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Register a new userA Generalized Method for Measuring Weak Lensing Magnification With Weighted Number Counts
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We present a derivation of a generalized optimally-weighted estimator for the weak lensing magnification signal, including a calculation of errors. With this estimator, we present a local method for optimally estimating the local effects of magnification from weak gravitational lensing, using a comparison of number counts in an arbitrary region of space to the expected unmagnified number counts. We show that when equivalent lens and source samples are used, this estimator is simply related to the optimally-weighted correlation function estimator used in past work and vice-versa, but this method has the benefits that it can calculate errors with significantly less computational time, that it can handle overlapping lens and source samples, and that it can easily be extended to mass-mapping. We present a proof-of-principle test of this method on data from the CFHTLenS, showing that its calculated magnification signals agree with predictions from model fits to shear data. Finally, we investigate how magnification data can be used to supplement shear data in determining the best-fit model mass profiles for galaxy dark matter haloes. We find that at redshifts greater than z ~ 0.6, the inclusion of magnification can often significantly improve the constraints on the components of the mass profile which relate to galaxies local environments relative to shear alone, and in high-redshift, low- and medium-mass bins, it can have a higher signal-to-noise than the shear signal.
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Galaxy-galaxy lensing is an essential tool for probing dark matter halos and constraining cosmological parameters. While galaxy-galaxy lensing measurements usually rely on shear, weak-lensing magnification contains additional constraining information. Using the fundamental plane (FP) of elliptical galaxies to anchor the size distribution of a background population is one method that has been proposed for performing a magnification measurement. We present a formalism for using the FP residuals of elliptical galaxies to jointly estimate the foreground mass and background redshift errors for a stacked lens scenario. The FP residuals include information about weak-lensing magnification $kappa$, and therefore foreground mass, since to first order, nonzero $kappa$ affects galaxy size but not other FP properties. We also present a modular, extensible code that implements the formalism using emulated galaxy catalogs of a photometric galaxy survey. We find that combining FP information with observed number counts of the source galaxies constrains mass and photo-z error parameters significantly better than an estimator that includes number counts only. In particular, the constraint on the mass is 17.0% if FP residuals are included, as opposed to 27.7% when only number counts are included. The effective size noise for a foreground lens of mass $M_H=10^{14}M_odot$, with a conservative selection function in size and surface brightness applied to the source population, is $sigma_{kappa,mathrm{eff}}=0.250$. We discuss the improvements to our FP model necessary to make this formalism a practical companion to shear analyses in weak lensing surveys.
Measuring weak lensing cosmic magnification signal is very challenging due to the overwhelming intrinsic clustering in the observed galaxy distribution. In this paper, we modify the Internal Linear Combination (ILC) method to reconstruct the lensing signal with an extra constraint to suppress the intrinsic clustering. To quantify the performance, we construct a realistic galaxy catalogue for the LSST-like photometric survey, covering 20000 $deg^{2}$ with mean source redshift at $z_{s}sim 1$. We find that the reconstruction performance depends on the width of the photo-z bin we choose. Due to the correlation between the lensing signal and the source galaxy distribution, the derived signal has smaller systematic bias but larger statistical uncertainty for a narrower photo-z bin. We conclude that the lensing signal reconstruction with the Modified ILC method is unbiased with a statistical uncertainty $<5%$ for bin width $Delta z^{P} = 0.2$.
We propose counting peaks in weak lensing (WL) maps, as a function of their height, to probe models of dark energy and to constrain cosmological parameters. Because peaks can be identified in two-dimensional WL maps directly, they can provide constraints that are free from potential selection effects and biases involved in identifying and determining the masses of galaxy clusters. We have run cosmological N-body simulations to produce WL convergence maps in three models with different constant values of the dark energy equation of state parameter, w=-0.8, -1, and -1.2, with a fixed normalization of the primordial power spectrum (corresponding to present-day normalizations of sigma8=0.742, 0.798, and 0.839, respectively). By comparing the number of WL peaks in 8 convergence bins in the range of -0.1 < kappa < 0.2, in multiple realizations of a single simulated 3x3 degree field, we show that the first (last) pair of models can be distinguished at the 95% (85%) confidence level. A survey with depth and area (20,000 sq. degrees), comparable to those expected from LSST, should have a factor of approx. 50 better parameter sensitivity. We find that relatively low-amplitude peaks (kappa = 0.03), which typically do not correspond to a single collapsed halo along the line of sight, account for most of this sensitivity. We study a range of smoothing scales and source galaxy redshifts (z_s). With a fixed source galaxy density of 15/arcmin^2, the best results are provided by the smallest scale we can reliably simulate, 1 arcminute, and z_s=2 provides substantially better sensitivity than z_s< 1.5.
We develop and apply an analytic method to predict peak counts in weak-lensing surveys. It is based on the theory of Gaussian random fields and suitable to quantify the level of spurious detections caused by chance projections of large-scale structures as well as the shape and shot noise contributed by the background galaxies. We compare our method to peak counts obtained from numerical ray-tracing simulations and find good agreement at the expected level. The number of peak detections depends substantially on the shape and size of the filter applied to the gravitational shear field. Our main results are that weak-lensing peak counts are dominated by spurious detections up to signal-to-noise ratios of 3--5 and that most filters yield only a few detections per square degree above this level, while a filter optimised for suppressing large-scale structure noise returns up to an order of magnitude more.
We test the impact of some systematic errors in weak lensing magnification measurements with the COSMOS 30-band photo-$z$ Survey flux limited to $I_{auto}<25.0$ using correlations of both source galaxy counts and magnitudes. Systematic obscuration effects are measured by comparing counts and magnification correlations. We use the ACS-HST catalogs to identify potential blending objects (close pairs) and perform the magnification analyses with and without blended objects. We find that blending effects start to be important ($sim$ 0.04~mag obscuration) at angular scales smaller than 0.1 arcmin. Extinction and other systematic obscuration effects can be as large as 0.10~mag (U-band) but are typically smaller than 0.02~mag depending on the band. After applying these corrections, we measure a $3.9sigma$ magnification signal that is consistent for both counts and magnitudes. The corresponding projected mass profiles of galaxies at redshift $z simeq 0.6$ ($M_I simeq -21$) is $Sigma= 25pm 6 M_{sun}h^3/pc^2$ at 0.1 Mpc/h, consistent with NFW type profile with $M_{200} simeq 2 times 10^{12} M_{sun} h/pc^2$. Tangential shear and flux-size magnification over the same lenses show similar mass profiles. We conclude that magnification from counts and fluxes using photometric redshifts has the potential to provide complementary weak lensing information in future wide field surveys once we carefully take into account systematic effects, such as obscuration and blending.
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