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Register a new userIntrinsic alignment contamination to CMB lensing-galaxy weak lensing correlations from tidal torquing
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Correlations of galaxy ellipticities with large-scale structure, due to galactic tidal interactions, provide a potentially significant contaminant to measurements of cosmic shear. However, these intrinsic alignments are still poorly understood for galaxies at the redshifts typically used in cosmic shear analyses. For spiral galaxies, it is thought that tidal torquing is significant in determining alignments resulting in zero correlation between the intrinsic ellipticity and the gravitational potential in linear theory. Here, we calculate the leading-order correction to this result in the tidal-torque model from non-linear evolution, using second-order perturbation theory, and relate this to the contamination from intrinsic alignments to the recently-measured cross-correlation between galaxy ellipticities and the CMB lensing potential. On the scales relevant for CMB lensing observations, the squeezed limit of the gravitational bispectrum dominates the correlation. Physically, the large-scale mode that sources CMB lensing modulates the small-scale power and hence the intrinsic ellipticity, due to non-linear evolution. We find that the angular cross-correlation from tidal torquing has a very similar scale dependence as in the linear alignment model, believed to be appropriate for elliptical galaxies. The amplitude of the cross-correlation is predicted to depend strongly on the formation redshift, being smaller for galaxies that formed at higher redshift when the bispectrum of the gravitational potential was smaller. Finally, we make simple forecasts for constraints on intrinsic alignments from the correlation of forthcoming cosmic shear measurements with current CMB lensing measurements. We note that cosmic variance can be significantly reduced in measurements of the difference in the intrinsic alignments for elliptical and spiral galaxies if these can be separated (e.g., using colour).
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Intrinsic galaxy alignments constitute the major astrophysical systematic of forthcoming weak gravitational lensing surveys but also yield unique insights into galaxy formation and evolution. We build analytic models for the distribution of galaxy shapes based on halo properties extracted from the Millennium Simulation, differentiating between early- and late-type galaxies as well as central galaxies and satellites. The resulting ellipticity correlations are investigated for their physical properties and compared to a suite of current observations. The best-faring model is then used to predict the intrinsic alignment contamination of planned weak lensing surveys. We find that late-type galaxy models generally have weak intrinsic ellipticity correlations, marginally increasing towards smaller galaxy separation and higher redshift. The signal for early-type models at fixed halo mass strongly increases by three orders of magnitude over two decades in galaxy separation, and by one order of magnitude from z=0 to z=2. The intrinsic alignment strength also depends strongly on halo mass, but not on galaxy luminosity at fixed mass, or galaxy number density in the environment. We identify models that are in good agreement with all observational data, except that all models over-predict alignments of faint early-type galaxies. The best model yields an intrinsic alignment contamination of a Euclid-like survey between 0.5-10% at z>0.6 and on angular scales larger than a few arcminutes. Cutting 20% of red foreground galaxies using observer-frame colours can suppress this contamination by up to a factor of two.
Correlations between the intrinsic shapes of galaxies and the large-scale galaxy density field provide an important tool to investigate galaxy intrinsic alignments, which constitute a major astrophysical systematic in cosmological weak lensing (cosmic shear) surveys, but also yield insight into the formation and evolution of galaxies. We measure galaxy position-shape correlations in the MegaZ-LRG sample for more than 800,000 luminous red galaxies, making the first such measurement with a photometric redshift sample. In combination with a re-analysis of several spectroscopic SDSS samples, we constrain an intrinsic alignment model for early-type galaxies over long baselines in redshift (z ~ 0.7) and luminosity (4mag). We develop and test the formalism to incorporate photometric redshift scatter in the modelling. For r_p > 6 Mpc/h, the fits to galaxy position-shape correlation functions are consistent with the scaling with r_p and redshift of a revised, nonlinear version of the linear alignment model for all samples. An extra redshift dependence proportional to (1+z)^n is constrained to n=-0.3+/-0.8 (1sigma). To obtain consistent amplitudes for all data, an additional dependence on galaxy luminosity proportional to L^b with b=1.1+0.3-0.2 is required. The normalisation of the intrinsic alignment power spectrum is found to be (0.077 +/- 0.008)/rho_{cr} for galaxies at redshift 0.3 and r band magnitude of -22 (k- and evolution-corrected to z=0). Assuming zero intrinsic alignments for blue galaxies, we assess the bias on cosmological parameters for a tomographic CFHTLS-like lensing survey. Both the resulting mean bias and its uncertainty are smaller than the 1sigma statistical errors when using the constraints from all samples combined. The addition of MegaZ-LRG data reduces the uncertainty in intrinsic alignment bias on cosmological parameters by factors of three to seven. (abridged)
We study the impact of lensing corrections on modeling cross correlations between CMB lensing and galaxies, cosmic shear and galaxies, and galaxies in different redshift bins. Estimating the importance of these corrections becomes necessary in the light of anticipated high-accuracy measurements of these observables. While higher order lensing corrections (sometimes also referred to as post Born corrections) have been shown to be negligibly small for lensing auto correlations, they have not been studied for cross correlations. We evaluate the contributing four-point functions without making use of the Limber approximation and compute line-of-sight integrals with the numerically stable and fast FFTlog formalism. We find that the relative size of lensing corrections depends on the respective redshift distributions of the lensing sources and galaxies, but that they are generally small for high signal-to-noise correlations. We point out that a full assessment and judgement of the importance of these corrections requires the inclusion of lensing Jacobian terms on the galaxy side. We identify these additional correction terms, but do not evaluate them due to their large number. We argue that they could be potentially important and suggest that their size should be measured in the future with ray-traced simulations. We make our code publicly available.
In recent years, weak lensing of the cosmic microwave background (CMB) has emerged as a powerful tool to probe fundamental physics, such as neutrino masses, primordial non-Gaussianity, dark energy, and modified gravity. The prime target of CMB lensing surveys is the lensing potential, which is reconstructed from observed CMB temperature $T$ and polarization $E$ and $B$ fields. Until very recently, this reconstruction has been performed with quadratic estimators (QEs), which, although known to be suboptimal for high-sensitivity experiments, are numerically efficient, and useful to make forecasts and cross-check the results of more sophisticated likelihood-based methods. It is expected that ongoing and near-future CMB experiments such as AdvACT, SPT-3G and the Simons Observatory (SO), will also rely on QEs. Here, we review different QEs, and clarify their differences. In particular, we show that the Hu-Okamoto (HO02) estimator is not the absolute optimal lensing estimator that can be constructed out of quadratic combinations of $T, E$ and $B$ fields. Instead, we derive the global-minimum-variance (GMV) lensing quadratic estimator. Although this estimator can be found elsewhere in the literature, it was erroneously described as equivalent to the HO02 estimator, and has never been used in real data analyses. Here, we show explicitly that the HO02 estimator is suboptimal to the GMV estimator, with a reconstruction noise larger by up to $sim 9%$ for a SO-like experiment. We further show that the QE used in the Planck, and recent SPT lensing analysis are suboptimal to both the HO02 and GMV estimator, and would have a reconstruction noise up to $sim 11%$ larger than that of the GMV estimator for a SO-like experiment. In addition to clarifying differences between different QEs, this work should thus provide motivation to implement the GMV estimator in future lensing analyses relying on QEs.
Weak gravitational lensing of background galaxies provides a direct probe of the projected matter distribution in and around galaxy clusters. Here we present a self-contained pedagogical review of cluster--galaxy weak lensing, covering a range of topics relevant to its cosmological and astrophysical applications. We begin by reviewing the theoretical foundations of gravitational lensing from first principles, with special attention to the basics and advanced techniques of weak gravitational lensing. We summarize and discuss key findings from recent cluster--galaxy weak-lensing studies on both observational and theoretical grounds, with a focus on cluster mass profiles, the concentration--mass relation, the splashback radius, and implications from extensive mass calibration efforts for cluster cosmology.
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