Computing an Image of Objects Hiding Behind a Black Hole

Undergraduate Review Volume 18 Article 6 2024 Computing an Image of Objects Hiding Behind a Black Hole Shanon Harding Follow this and additional works at: https://vc.bridgew.edu/undergrad_rev Part of the Physical Sciences and Mathematics Commons Recommended Citation Harding, Shanon (2024). Computing an Image of Objects Hiding Behind a Black Hole. Undergraduate Review, 18, 18-33. Available at: https://vc.bridgew.edu/undergrad_rev/vol18/iss1/6 This item is available as part of Virtual Commons, the open-access institutional repository of Bridgewater State University, Bridgewater, Massachusetts. Copyright © 2024 Shanon Harding BARTLETT COLLEGE OF SCIENCE AND MATHEMATICS Computing an Image of Objects Hiding Behind a Black Hole SHANNON HARDING 1 Abstract Gravitational lensing is the bending of light rays around a black hole. The goal of this project was to produce a computer code that would model light rays coming from a grid of objects set behind a rotating black hole. Using these light rays, we produced an image illustrating how this background of objects would appear to an observer on Earth. This was done by creating a MATLAB code to model the paths of multiple light rays at a time. This code was then used to help check and correct a C++ code that produced an image. Over the semester, we have worked to successfully increase the accuracy of the final image by fine-tuning our C++ code. 2 Gravitational Lensing Gravitational lensing is the bending of light rays around a supermassive object in space, such as a black hole. In our everyday lives, we experience light rays that move in straight lines, like rays of sunlight shining through the clouds, a laser bouncing off a mirror, or a light passing through a prism and producing the rainbow. However, around a supermassive object, spacetime becomes curved, and therefore, so do the paths of light rays. To understand the curvature of spacetime, imagine a blanket stretched tight. If a bowling ball is placed in the center, it will cause a significant dip in the blanket at that spot. A black hole creates a similar effect in the spacetime around it. When the blanket is stretched tight, rolling a ping-pong ball across it should cause it to travel in a straight line. However, with the bowling ball in the center of the blanket, the path of the ping-pong ball will curve. Light rays around a black hole will curve in a similar manner (Fig. 1). 2.1 Interpreting Gravitational Lensing Images Studying gravitational lensing is important to understanding regions behind black holes. The bending of light rays from these regions causes objects to appear distorted in size, shape, location, and brightness. Figure 2 shows how the location can be distorted, as the observer’s eye interprets the light rays as if they had traveled in a straight line. However, Figure 2 does not depict the distortion in brightness, shape, or size. Each light ray would correspond to only one point on the object, not the entire object itself. Therefore, the observer would not see exact copies like depicted but would instead see distorted images of the object. The distortion can be observed in Figure 3, an image of a galaxy cluster taken by the Hubble Space Telescope. Some of the galaxies are indicated by yellow areas, and the two brightest galaxies in the center have enough mass to create a gravitational lens. The arcs are distorted images of galaxies far behind the cluster. The gravitational lens amplifies the light from distant, faint objects, allowing astronomers to examine the details of galaxies BRIDGEWATER STATE UNIVERSITY | 18 BARTLETT COLLEGE OF SCIENCE AND MATHEMATICS that would otherwise not be visible from Earth. It also magnifies, multiplies, and stretches the images of these galaxies. In the case of objects like galaxy clusters, which do not have symmetrical matter distribution, these gravitational lensing images can also be used to map this distribution. Most matter in the universe is not visible and is called dark matter. By studying the lensing caused by the significant amount of both visible and dark matter, astronomers can map its distribution. Figure 1: On the left, a light ray bends around a black hole placed at the origin. On the right, four light rays originating from the same point bend around a black hole. One ray falls into the black hole, another goes off in a separate direction, and the other two intersect on the other side of the black hole. [Kling, et al] Figure 2: Light rays from a galaxy bend around a black hole to reach an observer on the other side. The observer then interprets the light rays as having traveled in a straight line and therefore sees different images of the galaxy.and the other two intersect on the other side of the black hole. [Kling, et al] 19 | THE UNDERGRADUATE REVIEW 2024 BARTLETT COLLEGE OF SCIENCE AND MATHEMATICS Figure 3: An image of the galaxy cluster Abell 370, taken by the Hubble Space Telescope. 2.2 Intriguing Images of Gravitational Lensing Some gravitational lensing images have distinctive shapes. For example, Figure 4 depicts an object nicknamed “The Dragon” due to its shape. The dragon is thought by astronomers to be multiple distorted images of a single spiral galaxy behind the galaxy cluster Abell 370. Figure 4: “The Dragon” The Einstein Ring is another distinct shape seen in images of gravitational lens- ing. Lensing usually produces multiple, seperate images of the object, but the Hubble Space Telescope has found many cases where the lens is aligned precisely between the object and Earth so that an almost perfectly symmetrical ring of light is formed. Figure 5 shows how a single, distant blue galaxy appears as a ring of light around a luminous red galaxy. BRIDGEWATER STATE UNIVERSITY | 20 BARTLETT COLLEGE OF SCIENCE AND MATHEMATICS Figure 5: An Einstein Ring Most notably, images of black holes demonstrate the gravitational lensing that they themselves cause. Black holes cannot be seen because they cannot reflect or emit light. However, they can be imaged because they bend light around them, creating a ring just beyond the event horizon, the point where light can no longer escape the black hole. Figure 6 is the image of M87*, a black hole at the center of the Messier 87 galaxy. While M87* cannot be directly seen, the ring of light bending around the black hole clearly reveals its presence. Figure 6: The first image of a black hole, called M87*, located at the center of the Messier 87 galaxy. 3 The Mathematics The curvature of spacetime is described by an equation called a metric. In this project, we use the Kerr metric, which describes the spacetime around a rotating black hole. This is an important distinction from the Schwarzschild case, where the black hole is not rotating, because rotation causes asymmetry in the curvature of the surrounding spacetime. The Kerr metric is described by the equation 21 | THE UNDERGRADUATE REVIEW 2024 BARTLETT COLLEGE OF SCIENCE AND MATHE (...truncated)