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How large would a bucket of water have to be to put out the sun?

Category: Space
Published: June 30, 2015

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No amount of water thrown on the sun would cause it to go out. Instead, any amount of water would cause the sun to burn even more. The burning of the sun is nuclear fusion, not chemical combustion. Campfires and candle flames are examples of chemical combustion. In combustion, the electronic bonds between atoms are rearranged without the nuclei of the atoms themselves changing at all. When you throw water on a campfire, the water absorbs heat from the fuel, cooling it to the point that the reaction cannot be sustained. Why are hot temperatures required for combustion? Before new chemical bonds can be formed (which is what releases all the energy that makes a fire bright and hot), the existing chemical bonds between the atoms must first be broken. It takes energy to break apart existing bonds. In a self-sustaining reaction such as combustion, the most common source of this energy is thermal energy due to high temperature. Note that the water thrown on a campfire also puts it out by smothering it, i.e. by preventing oxygen in the air from reaching the wood and taking part in the reaction.

Public Domain Image, source: Christopher S. Baird.

The sun is not a giant campfire. Rather, the sun is more similar to a giant hydrogen bomb going off. In nuclear fusion, the nuclei of atoms are pushed together so hard that they stick together and become new, heavier nuclei. While high temperature certainly plays a role in knocking nuclei close enough together that they experience fusion, the ultimate driver of nuclear fusion in stars is high pressure. To be more accurate, temperature and pressure are intimately linked, but it is ultimately the pressure in the star that creates the high temperature that drives fusion. This high pressure is caused by the star's own gravity. The more mass an object has, the more gravity it creates. This gravity pulls on everything, including the object itself. Simply put, a star is so massive that it gravitationally crushes itself to the point that its atoms fuse together.

Throwing water on the sun would simply increase the sun's mass, which would increase its gravity. This stronger gravity would crush the sun even more, leading to more nuclear fusion. In general, the larger the mass of the star, the more nuclear fusion it experiences and the more energy it pumps out into space per second. It's not just that more mass means more atoms to fuse together. More mass also means more gravity to crush the star more tightly together and thereby increase the fusion in the material that was already there. For this reason, the total energy output of a star per second (its luminosity L) is not usually linearly proportional to its mass M. In fact, for a star that has a mass near that of our sun, its energy output is proportional to the fourth power of its mass. This means that doubling the mass of the star will cause it to output 16 times more energy per second and shine 16 times brighter! For this reason, throwing water on the sun would just cause it to burn stronger and brighter. Note that the sun is so gigantic that throwing a human-sized bucket of water on the sun would do effectively nothing. In order to get the sun to increase its luminosity by just one percent, we would have to throw on an amount of water that is equivalent in mass to about 800 earths. Simply put, the sun is so enormous that we puny humans can't do anything to change it much.

Interestingly, for supermassive stars (twenty times as massive as our sun or more), the relationship between luminosity and mass is linear. This is because radiation pressure becomes significant. When a bit of light reflects off of a surface, it exerts a very small push on the surface. For this reason, a steady stream of light exerts a steady pressure on a surface it is hitting, called radiation pressure. In a star, the light generated inside the star hits the outer layers of the star and exerts on these layers an outwards push. In this way, the outward radiation pressure can counteract the inward pressure due to gravity along with the outward gas pressure. For stars that have about the same mass as our sun, the radiation pressure is too small to have much of an effect, and gas pressure is what balances out gravitational pressure. However, in supermassive stars, there is so much light generated in the core that the light's outward pressure becomes significant. The radiation pressure becomes the dominant outwards pressure that cancels gravity, and not the gas pressure. Adding more mass to such a star does not significantly increase the fusion of the material that was already there. It simply adds more atoms to participate in the fusion. This is why the luminosity-mass relation for supermassive stars is linear and not quartic.

There is an important distinction between normal stars and supermassive stars. For stars about the mass of our sun, adding mass has the dominant effect of increasing gravity. Therefore, no matter what you throw on such stars, the effect will be about the same. Throwing a hundred earth masses of water on the sun will have about the same effect as throwing on a hundred earth masses of gasoline. Although gasoline experiences chemical combustion better than water, nuclear fusion is so much more powerful than combustion that combustion effects can be completely ignored in the sun. In contrast, for supermassive stars, adding mass has two significant effects: increasing the overall gravity and providing more atoms to fuse. In these huge stars, radiation pressure does such a good job of counteracting gravity that the effect of providing more atoms to fuse becomes significant in comparison. Therefore, throwing a hundred earth masses of hydrogen (which fuses really well) on a supermassive star will increase its brightness much more than throwing on a hundred earth masses of uranium (which fuses very poorly). Again, it's the nuclear composition of the atoms that you are throwing on that is important and not the chemical properties, since chemical effects are dwarfed by nuclear effects in stars.

Topics: combustion, gravity, luminosity, mass, nuclear fusion, reaction, star, sun, supermassive