Galaxy Clusters: Your Home for Wings. Lensing. Dark Matter.

Paper Title: BUFFALO Wild Wings: A High Precision Free-Form Lens Model of MACSJ0416 with Constraints on Dark Matter from Substructure and Highly Magnified Arcs

Authors: Derek Perera, Liliya L. R. Williams, Jori Liesenborgs, Patrick L. Kelly, Sarah H. Taft, Sung Kei Li, Mathilde Jauzac, Jose M. Diego, Priyamvada Natarajan, Charles L. Steinhardt, Andreas L. Faisst, R. Michael Rich

First-author institution: The University of Minnesota

Status: Uploaded to ArXiV

In February 1919, two groups of researchers traveled far and wide to observe a total solar eclipse that was set to cut across South America and Africa. The goal of the expedition was to observe possible gravitational lensing—the bending of light due to strong gravity—of the stars nearest the sun in the sky. Gravitational lensing is a natural result and unique feature of Einstein’s theory of general relativity. In a Newtonian framework, massless particles like photons are not impacted by gravitational forces, but when gravity is the result of Einstein’s curved spacetime, even light is influenced by it. The researchers found, of course, that the mass of the sun bends light from background stars, providing a key piece of early evidence for Einstein’s work. 

In the century since, astronomers have developed gravitational lensing as an essential instrument in the cosmologist’s toolkit. There are two primary ways gravitational lensing is used in research. More obviously, we can use gravitational lenses like magnifying glasses, allowing us to study objects at significantly further distances than would otherwise be possible. This was the case with the star Earendel, discovered in 2022. Additionally, astronomers have learned to use the images of gravitationally-lensed sources to study the structure of the lens itself. While the original observations of gravitational lensing used the Sun as the lens, modern-day lensing studies (more often than not) make use of entire galaxy clusters. Today’s authors—as part of the Beyond Ultra-deep Frontier Fields And Legacy Observations (BUFFALO) survey—use lensed observations to help ascertain the dark matter distribution in galaxy cluster MACS J0416.1-2403.

The majority of the matter content in a galaxy cluster is dark matter. As such, it is insufficient to try to reconstruct the general mass distribution of a cluster using only visible matter observations. While dark matter does not interact with light, its mass still bends spacetime, making lensing a powerful tool for indirect dark matter observations. In general terms, this is possible because a galaxy cluster lens—unlike the glass lens in a magnifying glass—is not uniform. This means that instead of a single magnified image, multiple images of background sources are created. The apparent locations of these images are sensitive to the unique mass distribution of the lensing cluster.

Figure 1: An image of the MACS J0416.1-2403 cluster. Blue circles indicate observed lensed images, while red crosses are galaxies in the lensing cluster. The two brightest cluster galaxies (BCGs) are labeled in green. The yellow and green boxes highlight two arcs of particular interest. Image Credit: Figure 1 of today’s paper.

Using observations of 237 spectroscopically-confirmed lensed images from a number of surveys (including BUFFALO) and GRALE (a lens inversion and simulation code), the authors create several 2-D model mass distributions for the lensing cluster. The simplest “free-form” model is created by constructing a large grid of overlapping Plummer spheres, adjusting the relative masses of each, and seeing how well the distribution recreates the observed images. Regions of the model with greater density are subdivided into smaller spheres to obtain better resolution of the substructure. 

In addition to this base free-form model, today’s paper creates several “hybrid” models, which additionally include a number of physically-motivated parametric models for a selection of the galaxies in the cluster. The authors were especially interested in re-creating the well-studied structure of a particular image arc, called the Spock arc. As such, they prioritize applying parametric models to the two brightest cluster galaxies (BCGs) and the smaller galaxies that are closest to the Spock arc.

Figure 2: The 2-D mass density distribution simple lens model. Observed images are indicated with blue dots, and reconstructed images with red triangles. The BCGs are labeled in blue, while the new unaffiliated mass peaks (M1, M2) are in green. Image credit: Figure 2 of today’s paper.

The quality of the various models is determined by comparing the distance between the observed locations of the lensed images with the reconstructed locations from the simulation. They find that adding parametric models does not significantly improve upon the base free-form model. 

In their analysis, the authors highlight that a number of reconstructed lensed images from the model have not been observed, which is due to expected limitations of our observations. In addition, they note three observed images that are not correctly reconstructed. On a cluster-sized scale, these are not of particular concern, and could be an interesting point of future research with an additional hybrid model. Finally, their model contains two large mass substructures (M1, M2) that are not affiliated with any observed galaxies. It is understood that such structures are either dark matter structures, or arise from very dim galaxies that we have failed to observe. These serve as an important frontier of future research. 

Ultimately, the free-form model developed by today’s paper is the most accurate mass model of MACS J0416.1-2403 to date, correctly recreating the locations of over nearly 237 images with greater precision than previously achieved. The model also recreates the locations of the two brightest galaxies in the cluster to within observational uncertainty. Together, these indicate that the model is simultaneously re-creating the observed matter density, as well as yielding insight into the overall structure of the unobservable dark matter.

Astrobite edited by: Alexandra Masegian

Featured image credit: The BUFFALO Survey

About Catherine Slaughter

Catherine is a new author and a Ph.D. candidate in astrophysics at the University of Minnesota. Her research primarily deals with stellar population astrophysics in local dwarf galaxies, with particular focus on the intersection between computational and observational research methods. Prior to moving to Minnesota, she completed her B.A. in Physics and Astronomy at Dartmouth College, and M.Sc. in Astronomy Research at Leiden University.

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