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1. Einstein beams carrying orbital angular momentum

   Rodriguez-Fajardo, V; Nguyen, T; Hocek, K; Freedman, J; Galvez, E (March 2023, Proceedings of SPIE)

   Andrews, D; Galvez, E; Rubinsztein-Dunlop (Ed.)

   Einstein beams are coherent optical beams generated by the conditions of gravitational lensing. In the ray picture, Einstein beams are formed by the intersection of light rays deflected by a lensing mass, similar to nondiffracting Bessel beams, but with the difference that adjacent rays diverge slightly. When accounting for the wave properties of light, they form beam-like diffraction patterns that preserve their shape but expand as the light propagates. The addition of a topological charge to the light, leads to more complex patterns carrying orbital angular momentum. For symmetric lensing conditions, Einstein beams carry modes described by confluent hypergeometric functions, which can be approximated by Bessel functions. A theoretical analysis of this is presented here. In astrophysical observations, many of these features can only be inferred because conditions of coherence and alignment make them difficult to observe. Studies of Einstein beams in the laboratory can be used to inform astrophysical observations and discover new non-astrophysical laboratory applications. 

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2. Detecting low-mass haloes with strong gravitational lensing I: the effect of data quality and lensing configuration

   https://doi.org/10.1093/mnras/stab3537  

   Despali, Giulia; Vegetti, Simona; White, Simon D. M.; Powell, Devon M.; Stacey, Hannah R.; Fassnacht, Christopher D.; Rizzo, Francesca; Enzi, Wolfgang (December 2021, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT This paper aims to quantify how the lowest halo mass that can be detected with galaxy-galaxy strong gravitational lensing depends on the quality of the observations and the characteristics of the observed lens systems. Using simulated data, we measure the lowest detectable NFW mass at each location of the lens plane, in the form of detailed sensitivity maps. In summary, we find that: (i) the lowest detectable mass Mlow decreases linearly as the signal-to-noise ratio (SNR) increases and the sensitive area is larger when we decrease the noise; (ii) a moderate increase in angular resolution (0.07″ versus 0.09″) and pixel scale (0.01″ versus 0.04″) improves the sensitivity by on average 0.25 dex in halo mass, with more significant improvement around the most sensitive regions; (iii) the sensitivity to low-mass objects is largest for bright and complex lensed galaxies located inside the caustic curves and lensed into larger Einstein rings (i.e rE ≥ 1.0″). We find that for the sensitive mock images considered in this work, the minimum mass that we can detect at the redshift of the lens lies between 1.5 × 108 and $$3\times 10^{9}\, \mathrm{M}_{\odot }$$. We derive analytic relations between Mlow, the SNR and resolution and discuss the impact of the lensing configuration and source structure. Our results start to fill the gap between approximate predictions and real data and demonstrate the challenging nature of calculating precise forecasts for gravitational imaging. In light of our findings, we discuss possible strategies for designing strong lensing surveys and the prospects for HST, Keck, ALMA, Euclid and other future observations. 

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3. Inferring the Intermediate-mass Black Hole Number Density from Gravitational-wave Lensing Statistics

   https://doi.org/10.3847/2041-8213/ac7052  

   Gais, Joseph; Ng, Ken K. Y.; Seo, Eungwang; Wong, Kaze W. K.; Li, Tjonnie G. F. (June 2022, The Astrophysical Journal Letters)

   Abstract The population properties of intermediate-mass black holes remain largely unknown, and understanding their distribution could provide a missing link in the formation of supermassive black holes and galaxies. Gravitational-wave observations can help fill in the gap from stellar mass black holes to supermassive black holes with masses between ∼100–10⁴M_⊙. In our work, we propose a new method for examining lens populations through lensing statistics of gravitational waves, here focusing on inferring the number density of intermediate-mass black holes through hierarchical Bayesian inference. Simulating ∼200 lensed gravitational-wave signals, we find that existing gravitational-wave observatories at their design sensitivity could either constrain the number density of 10⁶Mpc⁻³within a factor of 10, or place an upper bound of ≲10⁴Mpc⁻³if the true number density is 10³Mpc⁻³. More broadly, our method leaves room for incorporation of additional lens populations, providing a general framework for probing the population properties of lenses in the universe. 

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4. Einstein beams and the diffractive aspect of gravitationally-lensed light

   https://doi.org/10.1088/1367-2630/ace98e  

   Rodríguez-Fajardo, V.; Nguyen, T. P.; Hocek, K. S.; Freedman, J. M.; Galvez, E. J. (August 2023, New Journal of Physics)

   Abstract The study of light lensed by cosmic matter has yielded much information about astrophysical questions. Observations are explained using geometrical optics following a ray-based description of light. After deflection the lensed light interferes, but observing this diffractive aspect of gravitational lensing has not been possible due to coherency challenges caused by the finite size of the sources or lack of near-perfect alignment. In this article, we report on the observation of these wave effects of gravitational lensing by recreating the lensing conditions in the laboratory via electro-optic deflection of coherent laser light. The lensed light produces a beam containing regularities, caustics, and chromatic modulations of intensity that depend on the symmetry and structure of the lensing object. We were also able to observe previous and new geometric-optical lensing situations that can be compared to astrophysical observations. This platform could be a useful tool for testing numerical/analytical simulations, and for performing analog simulations of lensing situations when they are difficult to obtain otherwise. We found that laboratory lensed beams constitute a new class of beams, with long-range, low expansion, and self-healing properties, opening new possibilities for non-astrophysical applications. 

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5. From Images to Dark Matter: End-to-end Inference of Substructure from Hundreds of Strong Gravitational Lenses

   https://doi.org/10.3847/1538-4357/aca525  

   Wagner-Carena, Sebastian; Aalbers, Jelle; Birrer, Simon; Nadler, Ethan O.; Darragh-Ford, Elise; Marshall, Philip J.; Wechsler, Risa H. (January 2023, The Astrophysical Journal)

   Abstract Constraining the distribution of small-scale structure in our universe allows us to probe alternatives to the cold dark matter paradigm. Strong gravitational lensing offers a unique window into small dark matter halos (<10¹⁰M_⊙) because these halos impart a gravitational lensing signal even if they do not host luminous galaxies. We create large data sets of strong lensing images with realistic low-mass halos, Hubble Space Telescope (HST) observational effects, and galaxy light from HST’s COSMOS field. Using a simulation-based inference pipeline, we train a neural posterior estimator of the subhalo mass function (SHMF) and place constraints on populations of lenses generated using a separate set of galaxy sources. We find that by combining our network with a hierarchical inference framework, we can both reliably infer the SHMF across a variety of configurations and scale efficiently to populations with hundreds of lenses. By conducting precise inference on large and complex simulated data sets, our method lays a foundation for extracting dark matter constraints from the next generation of wide-field optical imaging surveys. 

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