clustering redshifts – calibration of the weak lensing source redshift distributions with redMaGiC and BOSS/eBOSS." Monthly Notices of the Royal Astronomical Society 510, no. 1 (November 18, 2021): 1223–47. http://dx.doi.org/10.1093/mnras/stab3311.

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ABSTRACT We present the calibration of the Dark Energy Survey Year 3 (DES Y3) weak lensing (WL) source galaxy redshift distributions n(z) from clustering measurements. In particular, we cross-correlate the WL source galaxies sample with redMaGiC galaxies (luminous red galaxies with secure photometric redshifts) and a spectroscopic sample from BOSS/eBOSS to estimate the redshift distribution of the DES sources sample. Two distinct methods for using the clustering statistics are described. The first uses the clustering information independently to estimate the mean redshift of the source galaxies within a redshift window, as done in the DES Y1 analysis. The second method establishes a likelihood of the clustering data as a function of n(z), which can be incorporated into schemes for generating samples of n(z) subject to combined clustering and photometric constraints. Both methods incorporate marginalization over various astrophysical systematics, including magnification and redshift-dependent galaxy-matter bias. We characterize the uncertainties of the methods in simulations; the first method recovers the mean z of tomographic bins to RMS (precision) of ∼0.014. Use of the second method is shown to vastly improve the accuracy of the shape of n(z) derived from photometric data. The two methods are then applied to the DES Y3 data.

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Shirasaki, Masato, Takashi Hamana, Masahiro Takada, Ryuichi Takahashi, and Hironao Miyatake. "Mock galaxy shape catalogues in the Subaru Hyper Suprime-Cam Survey." Monthly Notices of the Royal Astronomical Society 486, no. 1 (March 16, 2019): 52–69. http://dx.doi.org/10.1093/mnras/stz791.

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Abstract We use the full-sky ray-tracing weak lensing simulations to generate 2268 mock catalogues for the Subaru Hyper Suprime-Cam (HSC) survey first-year shear catalogue. Our mock catalogues take into account various effects as in the real data: the survey footprints, inhomogeneous angular distribution of source galaxies, statistical uncertainties in photometric redshift (photo-z) estimate, variations in the lensing weight, and the statistical noise in galaxy shape measurements including both intrinsic shapes and the measurement errors. We then utilize our mock catalogues to evaluate statistical uncertainties expected in measurements of cosmic shear two-point correlations ξ± with tomographic redshift information for the HSC survey. We develop a quasi-analytical formula for the Gaussian sample variance properly taking into account the number of source pairs in the survey footprints. The standard Gaussian formula significantly overestimates or underestimates the mock results by 50 per cent level. We also show that different photo-z catalogues or the six disconnected fields, rather than a consecutive geometry, cause variations in the covariance by ${\sim } 5{{\ \rm per\ cent}}$. The mock catalogues enable us to study the chi-square distribution for ξ±. We find the wider distribution than that naively expected for the distribution with the degrees of freedom of data vector used. Finally, we propose a method to include non-zero multiplicative bias in mock shape catalogue and show that the non-zero multiplicative bias can change the effective shape noise in cosmic shear analyses. Our results suggest an importance of estimating an accurate form of the likelihood function (and therefore the covariance) for robust cosmological parameter inference from the precise measurements.

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Abruzzo, Matthew W., and Zoltán Haiman. "The impact of photometric redshift errors on lensing statistics in ray-tracing simulations." Monthly Notices of the Royal Astronomical Society 486, no. 2 (April 18, 2019): 2730–53. http://dx.doi.org/10.1093/mnras/stz1016.

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Abstract Weak lensing surveys are reaching sensitivities at which uncertainties in the galaxy redshift distributions n(z) from photo-z errors degrade cosmological constraints. We use ray-tracing simulations and a simple treatment of photo-z errors to assess cosmological parameter biases from uncertainties in n(z) in an LSST-like survey. We use lensing peak counts and the power spectrum to infer cosmological parameters, and find that the latter is somewhat more resilient to photo-z errors. We place conservative lower limits on the survey size at which different types of photo-z errors significantly degrade (${\sim }50{{\ \rm per\ cent}}$) ΛCDM (cold dark matter, wCDM) parameter constraints. A residual constant photo-z bias of |δz| < 0.003(1 + z), the current LSST requirement, does not significantly degrade surveys smaller than ≈1300 (≈490) deg2 using peaks and ≈6500 (≈4900) deg2 using the power spectrum. Surveys smaller than ≈920 (≈450) deg2 and ≈4600 (≈4000) deg2 avoid 25 per cent degradation. Adopting a recent prediction for LSST’s full photo-z probability distribution function (PDF), we find that simply approximating n(z) with the photo-z galaxy distribution computed from this PDF significantly degrades surveys as small as ≈60 (≈65) deg2 using peaks or the power spectrum. If the centroid bias in each tomographic bin is removed from the photo-z galaxy distribution, using peaks or the power spectrum still significantly degrades surveys larger than ≈200 (≈255) or ≈248 (≈315) deg2; 25 per cent degradations occur at survey sizes of ≈140 (≈180) deg2 or ≈165 (≈210) deg2. These results imply that the expected broad photo-z PDF significantly biases parameters, which must be further mitigated using more sophisticated photo-z treatments.

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Harnois-Déraps, Joachim, Nicolas Martinet, Tiago Castro, Klaus Dolag, Benjamin Giblin, Catherine Heymans, Hendrik Hildebrandt, and Qianli Xia. "Cosmic shear cosmology beyond two-point statistics: a combined peak count and correlation function analysis of DES-Y1." Monthly Notices of the Royal Astronomical Society 506, no. 2 (June 12, 2021): 1623–50. http://dx.doi.org/10.1093/mnras/stab1623.

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ABSTRACT We constrain cosmological parameters from a joint cosmic shear analysis of peak-counts and the two-point shear correlation functions, as measured from the Dark Energy Survey (DES-Y1). We find the structure growth parameter $S_8\equiv \sigma _8\sqrt{\Omega _{\rm m}/0.3} = 0.766^{+0.033}_{-0.038}$ which, at 4.8 per cent precision, provides one of the tightest constraints on S8 from the DES-Y1 weak lensing data. In our simulation-based method we determine the expected DES-Y1 peak-count signal for a range of cosmologies sampled in four w cold dark matter parameters (Ωm, σ8, h, w0). We also determine the joint covariance matrix with over 1000 realizations at our fiducial cosmology. With mock DES-Y1 data we calibrate the impact of photometric redshift and shear calibration uncertainty on the peak-count, marginalizing over these uncertainties in our cosmological analysis. Using dedicated training samples we show that our measurements are unaffected by mass resolution limits in the simulation, and that our constraints are robust against uncertainty in the effect of baryon feedback. Accurate modelling for the impact of intrinsic alignments on the tomographic peak-count remains a challenge, currently limiting our exploitation of cross-correlated peak counts between high and low redshift bins. We demonstrate that once calibrated, a fully tomographic joint peak-count and correlation functions analysis has the potential to reach a 3 per cent precision on S8 for DES-Y1. Our methodology can be adopted to model any statistic that is sensitive to the non-Gaussian information encoded in the shear field. In order to accelerate the development of these beyond-two-point cosmic shear studies, our simulations are made available to the community upon request.

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Heavens, Alan F., Elena Sellentin, Damien de Mijolla, and Alvise Vianello. "Massive data compression for parameter-dependent covariance matrices." Monthly Notices of the Royal Astronomical Society 472, no. 4 (September 12, 2017): 4244–50. http://dx.doi.org/10.1093/mnras/stx2326.

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Abstract We show how the massive data compression algorithm MOPED can be used to reduce, by orders of magnitude, the number of simulated data sets which are required to estimate the covariance matrix required for the analysis of Gaussian-distributed data. This is relevant when the covariance matrix cannot be calculated directly. The compression is especially valuable when the covariance matrix varies with the model parameters. In this case, it may be prohibitively expensive to run enough simulations to estimate the full covariance matrix throughout the parameter space. This compression may be particularly valuable for the next generation of weak lensing surveys, such as proposed for Euclid and Large Synoptic Survey Telescope, for which the number of summary data (such as band power or shear correlation estimates) is very large, ∼104, due to the large number of tomographic redshift bins which the data will be divided into. In the pessimistic case where the covariance matrix is estimated separately for all points in an Monte Carlo Markov Chain analysis, this may require an unfeasible 109 simulations. We show here that MOPED can reduce this number by a factor of 1000, or a factor of ∼106 if some regularity in the covariance matrix is assumed, reducing the number of simulations required to a manageable 103, making an otherwise intractable analysis feasible.

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Munshi, Dipak, Peter Coles, and Martin Kilbinger. "Tomography and weak lensing statistics." Journal of Cosmology and Astroparticle Physics 2014, no. 04 (April 2, 2014): 004. http://dx.doi.org/10.1088/1475-7516/2014/04/004.

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Amara, Adam, and Alexandre Réfrégier. "Optimal surveys for weak-lensing tomography." Monthly Notices of the Royal Astronomical Society 381, no. 3 (October 10, 2007): 1018–26. http://dx.doi.org/10.1111/j.1365-2966.2007.12271.x.

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Schäfer, Björn Malte, and Lavinia Heisenberg. "Weak lensing tomography with orthogonal polynomials." Monthly Notices of the Royal Astronomical Society 423, no. 4 (June 8, 2012): 3445–57. http://dx.doi.org/10.1111/j.1365-2966.2012.21137.x.

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Hu, Wayne. "Power Spectrum Tomography with Weak Lensing." Astrophysical Journal 522, no. 1 (September 1, 1999): L21—L24. http://dx.doi.org/10.1086/312210.

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Hollenstein, Lukas, Domenico Sapone, Robert Crittenden, and Björn Malte Schäfer. "Constraints on early dark energy from CMB lensing and weak lensing tomography." Journal of Cosmology and Astroparticle Physics 2009, no. 04 (April 16, 2009): 012. http://dx.doi.org/10.1088/1475-7516/2009/04/012.

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Zhan, Hu. "Cosmic tomographies: baryon acoustic oscillations and weak lensing." Journal of Cosmology and Astroparticle Physics 2006, no. 08 (August 24, 2006): 008. http://dx.doi.org/10.1088/1475-7516/2006/08/008.

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Cai, Yan-Chuan, and Gary Bernstein. "Combining weak-lensing tomography and spectroscopic redshift surveys." Monthly Notices of the Royal Astronomical Society 422, no. 2 (March 15, 2012): 1045–56. http://dx.doi.org/10.1111/j.1365-2966.2012.20676.x.

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Ding, Zhejie, Hee-Jong Seo, Eric Huff, Shun Saito, and Douglas Clowe. "Detecting baryon acoustic oscillations in dark matter from kinematic weak lensing surveys." Monthly Notices of the Royal Astronomical Society 487, no. 1 (May 9, 2019): 253–67. http://dx.doi.org/10.1093/mnras/stz1257.

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Abstract:

Abstract We investigate the feasibility of extracting baryon acoustic oscillations (BAO) from cosmic shear tomography. We particularly focus on the BAO scale precision that can be achieved by future spectroscopy-based, kinematic weak lensing (KWL) surveys in comparison to the traditional photometry-based weak lensing surveys. We simulate cosmic shear tomography data of such surveys with a few simple assumptions to focus on the BAO information, extract the spatial power spectrum, and constrain the recovered BAO feature. Due to the small shape noise and the shape of the lensing kernel, we find that a Dark Energy Task Force Stage IV version of such KWL survey can detect the BAO feature in dark matter by 3σ and measure the BAO scale at the precision level of 4 per cent, while it will be difficult to detect the feature in photometry-based weak lensing surveys. With a more optimistic assumption, a KWL-Stage IV could achieve a ${\sim } 2{{\ \rm per\ cent}}$ BAO scale measurement with 4.9σ confidence. A built-in spectroscopic galaxy survey within such KWL survey will allow cross-correlation between galaxies and cosmic shear, which will tighten the constraint beyond the lower limit we present in this paper and therefore possibly allow a detection of the BAO scale bias between galaxies and dark matter.

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Journal articles on the topic 'Tomographic Weak Lensing'

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