Strong Lensing



  • Danny Goldstein (U.C. Berkeley) - dgold at 
  • Tom Collett (Portsmouth) - thomas.collett at

Strong gravitational lensing refers to the multiple imaging of a background object (“the source” or “deflector”) by a massive foreground object (“the lens”) (e.g., Schneider et al. 2006b; Treu 2010). The resulting angular separation, time delay, and morphological distortion all depend on the lens geometry, quantified in terms of combinations of the three angular diameter distances between observer, lens and source (Refsdal 1964; Blandford & Narayan 1992). These observables are also affected by the mass distribution of the lens, which must be modeled simultaneously using high resolution follow-up imaging and spectroscopy.

Strong lensing provides at least two independent ways to measure dark energy parameters based on LSST data. The first one, gravitational time delays, has a venerable history and is now, in our opinion, mature for precision cosmology (Refsdal 1964; Suyu et al. 2010, 2012, 2013). The second one, the analysis of systems with multiple sets of multiple images (Gavazzi et al. 2008; Jullo et al. 2010, Collett et al. 2013a), is a more recent development and will require more research and development work in order to quantify precisely its systematics and assess its potential. 

Time Delay Distance Cosmography

Strong gravitational lensing time delays measure a combination of distances that is sensitive primarily to the Hubble constant, but also to the other parameters of the world model: when many lenses with different lens and source redshifts are combined, internal degeneracies are broken and dark energy parameters can be measured (Coe & Moustakas 2009). The time-delay distance provides significant complementarity with other dark energy probes to determine, e.g., the dark energy equation of state, matter density, Hubble constant, and sum of neutrino masses (e.g., Linder 2011; Collett et al. 2012; Weinberg et al. 2012). Furthermore, the main systematics coming from the lens-mass modeling and line-of-sight dark matter, are interesting astrophysically in themselves: dark matter substructure and galaxy mass profiles (e.g., Treu 2010, and references therein). LSST’s wide-field, time-domain survey will be superb for obtaining large samples of time delay systems and, with follow up spectroscopy and high resolution imaging for the lens model, delivering distance-ratio constraints. An exciting prospect is the use of time delays to test gravity on precisely those scales where we expect screening mechanisms to become active. 

How Will LSST Help?

We anticipate that dark energy measurements from strong lensing with LSST will differ from previous or concurrent strong-lens surveys in the following key ways:

  1. A high-yield lens search requires all four of the properties offered by LSST: wide area, depth, high image resolution, and spectral coverage to distinguish lens and source light. Other surveys – current, planned, or concurrent with LSST – will lack at least one of these properties. Only SKA is likely to surpass LSST in terms of raw yield; Euclid will perform comparably well, but will only overlap with LSST in the Southern half of the sky. LSST should be able to detect ≈ 8000 time-delay lenses (including both AGN and supernovae); the combination of LSST and Euclid imaging is an exciting prospect for efficient lens identification.

  2. Time-domain information will be available from within the survey, enabling the measurement of time delays for thousands of lens systems for the first time. Precursor surveys such as DES, HSC, and PS1, which should find lensed AGN in large numbers, will be reliant on monitoring follow-up, and so will likely achieve only a few hundred measured time delays, with enormous effort. LSST should provide precision time delays for over a thousand lenses.

In short, LSST’s strengths are the size of its lens sample, which should be an order of magnitude more in most lens classes (and even more in others), and its ability to provide measured time delays for the majority of suitable variable-source systems. On top of this, the simultaneous optical galaxy and weak shear surveys carried out by LSST will provide a detailed picture of the environment of each lens, both local and along the line of sight; this will enable weak lensing contamination to be modeled during the distance estimation (Collett et al 2013b).

What Are We Working On?

Practical problems that need to be solved to make strong lens cosmography work include lens detection (which will be very sensitive to the image quality and the deblender performance); image and light-curve modeling (which can be both CPU and skilled-labor intensive); obtaining and analyzing follow-up data; interpreting the whole sample of lenses in the context of a well-studied subset; and finding sufficient experienced researchers to accomplish all these tasks. 


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