# What affects the evolution curve of a star's luminosity as a function of time?

Take a star of a given mass (say $1.0\ \mathrm{M_{\odot}}$ or $1.1\ \mathrm{M_{\odot}}$), what affects the star's luminosity as a function of time and how much? (metallicity?, rotation?)

It seems to me that stellar evolution is basically set by the laws of physics; if we know certain parameters (e.g., mass). Of course, that's the trick since we can't directly measure the mass of a star with no companion(s).

I have run across a few issues with published values being in conflict. For example, this study gives the age of Zeta Tucanae as being about $2.1-3.8\ \mathrm{Gyr}$. However, mass/radius/luminosity is given as 0.99/1.08/1.26 relative to sun (Wikipedia sources). If you look at an evolutionary plot of the Sun something is wrong here. (I'm guessing mass.) By the way [Fe/H] is given as -0.18.

• It's not the metallicity. A star's luminosity depends on its size and its temperature. As a star gets older, these change, especially when it enters its giant stage. – Phiteros Apr 24 '17 at 1:02
• @Phiteros What makes you think metallicity won't play a role in this? Every feature of a star is tied to every other feature by physics. – zephyr Apr 24 '17 at 1:52
• Are you asking specifically about stars on the main sequence or stars in their post-main sequence phases? Because those are drastically different answers. – zephyr Apr 24 '17 at 1:58
• Not nearly as much as the temperature and size. Specifically, the luminosity of a star follows the Stefan-Boltzmann law: $F=\sigma T^4$. That's also where the size comes into play: $F=\frac{L}{4\pi R^2}$. – Phiteros Apr 24 '17 at 6:24
• @Phiteros You are correct, but that's only a first order answer. As Rob says in his answer, if you dig down a bit further and really look at stellar equations, you'll see things like metallicity do play a part. I'm not saying they're a huge factor, but you can't discount the metallicity completely. – zephyr Apr 24 '17 at 13:21

I think this question is too broad, but I'll take a stab at it.

The Russell-Vogt (or sometimes Vogt-Russell) theorem is that the position of a star in the HR diagram is determined by its mass and composition.

The luminosity is determined mostly by its central temperature and composition. In turn, the central temperature depends on mass and radius and the radius depends on the luninosity and effective temperature.

Thus the question you ask fills textbooks. But to first order. The time dependence of luminosity is set by the time dependence of mass - ie mass loss (or gain) and the rate of change of composition, particularly in the nuclear burning regions of a star.

In a star like the Sun, mass loss is relatively unimportant, so it is the rate at which hydrogen is turned into helium in the core that sets the timescale for luminosity evolution. Other processes that alter the core composition like mixing (due to convection, rotational mixing or diffusion) are thought to be second order effects.

Restricting myself to the main sequence as an example. The luminosity of the Sun is set by the core temperature. The the nuclear reactions become faster as the mean particle weight increases and the core contracts and the temperature rises to maintain hydrostatic equilibrium. The rate at which this occurs is given by the luminosity of the star divided by the amount of H available (proportional to the mass of the star).

Overall chemical composition drives this as a second order effect. A lower metallicity star is less opaque to radiation. The radiation escapes more efficiently and the star is smaller and hotter at the surface for the same luminosity. Smaller stars are hotter in the middle for the same mass and thus more luminous. Thus the luminosity evolution of low metallicity stars is faster than those of higher metallicity. See for example Figs 1 and 2 of Bazan & Mathews (1990).

• Your last paragraph (and the paper mentioned) seem to explain the special case I used as an example (Zeta Tucanae). The high end of the age estimate given in the paper I cited is 3.8Ga yet the sun will probably be at the luminosity of ZTuc about 2/3 of the way thru it's lifetime. The simplistic view here is that ZTuc will only spend about 5.7Ga on the main sequence. This is significantly shorter than the sun and the faster "heating" would be something to consider when looking for habitability. Do you think this is a fair statement?? – Jack R. Woods May 9 '17 at 23:53