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Quanta Magazine's Two Weeks In, the Webb Space Telescope Is Reshaping Astronomy highlights two submissions to arXiv soon after the first images were released: "Three days later, just minutes before the daily deadline on arxiv.org..." It certainly sounds exciting!

The first deep field images from the James Webb Space Telescope (JWST) of the galaxy cluster SMACS~J0723.3-7327 reveal a wealth of new lensed images at uncharted infrared wavelengths, with unprecedented depth and resolution. Here we securely identify 14 new sets of multiply imaged galaxies totalling 42 images, adding to the five sets of bright and multiply-imaged galaxies already known from Hubble data. We find examples of arcs crossing critical curves with magnification factors of at least 150, allowing detailed community follow-up, including JWST spectroscopy for precise redshift determinations, chemical abundances and detailed internal gas dynamics of very distant, young galaxies. We also detect an Einstein cross candidate only visible thanks to JWST's superb resolution. Our parametric lens model is available at this https URL , and will be regularly updated using additional spectroscopic redshifts. The model reproduces very well the multiple images, and allows for accurate magnification estimates of high-redshift galaxies. This work represents a first taste of the enhanced power JWST will have for lensing-related science.

Exploiting the fundamentally achromatic nature of gravitational lensing, we present a lens model for the massive galaxy cluster SMACSJ0723.3-7323 (SMACS J0723, z=0.388) that significantly improves upon earlier work. Building on strong-lensing constraints identified in prior Hubble Space Telescope (HST) observations, the mass model utilizes 21 multiple-image systems, 16 of which were newly discovered in Early Release Observation (ERO) data from the James Webb Space Telescope (JWST). The resulting lens model maps the cluster mass distribution to an RMS spatial precision of 1.08'' and is publicly available at this https URL . Consistent with previous analyses, our study shows SMACSJ0723.3-7323 to be well described by a single large-scale component centered on the location of the brightest cluster galaxy, however JWST data point to the need for two additional diffuse components west of the cluster, which in turn accounts for all the currently identified multiply imaged systems. A comparison of the galaxy distribution, the mass distribution, and gas distribution in the core of SMACS0723 based on HST, JWST, and Chandra data reveals a fairly concentrated regular elliptical profile along with tell-tale signs of recent merger activity, possibly proceeding aligned closely to our line of sight. The exquisite sensitivity of JWST's NIRCAM reveals in spectacular fashion both the extended intra-cluster-light distribution and numerous star-forming clumps in magnified background galaxies. The high-precision lens model derived here for SMACSJ0723-7323 demonstrates impressively the power of combining HST and JWST data for unprecedented studies of structure formation and evolution in the distant Universe.

While the groups chose different algorithms for title selection ("unscrambling" vs "precision modeling") I wonder if they used similar variations on the same technique?

Question: How do they do this? How do astronomers unscramble or precision-model the undistorted image from an observed image gravitationally lensed by a complex (or at least lumpy) gravitational field. Is there an easy way to explain it as a straightforward algorithm, or is it more like solving a jigsaw puzzle - a long series of guesses and decisions and tests?

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    $\begingroup$ Maybe you could un-scramble an egg with a computer? :) $\endgroup$ Jul 26 at 0:32
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    $\begingroup$ Basically, when you scramble an egg, you also change its chemistry. The energy you have input into it by the whisking action, and the fact that parts were in contact which would not have been in contact normally, all that changes its nature. When light goes through a lens, gravitational or otherwise, its nature is not changed. It’s twisted, but it still remains light. $\endgroup$ Jul 26 at 4:14
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    $\begingroup$ The short answer is that gravitational distorsions are non linear but not too strongly non linear, and with significant coherence, so it is in effect possible to reverse them to some extend. You could probably un scramble the egg if you had a snapshot an instant after it started breaking. $\endgroup$
    – chris
    Jul 26 at 8:48
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    $\begingroup$ It's a bit of a chicken-and-egg situation. ;) The lensing mass distribution determines the distortion, but we measure that mass distribution from the distortion. So you start with approximate models of the masses and the undistorted field, ray-trace, and gradually refine the models, possibly using a process similar to a multidimensional version of the Remez algorithm. en.wikipedia.org/wiki/Remez_algorithm Maybe some Fourier magic is used, too. $\endgroup$
    – PM 2Ring
    Jul 26 at 17:05
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    $\begingroup$ It helps that the mass distribution of a cluster of galaxies is mostly from the intracluster medium (gas and dark matter between the galaxies), and its lensing effects are well approximated by a simple spheroid. The individual galaxies are almost insignificant perturbations to that unless the image lies right on a galaxy. With this JWST data one can apparently make out some additional low mass subclumps of galaxies. $\endgroup$
    – eshaya
    Jul 26 at 18:24

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