Galaxies obey a set of strict dynamical laws, which imply a close coupling between the visible matter (stars and gas) and the observed dynamics (set by dark matter in the standard cosmological context). Here we review recent results from weak gravitational lensing, which allows studying the empirical laws of galaxy dynamics out to exceedingly large radii in both late-type galaxies (LTGs) and early-type galaxies (ETGs). We focus on three laws: (1) the circular velocity curves of both LTGs and ETGs remain indefinitely flat out to several hundreds of kpc; (2) the same baryonic Tully-Fisher relation is followed by LTGs and ETGs; (3) the same radial acceleration relation (RAR) is followed by LTGs and ETGs. Combining galaxy data with Solar System data, the RAR covers about 16 orders of magnitude in the Newtonian baryonic acceleration. Remarkably, these empirical facts were predicted a priori by MOND.
Kinematic weak lensing describes the distortion of a galaxy's projected velocity field due to lensing shear, an effect recently reported for the first time by Gurri et al. based on a sample of 18 galaxies at $z \sim 0.1$. In this paper, we develop a new formalism that combines the shape information from imaging surveys with the kinematic information from resolved spectroscopy to better constrain the lensing distortion of source galaxies and to potentially address systematic errors that affect conventional weak-lensing analyses. Using a Bayesian forward model applied to mock galaxy observations…
The combination of strong gravitational lensing and stellar kinematics provides a powerful and robust method to investigate the mass and dynamical structure of early-type galaxies. We demonstrate this approach by analysing two massive ellipticals from the XLENS Survey for which both high-resolution HST imaging and X-Shooter spectroscopic observations are available. We adopt a flexible axisymmetric two-component mass model for the lens galaxies, consisting of a generalised NFW dark halo and a realistic self-gravitating stellar mass distribution. For both systems, we put constraints on the dark …
Application of the most robust method of measuring black hole masses, spatially resolved kinematics of gas and stars, is presently limited to nearby galaxies. The Atacama Large Millimeter/sub-millimeter Array (ALMA) and thirty meter class telescopes (the Thirty Meter Telescope, the Giant Magellan Telescope, and the European Extremely Large Telescope) with milli-arcsecond resolution are expected to extend such measurements to larger distances. Here, we study the possibility of exploiting the angular magnification provided by strong gravitational lensing to measure black hole masses at high reds…
The stellar velocity anisotropy of strong lensing massive elliptical galaxies and its role in the inference of the Hubble parameter $H_0$ using spatially resolved kinematics
American Museum of Natural History（美国自然历史博物馆）；The Graduate Center of the City University of New York（纽约市立大学研究生中心）；Lehman College of the CUNY（纽约市立大学雷曼学院）；Borough of Manhattan Community College, City University of New York（纽约市立大学曼哈顿社区学院）
The degeneracy between disc and halo contributions in spiral galaxy rotation curves makes it difficult to obtain a full understanding of the distribution of baryons and dark matter in disc galaxies like our own Milky Way. Using mock data, we study how constraints on dark matter profiles obtained from kinematics, strong lensing, or a combination of the two are affected by assumptions about the halo model. We compare four different models: spherical isothermal and Navarro-Frenk-White halos, along with spherical and elliptical Burkert halos. For both kinematics and lensing we find examples where …
We present a joint strong lensing and stellar dynamical framework for future time-delay cosmography purposes. Based on a pixelated source reconstruction and the axisymmetric Jeans equations, we are capable of constraining cosmological distances and hence the current expansion rate of the Universe ($H_0$) to the few percent level per lens, when high signal-to-noise integral field unit (IFU) observations from the next generation of telescopes become available. For illustrating the power of this method, we mock up IFU stellar kinematic data of the prominent lens system RXJ1131-1231, given the spe…
We discuss constraints on the mass density distribution (parameterized as $ρ\propto r^{-γ}$) in early-type galaxies provided by strong lensing and stellar kinematics data. The constraints come from mass measurements at two `pinch' radii. One `pinch' radius $r_1=2.2 R_{Einst}$ is defined such that the Einstein (i.e. aperture) mass can be converted to the spherical mass almost independently of the mass-model. Another `pinch' radius $r_2=R_{opt}$ is chosen so that the dynamical mass, derived from the line-of-sight velocity dispersion, is least sensitive to the anisotropy of stellar orbits. We ver…
Determination of cluster masses is a fundamental tool for cosmology. Comparing mass estimates obtained by different probes allows to understand possible systematic uncertainties. The cluster Abell 315 is an interesting test case, since it has been claimed to be underluminous in X-ray for its mass (determined via kinematics and weak lensing). We have undertaken new spectroscopic observations with the aim of improving the cluster mass estimate, using the distribution of galaxies in projected phase space. We identified cluster members in our new spectroscopic sample. We estimated the cluster mass…
In this paper, we measure the optical-to-virial velocity ratios Vopt/V200c of disk galaxies in the Sloan Digital Sky Survey (SDSS) at a mean redshift of <z> = 0.07 and with stellar masses 10^9 M_sun < M_* < 10^11 M_sun. Vopt/V200c, the ratio of the circular velocity measured at the virial radius of the dark matter halo (\sim150 kpc) to that at the optical radius of the disk (\sim10 kpc), is a powerful observational constraint on disk galaxy formation. It links galaxies to their dark matter haloes dynamically and constrains the total mass profile of disk galaxies over an order of magnitude in l…
Kinematic Mapping of Giant Arcs: A New Method to Locate Lensing Critical Curves
University of California, Berkeley（加州大学伯克利分校）；Wuhan University（武汉大学）；Shanghai Jiao-Tong University（上海交通大学）；Fudan University（复旦大学）；Berkeley Center for Cosmological Physics, University of California, Berkeley（加州大学伯克利分校伯克利宇宙物理学中心）；University of California, Los Angeles（加州大学洛杉矶分校）；Instituto de Física de Cantabria (CSIC-UC)（坎塔布里亚物理研究所（西班牙高等科学研究委员会-坎塔布里亚大学））；Center for Astrophysics, Harvard & Smithsonian（哈佛史密森天体物理中心）；Chiba University（千叶大学）
Gravitational lensing time delays offer an avenue to measure the Hubble parameter $H_0$, with some analyses suggesting a tension with early-type probes of $H_0$. The lensing measurements must mitigate systematic uncertainties due to the mass modelling of lens galaxies. In particular, a core component in the lens density profile would form an approximate local mass sheet degeneracy and could bias $H_0$ in the right direction to solve the lensing tension. We consider ultralight dark matter as a possible mechanism to generate such galactic cores. We show that cores of roughly the required propert…
MaNGA DynPop -- IV. Stacked total density profile of galaxy groups and clusters from combining dynamical models of integral-field stellar kinematics and galaxy-galaxy lensing
Gravitational lensing offers a competitive method to measure $H_0$ with the goal of 1% precision. A major obstacle comes in the form of lensing degeneracies, such as the mass sheet degeneracy (MSD), which make it possible for a family of density profiles to reproduce the same lensing observables but return different values of $H_0$. The modeling process artificially selects one choice from this family, potentially biasing $H_0$. The effect is more pronounced when the profile of a given lens is not perfectly described by the lens model, which will always be the case to some extent. To explore t…
The kinematics of satellite galaxies moving in a dark matter halo are a direct probe of the underlying gravitational potential. Thus, the phase-space distributions of satellites represent a powerful tool to determine the galaxy-halo connection from observations. By stacking the signal of a large number of satellite galaxies this potential can be unlocked even for haloes hosting a few satellites on average. In this work, we test the impact of various modelling assumptions on constraints derived from analysing satellite phase-space distributions in the non-linear, 1-halo regime. We discuss their…
We present an improved determination of the total mass distribution of three CLASH/HFF massive clusters, MACS J1206.2-0847 (z=0.44), MACS J0416.1-2403 (z=0.40), Abell S1063 (z=0.35). We specifically reconstruct the sub-halo mass component with robust stellar kinematics information of cluster galaxies, in combination with precise strong lensing models based on large samples of spectroscopically identified multiple images. We use VLT/MUSE integral-field spectroscopy in the cluster cores to measure the stellar velocity dispersion, $σ$, of 40-60 member galaxies per cluster, covering 4-5 magnitudes…
Model-Independent Measurement of Baryon Gas Fractions through Galaxy-Galaxy Lensing and the Kinematic Sunyaev-Zel'dovich Effect
University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Berkeley Center for Cosmological Physics（伯克利宇宙物理学中心）；University of Cambridge（剑桥大学）；Kavli Institute for Cosmology Cambridge（卡弗里宇宙学剑桥研究所）；Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）
We present results from the KMOS lensing survey-KLENS which is exploiting gravitational lensing to study the kinematics of 24 star forming galaxies at $1.4<z<3.5$ with a median mass of $\rm log(M_\star/M_\odot)=9.6$ and median star formation rate (SFR) of $\rm 7.5\,M_\odot\,yr^{-1}$. We find that 25% of these low-mass/low-SFR galaxies are rotation dominated, while the majority of our sample shows no velocity gradient. When combining our data with other surveys, we find that the fraction of rotation dominated galaxies increases with the stellar mass, and decreases for galaxies with a positive o…
For lensing galaxies we introduce a formal velocity dispersion sigma_lens, based on enclosed mass and the virial theorem. This is calculated from an ensemble of pixelated lens models, and found to be fairly model independent. A sample of 18 well-known early-type lensing galaxies and two clusters is found to be consistent with the equality of sigma_lens and the kinematic velocity dispersion sigma_obs. Both the early-type lensing galaxies and the clusters can thus be determined as being virialized. In a second step we calculate the I-band luminosity and the total mass content for the sample of l…
Dynamical modelling of Integral-Field-Unit (IFU) stellar kinematics is a powerful tool to unveil the dynamical structure and mass build-up of galaxies in the local Universe, while gravitational lensing is nature's cosmic telescope to explore the properties of galaxies beyond the local Universe. We present a new approach which unifies dynamical modelling of galaxies with the magnification power of strong gravitational lensing, to reconstruct the structural and dynamical properties of high-redshift galaxies. By means of axisymmetric Jeans modelling, we create a dynamical model of the source gala…
We report observations of CO(J=2-1) and CO(J=3-2) line emission towards the quadruply-lensed quasar RXS J1131-1231 at z = 0.654 obtained using the Plateau de Bure Interferometer (PdBI) and the Combined Array for Research in Millimeter-wave Astronomy (CARMA). Our lens modeling shows that the asymmetry in the double-horned CO(J = 2-1) line profile is mainly a result of differential lensing, where the magnification factor varies from ~3 to ~9 across different kinematic components. The intrinsically symmetric line profile and a smooth source-plane velocity gradient suggest that the host galaxy is …
We investigate the matter distribution of a spiral galaxy with a counter-rotating stellar core, SDSS J1331+3628 (J1331), independently with gravitational lensing and stellar dynamical modelling. By fitting a gravitational potential model to a quadruplet of lensing images around J1331's bulge, we tightly constrain the mass inside the Einstein radius R_ein = (0.91 +/- 0.02)'' (~= 1.83 +/- 0.04 kpc) to within 4%: M_ein = (7.8 +/- 0.3) x 10^10 M_Sun. We model observed long-slit major axis stellar kinematics in J1331's central regions by finding Multi-Gaussian Expansion (MGE) models for the stellar…
Lensing by galaxy clusters is a versatile probe of cosmology and extragalactic astrophysics, but the accuracy of some of its predictions is limited by the simplified models adopted to reduce the (otherwise untractable) number of degrees of freedom. We aim at cluster lensing models where the parameters of all cluster-member galaxies are free to vary around some common scaling relations with non-zero scatter, and deviate significantly from them if and only if the data require it. We have devised a Bayesian hierarchical inference framework, which enables the determination of all lensing parameter…
The Initial Mass Function (IMF) for massive galaxies can be constrained by combining stellar dynamics with strong gravitational lensing. However, this method is limited by degeneracies between the density profile of dark matter and the stellar mass-to-light ratio. In this work we reduce this degeneracy by combining weak lensing together with strong lensing and stellar kinematics. Our analysis is based on two galaxy samples: 45 strong lenses from the SLACS survey and 1,700 massive quiescent galaxies from the SDSS main spectroscopic sample with weak lensing measurements from the Hyper Suprime-Ca…
We present the X-shooter Lens Survey (XLENS) data. The main goal of XLENS is to disentangle the stellar and dark matter content of massive early-type galaxies (ETGs), through combined strong gravitational lensing, dynamics and spectroscopic stellar population studies. The sample consists of 11 lens galaxies covering the redshift range from $0.1$ to $0.45$ and having stellar velocity dispersions between $250$ and $380\,\mathrm{km}\,\mathrm{s}^{-1}$. All galaxies have multi-band, high-quality HST imaging. We have obtained long-slit spectra of the lens galaxies with X-shooter on the VLT. We are a…
The Baryonic Mass-Halo Mass Relation of Extragalactic Systems
Case Western Reserve University（凯斯西储大学）；Max Planck Institute for Extraterrestrial Physics（马克斯·普朗克地外物理研究所）；Università degli Studi di Firenze（佛罗伦萨大学）；INAF — Arcetri Astrophysical Observatory（意大利国家天体物理研究所——阿切特里天文台）；University of Oregon（俄勒冈大学）；Nanjing University（南京大学）
We determine the inner density profiles of massive galaxy clusters (M$_{200}$ > $5 \times 10^{14}$ M$_{\odot}$) in the Cluster-EAGLE (C-EAGLE) hydrodynamic simulations, and investigate whether the dark matter density profiles can be correctly estimated from a combination of mock stellar kinematical and gravitational lensing data. From fitting mock stellar kinematics and lensing data generated from the simulations, we find that the inner density slopes of both the total and the dark matter mass distributions can be inferred reasonably well. We compare the density slopes of C-EAGLE clusters with…
The low-mass end of the stellar Initial Mass Function (IMF) is constrained by focusing on the baryon-dominated central regions of strong lensing galaxies. We study in this letter the Einstein Cross (Q2237+0305), a z=0.04 barred galaxy whose bulge acts as lens on a background quasar. The positions of the four quasar images constrain the surface mass density on the lens plane, whereas the surface brightness (H-band NICMOS/HST imaging) along with deep spectroscopy of the lens (VLT/FORS1) allow us to constrain the stellar mass content, for a range of IMFs. We find that a classical single power law…
We analyse the stellar kinematics of the z=0.169 brightest cluster galaxy (BCG) in Abell 1201, using integral field observations with VLT/MUSE. This galaxy has a gravitationally-lensed arc located at unusually small radius ($\sim$5 kpc), allowing us to constrain the mass distribution using lensing and stellar dynamical information over the same radial range. We measure a velocity dispersion profile which is nearly flat at $σ$ $\approx$ 285 km/s in the inner $\sim$5 kpc, and then rises steadily to $σ$ $\approx$ 360 km/s at $\sim$30 kpc. We analyse the kinematics using axisymmetric Jeans models,…
The Stellar IMF and Dark Matter Halo of ESO0286: Constraints from Strong Lensing and Dynamics
Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理学研究所）；Technical University of Munich（慕尼黑工业大学）；Max-Planck-Institut für extraterrestrische Physik（马克斯·普朗克地外物理学研究所）；Université de Genève（日内瓦大学）；Institute of Cosmology and Gravitation, University of Portsmouth（朴茨茅斯宇宙学与引力研究所）
We present an end-to-end methodology to measure the effects of weak lensing on individual galaxy-galaxy systems exploiting their kinematic information. Using this methodology, we have measured a shear signal from the velocity fields of 18 weakly-lensed galaxies. We selected a sample of systems based only on the properties of the sources, requiring them to be bright (apparent $i$-band magnitude $ < 17.4$) and in the nearby Universe ($z < 0.15$). We have observed the velocity fields of the sources with WiFeS, an optical IFU on a 2.3m telescope, and fitted them using a simple circular motion mode…
The study of strong-lensing systems conventionally involves constructing a mass distribution that can reproduce the observed multiply-imaging properties. Such mass reconstructions are generically non-unique. Here, we present an alternative strategy: instead of modelling the mass distribution, we search cosmological galaxy-formation simulations for plausible matches. In this paper we test the idea on seven well-studied lenses from the SLACS survey. For each of these, we first pre-select a few hundred galaxies from the EAGLE simulations, using the expected Einstein radius as an initial criterion…
Dynamical models of cluster members to probe the total mass properties of cluster subhalos. I. A comparison with parametric strong lensing models
Università degli Studi di Milano（米兰大学）；INAF – IASF Milano（意大利国家天体物理研究所-米兰天文物理研究所）；Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara（费拉拉大学地球与物理系）；Institute of Cosmology and Gravitation, University of Portsmouth（朴茨茅斯宇宙学与引力研究所）；INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna（意大利国家天体物理研究所-博洛尼亚天文物理与空间科学观测站）；Università di Salerno（萨莱诺大学）；INAF – Osservatorio Astronomico di Capodimonte（意大利国家天体物理研究所-卡波迪蒙特天文台）
We investigate the internal structure of elliptical galaxies at $z\sim 0.2$ from a joint lensing-dynamics analysis. We model Hubble Space Telescope images of a sample of 23 galaxy-galaxy lenses selected from the Sloan Lens ACS (SLACS) survey. Whereas the original SLACS analysis estimated the logarithmic slopes by combining the kinematics with the imaging data, we estimate the logarithmic slopes only from the imaging data. We find that the distribution of the lensing-only logarithmic slopes has a median $2.08\pm0.03$ and intrinsic scatter $0.13 \pm 0.02$, consistent with the original SLACS anal…
MUSE-DARK-II: 3D morpho-kinematic modelling of lensed galaxies. Tully-Fisher relation of $z \sim 1$ star-forming galaxies
Universite Claude Bernard Lyon 1, CRAL UMR5574, ENS de Lyon, CNRS（里昂第一大学，CRAL UMR5574，里昂高等师范学校，法国国家科学研究中心）；Leibniz-Institut für Astrophysik Potsdam (AIP)（波茨坦莱布尼茨天体物理研究所）；Observatoire Astronomique de Strasbourg, Université de Strasbourg, CNRS, UMR 7550（斯特拉斯堡天文台，斯特拉斯堡大学，法国国家科学研究中心）；French-Chilean Laboratory for Astronomy, IRL 3386, CNRS and Universidad de Concepción, Departamento de Astronomía（法智天文学联合实验室，法国国家科学研究中心与康塞普西翁大学天文学系）；Aix Marseille Univ, CNRS, CNES, LAM（艾克斯-马赛大学，法国国家科学研究中心，法国国家空间研究中心）；IRAP, Université de Toulouse, CNRS, CNES（天体物理研究研究所，图卢兹大学，法国国家科学研究中心，法国国家空间研究中心）
Exploiting the relative proximity of the nearby strong-lens galaxy SNL-1, we present a critical comparison of the mass estimates derived from independent modelling techniques. We fit triaxial orbit-superposition dynamical models to spatially-resolved stellar kinematics, and compare to the constraints derived from lens modelling of high-resolution photometry. From the dynamical model, we measure the total (dynamical) mass enclosed within a projected aperture of radius the Einstein radius to be $\log_{10} M_{\mathrm{Ein.}} = 11.00 \pm 0.02$, which agrees with previous measurements from lens mode…
