Warm dark matter chills out: constraints on the halo mass function and the free-streaming length of dark matter with 8 quadruple-image strong gravitational lenses
Daniel Gilman, Simon Birrer, Anna Nierenberg, Tommaso Treu, Xiaolong Du, Andrew Benson
The free-streaming length of dark matter depends on fundamental dark matter physics, and determines the abundance and concentration of dark matter halos on sub-galactic scales. Using the image positions and flux ratios from eight quadruply-imaged quasars, we constrain the free-streaming length of dark matter and the amplitude of the subhalo mass function (SHMF). We model both main deflector subhalos and halos along the line of sight, and account for warm dark matter (WDM) free-streaming effects on the mass function and mass-concentration relation. By calibrating the scaling of the SHMF with host halo mass and redshift using a suite of simulated halos, we infer a global normalization for the SHMF. We account for finite-size background sources, and marginalize over the mass profile of the main deflector. Parameterizing dark matter free-streaming through the half-mode mass $m_{\rm{hm}}$, we constrain the thermal relic particle mass $m_{\rm{DM}}$ corresponding to $m_{\rm{hm}}$. At $95 \%$ CI: $m_{\rm{hm}} < 10^{7.8} M_{\odot}$ ($m_{\rm{DM}} > 5.2 \ \rm{keV}$). We disfavor $m_{\rm{DM}} = 4.0 \rm{keV}$ and $ m_{\rm{DM}} = 3.0 \rm{keV}$ with likelihood ratios of 7:1 and 30:1, respectively, relative to the peak of the posterior distribution. Assuming cold dark matter, we constrain the projected mass in substructure between $10^6 - 10^{9} M_{\odot}$ near lensed images. At $68 \%$ CI, we infer $2.0 - 6.1 \times 10^{7} M_{\odot} \rm{kpc^{-2}}$, corresponding to mean projected mass fraction $\bar{f}_{\rm{sub}} = 0.035_{-0.017}^{+0.021}$. At $95 \%$ CI, we obtain a lower bound on the projected mass of $0.6 \times 10^{7} M_{\odot} \rm{kpc^{-2}}$, corresponding to $\bar{f}_{\rm{sub}} > 0.005$. These results agree with the predictions of cold dark matter.
We report the serendipitous discovery of the first gravitationally lensed quasar candidate from Pan-STARRS. The grizy images reveal four point-like images with magnitudes between 14.9 mag and 18.1 mag. The colors of the point sources are similar, and they are more consistent with quasars than with stars or galaxies. The lensing galaxy is detected in the izy bands, with an inferred photometric redshift of ~0.6, lower than that of the point sources. We successfully model the system with a singular isothermal ellipsoid with shear, using the relative positions of the five objects as constraints. W…
We investigate the weak lensing effect by line-of-sight structures with a surface mass density of <~10^8 solar mass/arcsec^2 in QSO-galaxy quadruple lens systems. Using high-resolution N-body simulations in warm dark matter (WDM) models and observed four quadruple lenses that show anomalies in the flux ratios, we obtain constraints on the mass of thermal WDM, m_WDM>= 1.3keV(95%CL) assuming that the density of the primary lens is described by a singular isothermal ellipsoid (SIE). The obtained constraint is consistent with those from Lyman-$α$ forests and the number counts of high-redshift gala…
Time delays in gravitational lenses can be used to determine the Hubble constant and the lens potential. In future surveys, many gravitational lenses can be discovered, and their time delays and image positions can in principle be measured. Using an elliptical power-law potential, we show that combinations of image positions and time delays for quadruple lenses yield simple analytical expressions that are connected with observable quantities. These relations can be used to obtain the approximate axis ratio q, the Einstein radius and the slope. We apply this method to RX J1131-1231, and show th…
We report the discovery of a candidate to quadrupole gravitationally lensed system KiDS0239-3211 based on the public data release 3 of the KiDS survey and machine learning techniques.
The quadruple image configurations of gravitational lenses with vanishing ellipticity are examined. Even though such lenses asymptotically approach circularity, the configurations are stable if the position of the source relative to the vanishing diamond caustic is held constant. The configurations are the solutions of a quartic equation, an "Asymptotically Circular Lens Equation" (ACLE), parameterized by a single complex quantity. Several alternative parameterizations are examined. Relative magnifications of the images are derived. When a non-vanishing quadrupole, in the form of an external s…
We present mid-infrared imaging at 11.7 $μ$m for the quadruple lens systems, MG0414+0534 and Q2237+030, using the cooled mid-infrared camera and spectrometer (COMICS) attached on the Subaru telescope. MG0414+0534 is characterized by a bright pair of lensed images (A1, A2) and their optical flux ratio A2/A1 deviates significantly from the prediction of a smooth lens model. Q2237+030 is comprised of four lensed images, which are significantly affected by microlensing in a foreground lensing galaxy. Our mid-infrared observations of these lensed images have revealed that the mid-infrared flux rati…
Quadruply lensed quasars are extremely rare objects, but incredibly powerful cosmological tools. Only few dozen are known in the whole sky. Here we present the spectroscopic confirmation of two new quadruplets WG0214-2105 and WG2100-4452 discovered by Agnello & Spiniello (2018) within the Dark Energy Survey (DES) public footprints. We have conducted spectroscopic follow-up of these systems with the Southern African Large Telescope as part of a program that aims at confirming the largest possible number of optically selected strong gravitational lensing systems in the Equatorial and Southern He…
We report the $4 \, σ$ detection of a faint object with a flux of ~ 0.3 mJy, in the vicinity of the quadruply lensed QSO MG0414+0534 using the Atacama Large Millimeter/submillimeter array (ALMA) Band 7. The object is most probably a dusty dark dwarf galaxy, which has not been detected in either the optical, near-infrared (NIR) or radio (cm) bands. An anomaly in the flux ratio of the lensed images observed in Band 7 and the mid-infrared (MIR) band and the reddening of the QSO light color can be simultaneously explained if we consider the object as a lensing substructure with an ellipticity ~ 0.…
We investigate the weak lensing effects of line-of-sight structures on quadruple images in quasar-galaxy strong lens systems based on N-body and ray-tracing simulations that can resolve halos with a mass of 10^5 solar mass. The intervening halos and voids disturb the magnification ratios of lensed images as well as their relative positions due to lensing. The magnification ratios typically change by O(10%) when the shifts of relative angular positions of lensed images are constrained to <0.004 arcsec. The constrained amplitudes of projected density perturbations due to line-of-sight structures…
We report the serendipitous discovery of a quadruply lensed source at $z_{\rm s}=3.76$, HSC~J115252+004733, from the Hyper Suprime-Cam (HSC) Survey. The source is lensed by an early-type galaxy at $z_{\rm l}=0.466$ and a satellite galaxy. Here, we investigate the properties of the source by studying its size and luminosity from the imaging and the luminosity and velocity width of the Ly-$α$ line from the spectrum. Our analyses suggest that the source is most probably a low-luminosity active galactic nucleus (LLAGN) but the possibility of it being a compact bright galaxy (e.g., a Lyman-$α$ emit…
We explore the weak lensing effect by line-of-sight halos and sub-halos with a mass of M < 10^7 solar mass in QSO-galaxy strong lens systems with quadruple images in a concordant LCDM universe. Using a polynomially fitted non-linear power spectrum P(k) obtained from N-body simulations that can resolve halos with a mass of M ~ 10^5 solar mass, or structures with a comoving wavenumber of k ~ 3*10^2 h/Mpc, we find that the ratio of magnification perturbation due to intervening halos to that of a primary lens is typically ~10 per cent and the predicted values agree well with the estimated values f…
Inferring cosmological parameters from time-delay strong lenses requires a significant investment of telescope time; it is therefore tempting to focus on the systems with the brightest sources, the highest image multiplicities and the widest image separations. We investigate if this selection bias can influence the properties of the lenses studied and the cosmological parameters that are inferred. Using a population of lenses with ellipsoidal powerlaw density profiles, we build a sample of double and quadruple image systems. Assuming reasonable thresholds on image separation and flux, based on…
Mock Catalogs of Strongly Lensed Gravitational Waves via A Halo Model Approach with Ground-based Detectors
School of Physics and Technology, Wuhan University（武汉大学物理科学与技术学院）；National Centre for Nuclear Research（波兰国家核研究中心）；School of Physics and Optoelectronic, Yangtze University（长江大学物理与光电工程学院）
We develop a robust method to model quadruply lensed quasars, relying heavily on the work of Witt (1996), who showed that for elliptical potentials, the four image positions, the source, and the lensing galaxy lie on a right hyperbola. For the singular isothermal elliptical potential, there exists a complementary ellipse centered on the source which also maps through the four images, with the same axis ratio as the potential but perpendicular to it. We first solve for Witt's hyperbola, reducing the allowable space of models to three dimensions. We then obtain the best fitting complementary ell…
The mass-concentration relation of dark matter halos reflects the assembly history of objects in hierarchical structure formation scenarios, and depends on fundamental quantities in cosmology such as the slope of the primordial matter power-spectrum. This relation is unconstrained by observations on sub-galactic scales. We derive the first measurement of the mass-concentration relation using the image positions and flux ratios from eleven quadruple-image strong gravitational lenses (quads) in the mass range $10^{6} - 10^{10} M_{\odot}$, assuming cold dark matter. Our analysis framework include…
We report upon the follow up of 34 candidate lensed quasars found in the Dark Energy Survey using NTT-EFOSC, Magellan-IMACS, KECK-ESI and SOAR-SAMI. These candidates were selected by a combination of double component fitting, morphological assessment and color analysis. Most systems followed up are indeed composed of at least one quasar image and 13 with two or more quasar images: two lenses, four projected binaries and seven Nearly Identical Quasar Pairs (NIQs). The two systems confirmed as genuine gravitationally lensed quasars are one quadruple at $z_s=1.713$ and one double at $z_s=1.515$. …
JWST lensed quasar dark matter survey IV: Stringent warm dark matter constraints from the joint reconstruction of extended lensed arcs and quasar flux ratios
University of Chicago（芝加哥大学）；University of California, Merced（加州大学默塞德分校）；University of California, Los Angeles（加州大学洛杉矶分校）；Stony Brook University（石溪大学）；Carnegie Institution for Science（卡内基科学机构）；University of California, Davis（加州大学戴维斯分校）；The University of Tokyo（东京大学）
(abridged) Gravitationally lensed quasars can be used as powerful cosmological and astrophysical probes. We can (i) infer the Hubble constant based on the time-delay technique, (ii) unveil substructures along the l.o.s. toward distant galaxies, and (iii) compare the shape and the slope of baryons and dark matter distributions in galaxies. To reach these goals, we need high-accuracy astrometry and morphology measurements of the lens. In this work, we first present new astrometry for 11 lenses with measured time delays. Using MCS deconvolution on NIC2 HST images, we reached an astrometric accura…
The free-streaming length of dark matter from JWST observations of 28 strong gravitational lenses
University of Chicago（芝加哥大学）；University of California, Merced（加州大学默塞德分校）；University of California, Los Angeles（加州大学洛杉矶分校）；University of California, Irvine（加州大学尔湾分校）；Universidad Andres Bello（安德斯·贝略大学）；California Polytechnic State University（加州州立理工大学）；Carnegie Institution for Science（卡内基科学机构）；Stony Brook University（石溪大学）；California Institute of Technology（加州理工学院）；University of Southampton（南安普顿大学）
We present the second report of our systematic search for strongly lensed quasars from the data of the Sloan Digital Sky Survey (SDSS). From extensive follow-up observations of 136 candidate objects, we find 36 lenses in the full sample of 77,429 spectroscopically confirmed quasars in the SDSS Data Release 5. We then define a complete sample of 19 lenses, including 11 from our previous search in the SDSS Data Release 3, from the sample of 36,287 quasars with i<19.1 in the redshift range 0.6<z<2.2, where we require the lenses to have image separations of 1"<θ<20" and i-band magnitude difference…
Discrepancies between the observed and model-predicted radio flux ratios are seen in a number of quadruply-lensed quasars. The most favored interpretation of these anomalies is that CDM substructures present in lensing galaxies perturb the lens potentials and alter image magnifications and thus flux ratios. So far no consensus has emerged regarding whether or not the predicted CDM substructure abundance fully accounts for the lensing flux anomaly observations. Accurate modeling relies on a realistic lens sample in terms of both the lens environment and internal structures and substructures. In…
Core formation and runaway core collapse in models with self-interacting dark matter (SIDM) significantly alter the central density profiles of collapsed halos. Using a forward modeling inference framework with simulated datasets, we demonstrate that flux ratios in quadruple image strong gravitational lenses can detect the unique structural properties of SIDM halos, and statistically constrain the amplitude and velocity dependence of the interaction cross section in halos with masses between $10^6 - 10^{10} M_{\odot}$. Measurements on these scales probe self-interactions at velocities below $3…
The central ambition of the modern time delay cosmography consists in determining the Hubble constant $H_0$ with a competitive precision. However, the tension with $H_0$ obtained from the Planck satellite for a spatially-flat $Λ$CDM cosmology suggests that systematic errors may have been underestimated. The most critical one probably comes from the degeneracy existing between lens models that was first formalized by the well-known mass-sheet transformation (MST). In this paper, we assess to what extent the source position transformation (SPT), a more general invariance transformation which con…
Ultra-light dark matter (ULDM) refers to a class of theories, including ultra-light axions, in which particles with mass $m_ψ < 10^{-20}\, \rm{eV}$ comprise a significant fraction of the dark matter. A galactic scale de Broglie wavelength distinguishes these theories from cold dark matter (CDM), suppressing the overall abundance of structure on sub-galactic scales, and producing wave-like interference phenomena in the density profiles of halos. With the aim of constraining the particle mass, we analyze the flux ratios in a sample of eleven quadruple-image strong gravitational lenses. We accoun…
