We develop a unified, analytic framework for gravitational lensing by Kerr black holes. In this first paper we present a new, general lens equation and magnification formula governing lensing by a compact object. Our lens equation assumes that the source and observer are in the asymptotically flat region and does not require a small angle approximation. Furthermore, it takes into account the displacement that occurs when the light ray's tangent lines at the source and observer do not meet on the lens plane. We then explore our lens equation in the case when the compact object is a Kerr black hole. Specifically, we give an explicit expression for the displacement when the observer is in the equatorial plane of the Kerr black hole as well as for the case of spherical symmetry.
In the context of strong gravitational lensing, the magnification of image is of crucial importance to constrain various lens models. For several commonly used quadruple lens models, the magnification invariants, defined as the sum of the signed magnifications of images, have been analytically derived when the image multiplicity is a maximum. In this paper, we further study the magnification of several disk lens models, including (a) exponential disk lens, (b) Gaussian disk lens, (c) modified Hubble profile lens, and another two of the popular three-dimensional symmetrical lens model, (d) NFW …
The magnification of galaxies in modern galaxy surveys induces additional correlations in the cosmic shear, galaxy-galaxy lensing and clustering observables used in modern lensing "3x2pt" analyses, due to sample selection. In this paper, we emulate the magnification contribution to all three observables utilising the SLICS simulations suite, and test the sensitivity of the cosmological model, galaxy bias and redshift distribution calibration to un-modelled magnification in a Stage-IV-like survey using Monte-Carlo sampling. We find that magnification cannot be ignored in any single or combined …
With increasing sensitivities of the current ground-based gravitational-wave (GW) detectors, the prospects of detecting a strongly lensed GW signal are going to be high in the coming years. When such a signal passes through an intervening lensing galaxy or galaxy cluster, the embedded stellar-mass microlenses lead to interference patterns in the signal that may leave observable signatures. In this work, we present an extensive study of these wave effects in the LIGO/Virgo frequency band ($10$-$10^4$ Hz) due to the presence of the microlens population in galaxy-scale lenses for the first time. …
Effect of gravitational magnification on the measurement of distance modulus of type Ia supernovae is presented. We investigate a correlation between magnification and Hubble residual to explore how the magnification affects the estimation of cosmological parameters. We estimate magnification of type Ia supernovae in two distinct methods: one is based on convergence mass reconstruction under the weak lensing limit and the other is based on the direct measurement from galaxies distribution. Both magnification measurements are measured from Subaru Hyper Suprime-Cam survey catalogue. For both mea…
Gravitational waves (GWs) may be magnified or de-magnified due to lensing. This phenomenon will bias the distance estimation based on the matched filtering technique. Via the multi-sphere ray-tracing technique, we study the GW magnification effect and selection effect with particular attention to the stellar-mass binary black holes (BBHs). We find that, for the observed luminosity distance $\lesssim 3~\mathrm{Gpc}$, which is the aLIGO/Virgo observational horizon limit, the average magnification keeps as unity, namely unbiased estimation, with the relative distance uncertainty $σ(\hat{d})/\hat{…
Many distant objects can only be detected, or become more scientifically valuable, if they have been highly magnified by strong gravitational lensing. We use EAGLE and BAHAMAS, two recent cosmological hydrodynamical simulations, to predict the probability distribution for both the lens mass and lens redshift when point sources are highly magnified by gravitational lensing. For sources at a redshift of two, we find the distribution of lens redshifts to be broad, peaking at z=0.6. The contribution of different lens masses is also fairly broad, with most high-magnification lensing due to lenses w…
The effect of ionized gas on the propagation of radio signals is known as plasma lensing. Unlike gravitational lensing, plasma lensing causes both magnification and strong de-magnification effects to background sources. We study the cross section of plasma lensing for two density profiles, the Gaussian and power-law models. In general, the cross section increases with the density gradient. Radio sources can be used to measure the free electron density along the line of sight. However, plasma lensing de-magnification causes an underestimate of the electron density. Such a bias increases with th…
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 …
Advances in upcoming weak lensing surveys pose new challenges for an accurate modeling of the lensing observables. The wide sky coverage of Euclid makes angular scales down to $l_\mathrm{min}=10$ accessible. At such large angular scales, general relativistic effects manifest themselves, and the lensing magnification cannot be correctly described by the standard lensing convergence only. The impact of line-of-sight velocities on the magnification angular power spectrum, referred to as the Doppler magnification, is already well recognized in literature. In particular, it was suggested that the D…
Weak lensing, Big Magnification: Recovering hidden lensing information from galaxy positions
Institute of Space Sciences (ICE, CSIC)（空间科学研究所）；Universitat Autònoma de Barcelona (UAB)（巴塞罗那自治大学）；Institut de Física d’Altes Energies (IFAE)（高能物理研究所）；The Barcelona Institute of Science and Technology（巴塞罗那科学技术研究院）
Recent works have shown that weak lensing magnification must be included in upcoming large-scale structure analyses, such as for the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST), to avoid biasing the cosmological results. In this work we investigate whether including magnification has a positive impact on the precision of the cosmological constraints, as well as being necessary to avoid bias. We forecast this using an LSST mock catalog and a halo model to calculate the galaxy power spectra. We find that including magnification has little effect on the precision of the cosmo…
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. …
The weak lensing magnification of Type Ia Supernovae (SNe Ia) is sensitive to the clustering of matter, and provides an independent cosmological probe complementary to SN Ia distance measurements. The Nancy Grace Roman Space Telescope is uniquely sensitive to this measurement as it can discover high redshift SNe Ia and measure them with high precision. We present a methodology for reconstructing the probability distribution of the weak lensing magnification $μ$ of SNe Ia, $p(μ)$, from observational data, and using it to constrain cosmological parameters. We find that the reconstructed $p(μ)$ c…
Lens models and magnification maps of the six Hubble Frontier Fields clusters
我们提出了强透镜模型，以及质量和放大率的地图，为核心的六个HST前沿领域的星系团。我们的参数透镜模型受到透镜背景星系的多个图像系统的位置和红移的约束。我们使用的光度红移和光谱红移的透镜背景源的组合，我们获得的（阿贝尔2744和阿贝尔S1063），从文献中收集，或好心提供的透镜社区。利用我们的结果，我们（1）比较了每个星团的质量分布和它的光分布，（2）量化了HFF星团的累积放大能力，（3）描述了我们的模型如何用于估计在所有红移和星团核心内任何位置的透镜背景源的放大率和图像多样性，以及（4）讨论我们的建模方法所产生的系统效应和注意事项。我们专门调查的影响，使用光谱和光度红移的限制所产生的模型的不确定性。我们发现，透镜星系的光度红移估计一般是在很好的协议与光谱红移，在可用的。然而，与松弛的红移先验相关联的灵活性可能会导致低估考虑透镜效应信号所需的大尺度结构的复杂性。因此，我们的研究结果强调了光谱弧红移的重要性，或严格的光度红移的限制，高精度透镜模型。我们的最佳拟合镜头模型（放大率，会聚，剪切，偏转场）和模型模拟的所有产品都可以通过Mikulski Archive for Space Telescopes获得。
In this paper we study gravitational lensing of gravitational wave events. The main point of the present work is to introduce a semi-analytic approach so that each ingredient can be varied and tested individually. Our analytic model for the source population is motivated by a numerical study and we compare semi-analytical and numerical results. We determine the expected magnification for events seen at a given observed luminosity distance. We find that while the probability of significant magnification of the observed LIGO-Virgo events is very small, the probability distribution of the magnifi…
Lens Models Under the Microscope: Comparison of Hubble Frontier Field Cluster Magnification Maps
利用大质量星系团的引力透镜放大能力，哈勃前沿场提供了高红移宇宙的六个补丁的深度视图。深度哈勃成像和特殊的透镜强度相结合，揭示了最大数量的多重成像星系，可用于约束星系团质量分布模型。然而，即使每个聚类具有$\mathcal{O}(100)$图像，与重建相关联的不确定性也是不可忽略的。本文的目的是展示模型放大预测的多样性。我们分别研究了Abell 2744和MACS J0416的7和9个质量模型，这些模型于2015年9月提交给Mikulski Archive for Space Telescopes供公众分发。模型预测值之间的离散度从常见低放大倍数（$μ\sim2$）下的30%增加到罕见高放大倍数（$μ\sim40$）下的70%。MACS J0416对$2<μ<10$的分散性小于Abell 2744。我们表明，放大率地图的基础上，不同的镜头反转技术通常彼此不同，超过他们引用的统计误差。这表明，一些模型低估了真正的不确定性，这主要是由于各种透镜简并。虽然精确的质量片简并被打破，但它的广义对应物至少在Abell 2744中没有被打破。其他的，本地简并也存在于这两个集群。我们的模型比较是互补的重建已知的合成质量分布的比较。通过关注观察到的星系团，我们可以识别出那些受到最好约束的星系团，从而提供遥远宇宙的最清晰视图。
Using the same lens galaxies, the ratios of tangential shears for different source galaxy redshifts is equal to the ratios of their corresponding angular-diameter distances. This is the so-called shear-ratio test (SRT) and it is valid when effects induced by the intervening large-scale structure (LSS) can be neglected. The dominant LSS effect is magnification bias which, on the one hand, induces an additional shear, and on the other hand, causes a magnification of the lens population. Our objective is to quantify the magnification bias for the SRT and show an easy-to-apply mitigation strategy …
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 $20\,000\ °^2$ 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…
Weak lensing of Type Ia supernovae (SNe Ia) is a systematic uncertainty in the use of SNe Ia as standard candles, as well as an independent cosmological probe, if the corresponding magnification distribution can be extracted from data. We study the peak brightness distribution of SNe Ia in the Pantheon sample, and find that the high $z$ sub-sample shows distinct weak lensing signatures compared to the low $z$ subsample: a long tail at the bright end due to high magnifications and a shift of the peak brightness toward the faint end, consistent with findings from earlier work. We have developed …
We present a statistical weak-lensing magnification analysis on an optically selected sample of 3029 \texttt{CAMIRA} galaxy clusters with richness $N>15$ at redshift $0.2\leq z <1.1$ in the Subaru Hyper Suprime-Cam (HSC) survey. We use two distinct populations of color-selected, flux-limited background galaxies, namely the low-$z$ and high-$z$ samples at mean redshifts of $\approx1.1$ and $\approx1.4$, respectively, from which to measure the weak-lensing magnification signal by accounting for cluster contamination as well as masking effects. Our magnification bias measurements are found to be …
The Hubble Frontier Fields data, along with multiple data sets obtained by other telescopes, have provided some of the most extensive constraints on cluster lenses to date. Multiple lens modeling teams analyzed the fields and made public a number of deliverables. By comparing these results, we can then undertake a unique and vital test of the state of cluster lens modeling. Specifically, we see how well the different teams can reproduce similar magnifications and mass profiles. We find that the circularly averaged mass profiles of the fields are remarkably constrained (scatter <5%) at distance…
Using data from the Pantheon SN Ia compilation and the Sloan Digital Sky Survey (SDSS), we propose an estimator for weak lensing convergence incorporating positional and photometric data of foreground galaxies. The correlation between this and the Hubble diagram residuals of the supernovae has $3.6σ$ significance, and is consistent with weak lensing magnification due to dark matter halos centered on galaxies. We additionally constrain the properties of the galactic haloes, such as the mass-to-light ratio $Γ$ and radial profile of the halo matter density $ρ(r)$. We derive a new relationship for…
