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Star Stories
Tales from the dark skies of Tenerife, brought to you by the guides of the stars!
Sirius Star and White Dwarfs.
By Stargazing Tenerife team, your guide to the dark skies of Tenerife.

Welcome everyone to our new topic in the blog section.  We are going to talk about The Violent Universe.  We start today talking about a star we have been observing on tour recently, Sirius.  Be warned there is a lot of science in here but hopefully I have kept the geeky math bits to a minimum.  In the early 19th century, Bessell used the world’s best telescope (designed by Fraunhofer) to discover that the star Sirius was wobbling backwards and forwards every 50 years. He concluded that it must have a massive but invisible companion.  He worked out that the mass of this companion was roughly 1 solar mass.  50 years later, the companion (known as Sirius B) was seen for the first time.  Curiously, it is around 1000 times fainter than the main star Sirius (now called Sirius A), despite having half its mass.  It was initially assumed that its faintness must be due to its cool temperature, but early in the 20th century, spectroscopy showed that Sirius B was extremely hot, 2.5 times hotter than Sirius A.  If it was so hot, why was it so small?  The only possibility was if it was extremely small.  Using the Stefan-Boltzman equation we were able to work out its size from the luminosities, which comes out as around 6000 km for Sirius B, i.e. slightly smaller than the Earth! Despite weighing as much as the Sun.  Sirius B is so small and so heavy that the force of gravity near its surface must be enormous. Using Newtons law of gravity it was possible to estimate the pressure in the centre of a star using a bit of calculus, if we assume that the density of the star is constant. In this case, we found the pressure gradient by balancing forces on a cylinder of star material (the pressure on the inside must exceed the pressure on the outside by enough to balance gravity), using the calculations, we could see that the pressure in the centre of Sirius B is vastly greater than that in the middle of the Sun.  All of which leaves us with two problems.  Firstly, given that Sirius B is much denser than the Sun, and hotter two, it should be doing nuclear fusion at a much faster rate than the Sun.  But it is clearly not – or it would be more luminous than the Sun.  So why isn’t it undergoing fusion?  Secondly, the gravity on Sirius B is so intense that no material could withstand it.  So why doesn’t its surface collapse inwards?  In the Sun, heat from fusion stops this collapse.  But there is no such heat in Sirius B – so what is holding its surface up?

“Astronomy compels the soul to look upwards and leads us from this world for another.”

– Plato

To explain how white dwarf stars can support their immense pressure, we need quantum mechanics. The first clues to quantum mechanics came from the discovery of emission- and absorption-lines in gas spectra. Why do gasses emit and absorb at particular narrow wavelengths and not over a wide range of wavelengths? P ρ pc = πG 2 3 ρ2R2 One possible answer came from an analogy with sound waves. Musical instruments also emit sound waves only at particular narrow frequencies, not at all frequencies. This is because the sound in generated by waves (string vibrations in the case of a guitar) but these waves are confined. In the case of a guitar, the waves must have zero amplitude at both ends of the string. This means that only certain discrete wavelengths are allowed (the harmonics).  If the electrons in an atom were actually waves, then the fact that they are trapped in the atom would confine them, and you would get certain distinct wavelengths (energy levels), just like you do for sound waves on a guitar string. But how could an electron be a wave? We know that if you fire a beam of electrons at a phosphorescent plate, you get a series of discrete pin-point flashes, not a spread-out wave pattern. That sounds like a particle, not a wave.  The very strange answer proposed by quantum mechanics is that electrons (and photons, protons, and pretty much everything else) are actually probability waves. If (and only if) you don’t measure exact positions, then electrons behave like waves, and do all the wave-like things, such as have discrete energy levels, interfere with themselves, diffract etc. But if you make a precise position measurement (say by having a phosphorescent plate), the “wave function collapses” and all of a sudden the electron has a definite position. What is this position? Well – it’s random, but the odds of it being in a particular region are proportional to the square of the amplitude of the probability wave at that location.  Two more quantum-mechanics laws:* *The Pauli Exclusion Principle. No two fermions (particles like electrons and neutrons) can be in the same state. So you can’t have all the 26 electrons in an iron atom in the ground state – once it fills up, further electrons have to go into progressively higher energy levels.

*The Heisenberg Uncertainty Principle. So, the more accurately you know one of these pair of variables, the less accurately you can know the other.

In the core of a white dwarf you have vast numbers of electrons compressed into a small space. Because of the Pauli exclusion principle, they cannot share space but must be in different states. This means each is confined into a small volume, which means (because of the Heisenberg uncertainty principle) that their momenta become quite uncertain (and hence large on average). Because they have large momenta, the electrons bash into things quite hard and fast, so they exert quite a strong pressure – the so-called “Degeneracy pressure”.

Using the degeneracy pressure and the central pressure we are able to determine the mass of a white dwarf.  Remarkably, this equation, based on huge approximations and basic physics, gets the size of a white dwarf correct to within a factor of two!

So white dwarfs are held up by amazing combination of gravity and quantum mechanics. But that still leaves the problem of how they formed in the first place, and why they are made of something other than Hydrogen and Helium, despite the fact that the universe is overwhelming made of Hydrogen and Helium. Most likely, white dwarfs start off as the cores of normal stars, like our Sun. In its centre, the star ends up burning hydrogen and helium to form carbon and oxygen. Eventually, the star swells up to become a red giant. Red giants are so large and low density that they only have a tenuous hold on their outer layers, and eventually most of the gas blows away into space, producing a planetary nebula, surrounding the naked core (a carbon-oxygen white dwarf).

How can white dwarfs be violent? The first clue came from the 19th century discovery of certain stars that occasionally become 100 times brighter – socalled “Dwarf Novae”. When spectra were first taken of these stars, it was found that they showed emission lines when faint, but during their explosions, they showed absorption lines.

For the next blog we will look at the different types of novae.  I look forward to explaining the processes involved in this remarkable stars!

So until next time, keep looking up in wonder at our universe not forgetting that even the best minds in the world are still learning on a daily basis.

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