# How To Weigh A Star

In Stars by Brian Koberlein0 Comments

The life of a star is determined by its mass. Large stars live short lives that end in supernova explosions, while smaller stars live longer, ending their lives as white dwarfs. Knowing the mass of a star helps us understand not only the life of a star, but the evolution of galaxies. But determining the mass of a star can be difficult.

The best way to weigh a star is to measure how strongly it pulls on another star. If two stars are a binary pair, the speed at which they orbit each other is governed by the gravitational pull between them. By measuring their orbits over time, we can determine the mass of each star. But many stars are solitary. The nearest star to them can be light years away, and its gravitational pull on these stars is too small to measure. So we need another way to determine its mass.

One alternative is to look at the temperature of a star. Larger mass stars burn hotter than smaller ones, so the higher a star’s temperature, the greater its mass. But this has a few downsides. For one, this relation between stellar temperature and mass is only true for main sequence stars. For another, stars get slightly hotter as they age. An old star with the Sun’s mass has a higher temperature than a young solar mass star.

A new way to measure a star’s mass looks at its surface gravity. A ball dropped near the surface of the Earth will fall at a rate of about 9.8 m/s2. This is Earth’s surface gravity. Far away from the Earth gravity is weaker. The Moon, for example, “falls” around the Earth at  only about 2.7 mm/s2. The surface gravity of a planet or star depends upon its mass and its diameter. By determining the distance to a star, we can use its apparent size to determine its diameter. Determining surface gravity is a bit more tricky.

If you bounce a ball against the ground, it takes a certain amount of time to rise to its maximum height and fall back to the ground. That time depends in part on surface gravity. If you were to bounce a ball in the same way on Mars, the time between bounces would be longer, because Mars has a smaller surface gravity. We can’t bounce balls on a star, but there are surface fluctuations that rise and fall. The surface of a star often churns a bit like boiling water, creating rising and falling pockets known as granules. The rate at which these granules rise and fall is determined by the star’s surface gravity. So by measuring the rate at which a star flickers in tiny ways, we can determine a star’s mass.

A recent paper looked at the observational limits of data from GAIA (currently gathering data) and TESS (planned to launch in March). They found that GAIA could determine a star’s mass give or take 25%, and TESS should be able to determine stellar mass to within 10%. Since these satellites will observe millions of stars, this could become a powerful tool in the study of stars.

Paper: Keivan G. Stassun, et al. Empirical, Accurate Masses and Radii of Single Stars with TESS and GaiaarXiv:1710.01460 (2017)