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Register a new userSuppressing the contribution of intrinsic galaxy alignments to the shear two-point correlation function
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Cosmological weak lensing gives rise to correlations in the ellipticities of faint galaxies. This cosmic shear signal depends upon the matter power spectrum, thus providing a means to constrain cosmological parameters. It has recently been proposed that intrinsic alignments arising at the epoch of galaxy formation can also contribute significantly to the observed correlations, the amplitude increasing with decreasing survey depth. Here we consider the two-point shear correlation function, and demonstrate that photometric redshift information can be used to suppress the intrinsic signal; at the same time Poisson noise is increased, due to a decrease in the effective number of galaxy pairs. The choice to apply such a redshift-depending weighting will depend on the characteristics of the survey in question. In surveys with a mean z of about 1, although the lensing signal dominates, the measurement error bars may soon become smaller than the intrinsic alignment signal; hence, in order not to be dominated by systematics, redshift information in cosmic shear statistics will become a necessity. We discuss various aspects of this.
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During the past few years, secure detections of cosmic shear have been obtained, manifest in the correlation of the observed ellipticities of galaxies. Constraints have already been placed on cosmological parameters, such as the normalisation of the matter power spectrum sigma_8. One possible systematic contaminant of the lensing correlation signal arises from intrinsic galaxy alignment, which is still poorly constrained. Unlike lensing, intrinsic correlations only pertain to galaxies with small physical separations, the correlation length being a few Mpc. We present a new method that harnesses this property, and isolates the lensing and intrinsic components of the galaxy ellipticity correlation function using measurements between different redshift slices. The observed signal is approximated by a set of template functions, making no strong assumptions about the amplitude or correlation length of any intrinsic alignment. We also show that the near-degeneracy between the matter density parameter Omega_m and sigma_8 can be lifted using correlation function tomography, even in the presence of an intrinsic alignment signal.
We present the integrated 3-point shear correlation function $izeta_{pm}$ -- a higher-order statistic of the cosmic shear field -- which can be directly estimated in wide-area weak lensing surveys without measuring the full 3-point shear correlation function, making this a practical and complementary tool to 2-point statistics for weak lensing cosmology. We define it as the 1-point aperture mass statistic $M_{mathrm{ap}}$ measured at different locations on the shear field correlated with the corresponding local 2-point shear correlation function $xi_{pm}$. Building upon existing work on the integrated bispectrum of the weak lensing convergence field, we present a theoretical framework for computing the integrated 3-point function in real space for any projected field within the flat-sky approximation and apply it to cosmic shear. Using analytical formulae for the non-linear matter power spectrum and bispectrum, we model $izeta_{pm}$ and validate it on N-body simulations within the uncertainties expected from the sixth year cosmic shear data of the Dark Energy Survey. We also explore the Fisher information content of $izeta_{pm}$ and perform a joint analysis with $xi_{pm}$ for two tomographic source redshift bins with realistic shape-noise to analyse its power in constraining cosmological parameters. We find that the joint analysis of $xi_{pm}$ and $izeta_{pm}$ has the potential to considerably improve parameter constraints from $xi_{pm}$ alone, and can be particularly useful in improving the figure of merit of the dynamical dark energy equation of state parameters from cosmic shear data.
We perform theoretical and numerical studies of the full relativistic two-point galaxy correlation function, considering the linear-order scalar and tensor perturbation contributions and the wide-angle effects. Using the gauge-invariant relativistic description of galaxy clustering and accounting for the contributions at the observer position, we demonstrate that the complete theoretical expression is devoid of any long-mode contributions from scalar or tensor perturbations and it lacks the infrared divergences in agreement with the equivalence principle. By showing that the gravitational potential contribution to the correlation function converges in the infrared, our study justifies an IR cut-off $(k_{text{IR}} leq H_0)$ in computing the gravitational potential contribution. Using the full gauge-invariant expression, we numerically compute the galaxy two-point correlation function and study the individual contributions in the conformal Newtonian gauge. We find that the terms at the observer position such as the coordinate lapses and the observer velocity (missing in the standard formalism) dominate over the other relativistic contributions in the conformal Newtonian gauge such as the source velocity, the gravitational potential, the integrated Sachs-Wolf effect, the Shapiro time-delay and the lensing convergence. Compared to the standard Newtonian theoretical predictions that consider only the density fluctuation and redshift-space distortions, the relativistic effects in galaxy clustering result in a few percent-level systematic errors beyond the scale of the baryonic acoustic oscillation. Our theoretical and numerical study provides a comprehensive understanding of the relativistic effects in the galaxy two-point correlation function, as it proves the validity of the theoretical prediction and accounts for effects that are often neglected in its numerical evaluation.
We study the effect of large scale tangled magnetic fields on the galaxy two-point correlation function in the redshift space. We show that (a) the magnetic field effects can be comparable the gravity-induced clustering for present magnetic field strength $B_0 simeq 5 times 10^{-8}$ G, (b) the absence of this signal from the present data gives an upper bound $B_0 la 3 times 10^{-8}$ G, (c) the future data can probe the magnetic fields of $simeq 10^{-8}$ G. A comparison with other constraints on the present magnetic field shows that they are marginally compatible.However if the magenetic fields corresponding to $B_0 simeq 10^{-8}$ G existed at the last scattering surface they will cause unacceptably large CMBR anisotropies.
The two-point correlation function of the galaxy distribution is a key cosmological observable that allows us to constrain the dynamical and geometrical state of our Universe. To measure the correlation function we need to know both the galaxy positions and the expected galaxy density field. The expected field is commonly specified using a Monte-Carlo sampling of the volume covered by the survey and, to minimize additional sampling errors, this random catalog has to be much larger than the data catalog. Correlation function estimators compare data-data pair counts to data-random and random-random pair counts, where random-random pairs usually dominate the computational cost. Future redshift surveys will deliver spectroscopic catalogs of tens of millions of galaxies. Given the large number of random objects required to guarantee sub-percent accuracy, it is of paramount importance to improve the efficiency of the algorithm without degrading its precision. We show both analytically and numerically that splitting the random catalog into a number of subcatalogs of the same size as the data catalog when calculating random-random pairs, and excluding pairs across different subcatalogs provides the optimal error at fixed computational cost. For a random catalog fifty times larger than the data catalog, this reduces the computation time by a factor of more than ten without affecting estimator variance or bias.
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