A Goddess Spurned and the Fate of the Sun

by Nicholas Mee on September 25, 2020

Taurus the Bull is one of the most prominent constellations in the night sky. The distinctive V-shaped head of the bull, on the right in the image below, is formed of the stars of the Hyades open cluster and the red giant Aldebaran is the bull’s angry red eye. To the left of Taurus is the magnificent constellation Orion the Hunter whose shoulder is the red supergiant Betelgeuse. 

Orion the Hunter and Taurus the Bull.

Mythological tales have been associated with these constellations since the earliest civilisations. The Epic of Gilgamesh, the oldest surviving masterpiece of world literature, was woven together from ancient Sumerian stories told over four thousand years ago. One such story tells of Ishtar, the Goddess of Love, identified with the planet Venus, and her desire for the mighty warrior king Gilgamesh. But her attempts at seduction fail and her advances are spurned. So the enraged goddess wreaks her revenge, sending the Bull of Heaven to strike Gilgamesh down. Undaunted and fearless, the noble Gilgamesh slays the bull with the help of his friend Enkidu. While Enkidu holds the bull by its tail, Gilgamesh plunges his sword between the bull’s horns into the back of its neck, as depicted below.

A clay impression of an Assyrian cylinder seal dating to the 7th or 8th century B.C. On the left Enkidu wields an axe and holds the Bull of Heaven by its tail. On the right Gilgamesh, king of Uruk, plunges his swords between the bull’s horns.

There can be little doubt that the Bull of Heaven represents the constellation Taurus, while Gilgamesh is sometimes identified with Orion, which seems reasonable given the proximity of these two constellations in the night sky.

The distinctive V-shaped head of Taurus the Bull. The red giant star Aldebaran is the bull’s angry red eye. Credit: Wikisky.

The bull’s eye Aldebaran was once a star much like the Sun. It gives us a good idea of how the Sun will appear in the distant future. 

The Future Sun

So how will the Sun evolve and what is its ultimate fate?

Within the Sun’s core hydrogen nuclei are gradually fusing to form helium nuclei, releasing a steady stream of energy. The flow of thermal energy from the nuclear furnace supports a star against its tendency to collapse under gravity. This balance is maintained for as long as the nuclear fuel holds out, which in the case of the Sun is around ten billion years. Currently, the Sun is nearly half way through its allotted time span.

The temperature of the Sun’s core is about sixteen million degrees. As the hydrogen fuel is depleted the star’s core gradually contracts and this raises its temperature and increases the star’s luminosity. The Sun is brighter today than it was billions of years ago and it will continue to brighten very slowly over the coming billions of years.

Eventually all the hydrogen in the core will be converted into helium, and with no hydrogen nuclear fuel left, the fusion reactions will cease, energy generation will stop and gravitational collapse can no longer be resisted. The helium core now contracts dramatically releasing gravitational binding energy, which raises its temperature significantly and as the energy escapes through the star’s outer layers it inflates into a red giant.

In around five billion years time the Sun will swell up into a bloated red giant, a vast glowing ball of gas millions of kilometres in diameter, to look very much like Aldebaran does today. Aldebaran has a bit more mass than the Sun (about 16% more), but has already used up the hydrogen in its core and swollen to enormous dimensions. Its outer layers are cooler than the Sun’s and this is why it shines with a reddish hue.

Aldebaran has a diameter of forty million miles or sixty million kilometres, which is over forty times the diameter of the Sun. Because of its great size, Aldebaran is over 500 times as bright as the Sun. Even at a distance of sixty-five light years it is among the brightest stars in the night sky. The Sun would be invisible to the naked eye at such a distance.

From left to right: Earth, Jupiter, the Sun, Aldebaran. Credit: Nicholas Mee.

The image above illustrates just how enormous Aldebaran is. From left to right we have the Earth, which is just visible as a small dot, then Jupiter, whose diameter is over ten times that of the Earth, then the Sun, with a diameter ten times that of Jupiter and finally the red giant Aldebaran, with a diameter over forty times that of the Sun. (You might need to click the image and enlarge it to see the Earth.)

Triple Alpha

Deep within a red giant the core continues to contract until a new round of fusion reactions kicks in. The helium created in the star’s hydrogen-fusing phase will become the nuclear fuel for a new round of fusion reactions. Atomic nuclei carry a positive electric charge due to the protons that they contain. This produces an electrostatic repulsion that prevents nuclei approaching close enough to fuse unless they are smashed together with great ferocity at very high temperatures. Hydrogen nuclei carry a single positive charge, but helium nuclei have a positive charge of two, so there is four times the electrostatic repulsion between two helium nuclei as between two hydrogen nuclei. Consequently, the temperature required for helium fusion is much higher than for hydrogen fusion.

There are no viable nuclei with atomic mass 5 or 8, so no energy is available from fusing a proton and a helium-4 nucleus or two helium-4 nuclei. Therefore, further fusion requires an essentially simultaneous collision of three helium-4 nuclei to form a carbon-12 nucleus. This is known as the triple alpha process because the helium nucleus is identical to an alpha particle. Such reactions are only possible when the temperature of the contracting core reaches an incredible 100 million degrees.

The Triple Alpha Process.

Some of the carbon-12 nuclei formed through the triple alpha process undergo a further fusion reaction with a helium-4 nucleus to form oxygen-16 nuclei. So within the core of a red giant helium is steadily converted into carbon and oxygen.

The helium-fusing phase of a star’s life is much shorter than its hydrogen-fusing phase. This is because helium fusion releases far less energy than hydrogen fusion and also, as the star has bloated into a much more luminous red giant, it is radiating energy away far more rapidly. The Sun’s helium-fusing phase might last a few hundred million years. In much more massive stars this phase can be very much shorter.

A Diamond in the Sky

The Eskimo Nebula. Credit: NASA, ESA, Andrew Fruchter (STScI), and the ERO team (STScI + ST-ECF).

So what happens when the helium nuclear fuel runs out? In a star like the Sun, the carbon-oxygen core contracts and the temperature rises again generating a surge of radiation that blasts away the already distended envelope of the red giant. The blazing hot core emerges as a white dwarf whose radiation sweeps the outer layers of the giant star off into space, illuminating and exciting the expanding gas clouds to create a planetary nebula. (These nebulae were so named because they sometimes look similar to planets through a low-power telescope, but they are totally different objects and have nothing to do with planets.)

Striking images of planetary nebulae have been produced by large telescopes such as the Hubble Space Telescope. The white dwarf can often be spotted as a brilliant dot in the centre of the nebula, as in the example shown here. Planetary nebulae do not last very long by astronomical standards. Within ten thousand years or so the gas clouds disperse and the show is over. The white dwarf is now just the dying ember of a dead star steadily radiating its heat into space and gradually cooling down over the course of billions of years. 

White dwarfs might be extremely hot, but they are very faint compared to ordinary stars. The white dwarf is the compressed core of a dead star and is similar in size to the Earth, so the mass of a star is squeezed into a volume comparable to that of a planet. The density of a white dwarf is at least a million times that of water. If we scooped out a spoonful of white dwarf material and transported it to Earth, it would weigh around ten tonnes.

The nearest white dwarf is about eight and a half light years away. It is the companion of Sirius, the brightest star in the night sky. Sirius is the principal star of Canis Major, the Big Dog, one of Orion’s hunting dogs, and can be seen on the far left in the image below. 

Sirius is the bright star to the left of Orion. Credit: Odd Høydalsvik.

Sirius A, the star we can see, and Sirius B, its white dwarf companion, orbit each other every fifty years or so. Sirius is known as the Dog Star, so Sirius B is sometimes nicknamed the Pup. 

Sirius A is the bright star in this image, its companion the white dwarf Sirius B is the small dot by the bottom left spike. Credit: NASA, ESA, H. Bond (STScI), and M. Barstow.

Although Sirius B has almost exactly the same mass as the Sun, it is only marginally bigger than the Earth. This makes it far too faint to see with the naked eye. It is notoriously difficult to spot even with a telescope. Sirius B is the small dot by the bottom left spike in this image of Sirius. (The diffraction spikes are optical artefacts of the lens system.)

Another look at the Earth, Jupiter, the Sun and Aldebaran in the image above gives us an idea of the great differences in size between a white dwarf such as Sirius B, an ordinary star such as the Sun and a red giant. Sirius B is similar in size to the Earth, but it has about one thousand times the mass of Jupiter. And despite the great disparities in size, Sirius B, the Sun and the red giant Aldebaran all have about the same mass. Billions of years from now the Sun will become a blazing-hot planet-sized cinder composed of carbon and oxygen, similar Sirius B.

And what of Betelgeuse, the shoulder of Orion? Betelgeuse is estimated to be at least fifteen times the mass of the Sun. It has swollen to an extraordinary size and is classed as a red supergiant. A much more dramatic future awaits this mighty star. I will discuss its fate in another blog post.

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