Unveiling the dark matter: Computational methods

In continuation of previous blog The darkness of the ‘Dark Matter’

Here I discuss some computational physics methods that may sound interesting to you, in terms of dark matter understating and discovery. Though this should involve a lot of alien kind of equations, I try to minimize their use in the current story. 

Cosmologists and physicists are hunting together for the elusive dark matter thought to pervade in the universe. How do you think they look for something that cannot  be seen? How do they model the effect of something they cannot percieve ordinarily? Let us start with a simple illustration. Imagine a heavier body and two lighter one revolving around the former in an elliptical orbit. On applying newtonian mechanics operating therein we can calculate the forces acting at an instant and also the orbital motion. Here we need to update the forces operating, with the changes in distances during their motion.  The calculation is simple as of now, but if we include more bodies, calculations get complicated. To make it appear closer to a galaxy make the centre heavier and the structure an non planar one together with an increase in density on moving towards the centre from the edge.

Such model can be implemented as a computer program and simulated to analyze the motion and evolution of galaxy over time. Ostriker and Pebbles tried such simulation called ‘N-body simulation’ in 1979. They tried to compute all the interacting forces and motion in a model consisting of mass points structured like a galaxy. They astonishingly found that such a system tends to a collapses to a bar shaped dense core in the galaxy model. But in such simulation, if a uniformly distributed mass is added in certain amount, the galactic model tends to show more stability depending on the mass added. This mathematically proves that there is some hidden mass in the galaxy accounting for the shape we observe an also gives an estimate for their mass. However, such simulation have evolved a lot from their ancestors with advent of technology and knowledge. (For those who are interested a possible pseudocode is in figure 1a)

Figure 1a (Left) showing a basic pseudocode for N-body simulation and on right showing the expected velocities (A) and actual velocities (B) at distances from the centre of the galaxy.

There are other computational method which further give the proof in favor of dark matter, but discussing all these will be beyond the scope of this story. Now lets talk about the modeling such dark matter. Modeling gives a better understanding of behavior, nature and interaction of dark matter.  There are few theories about the dark matter viz. cold dark matter, hot dark matter and warm dark matter as mentioned in the previous blog. Taking up the case of cold dark matter the particles move at a slow speed. The slow speed allows the individual galaxies to clump together, whereas in case of hot dark matter the high speed of particles fails to explain the theory of galactic formation. The obvious question that can come to you is why? The reason is very simple. The particles in hot dark matter are ultralight and therefore do not come up with enough gravitational force to explain the formation of galaxies. The cold dark matter on the other hand talks about heavier particles that can explain the the unexplained ones.

To model this, the N-body simulation can be extended with the particle velocity and mass parameters. Thus in our N-body simulations we consider the relative mass of particles that we uniformly add to our galactic system. To simulate a cold dark matter system we add heavier particles and for hot dark matter we add lighter particles. We also consider the velocities of the particles here and run the simulation. The simulation will show how the bodies in the system clump together. This simulation has been tried by many physicist. The model at the University of Illinois, consisted of hot dark matter, cold dark matter and baryons (a mixed model). This model seemed to match the observed distribution, both in terms of temperature and luminosity. But there are numerous possibilities the work still on to model the dark matter.

* I do not mention the bibliographic references here in the blog just to make it shorter, it can be provided if needed. 

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