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Register a new userWeak lensing post-Born effects are equivalent to pure lens-lens couplings
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Added by
Oliver Denton-Turner
Publication date
2021
fields
Physics
and research's language is
English
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We show that the so-called post-Born effects of weak lensing at 4th order are equivalent to lens-lens couplings in the Born Approximation. We demonstrate this by explicitly showing the equivalence of the canonical weak lensing approach at 4th order using the anisotropy remapping method, to that of the 4th order calculation of the lens-lens coupling effects using the Boltzmann equation approach that was first developed in [Phys. Rev. D89, 123006]. Furthermore, we argue that to incorporate true post-Born effects, i.e. taking into account non-straight photon paths, require the addition of a photon deflection term which has not been taken into account in the canonical formalism nor the Boltzmann method.
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We present a full-sky derivation of weak lensing observables in the Post-Friedmann (PF) formalism. Weak lensing has the characteristic of mixing small scales and large scales since it is affected by inhomogeneities integrated along the photon trajectory. With the PF formalism, we develop a modelling of lensing observables which encompasses both leading order relativistic effects and effects that are due to the fully non-linear matter distribution at small scales. We derive the reduced shear, convergence and rotation up to order $1/c^4$ in the PF approximation, accounting for scalar, vector and tensor perturbations, as well as galaxies peculiar velocities. We discuss the various contributions that break the Kaiser-Squires relation between the shear and the convergence at different orders. We pay particular attention to the impact of the frame-dragging vector potential on lensing observables and we discuss potential ways to measure this effect in future lensing surveys.
We present weak lensing mass estimates of seven shear-selected galaxy cluster candidates from the Deep Lens Survey. The clusters were previously identified as mass peaks in convergence maps of 8.6 sq. deg of R band imaging, and followed up with X-ray and spectroscopic confirmation, spanning a redshift range 0.19 - 0.68. Most clusters contained multiple X-ray peaks, yielding 17 total mass concentrations. In this paper, we constrain the masses of these X-ray sources with weak lensing, using photometric redshifts from the full set of BVRz imaging to properly weight background galaxies according to their lensing distance ratios. We fit both NFW and singular isothermal sphere profiles, and find that the results are insensitive to the assumed profile. We also show that the results do not depend significantly on the assumed prior on the position of the mass peak, but that this may become an issue in future larger samples. The inferred velocity dispersions for the extended X-ray sources range from 250-800 km/s, with the exception of one source for which no lensing signal was found. This work further establishes shear selection as a viable technique for finding clusters, but also highlights some unresolved issues such as determination of the mass profile center without biasing the mass estimate, and fully accounting for line-of-sight projections. A follow-up paper will examine the mass-X-ray scaling relations of these clusters.
The information about the mass density of galaxy clusters provided by the gravitational lens effect has inspired many inversion techniques. In this article, updates to the previously introduced method in Grale are described, and explored in a number of examples. The first looks into a different way of incorporating time delay information, not requiring the unknown source position. It is found that this avoids a possible bias that leads to over-focusing the images, i.e. providing source position estimates that lie in a considerably smaller region than the true positions. The second is inspired by previous reconstructions of the cluster of galaxies MACS J1149.6+2223, where a multiply-imaged background galaxy contained a supernova, SN Refsdal, of which four additional images were produced by the presence of a smaller cluster galaxy. The inversion for the cluster as a whole, was not able to recover sufficient detail interior to this quad. We show how constraints on such different scales, from the entire cluster to a single member galaxy, can now be used, allowing such small scale substructures to be resolved. Finally, the addition of weak lensing information to this method is investigated. While this clearly helps recover the environment around the strong lensing region, the mass sheet degeneracy may make a full strong and weak inversion difficult, depending on the quality of the ellipticity information at hand. We encounter ring-like structure at the boundary of the two regimes, argued to be the result of combining strong and weak lensing constraints, possibly affected by degeneracies.
We introduce the skew-spectrum statistic for weak lensing convergence $kappa$ 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 $kappa$ 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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