Layman’s Astronomy 1.02: Stars, Waves and Nuclear Fusion.

Important note: This article has been corrected. It suggested radiation was the main source of outward pressure in stars. As this is only the case in high mass stars, I’ve changed it to make it less misleading. The corrected paragraph is the first one under “What are stars made of?”

Introduction

This is the first of two posts on stars. This time, we’re going to introduce two fundamental forces1, electromagnetic radiation, and nuclear fusion; these are all concepts you’re going to need, as the next post will go over a star’s life in detail, looking at the different stages of evolution and why they occur.

A few words about waves

A wave is a periodic2 disturbance. Consider sea waves (before they reach shore): the up/down motion we observe3 is a periodic disturbance in the water.

The properties of a wave are determined by its frequency: how many oscillations it completes4 each second; a wave with a higher frequency carries more energy, and one with lower frequency carries less. This is inextricably linked to its wavelength: how much physical space is taken up by one complete oscillation – the two are inversely proportional5.

Click for a larger version

Starlight: Electromagnetic Radiation

Most waves have a medium: some sort of material they travel through (for example, in the sea analogy above, the medium is the water).  Electromagnetic wavesotherwise known as electromagnetic radiation (or, colloquially, light), are unique in that they are capable of travelling through a vacuum6 – they don’t require a medium at all7.  The range of frequencies an electromagnetic wave can take is called the Electromagnetic Spectrum. This encompasses Gamma rays, X-rays, Ultraviolet light, visible light, Infra-red, microwaves and radio-waves – despite referring to them as distinct things in everyday terms, they are in fact all the same physical phenomenon, we’ve simply named different parts of the spectrum for convenience. All this is much easier to understand summed up in one image, so I made one for you.

Click for a larger version

Stars emit electromagnetic radiation at all frequencies. Why? Find out in extra credits!

What are stars made of?

By NASA/Solar Dynamics Observatory (AIA) [Public domain], via Wikimedia Commons

By NASA/Solar Dynamics Observatory (AIA)

The traditional image of a star is one of an enormous fireball – but the truth is nothing’s actually burning in the everyday sense. Stars are very large8 clouds of (mostly Hydrogen) gas that get tremendously hot as a result of the nuclear fusion occurring in their cores. This means that the gas particles in the core are moving very quickly. The hotter, faster moving particles “push” outwards against the cooler, slower moving ones. This is known as thermal pressure. Additionally, these reactions create an enormous amount of electromagnetic radiation which, as it makes its way from the core to the surface, exerts extra outward pressure on the gas. In smaller stars, thermal pressure dominates, while radiation pressure becomes an important factor in large stars, and indeed places an upper limit on how large a star can be. We’ll look at this in a later post. These sources of pressure are the only thing preventing the entire cloud collapsing under gravity, and the balance between said forces (inward gravity and outward thermal and radiation pressure) is the driving mechanism behind most of a star’s evolution, which we’ll be covering next week. As it’s an important concept, I made you an animation to clear it up a bit.

GIF

Nuclear Fusion

I think it’s worth starting this section with a (very) brief crash course on atoms. Put simply, atoms consist of a nucleus made up of protons and neutrons, with a “cloud” of electrons orbiting it.

  • Protons are (relatively) large, heavy subatomic particles that carry a positive charge.
  • Neutrons are similar to protons in size, weight and makeup, but do not carry a charge.
  • Electrons are extremely small, extremely light fundamental particles9 that carry a negative charge.

The simplest example of fusion is straightforward: two nuclei collide and form a single larger one, releasing energy in the process. Where does this energy come from? On average, the nucleons10 in the new, larger nucleus are more tightly bound11 than they were in their original, smaller one.12 In nuclei, binding energy and mass are closely related: the new, more tightly bound nucleus’ mass is slightly lower than that of the two originals. This small bit of “missing” mass manifests itself as a release of energy, given by Einstein’s famous formula E=mc2. “c” here represents the speed of light, a relatively large number13, so the tiny difference in mass between the initial and final states results in an appreciable amount of energy being released.

This doesn’t explain why fusion only occurs in the cores of stars and not, say in your living room. In everyday life, one of the reasons we can’t walk through walls or go falling through the floor is due to the Electromagnetic Force: the electrons in the atoms that make up your skin (or clothes) repel those in the atoms that make up the wall/floor as they’re both negatively charged14. Without this, the universe as we know it wouldn’t exist15. It’s this electromagnetic repulsion that prevents fusion under normal circumstances: protons have a positive charge, so if two get too close together, they repel each other.

So why don’t atomic nucleii, which are made up of positive protons and neutral neutrons, get blown apart by the repulsive force between the protons? There’s something else pulling them together: The Strong Nuclear Force, a very short range, very strong16 attractive force. So, if protons get close enough together, the strong force prevents them from flying apart. The repulsive, electromagnetic “wall” they have to punch through to do this is called the Coulomb barrier. Imagine holding two like-charged magnets, each covered in velcro. Pushing them together is difficult, but if you can overcome the repulsion and get them close enough, they’ll stick.

The diagram below shows how the total or net force17 experienced by two charged particles changes as they get closer together. A net force above the horizontal axis represents repulsion, while one below represents attraction. Another way physicists sometimes think about this is as a well. Imagine pushing a ball up the red slope (going left). It’d take a lot of work, but once you got over the top, the ball would fall into the green section (the well, in this case), and require a large amount of energy to get out.

Coulomb diagram

Click for larger version

This is why fusion requires such high temperatures to “ignite”18: at the particle level, “temperature” is a measure of much kinetic energy19 particles have  – if you get the gas hot enough, some protons will have enough energy to get past the Coulomb barrier and fuse. The specifics of which particles are fusing into what, and how this affects the star’s behaviour, will be the subject of next week’s post.

Extra credits

Random walk: The Photon Disco

Imagine you’re in the middle of a crowded dance floor, and you want to reach the edge. You set out in a certain direction, but people keep bumping into you, and each time somebody does, you’re sent off in a new, different direction. This in physics is called a random walk.20

Radiation is produced in the core of the star (the outer layers aren’t hot enough to support fusion); this is the middle of our “dance floor”. As it travels outwards, it repeatedly interacts with the particles around it, each time being redirected randomly and losing some energy. The result of this is twofold: first, photons21 take a very long time to escape the star – they only travel ~1cm between collisions, resulting in a travel time of hundreds of thousands of years. For comparison, once it’s escaped the star, sunlight reaches the Earth in about 7 minutes! The second is that the amount of energy a photon escapes with, and therefore which part of the electromagnetic spectrum we classify it in, is also randomized22 – this is why stars emit radiation at all frequencies.

If (like me) you’re particularly nerdy, AstronomyCentre.org have a little Java app you can play with that simulates random walks. As it visualizes this concept very nicely, I’ve recorded a simulation and included it below. The red line represents the photon’s path out of the star. (Might take a little while to load)

GIF

Benji Sidi

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