Observing Time Dilation and General Relativity in a Dual Supermassive Blackhole System

Hello everyone, My name is Sebastian Gibbs and I am a rising senior at Gettysburg College. I am a physics major from Bethlehem, PA and I am conducting my research with Dr. Ryan E Johnson. This is my first year conducting research for X-Sig at Gettysburg College, and it has been going very well so far. Along with this being my first time doing research, this is also my first time coding which has been a challenge, but I have been developing and learning everyday which has enhanced my skill set. My research is a continuation of Sheldon Johnson’s research who graduated last year from Gettysburg (Class of 2022). My research deals with the gravitational aspect of time dilation as proposed by Albert Einstein’s Theory of General Relativity. This has led me to model the first direct dynamical detection of a dual supermassive blackhole system at sub-kiloparsec separation. General relativity is a concept that involves the curving or warping of space from the invisible force that we interact with daily. The theory of General Relativity is founded on the idea that massive objects cause a distortion in space time which leads to the subject of time dilation. In physics and relativity, time dilation is recognized as the slowing of time perceived by one observer compared to another, depending on their relative motion. Along with this, time dilation can also be affected by gravity which is the spark of motivation for this project. In my research with Professor Johnson, we are attempting to replicate the dual supermassive blackhole system (Voggel,2022) using three-dimensional visualizations on a computer software program which is named python in order to visually perceive time dilation. The overall goal for this project is to observe paths of constant time through intersecting gravitational fields.

Figure I of creating the Dual Blackhole System

Here is one of the first three-dimensional visualizations that me and Dr. Johnson have created from the data that we collected about the blackhole system from the constellation NGC 7727 which is approximately 89 million light years away. This was the first blackhole that we replicated and coded into python. The initial goal for this was to create a perfectly spherical object with the data we obtained about the blackhole system. In order to perform this we had to code in the X,Y, and Z spherical coordinates and develop a random number generator to select various positions on the sphere within the three-dimensional grid everytime we ran the cell. We also implemented a modified version of The Schwarzschild Equation into the cell in order to view the time dilation within the replicated sphere. In order to view the time dilation within the coded sphere we had to adjust the amount of contours that appeared, and choose a specific color scale that best represents the amount of contours as well. The contours within the 3d figures are the different shades of color that transition inside of the sphere as it approaches its core. The side color scale bar guides the reader to understand the different intensities of time dilation that is apparent within the sphere. As we can see above (Figure 1), the time dilation transitions from low intensity (Outer shell of the sphere) to very high intensity (the glowing yellow in the middle) which shows how time is being affected from the gravitational field of the blackhole. As the contours approach the core of the sphere, time continuously slows down. Once we got to the point where the sphere appeared to be like the figure above, we moved on to replicating another blackhole within python to truly create the dual supermassive blackhole system.

Figure II of creating the Dual Blackhole System (View from the X coordinate)
Figure III 3d visualization from the Y coordinate

The existence of stellar-mass binary black holes was discovered in the year 2015 which makes this a fairly new phenomenon in the astrophysics field. Most black holes usually have masses between three and ten solar masses which makes these specific black holes astounding. These discovered merging black holes are approximately 30 solar masses each and about 1.3 billion light years away. The reason why these black holes were able to be detected is because of LIGO (Laser Interferometer Gravitational-Wave Observatory) which observed the gravitational wave signature of the two merging black holes (Caltech, 2022).

In this past week, Professor Johnson and I have modeled the first, and newly discovered, dual supermassive blackhole system (See Figure 2 and 3). While creating this visualization, we calculated the mass ratio between the two black holes in the system. The smaller blackhole which is visualized in the color purple is approximately 6.33×10^6 solar masses (a solar mass is the mass of the Sun, ~2e30 kg). The larger blackhole in the 3d visualization is approximately 1.54 ×10^8 solar masses. Most galaxies, including our own Milky Way Galaxy, contain supermassive black holes which can reach up to millions or billions of solar masses.

We calculated the Schwarzchild radius of each black hole in the binary system, and we were able to compute this by using The Schwarzchild radius equation which is (Cosmos, 2022). Because our simulation space was not large enough to encompass the astronomical units of the positional data, and in an effort to faithfully reproduce the size and relative positions of these supermassive black holes, we used the black hole diameters (specifically the larger black hole’s diameter) as a scale for expressing the separation distance between the two. Since the larger supermassive black holes radius was 2.83 x 10^8 miles, and the separation distance was 9.58 x 10^8 miles, then the seperation distance measured in black hole diameters is approximately 3.38. We can observe this separation distance in the figure below.

Figure IV, Separation distance of approximately 3.38 large black hole diameters within the 3d grid.

Now comparing the masses of the first detected binary system to the binary system that Professor Johnson and I are researching is astonishing. If we take the mass of the smaller blackhole in our research (6.33×10^6 solar masses) and compared it to one of the detected black holes from 2015 ( 30 solar masses) we would see that the smaller blackhole that we are researching is approximately 211,000 times as massive as one of the discovered black holes in the first binary system. In calculating the mass ratio of the black holes in our research, we found that the larger black hole in NGC 7727 is around 25 times more massive than the other blackhole. We coded this calculation into python which then created this size difference within the 3d grid (See Figure 2). We also changed the color scheme in this visualization in order to enhance the perspective of time dilation within the blackhole system. The next step for this research project is to find a constant path of time around the time dilation in the 3d grid.

Along with having to code for most of the day, Dr. Johnson has established a mandatory hacky sack session daily in order for us not to be stuck inside for all eight hours. Since the start of summer research, I believe it is safe to say that my hacky sacking skills have developed pretty well along with my fellow research partners within the Johnson lab. Dr. Johnson has made multiple connections with hacky sacking and life lessons which I believe is pretty common since I hear about them every year from past researchers who have worked with him. The one connection that will stick with me from hacky sacking is having the ability to stay consistent. This idea of consistency comes from the daily act of performing this activity. The more consistent someone is, the more development and growth they will see and receive. This is also true on the coding side of things. As I have stayed consistent with coding everyday at work, I have noticed a lot of development and improvement in this activity as well.

I have enjoyed my research experience so far with Dr. Johnson, and I expect this level of enjoyment to rise from this point on. Dr. Johnson has been my mentor, and advisor since my freshman year and we have always had a strong connection and understanding with one another. Working with Dr. Johnson has allowed me to expand my knowledge about physics and develop an abstract way of thinking. He also has the ability to teach in a versatile manner which allows students from any background to develop and understand the subject that is being taught. I’m very grateful for this opportunity to explore time dilation and special relativity since it will allow physicists like myself to be able to understand gravity, time, and space in an advanced manner. This research can potentially create paths for future space travel. Creating visual projections of these massive entities along with astronomical space data may dispense a plan for future celestial expeditions.

References

111Caltech. (2021). LIGO Lab: Caltech: MIT. Caltech. Retrieved July 6, 2022, from https://www.ligo.caltech.edu/

111Swinburne University. (n.d.). Schwarzschild radius: Cosmos. Schwarzschild Radius | COSMOS. Retrieved June 30, 2022, from https://astronomy.swin.edu.au/cosmos/S/Schwarzschild+Radius

111Voggel, K. T., Seth, A. C., Baumgardt, H., Husemann, B., Neumayer, N., Hilker, M., Pechetti, R., Mieske, S., Dumont, A., & Georgiev, I. (2022). First direct dynamical detection of a dual supermassive black hole system at sub-kiloparsec separation. Astronomy & Astrophysics, 658. https://doi.org/10.1051/0004-6361/202140827

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