Liliya Williams is a Professor of Astrophysics working on the distribution of dark matter throughout the Universe. Using luminous matter such as stars and gas, Williams can trace dark matter and find patterns in the distribution.
One of the goals of this research is to try to understand the nature of dark matter particle, one of the great unsolved mysteries of physics. Williams approach is to ask where is dark matter in order to understand what is dark matter.
Dark matter often appears in clumps in galaxies and is not evenly spread throughout the Universe. If the Dark Matter particle was “hot” or had energy, one would expect it to spread out like steam in an even pattern. If it was entirely “cold” and had no internal momenta and only mass, it would be very clumped. If it was a bit “warm” and had some internal momenta, the extent of the clumps would be larger. Physicists have compared these patterns to simulations in the past, but Williams is attempting to build a model with equations that will be able to analyze the dark matter distribution based on real physics of what is known about the particle.
Another diagnostic that Williams uses can tell whether the particles interact with themselves through anything other than gravity. “We know it interacts with gravity, because that’s how we know it exists.” Williams uses the analogy two clusters of galaxies moving toward each other in space, as they approach each other and collide, if there is any type of interaction apart from gravity, what you’d expect, is that the dark matter belonging to the smaller cluster will become somewhat detached from the ordinary matter, and it will be lagging behind. “Think of it as molasses, it’s hard for one entity to swim though molasses, and as a smaller clump swims through, it’s going to drag behind, moving through something less dense, and some is going to get pulled away.” Stars are going to swim right through, but dark matter will have some dragged away. Williams is able to detect this using gravitational lensing or the deflection of light from background sources. “We are looking though clusters of galaxies. You see the images, and based on the location of objects within the images we can reconstruct the mass, both the visible and the invisible.”
Taking what Williams has learned from these observations, she is building a model that will help her solve many of the unknown aspects of the physics of Dark Matter. “We think we have something that actually works.” If so this would represent a huge breakthrough since physicsts have been attempting to place mathematical limits on Dark matter since the 1950s. Williams’ model agrees with simulations, but the trick is making sure it agree with observations. “An observed system is never as clean as the one you can make in your computer.”
The third and most difficult test is to prove that the theoretical principals that you used to arrive at a conclusion are valid. “We are using the principal of maximum entropy, widely used in physics, but we are using a slightly modified version. “It hasn’t been proven that our specific version is valid. Proving that is challenging.” Williams says. When she has proved that her model is valid, then Williams’ can start making actual predictions based on her model.
To understand the importance of a mathematical model, Williams compares it to physicists knowledge of stars. “We can predict what the properties of stars are on the surface and deep inside as well, because we understand how the physics of gas works, we know the temperature at the center, the density, and we know its structure. We don’t have an equivalent knowledge about the distribution of dark matter. I can make equations about the sun and solve them. I can not for dark matter. “