Binary Blackhole #1 Over Time
Although black holes likely exist abundantly in the universe, they are notoriously hard to see hence why there is not a lot of data to work with. As a result, astronomers use computer simulations to help future observatories develop more precision and therefore spot more mergers in future missions. Specifically, we use sets of equations that are either too complex or just need to be repeated a substantial amount of times and run them in python scripts to create a vast amount of data. With this data set, we are then able to create tables and plots, which helps us illustrate how the black holes affect each other in the system. To find the time at which they collide we look at the properties of both black holes that lead up to the merging event.
Black holes are a region of spacetime where gravity is so strong that nothing, not even particles, electromagnetic radiation, or even light could escape. Since black holes distort space-time it's hard to study their phenomenon. Since black holes emit an enormous amount of gravitational waves we use observatories (LIGOS) to detect these gravitational waves. The properties of the black holes get distorted in places like the accretion disk. In this instance, we are using the gravitational waves because of their consistency when applied to calculations. The main processes that lead to the formation of binary black holes are the isolated evolution of massive binary stars. The physics of core-collapse supernovae and the process of planetary envelopment are two of the main sources of uncertainty about this formation channel. Alternatively, two black holes can form a binary by dynamic encounters in a dense star cluster. The theory behind the formation of black holes is based on general relativity regarding sufficiently compact mass. If the star is massive enough it can collapse directly to form a black hole without a supernova explosion in less than half a second. A black hole can also form via the collapse of a neutron star into a black hole if the neutron star accretes so much material from a nearby companion star, or merges with the companion star that it gets pushed over the neutron star mass limit and collapses to become a black hole. This process could take a long time, maybe a million years or more depending on how quickly it accretes the material. Once the neutron star is over the mass limit, which is at a mass of about 3 solar masses, the collapse into a black hole occurs in less than a second.
Binary Black holes (BBH’s) are simply two black holes orbiting each other. They have a lifecycle that’s three stages, Inspiral, Merger, Ringdown. During this process, these black holes are always emitting gravitational waves which is how we “see” all of this. Inspiral is the first stage, where there is a gradually shrinking orbit with weak gravitational waves. When the black holes are close, the speed increases and gravitational wave emission increases which also causes the orbit to then shrink rapidly. Finally, the orbit plunges to the point where the two Black holes meet. This is the Merger, where the gravitational wave emission peaks. Right after, the last and most visual event forms. The Ringdown, the now single black hole, forms a sphere of photons because of the strength of gravity.
Below is a graph demonstrating how the recorded gravitational waves are being emitted throughout the lifecycle of a binary black hole system.
The data set we start with has Eccentricity(e)¹ ², Distance (AU)¹ ² ³, Masses in solar masses¹ ² ³, Effective Spin (chi)¹ ² ³, and maximum time. After we put these through python code we get pages of data with 20 columns. Time, e¹(1-3), j²(1-3),e²(1-3),j²(1-3), S¹(1-3), S²(1-3), a¹ Based on the initial set of data we can manipulate it and find how changing one variable changes the outcomes. Using the data, graphs were made by making the intensity of eccentricity vectors to help determine how close the black hole would orbit over time.
This is a vector graph showing the intensity of eccentricity. As you can see by the data, the intensity of the eccentricity increases and decreases drastically. This means that their orbit is ovular because as you can see it has high ups and low downs. The ups being when they are farthest and the downs being when they are the closest. The second black hole also follows the same curve which is expected but at a lower intensity of about half which shows a difference in mass.
The second black hole also follows the same curve which is expected but at a lower intensity of about half which shows a difference in mass.
When the eccentricity reaches certain points it has an effect on the orbital period and the semi-major axis because the orbit changes as the black holes gravitational waves act on each other.
It seems like the gravitational waves emitted by both black holes have an effect on the orbital path which affects both the eccentricity and the semi-major axis along with it.
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Thanks to the CIERA REU program at Northwestern University, and thanks to all staff here helping not only us but much more conduct research during the 2021 Summer. To end, a special thanks goes to Giacomo Fragione and Frederic A. Rasio for their role as advisors and meteors during this time. This material is based upon work supported by the National Science Foundation under Grant No. AST-1757792.