mass - How do we know the masses of single stars?

I have recently read that we can only know the masses of stars in binary systems, because we use Kepler's third law to indirectly measure the mass. However, it is not hard to find measurements for the mass of stars not in binary systems. So how is the mass of these stars determined?

Answer

The Hertzsprung–Russell diagram is the key to determining masses of individual stars. For stars on the main sequence, their properties are essentially determined by their mass. Age and metallicity are also interrelated factors, but of considerably less importance than mass. That is, if you tell me the mass of a star on the main sequence, I can tell you its temperature, luminosity, radius, etc., to reasonably good accuracy. This means that if you are able to measure the luminosity and temperature of a star, I can put it on a Hertzsprung–Russell diagram, and tell you how massive it is. Of course, calibrating this relationship in the first place required measuring the masses of stars directly using stars in binary systems, as you mention.

[Edit: I did not notice that the star you linked to specifically was Arcturus, for which this does not directly apply.] For a giant like Arcturus, masses are often determined in a bit more complicated manner. The Hertzsprung–Russell diagram still provides a guide, in developing models of stellar evolution that can produce the observed patterns of non-main-sequence stars on the HR diagram. As Arcturus is no longer on the main sequence, these stellar evolution models are used to find the mass that produces the combination of temperature, luminosity, and radius observed, from which a mass can be inferred.