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Register a new userLensing corrections on galaxy-lensing cross correlations and galaxy-galaxy auto correlations
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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.
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Cluster weak lensing is a sensitive probe of cosmology, particularly the amplitude of matter clustering $sigma_8$ and matter density parameter $Omega_m$. The main nuisance parameter in a cluster weak lensing cosmological analysis is the scatter between the true halo mass and the relevant cluster observable, denoted $sigma_{ln Mc}$. We show that combining the cluster weak lensing observable $Delta Sigma$ with the projected cluster-galaxy cross-correlation function $w_{p,cg}$ and galaxy auto-correlation function $w_{p,gg}$ can break the degeneracy between $sigma_8$ and $sigma_{ln Mc}$ to achieve tight, percent-level constraints on $sigma_8$. Using a grid of cosmological N-body simulations, we compute derivatives of $Delta Sigma$, $w_{p,cg}$, and $w_{p,gg}$ with respect to $sigma_8$, $Omega_m$, $sigma_{ln Mc}$ and halo occupation distribution (HOD) parameters describing the galaxy population. We also compute covariance matrices motivated by the properties of the Dark Energy Suvery (DES) cluster and weak lensing survey and the BOSS CMASS galaxy redshift survey. For our fiducial scenario combining $Delta Sigma$, $w_{p,cg}$, and $w_{p,gg}$ measured over $0.3-30.0 ; h^{-1} ; mathrm{Mpc}$, for clusters at $z=0.35-0.55$ above a mass threshold $M_capprox 2times 10^{14} ; h^{-1} ; mathrm{M_{odot}}$, we forecast a $1.4%$ constraint on $sigma_8$ while marginalizing over $sigma_{ln Mc}$ and all HOD parameters. Reducing the mass threshold to $1times 10^{14} ; h^{-1} ; mathrm{M_{odot}}$ and adding a $z=0.15-0.35$ redshift bin sharpens this constraint to $0.8%$. The small scale $(r_p < 3.0 ; h^{-1} ; mathrm{Mpc})$ ``mass function and large scale $(r_p > 3.0 ; h^{-1} ; mathrm{Mpc})$ ``halo-mass cross-correlation regimes of $Delta Sigma$ have comparable constraining power, allowing internal consistency tests from such an analysis.
We explore the effects of incorporating redshift uncertainty into measurements of galaxy clustering and cross-correlations of galaxy positions and cosmic microwave background (CMB) lensing maps. We use a simple Gaussian model for a redshift distribution in a redshift bin with two parameters: the mean, $z_0$, and the width, $sigma_z$. We vary these parameters, as well as a galaxy bias parameter, $b_{text{g}}$, and a matter fluctuations parameter, $sigma_8$, for each redshift bin, as well as the parameter $Omega_{text{m}}$, in a Fisher analysis across 12 redshift bins from $z=0-7$. We find that incorporating redshift uncertainties degrades constraints on $sigma_8(z)$ in the Large Synoptic Survey Telescope (LSST)/CMB-S4 era by about a factor of 10 compared to the case of perfect redshift knowledge. In our fiducial analysis of LSST/CMB-S4 including redshift uncertainties, we project constraints on $sigma_8(z)$ for $z<3$ of less than $5 %$. Galaxy imaging surveys are expected to have priors on redshift parameters from photometric redshift algorithms and other methods. When adding priors with the expected precision for LSST redshift algorithms, the constraints on $sigma_8(z)$ can be improved by a factor of 2-3 compared to the case of no prior information. We also find that `self-calibrated constraints on the redshift parameters from just the autocorrelation and cross-correlation measurements (with no prior information) are competitive with photometric redshift techniques. In the LSST/CMB-S4 era, we find uncertainty on the redshift parameters ($z_0,sigma_z$) to be below 0.004(1+z) at $z<1$. For all parameters, constraints improve significantly if smaller scales can be used. We also project constraints for nearer term survey combinations, Dark Energy Survey (DES)/SPT-SZ, DES/SPT-3G, and LSST/SPT-3G, and analyze how our constraints depend on a variety of parameter and model choices.
Galaxy clustering on very large scales can be probed via the 2-point correlation function in the general case of wide and deep separations, including all the lightcone and relativistic effects. Using our recently developed formalism, we analyze the behavior of the local and integrated contributions and how these depend on redshift range, linear and angular separations and luminosity function. Relativistic corrections to the local part of the correlation can be non-negligible but they remain generally sub-dominant. On the other hand, the additional correlations arising from lensing convergence and time-delay effects can become very important and even dominate the observed total correlation function. We investigate different configurations formed by the observer and the pair of galaxies, and we find that the case of near-radial large-scale separations is where these effects will be the most important.
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).
We study moderate gravitational lensing where a background galaxy is magnified substantially, but not multiply imaged, by an intervening galaxy. We focus on the case where both the lens and source are elliptical galaxies. The signatures of moderate lensing include isophotal distortions and systematic shifts in the fundamental plane and Kormendy relation, which can potentially be used to statistically determine the galaxy mass profiles. These effects are illustrated using Monte Carlo simulations of galaxy pairs where the foreground galaxy is modelled as a singular isothermal sphere model and observational parameters appropriate for the Large Synoptic Survey Telescope (LSST). The range in radius probed by moderate lensing will be larger than that by strong lensing, and is in the interesting regime where the density slope may be changing.
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