We present a method to include lensing selection effects due to the finite horizon of a given detector when studying lensing of gravitational wave (GW) sources. When selection effects are included, the mean of the magnification distribution is shifted from one to higher values for sufficiently high-redshift sources. This introduces an irreducible (multiplicative) bias on the luminosity distance reconstruction, in addition to the typical source of uncertainty in the distance determination. We apply this method to study lensing of GWs emitted by massive black hole binary mergers at high redshift detectable by LISA. We estimate the expected bias induced by selection effects on the luminosity distance reconstruction as function of cosmological redshift, and discuss its implications for cosmological and astrophysical analyses with LISA. We also reconstruct the distribution of lensing magnification as a function of the observed luminosity distance to a source, that is the observable quantity in the absence of an electromagnetic counterpart. Lensing provides the dominant source of errors in distance measurements of high-redshift GW sources. Its full characterisation, including the impact of selection effects, is of paramount importance to correctly determine the astrophysical properties of the underlying source population and to be able to use gravitational wave sources as a new cosmological probe.
We discuss strong gravitational lensing of gravitational waves from merging of massive black hole binaries in the context of the LISA mission. Detection of multiple events would provide invaluable information on competing theories of gravity, evolution and formation of structures and, with complementary observations, constraints on H_0 and other cosmological parameters. Most of the optical depth for lensing is provided by intervening massive galactic halos, for which wave optics effects are negligible. Probabilities to observe multiple events are sizable for a broad range of formation historie…
LISA might detect gravitational waves from mergers of massive black hole binaries strongly lensed by intervening galaxies (Sereno et al. 2010). The detection of multiple gravitational lensing events would provide a new tool for cosmography. Constraints on cosmological parameters could be placed by exploiting either lensing statistics of strongly lensed sources or time delay measurements of lensed gravitational wave signals. These lensing methods do not need the measurement of the redshifts of the sources and the identification of their electromagnetic counterparts. They would extend cosmologic…
The Laser Interferometer Space Antenna's (LISA's) observation of supermassive binary black holes (SMBBH) could provide a new tool for precision cosmography. Inclusion of sub-dominant signal harmonics in the inspiral signal allows for high-accuracy sky localization, dramatically improving the chances of finding the host galaxy and obtaining its redshift. A SMBBH merger can potentially have component masses from a wide range ($10^5 - 10^8\,\Ms$) over which parameter accuracies vary considerably. We perform an in-depth study in order to understand (i) what fraction of possible SMBBH mergers allow…
We determine the cosmic expansion rate from supernovae of type Ia to set up a data-based distance measure that does not make assumptions about the constituents of the universe, i.e. about a specific parametrisation of a Friedmann cosmological model. The scale, determined by the Hubble constant $H_0$, is the only free cosmological parameter left in the gravitational lensing formalism. We investigate to which accuracy and precision the lensing distance ratio $D$ is determined from the Pantheon sample. Inserting $D$ and its uncertainty into the lensing equations for given $H_0$, esp. the time-del…
When light from a distant source object, like a galaxy or a supernova, travels towards us, it is deflected by massive objects that lie on its path. When the mass density of the deflecting object exceeds a certain threshold, multiple, highly distorted images of the source are observed. This strong gravitational lensing effect has so far been treated as a model-fitting problem. Using the observed multiple images as constraints yields a self-consistent model of the deflecting mass density and the source object. As several models meet the constraints equally well, we develop a lens characterisatio…
Strong-lensing effects in high-redshift massive black-hole binary population inference
University of Chinese Academy of Sciences（中国科学院大学）；Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）
The cross-correlation of gravitational wave strain with upcoming galaxy surveys probe theories of gravity in a new way. This method enables testing the theory of gravity by combining the effects from both gravitational lensing of gravitational waves and the propagation of gravitational waves in spacetime. We find that within 10 years, the combination of the Advanced-LIGO and VIRGO detector networks with planned galaxy surveys should detect weak gravitational lensing of gravitational waves in the low redshift Universe ($z<0.5$). With the next generation gravitational wave experiments such as Vo…
We consider the problem of characterisation of burst sources detected with the Laser Interferometer Space Antenna (LISA) using the multi-modal nested sampling algorithm, MultiNest. We use MultiNest as a tool to search for modelled bursts from cosmic string cusps, and compute the Bayesian evidence associated with the cosmic string model. As an alternative burst model, we consider sine-Gaussian burst signals, and show how the evidence ratio can be used to choose between these two alternatives. We present results from an application of MultiNest to the last round of the Mock LISA Data Challenge, …
As established in previous papers of this series, observables in highly distorted and magnified multiple images caused by the strong gravitational lensing effect can be used to constrain the distorting properties of the gravitational lens at the image positions. If the background source is extended and contains substructure, like star forming regions, which is resolved in multiple images, all substructure that can be matched across a minimum of three multiple images can be used to infer the local distorting properties of the lens. In this work, we replace the manual feature selection by an aut…
The detectability of gravitational waves originating from primordial black holes or other large macroscopic dark-matter candidates inspiraling into Sagittarius ${\rm A}^{\!*}$ is investigated. It is shown that LISA should be a formidable machine to detect the stochastic signal from the accumulated collection of such objects that have been gravitationally captured by Sgr$\,{\rm A}^{\!*}$, provided they have masses above $\sim 10^{-20}\,M_{\odot}$. This is especially so, if they are the main component of the dark matter, and the dark-matter density at Sagittarius ${\rm A}^{\!*}$ exceeds its valu…
Based on the standard gravitational lensing formalism with its effective, projected lensing potential in a given background cosmology, we investigate under which transformations of the source position and of the deflection angle the observable properties of the multiple images, i.e. the time delay differences, the relative image positions, relative shapes, and magnification ratios, remain invariant. As these observables only constrain local lens properties, we derive general, local invariance transformations in the areas covered by the multiple images. We show that the known global invariance …
Gravitational lensing of gravitational waves (GWs) is a powerful probe of the matter distribution in the universe. Here we revisit the wave-optics effects induced by dark matter (DM) halos on the GW signals of merging massive black hole binaries (MBHBs), and we study the possibility of discerning these effects using the Laser Interferometer Space Antenna (LISA). In particular, we include the halos in the low-mass range of $\rm 10^5-10^8\, M_\odot$ since they are the most numerous according to the cold DM model. We simulate the lensed signals corresponding to a wide range of impact parameters, …
Continuous gravitational waves are analogous to monochromatic light and therefore could be used to detect wave effects like interference or diffraction. This would be possible with strongly lensed gravitational waves. This article reviews and summaries the theory of gravitational lensing in the context of gravitational waves in two different regimes: geometric optics and wave optics, for two widely used lens models such as point mass lens and Singular Isothermal Sphere (SIS). Observable effects due to wave nature of gravitational waves are discussed. As a consequence of interference GWs produc…
To recognize gravitational wave lensing events and being able to differentiate between similar lens models will be of crucial importance once one will be observing several lensing events of gravitational waves per year. In this work, we study the lensing of gravitational waves in the context of LISA sources and wave-optics regime. While different papers before ours studied microlensing effects enhanced by simultaneous strong lensing, we focus on frequency (time) dependent phase effects produced by one lens that will be visible with only one lensed image. We will show how, in the interference r…
We investigate the impact of higher-order gravitational lens properties and properties of the background source on our approach to directly infer local lens properties from observables in multiple images of strong gravitationally lensed extended, static background sources developed in papers I to VI. As the degeneracy between local lens and source properties only allows to determine relative local lens properties between the multiple image positions, we cannot distinguish common scalings and distortions caused by lensing from intrinsic source characteristics. The consequences of this degenerac…
In galaxy-galaxy strong gravitational lensing, Einstein rings are generated when the lensing galaxy has an axisymmetric lensing potential and the source galaxy is aligned with its symmetry centre along the line of sight. Using a Taylor expansion around the Einstein radius and eliminating the unknown source, I derive a set of analytic equations that determine differences of the deflection angle of the perturber weighted by the convergence of the axisymmetric lens and ratios of the convergences at the positions of the arcs from the measurable thickness of the arcs. In the same manner, asymmetrie…
Tracing small-scale structure formation through cosmic time with strong gravitational lensing: A case for a next-generation sub-millimetre/millimetre interferometer
European Southern Observatory (ESO)（欧洲南方天文台）；Kapteyn Astronomical Institute, University of Groningen（格罗宁根大学卡普坦天文研究所）；South African Radio Astronomy Observatory (SARAO)（南非射电天文观测台）；Department of Physics, University of Pretoria（比勒陀利亚大学物理系）；Pole Scientific, Catholic University of Lyon（里昂天主教大学科学部门）；Instituto de Física y Astronomía, Universidad de Valparaíso（瓦尔帕莱索大学物理与天文学研究所）；Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理学研究所）；Department of Physics, University of Oxford（牛津大学物理系）；Observatoire de Paris, LUX, Collège de France, CNRS, PSL University, Sorbonne University（巴黎天文台，卢克斯，法兰西公学院，法国国家科学研究中心，巴黎文理研究大学，索邦大学）；Dipartimento di Fisica e Astronomia Augusto Righi , Università di Bologna（博洛尼大学奥古斯托·里吉物理与天文学系）；INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna（意大利国家天体物理研究所博洛尼亚空间科学与天文学观测台）；INFN – Sezione di Bologna（意大利国家核物理研究所博洛尼亚分部）
The gravitational waves (GWs) emitted by inspiraling binary black holes, expected to be detected by the Laser Interferometer Space Antenna (LISA), could be used to determine the luminosity distance to these sources with the unprecedented precision of <~ 1%. We study cosmological parameter constraints from such standard sirens, in the presence of gravitational lensing by large-scale structure. Lensing introduces magnification with a probability distribution function (PDF) whose shape is highly skewed and depends on cosmological parameters. We use Monte-Carlo simulations to generate mock samples…
Emulating redshift mixing due to blending in weak gravitational lensing
Ludwig-Maximilians Universität München（慕尼黑大学）；Excellence Cluster ORIGINS（ORIGINS卓越集群）；Ruhr University Bochum（波鸿鲁尔大学）；Leiden University（莱顿大学）；Princeton University（普林斯顿大学）
An Opacity-Free Test of the Cosmic Distance Duality Relation Using Strongly Lensed Gravitational Wave Signals with Space-Based Detector Networks
Center for Gravitational Wave Experiment, National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences（中国科学院力学研究所微重力实验室引力波实验中心）；Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台暗物质与空间天文重点实验室）；School of Astronomy and Space Science, University of Science and Technology of China（中国科学技术大学天文与空间科学学院）；Department of Astronomy, Beijing Normal University（北京师范大学天文系）；Kavli Institute for Astronomy and Astrophysics, Peking University（北京大学科维理天文与天体物理研究所）；Taiji Laboratory for Gravitational Wave Universe (Beijing/Hangzhou), University of Chinese Academy of Sciences（中国科学院大学太极引力波宇宙实验室（北京/杭州））；Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院）；School of Physics Science And Technology, Wuhan Un（武汉大物理学科学与技术学院）
[Abridged] Aims: This work focuses on one lensed system, HATLAS J142935.3-002836 (H1429-0028), selected in the Herschel-ATLAS field. Gathering a rich, multi-wavelength dataset, we aim to confirm the lensing hypothesis and model the background source's morphology and dynamics, as well as to provide a full physical characterisation. Methods: Multi-wavelength high-resolution data is utilised to assess the nature of the system. A lensing-analysis algorithm which simultaneously fits different wavebands is adopted to characterise the lens. The background galaxy dynamical information is studied by re…
AMPM II. A Lunar-Mass Primordial Black Hole Microlensing Candidate in the Milky Way Halo
Swinburne University of Technology（斯威本科技大学）；ARC Centre of Excellence for Dark Matter Particle Physics（暗物质粒子物理卓越研究中心）；Australian National University（澳大利亚国立大学）；NSF NOIRLab National Optical-Infrared Astronomy Research Laboratory（美国国家光学红外天文研究实验室）；Cerro Tololo Inter-American Observatory（塞罗托洛美洲际天文台）
