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Register a new userMeasuring Lensing Magnification of Quasars by Large Scale Structure using the Variability-Luminosity Relation
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We introduce a technique to measure gravitational lensing magnification using the variability of type I quasars. Quasars variability amplitudes and luminosities are tightly correlated, on average. Magnification due to gravitational lensing increases the quasars apparent luminosity, while leaving the variability amplitude unchanged. Therefore, the mean magnification of an ensemble of quasars can be measured through the mean shift in the variability-luminosity relation. As a proof of principle, we use this technique to measure the magnification of quasars spectroscopically identified in the Sloan Digital Sky Survey, due to gravitational lensing by galaxy clusters in the SDSS MaxBCG catalog. The Palomar-QUEST Variability Survey, reduced using the DeepSky pipeline, provides variability data for the sources. We measure the average quasar magnification as a function of scaled distance (r/R200) from the nearest cluster; our measurements are consistent with expectations assuming NFW cluster profiles, particularly after accounting for the known uncertainty in the clusters centers. Variability-based lensing measurements are a valuable complement to shape-based techniques because their systematic errors are very different, and also because the variability measurements are amenable to photometric errors of a few percent and to depths seen in current wide-field surveys. Given the data volume expected from current and upcoming surveys, this new technique has the potential to be competitive with weak lensing shear measurements of large scale structure.
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Accurate measurement of galaxy cluster masses is an essential component not only in studies of cluster physics, but also for probes of cosmology. However, different mass measurement techniques frequently yield discrepant results. The SDSS MaxBCG catalogs mass-richness relation has previously been constrained using weak lensing shear, Sunyaev-Zeldovich (SZ), and X-ray measurements. The mass normalization of the clusters as measured by weak lensing shear is >~25% higher than that measured using SZ and X-ray methods, a difference much larger than the stated measurement errors in the analyses. We constrain the mass-richness relation of the MaxBCG galaxy cluster catalog by measuring the gravitational lensing magnification of type I quasars in the background of the clusters. The magnification is determined using the quasars variability and the correlation between quasars variability amplitude and intrinsic luminosity. The mass-richness relation determined through magnification is in agreement with that measured using shear, confirming that the lensing strength of the clusters implies a high mass normalization, and that the discrepancy with other methods is not due to a shear-related systematic measurement error. We study the dependence of the measured mass normalization on the cluster halo orientation. As expected, line-of-sight clusters yield a higher normalization; however, this minority of haloes does not significantly bias the average mass-richness relation of the catalog.
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.
We show that a large-area imaging survey using narrow-band filters could detect quasars in sufficiently high number densities, and with more than sufficient accuracy in their photometric redshifts, to turn them into suitable tracers of large-scale structure. If a narrow-band optical survey can detect objects as faint as i=23, it could reach volumetric number densities as high as 10^{-4} h^3 Mpc^{-3} (comoving) at z~1.5 . Such a catalog would lead to precision measurements of the power spectrum up to z~3-4. We also show that it is possible to employ quasars to measure baryon acoustic oscillations at high redshifts, where the uncertainties from redshift distortions and nonlinearities are much smaller than at z<1. As a concrete example we study the future impact of J-PAS, which is a narrow-band imaging survey in the optical over 1/5 of the unobscured sky with 42 filters of ~100 A full-width at half-maximum. We show that J-PAS will be able to take advantage of the broad emission lines of quasars to deliver excellent photometric redshifts, sigma_{z}~0.002(1+z), for millions of objects.
Cluster gravitational lensing surveys like the Hubble Space Telescope Frontier Fields survey will detect distant galaxies 10-50 times fainter than any yet discovered. Using these surveys to measure the luminosity function of such faint, distant galaxies, however, requires that magnification maps built from the constraints of strongly-lensed images be accurate. For models that assume the cluster and nearby (correlated) structures are the only significant sources of lensing, a potential source of error in these maps comes from the fact that light rays also suffer weak deflections by uncorrelated large-scale structure along the line-of-sight, i.e. cosmic weak lensing (CWL). To demonstrate the magnitude of this effect, we calculate the magnification change which results when the same cluster-lens is placed along different lines of sight. Using a simple density profile for a cluster-lens at z~0.3-0.5 and the power spectrum of the matter density fluctuations responsible for CWL, we show that the typical magnifications of ~5(10) of sources at z=6-10 can differ by ~10-20(20-30)% from one line-of-sight to another. However, these fluctuations rise to greater than order unity near critical curves, indicating that CWL tends to make its greatest contribution to the most magnified images. We conclude that the neglect of CWL in determining the intrinsic luminosities of highly-magnified galaxies may introduce errors significant enough to warrant further effort to include this contribution in cluster-lens modeling. We suggest that methods of modeling CWL in galaxy-strong-lensing systems should be generalized to cluster-lensing systems.
Measurements of the galaxy number density in upcoming surveys such as Euclid and the SKA will be sensitive to distortions from lensing magnification and Doppler effects, beyond the standard redshift-space distortions. The amplitude of these contributions depends sensitively on magnification bias and evolution bias in the galaxy number density. Magnification bias quantifies the change in the observed number of galaxies gained or lost by lensing magnification, while evolution bias quantifies the physical change in the galaxy number density relative to the conserved case. These biases are given by derivatives of the number density, and consequently are very sensitive to the form of the luminosity function. We give a careful derivation of the magnification and evolution biases, clarifying a number of results in the literature. We then examine the biases for a variety of surveys, encompassing optical/NIR, 21cm galaxy and 21cm intensity mapping surveys.
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