Dark Matter #1: Galactic Rotation Curves

Vera Rubin – Researcher of Dark Matter

After the death of pioneering astronomer Vera Rubin, I suspect many more people have become intrigued by the term Dark Matter. Something else that often accompanies this term is Dark Energy. Both probably sound like mysterious or perhaps evil forces of nature to an ordinary person – at least I thought so, but then I learned Dark simply implied that it doesn’t interact with light.

A friend’s sister, a frequent reader of Passion for STEM and also a physics lover herself suggested that I write something on dark matter. At first, I thought this may be a difficult task (and I still do) because of the amount of uncertainty regarding what it actually is within the scientific community.

Everything we know that exists: us, all living things, all nonliving things, all the stars, galaxies, asteroids and cosmic dust collectively gather under one title – Baryonic Matter, and it accounts for less than 5% of the known Universe. The rest of the Universe under current calculation predictions is dark matter and dark energy, making up roughly 25% and 70% of the stuff in the Universe. This is rather overwhelming as what we know and experience is only less than a tiny fraction of reality. Since dark matter cannot be observed because it doesn’t interact with light, or as we say the electromagnetic force, there is no direct way of detecting it so how do physicists know that so much of the Universe’s mass is dark matter and not just ordinary matter like dust?

Evidence of dark matter comes from Galactic Rotation Curve calculations. Rotation curves allow us to calculate the quantity and location of mass within rotating galaxies. Let’s begin with our solar system. The Sun makes up roughly 99.8% of the entire mass of the Solar system, thus the majority of the mass is heavily concentrated at the centre. The orbital velocities of the eight planets vary from each other due to the different distances they are from the Sun suggesting the force of gravity on Neptune would be much weaker than of Jupiter which is closer and feels a stronger gravitational pull. This explains the variation of orbital periods in which for Jupiter is twelve years and Neptune is a hundred and sixty-five years. A graph with orbital velocities of all planets against the distance they are from the centre of mass can be plotted where we perceive a falling curve often called Keplerian Decline.

 

Line of Keplerian Decline

 

There is a steeply rising line within a small area of the graph in which the distance is close to zero. At zero distance the orbital speed is of course zero due to the strong force of gravity pulling the object in all directions. The Keplerian Decline behaviour is seen inside the distribution of mass with systems that follow Kepler’s laws like planets around a host star.

It would be reasonable to believe that some sort of Keplerian Decline curve would show up when we do a similar calculation with the Milky Way Galaxy, since the apparent distribution of mass for our galaxy resembles the mass distribution of the Solar System: the centre of the Milky Way is more compacted with mass than the outskirts which compared to the centre has little to no distribution of stars. However, something rather interesting is seen instead: not a falling but a flat rotation curve.

 

Bold line: Flat Rotation Curve, Dashed line: Theoretical Keplerian Decline

 

Like our previous graph, the behaviour is fairly similar at the centre, however instead of the gravitational pull getting weaker, the orbital velocities seem constantly high over a vast radii and the force of gravity remains strong even at the edge of the galaxy radius. The conclusion of the result is no matter how far out from the centre, everything is still inside the distribution of mass, therefore the mass continues to increase with the radius, this mass is Dark Matter and there’s a lot more of it than visible apparent matter. The exact result is seen with the majority of galaxies and exists in the form of a spherical halo rather than a disk like what we can see with the baryonic matter.

Well, dark matter doesn’t absorb, emit or reflect light thus interacts very weakly with ordinary matter making it close to impossible to detect and right now is only inferred by evidence such as galactic rotation curves and gravitational lensing. In the next post, I will discuss how Gravitational Lensing provides evidence for the existence of dark matter and the leading theories of what it may be.

P.S Apologies – the shortness of this post is due to the levels of school work I have at the moment, hopefully, this amount will decrease soon.

Author – Susan Chen

Susan is a 5th year high school student currently studying three STEM subjects at Scottish Higher level-Mathematics, Physics and Chemistry (Crash Course). She particularly loves ideas in cosmology and hopes to embark on an academic journey in the area of theoretical physics.