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# 12.17 Stellar Mass

Mass is a fundamental property of a star. Mass also turns out to be one of the most difficult stellar properties to measure. Astronomers estimate the mass of most stars based on a model of how stars evolve and radiate their energy. The starting point is our knowledge of the process of nuclear fusion that powers the star. We also know that hydrogen and helium are the two principal ingredients of the fusion process. A model of the power source allows us to predict how the temperature of the star varies in radius from the fusion core to the cooler photosphere. This prediction in turn allows us to hypothesize how density varies with radius. The final step is to mathematically convert the change of density with radius into a total mass. This sounds indirect, and it is! However, every step in the chain of logic is based on well-understood laws of physics.

Two supermassive stars orbiting one another in the open cluster Pismis 24. Click here for original source URL.

It is much simpler to calculate the mass of stars in orbit around each other. Then we can calculate stellar masses by an application of Kepler's Laws. Binary stars are quite common and this important way of measuring mass is often used by astronomers. After hundreds of different measurements, astronomers have deduced that stars range widely in mass from about a tenth to about a hundred times the mass of the Sun. The use of binaries to measure mass is crucial, because even if not all the stars we want to understand are in binary systems, the binaries allow the more indirect calculation to be checked.

What factors determine the range of possible star masses? Gravity can cause the collapse of gas clouds with an enormous range of masses. Why are there not enormous stars a thousand or more times the mass of the Sun? And why are there not pint-sized stars one hundredth the mass of the Sun or less? It turns out that physics limits the range of star masses.

Hertzsprung-Russell diagram showing color and size of stars. Click here for original source URL.

There are physical reasons for the mass limits on stars. If a cloud is dense and cool enough to contract but has less than about 8% of a solar mass, it will contract but never develop a high enough central pressure and temperature to reach a main sequence state (i.e. no extensive fusion of hydrogen). Proto stars from about 0.01 to 0.08 solar mass may heat up temporarily due to their gravitational contraction and may even develop a few feeble nuclear reactions (the first step in the proton-proton chain that make deuterium), but eventually they fade without settling on the main sequence for any appreciable time. Smaller objects, including even Jupiter-sized planets, also warm up temporarily due to their gravitational contraction; they may glow for a while in the infrared, but they fade before any nuclear reactions can start.

If the cloud is dense enough to contract but is more than about 200 solar masses, the contraction is violent and produces an extremely high central temperature and pressure. Under these conditions, so much energy is generated inside the new star that the star is very luminous and may blow itself apart almost immediately without spending much time on the main sequence. This rapid destruction leads to some of the most spectacular events in the night sky. In other words, very large gas clouds do collapse by gravity but the collapse is so violent that they're disrupted before a stable star is formed.