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Strong gravitational lenses with two background sources at widely separated redshifts are a promising independent probe of cosmological parameters. We can use these systems, known as double-source-plane lenses (DSPLs), to measure the ratio (β) of angular-diameter distances of the sources, which is sensitive to the matter density (Ω_m) and the equation-of-state parameter for dark-energy (w). However, DSPLs are rare and require high-resolution imaging and spectroscopy for detection, lens modeling, and measuringβ. Here, we report only the second DSPL ever used to measure cosmological parameters. We model the DSPLAGEL150745+052256 from the ASTRO 3D Galaxy Evolution with Lenses (AGEL) survey using Hubble Space Telescope/Wide-Field Camera 3 imaging and Keck Cosmic Web Imager spectroscopy. The spectroscopic redshifts for the deflector and two sources inAGEL1507 arez_defl= 0.594,z_S1 =  2.163, andz_S2= 2.591. We measure a stellar velocity dispersion ofσ_obs = 109 ± 27 km s⁻¹for the nearer source (S1). Usingσ_obsfor the main deflector (from literature) and S1, we test the robustness of our DSPL model. We measure $\beta =0.953_{-0.010}^{+0.008}$forAGEL1507 and infer Ω_m $=0.33_{-0.23}^{+0.38}$for ΛCDM cosmology. CombiningAGEL1507 with the published model of the Jackpot lens improves the precision on Ω_m(ΛCDM) andw(wCDM) by ∼10%. The inclusion of DSPLs significantly improves the constraints when combined with Planck’s cosmic microwave background observations, enhancing the precision onwby 30%. This paper demonstrates the potential constraining power of DSPLs and their complementarity to other standard cosmological probes. Tighter future constraints from larger DSPL samples discovered from ongoing and forthcoming large-area sky surveys would provide insights into the nature of dark energy. 

Double-source-plane strong gravitational lenses (DSPLs), with two sources at different redshifts, are independent cosmological probes of the dark energy equation of state parameterwand the matter density parameter Ω_m. We present the lens model for the DSPL AGEL035346−170639 and infer cosmological constraints from this system for flat Λ cold dark matter and flatwCDM cosmologies. From the joint posterior ofwand Ω_min the flatwCDM cosmology, we extract the following median values and 1σuncertainties: $w=-1.52_{-0.33}^{+0.49}$and ${\mathrm{\Omega }}_{\mathrm{m}}=0.192_{-0.131}^{+0.305}$from AGEL0353 alone. Combining our measurements with two previously analyzed DSPLs, we present the joint constraint on these parameters from a sample of three, the largest galaxy-scale DSPL sample used for cosmological measurement to date. The combined precision ofwfrom three DSPLs is higher by 15% over AGEL0353 alone. Combining DSPL and cosmic microwave background (CMB) measurements improves the precision ofwfrom CMB-only constraints by 39%, demonstrating the complementarity of DSPLs with the CMB. Despite their promising constraining power, DSPLs are limited by sample size, with only a handful discovered so far. Although ongoing and near-future wide-area sky surveys will increase the number of known DSPLs by up to two orders of magnitude, these systems will still require dedicated high-resolution imaging and spectroscopic follow-ups like those presented in this paper. Our ASTRO 3D Galaxy Evolution with Lenses collaboration is undertaking such follow-up campaigns for several newly discovered DSPLs and will provide cosmological measurements from larger samples of DSPLs in the future. 

Abstract Imaging data is the principal observable required to use galaxy-scale strong lensing in a multitude of applications in extragalactic astrophysics and cosmology. In this paper, we develop Lensing Exposure Time Calculator (L ensing ETC; https://github.com/ajshajib/LensingETC ) to optimize the efficiency of telescope-time usage when planning multifilter imaging campaigns for galaxy-scale strong lenses. This tool simulates realistic data tailored to specified instrument characteristics and then automatically models them to assess the power of the data in constraining lens model parameters. We demonstrate a use case of this tool by optimizing a two-filter observing strategy (in the IR and ultraviolet-visual (UVIS)) within the limited exposure time per system allowed by a Hubble Space Telescope (HST) Snapshot program. We find that higher resolution is more advantageous to gain constraining power on the lensing observables, when there is a trade-off between signal-to-noise ratio and resolution; for example, between the UVIS and IR filters of the HST. We also find that, whereas a point-spread function (PSF) with sub-Nyquist sampling allows the sample mean for a model parameter to be robustly recovered for both galaxy–galaxy and point-source lensing systems, a sub-Nyquist-sampled PSF introduces a larger scatter than a Nyquist-sampled one in the deviation from the ground truth for point-source lens systems. 

Abstract We present spectroscopic confirmation of candidate strong gravitational lenses using the Keck Observatory and Very Large Telescope as part of our ASTRO 3D Galaxy Evolution with Lenses ( AGEL ) survey. We confirm that (1) search methods using convolutional neural networks (CNNs) with visual inspection successfully identify strong gravitational lenses and (2) the lenses are at higher redshifts relative to existing surveys due to the combination of deeper and higher-resolution imaging from DECam and spectroscopy spanning optical to near-infrared wavelengths. We measure 104 redshifts in 77 systems selected from a catalog in the DES and DECaLS imaging fields ( r ≤ 22 mag). Combining our results with published redshifts, we present redshifts for 68 lenses and establish that CNN-based searches are highly effective for use in future imaging surveys with a success rate of at least 88% (defined as 68/77). We report 53 strong lenses with spectroscopic redshifts for both the deflector and source ( z src > z defl ), and 15 lenses with a spectroscopic redshift for either the deflector ( z defl > 0.21) or source ( z src ≥ 1.34). For the 68 lenses, the deflectors and sources have average redshifts and standard deviations of 0.58 ± 0.14 and 1.92 ± 0.59 respectively, and corresponding redshift ranges of z defl = 0.21–0.89 and z src = 0.88–3.55. The AGEL systems include 41 deflectors at z defl ≥ 0.5 that are ideal for follow-up studies to track how mass density profiles evolve with redshift. Our goal with AGEL is to spectroscopically confirm ∼100 strong gravitational lenses that can be observed from both hemispheres throughout the year. The AGEL survey is a resource for refining automated all-sky searches and addressing a range of questions in astrophysics and cosmology. 

Abstract: Detecting gravitationally lensed supernovae is among the biggest challenges in astronomy. It involves a combination of two very rare phenomena: catching the transient signal of a stellar explosion in a distant galaxy and observing it through a nearly perfectly aligned foreground galaxy that deflects light towards the observer. Here we describe how high-cadence optical observations with the Zwicky Transient Facility, with its unparalleled large field of view, led to the detection of a multiply imaged type Ia supernova, SN Zwicky, also known as SN 2022qmx. Magnified nearly 25-fold, the system was found thanks to the standard candle nature of type Ia supernovae. High-spatial-resolution imaging with the Keck telescope resolved four images of the supernova with very small angular separation, corresponding to an Einstein radius of only θ E  = 0.167″ and almost identical arrival times. The small θ E and faintness of the lensing galaxy are very unusual, highlighting the importance of supernovae to fully characterize the properties of galaxy-scale gravitational lenses, including the impact of galaxy substructures.