How old are small stars?
How old are small stars?
The answer depends on what you mean by small stars. I will explore two different interpretations here.
Stars like our Sun are powered by nuclear fusion of hydrogen into helium in their cores. This phase of evolution is called the “main sequence” because it is the longest part of a star’s lifetime. Stars on the main sequence span a large range of masses from some 40 times the mass of the Sun down to about 10% of the Sun’s mass. The more massive stars are bigger (take up more space) and the less massive stars are smaller. Let’s call the stars at the low-mass end of the main sequence the “small stars” (technical name: M dwarf stars).
The properties of stars on the main sequence are governed mostly by mass. Small stars are less massive (made up of less matter), so they have less nuclear fuel for the hydrogen to helium fusion that powers them. However, the gravitational force that holds them together is not as strong because they don’t have as much mass. The weaker gravitational pull causes as correspondingly lower temperature in the stellar interior. The rate of nuclear fusion in the core is very sensitive to the local temperature, proceeding very much slower at the lower temperatures of M dwarf stars. So even though there is less nuclear fuel available in small stars, that fuel is used up so much slower that the small stars actually live longer than larger, more massive stars! (A common analogy is to a very fuel efficient (e.g., hydrid) car with a smaller gas tank. Even though the gas tank doesn’t hold as much fuel, the car is so efficient that it can travel longer before needing a refill than a less efficient vehicle with a slightly larger tank.)
Stars with masses similar to the Sun have main sequence lifetimes of around 10 billion years. Down at the low mass end of the main sequence, stars will stably burn hydrogen into helium for trillions of years! But consider that the Milky Way galaxy is only around 13.6 billion year old. The low-mass stars in the Milky Way have not had nearly enough time to exhaust their fuel supplies. The M dwarf stars that formed early in the history of the Galaxy are close to 13.6 billion years old and still puttering along. M dwarf stars that formed more recently (there is ongoing star formation in the Milky Way) are younger. There are some relationships between the observed rotation periods and amount of stellar activity (like stellar flares) of M dwarf stars and their ages that make it possible to constrain ages of individual stars within this range.
You can find a simple calculator for main sequence lifetimes at this link.
But but but, there are stars even smaller than M dwarfs. The most common on these are the white dwarf stars. Since stars more massive than our Sun have main sequence lifetimes shorter than the age of the Galaxy, many of them have already run out of all fuel for nuclear burning. At this point, most stars shed their outer layers as beautiful planetary nebulae (which have nothing to do with planets!), while their cores contract under gravity to become hot dense objects called white dwarfs. Without the energy from nuclear fusion puffing the star up against the star’s gravitational pull anymore, the star gets compressed down to roughly the size of the Earth. White dwarfs evolve very differently from other stars. They start off very hot (hundreds of thousands of degrees!) and then cool off by radiating away energy as light and neutrinos. We can determine the temperatures of individual white dwarf stars by measuring their spectra or colors (hotter stars are bluer, cooler stars are redder). Since white dwarfs with lower temperatures (redder colors) have been cooling off for longer, determining ages of individual white dwarfs is fairly straightforward. This provides an independent method for determining the age of the Milky Way galaxy or other stellar populations: they’re only as old as their coolest white dwarfs. We call the field of determining the ages of stellar populations “cosmochronology.”
For a more detailed description of white dwarf cosmochronology, see this summary article on the seminal work of Winget et al. (1987).