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Register a new userThe importance of magnification effects in galaxy-galaxy lensing
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Magnification changes the observed number counts of galaxies on the sky. This biases the observed tangential shear profiles around galaxies, the so-called galaxy-galaxy lensing (GGL) signal, and the related excess mass profile. Correspondingly, inference of physical quantities, such as the mean mass profile of halos around galaxies, are affected by magnification effects. We use simulated shear and galaxy data of the Millennium Simulation to quantify the effect on shear and mass estimates from magnified lens and source number counts. The former are due to the large-scale matter distribution in the foreground of the lenses, the latter are caused by magnification of the source population by the matter associated with the lenses. The GGL signal is calculated from the simulations by an efficient fast-Fourier transform that can also be applied to real data. The numerical treatment is complemented by a leading-order analytical description of the magnification effects, which is shown to fit the numerical shear data well. We find the magnification effect is strongest for steep galaxy luminosity functions and high redshifts. For a lens redshift of $z_mathrm{d}=0.83$, a limiting magnitude of $22,mathrm{mag}$ in the $r$-band and a source redshift of $z_mathrm{s}=0.99$, we find that a magnification correction changes the shear profile up to $45%$ and the mass is biased by up to $55 %$. For medium-redshift galaxies the relative change in shear and mass is typically a few percent. As expected, the sign of the bias depends on the local slope of the lens luminosity function $alpha_mathrm{d}$, where the mass is biased low for $alpha_mathrm{d}<1$ and biased high for $alpha_mathrm{d}>1$. Whereas the magnification effect of sources is rarely than more $1%$, the statistical power of future weak lensing surveys warrants correction for this effect.
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We present a joint shear-and-magnification weak-lensing analysis of a sample of 16 X-ray-regular and 4 high-magnification galaxy clusters at 0.19<z<0.69 selected from the Cluster Lensing And Supernova survey with Hubble (CLASH). Our analysis uses wide-field multi-color imaging, taken primarily with Suprime-Cam on the Subaru Telescope. From a stacked shear-only analysis of the X-ray-selected subsample, we detect the ensemble-averaged lensing signal with a total signal-to-noise ratio of ~25 in the radial range of 200 to 3500kpc/h. The stacked tangential-shear signal is well described by a family of standard density profiles predicted for dark-matter-dominated halos in gravitational equilibrium, namely the Navarro-Frenk-White (NFW), truncated variants of NFW, and Einasto models. For the NFW model, we measure a mean concentration of $c_{200c}=4.01^{+0.35}_{-0.32}$ at $M_{200c}=1.34^{+0.10}_{-0.09} 10^{15}M_{odot}$. We show this is in excellent agreement with Lambda cold-dark-matter (LCDM) predictions when the CLASH X-ray selection function and projection effects are taken into account. The best-fit Einasto shape parameter is $alpha_E=0.191^{+0.071}_{-0.068}$, which is consistent with the NFW-equivalent Einasto parameter of $sim 0.18$. We reconstruct projected mass density profiles of all CLASH clusters from a joint likelihood analysis of shear-and-magnification data, and measure cluster masses at several characteristic radii. We also derive an ensemble-averaged total projected mass profile of the X-ray-selected subsample by stacking their individual mass profiles. The stacked total mass profile, constrained by the shear+magnification data, is shown to be consistent with our shear-based halo-model predictions including the effects of surrounding large-scale structure as a two-halo term, establishing further consistency in the context of the LCDM model.
We present a Bayesian framework to account for the magnification bias from both strong and weak gravitational lensing in estimates of high-redshift galaxy luminosity functions. We illustrate our method by estimating the $zsim8$ UV luminosity function using a sample of 97 Y-band dropouts (Lyman break galaxies) found in the Brightest of Reionizing Galaxies (BoRG) survey and from the literature. We find the luminosity function is well described by a Schechter function with characteristic magnitude of $M^star = -19.85^{+0.30}_{-0.35}$, faint-end slope of $alpha = -1.72^{+0.30}_{-0.29}$, and number density of $log_{10} Psi^star [textrm{Mpc}^{-3}] = -3.00^{+0.23}_{-0.31}$. These parameters are consistent within the uncertainties with those inferred from the same sample without accounting for the magnification bias, demonstrating that the effect is small for current surveys at $zsim8$, and cannot account for the apparent overdensity of bright galaxies compared to a Schechter function found recently by Bowler et al. (2014a,b) and Finkelstein et al. (2014). We estimate that the probability of finding a strongly lensed $zsim8$ source in our sample is in the range $sim 3-15 %$ depending on limiting magnitude. We identify one strongly-lensed candidate and three cases of intermediate lensing in BoRG (estimated magnification $mu>1.4$) in addition to the previously known candidate group-scale strong lens. Using a range of theoretical luminosity functions we conclude that magnification bias will dominate wide field surveys -- such as those planned for the Euclid and WFIRST missions -- especially at $z>10$. Magnification bias will need to be accounted for in order to derive accurate estimates of high-redshift luminosity functions in these surveys and to distinguish between galaxy formation models.
We study the importance of gravitational lensing in the modelling of the number counts of galaxies. We confirm previous results for photometric surveys, showing that lensing cannot be neglected in a survey like LSST since it would infer a significant shift of cosmological parameters. For a spectroscopic survey like SKA2, we find that neglecting lensing in the monopole, quadrupole and hexadecapole of the correlation function also induces an important shift of parameters. For ${Lambda}$CDM parameters, the shift is moderate, of the order of 0.6${sigma}$ or less. However, for a model-independent analysis, that measures the growth rate of structure in each redshift bin, neglecting lensing introduces a shift of up to 2.3${sigma}$ at high redshift. Since the growth rate is directly used to test the theory of gravity, such a strong shift would wrongly be interpreted as the breakdown of General Relativity. This shows the importance of including lensing in the analysis of future surveys. On the other hand, for a survey like DESI, we find that lensing is not important, mainly due to the value of the magnification bias parameter of DESI, $s(z)$, which strongly reduces the lensing contribution at high redshift. We also propose a way of improving the analysis of spectroscopic surveys, by including the cross-correlations between different redshift bins (which is neglected in spectroscopic surveys) from the spectroscopic survey or from a different photometric sample. We show that including the cross-correlations in the SKA2 analysis does not improve the constraints. On the other hand replacing the cross-correlations from SKA2 by cross-correlations measured with LSST improves the constraints by 10 to 20 %. Interestingly, for ${Lambda}$CDM parameters, we find that LSST and SKA2 are highly complementary, since they are affected differently by degeneracies between parameters.
We present a comprehensive analysis of strong-lensing, weak-lensing shear and magnification data for a sample of 16 X-ray-regular and 4 high-magnification galaxy clusters selected from the CLASH survey. Our analysis combines constraints from 16-band HST observations and wide-field multi-color imaging taken primarily with Subaru/Suprime-Cam. We reconstruct surface mass density profiles of individual clusters from a joint analysis of the full lensing constraints, and determine masses and concentrations for all clusters. We find internal consistency of the ensemble mass calibration to be $le 5% pm 6%$ by comparison with the CLASH weak-lensing-only measurements of Umetsu et al. For the X-ray-selected subsample, we examine the concentration-mass relation and its intrinsic scatter using a Bayesian regression approach. Our model yields a mean concentration of $c|_{z=0.34} = 3.95 pm 0.35$ at $M_{200c} simeq 14times 10^{14}M_odot$ and an intrinsic scatter of $sigma(ln c_{200c}) = 0.13 pm 0.06$, in excellent agreement with LCDM predictions when the CLASH selection function based on X-ray morphological regularity and the projection effects are taken into account. We also derive an ensemble-averaged surface mass density profile for the X-ray-selected subsample by stacking their individual profiles. The stacked mass profile is well described by a family of density profiles predicted for cuspy dark-matter-dominated halos, namely, the NFW, Einasto, and DARKexp models, whereas the single power-law, cored isothermal and Burkert density profiles are disfavored by the data. We show that cuspy halo models that include the two-halo term provide improved agreement with the data. For the NFW halo model, we measure a mean concentration of $c_{200c} = 3.79^{+0.30}_{-0.28}$ at $M_{200c} = 14.1^{+1.0}_{-1.0}times 10^{14}M_odot$, demonstrating consistency between complementary analysis methods.
Cosmological cluster-scale strong gravitational lensing probes the mass distribution of the dense cores of massive dark matter halos and the structures along the line of sight from background sources to the observer. It is frequently assumed that the primary lens mass dominates the lensing, with the contribution of secondary masses along the line of sight being neglected. Secondary mass structures may, however, affect both the detectability of strong lensing in a given survey and modify the properties of the lensing that is detected. In this paper, we utilize a large cosmological N-body simulation and a multiple lens plane (and many source planes) ray-tracing technique to quantify the influence of line of sight halos on the detectability of cluster-scale strong lensing in a cluster sample with a mass limit that encompasses current cluster catalogs from the South Pole Telescope. We extract both primary and secondary halos from the Outer Rim simulation and consider two strong lensing realizations: one with only the primary halos included, and the other contains all secondary halos down to a mass limit. In both cases, we use the same source information extracted from the Hubble Ultra Deep Field, and create realistic lensed images consistent with moderately deep ground-based imaging. The results demonstrate that down to the mass limit considered the total number of lenses is boosted by about 13-21% when considering the complete multi-halo lightcone. The increment in strong lens counts peaks at lens redshifts of 0.6 approximately with no significant effect at z<0.3. The strongest trends are observed relative to the primary halo mass, with no significant impact in the most massive quintile of the halo sample, but increasingly boosting the observed lens counts toward small primary halo masses, with an enhancement greater than 50% in the least massive quintile of the halo masses considered.
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