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Microlensing of Microlensing: Effects of Random Stars on the Double-Source-Plane Gravitational Lens

This paper presents the first numerical simulations of "microlensing of microlensing" in the double-source-plane gravitational lens J1721+8842, revealing that the interaction of light rays with compact masses in two foreground galaxies generates complex caustic features and distinct lightcurves for the six quasar images.

Original authors: Nada Salama, Daniel J. Ballard, Huimin Qu, Geraint F. Lewis, Karl Glazebrook

Published 2026-07-21

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CC BY 4.0

Original authors: Nada Salama, Daniel J. Ballard, Huimin Qu, Geraint F. Lewis, Karl Glazebrook

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, cosmic funhouse. Sometimes, the massive gravity of a galaxy or a cluster of galaxies acts like a warped mirror, bending the light from objects behind it. This is called gravitational lensing. It can stretch a distant galaxy into a long arc or, if the alignment is perfect, split a single object into multiple copies, like a kaleidoscope. Astronomers love this because it acts as a natural telescope, letting us see things that are too far away to see otherwise.

But the funhouse doesn't just have big mirrors; it also has tiny, invisible bumps. Inside the galaxies acting as lenses, there are billions of stars. As these stars move, they create tiny, shifting pockets of gravity that act like miniature lenses on top of the big one. This is microlensing. It's like looking at a streetlamp through a wavy window; the light flickers and brightens unpredictably. This effect is a double-edged sword: it messes up our measurements of time and distance, but it also gives us a way to weigh the invisible stars and black holes that make up the galaxy.

Now, imagine a scenario where the light from a distant object has to pass through two different funhouse mirrors before it reaches us. This is a double-source-plane lens. It's a rare cosmic coincidence where a galaxy sits in front of another galaxy, and both are in front of a super-bright beacon called a quasar. The light gets bent by the first (foreground) galaxy, then bent again by the second (intermediate) one. The big question for astronomers is: what happens when you add the tiny, wobbly bumps (microlensing) to this already complicated two-step dance? Does the light get even more chaotic?

In this paper, the authors take a deep dive into this specific cosmic puzzle. They focus on a real, recently discovered system called J1721+8842, which they affectionately nickname the "Einstein zig-zag." In this system, light from a distant quasar (the background source) travels toward us and is first bent by an intermediate galaxy. This deflection sends the light toward a foreground galaxy, which bends it one last time before it reaches Earth. This creates a "zig-zag" path for the light rays, resulting in six distinct images of the same quasar.

The team wanted to see what happens when you simulate microlensing of microlensing. Usually, scientists simulate how stars in one galaxy mess up the light from a background object. But here, the light has already been scrambled by the first galaxy's stars before it even hits the second galaxy's stars. To figure this out, the authors built a brand-new computer simulation. They didn't just guess; they wrote a custom code that runs on powerful graphics cards (GPUs) to track billions of light rays as they bounce through these two layers of gravitational chaos.

Their main finding is that this "compound microlensing" creates a much more chaotic and intricate mess than we ever saw before. In a normal single-lens system, the patterns of bright and dark spots (called caustics) look like a relatively simple web of folds and cusps. But in this double-lens "zig-zag" system, the simulations show that the web becomes incredibly dense and complex. They found strange new shapes in the light patterns, including "convexity violations" where the curves of the light traps bend the wrong way, and "lip" structures that are impossible to create with just one lens.

The authors also simulated what the light from the quasar would look like over time as it moves across these complex maps. They found that the brightness fluctuations (lightcurves) are wilder and more frequent. The peaks in brightness are not just bigger; they are more numerous and sharper because the light is being hit by two layers of stellar bumps instead of one. Interestingly, for some of the images, the second layer of microlensing actually made the light less bright at certain moments compared to if only one lens were present, showing that the interaction is not just a simple addition of effects but a complex interplay.

The paper concludes that while we have a good theoretical idea of how this should work, this is the first time anyone has actually run the numbers to see what it looks like in a realistic, high-density environment. The results suggest that if we want to use these rare double-lens systems to measure the expansion rate of the universe (the Hubble constant) or study the size of quasar disks, we have to account for this extra layer of chaos. The "microlensing of microlensing" creates a unique fingerprint that is distinct from single-lens systems, and understanding it is key to unlocking the secrets hidden in these cosmic zig-zags.

Technical Summary: Microlensing of Microlensing in Double-Source-Plane Systems

Problem Statement
Strong gravitational lensing has become a cornerstone for cosmological probes, particularly for measuring the Hubble constant ( $H_0$ ) via time delays. However, as precision goals tighten toward $\sim 1\%$ , the influence of gravitational microlensing—caused by compact objects (stars, black holes) within the lens galaxy—becomes a critical source of uncertainty. While microlensing in single-source-plane systems is well-studied, the discovery of Double-Source-Plane Lenses (DSPLs) introduces a new complexity: "compound microlensing." In DSPLs, a background source (e.g., a quasar) is lensed by an intermediate galaxy, which is itself lensed by a foreground galaxy. The light rays from the quasar undergo sequential deflection, meaning the microimages formed by the intermediate plane are subsequently microlensed by the foreground plane. The statistical characteristics of this "microlensing of microlensing," including the resulting caustic structures and lightcurves, had not been previously simulated or characterized.

Methodology
The authors present the first numerical simulations of compound microlensing, using the recently discovered "Einstein zig-zag" system J1721+8842 as a fiducial case. This system features a foreground lens at $z=0.184$ , an intermediate source plane (an early-type galaxy) at $z=1.885$ , and a background quasar source at $z=2.38$ .

Macromodeling: The authors fitted a macrolensing model to HST F814W data of J1721 to determine the convergence ( $\kappa$ ) and shear ( $\gamma$ ) at the positions of the six quasar images (A–F). They calculated the effective magnification and the specific contributions of the foreground lens and the intermediate source plane separately.
Ray-Shooting Framework: A novel, GPU-accelerated ray-shooting code written in JAX was developed to handle the multi-plane geometry. Unlike standard single-plane codes, this framework sequentially maps rays from the observer through the foreground lens plane, then to the intermediate plane, and finally to the source plane.
- The simulation treats the convergence on each plane as a sum of smooth mass and point masses (microlenses).
- The authors generated magnification maps containing $10^{10}$ rays, split into $10^4 \times 10^4$ pixels.
- Lightcurves were simulated by convolving the magnification maps with a Gaussian source profile (radius $10^{15}$ cm) and moving the source across the map at a transverse velocity of $600$ km/s.
Comparison: The study compares the compound microlensing results against single-plane microlensing scenarios (lensing by the intermediate plane alone and the foreground plane alone) to isolate the effects of the recursive deflection.

Key Contributions and Results

Complex Caustic Morphologies: The simulations reveal that compound microlensing produces significantly more complex caustic networks than single-plane microlensing. While single-plane maps exhibit standard metamorphoses (e.g., swallowtails, butterflies), the compound maps display "convexity violations."
Convexity Violations: The authors identify "caustics of the second kind," where one of the folds meeting at a cusp becomes locally concave relative to the caustic interior. This feature, theoretically predicted by Petters & Wicklin (1995) but never observed in realistic high-density simulations, is exclusive to the multi-plane configuration. Additionally, "lip" caustics, forbidden in single-plane lensing, appear in the compound maps.
Lightcurve Characteristics: The resulting lightcurves for the six quasar images show that compound microlensing retains the broad trends of single-plane events but introduces a secondary network of smaller-scale peaks. In some cases (specifically images D and F), the compound lightcurves are less magnified at certain points than the single-lens case, and the features of the first lensing event are sometimes less pronounced due to the intermingling of the second microlensing event.
Shear Alignment: The study notes that the lack of intrinsic alignment between the shear vectors of the two planes leads to shearing in multiple directions, further complicating the caustic structure compared to single-plane scenarios.

Significance and Claims
The paper claims to provide the first practical demonstration of compound microlensing, moving beyond theoretical classification to realistic simulation. The authors argue that understanding these effects is timely and necessary for maximizing the cosmological output of DSPLs. Specifically:

Cosmological Precision: As the community aims for $\sim 1\%$ precision on $H_0$ using time-delay lenses, microlensing signals (which can induce time delays of hours) must be accounted for. DSPLs offer tighter constraints on lens potentials, but only if the complex microlensing signatures are understood.
New Probes: The unique "zig-zag" geometry of systems like J1721 provides a testbed for studying how recursive deflection alters magnification maps and source size constraints.
Future Work: The authors acknowledge that their current work covers a limited parameter space (e.g., assuming static microlenses and specific mass functions). They state that a full statistical characterization requires exploring different shear alignments, initial mass functions, and smooth mass distributions, noting that future observations (e.g., JWST NIRSpec) could inform the velocity dispersion of stellar populations to refine these models.

The paper concludes that compound microlensing produces new, intricate microcaustic structures that distinguish it from single-plane lensing, necessitating a thorough understanding of these effects to fully utilize the potential of compoundly lensed quasars as cosmological probes.

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