Week 6-- Solar Evolution I

I. Protostar phase
After gravitational instability sets in at the Jeans mass, the gas that will become the Sun collapses and fragments and eventually determines the mass that will be our Sun. After that, collapse continues because the gas is very spread out and heat easily escapes. But eventually the Sun becomes a small enough ball (still much larger than ours) that radiation does not easily escape (check that the optical depth of a star increases like 1/R^2 if we keep the cross section per gram constant). At that point, contraction is stabilized (because adiabatic contraction is always stable in 3D), force balance sets in, and the star obeys the virial theorem. This means further contraction requires net heat loss, and is also very slow as a result.

At this stage, the star is very red, and very large, and indeed looks from the outside just like a "red giant", though it is not officially a red giant because, as we shall see, red giants require a shell undergoing fusion but the Sun at this early "protostar" phase is not undergoing fusion in its core or in any shell. The actual reason it looks like a red giant is that both types of stars are very large and either fully convective or nearly so. The Sun is so large at this protostar phase (by virtue of its history of being larger still) that it is extremely luminous, as luminous as it will ever be throughout its life.

II. Fully Convective Stars and the Hayashi Track
It was discovered by Hayashi that fully convective stars always have surface T fairly close to 3000 K, so they are always "red." Thus such stars, when plotted in the H-R diagram, are said to be on the "Hayashi track." The physical reason for this is a little complicated, but has to do with the fact that cool surfaces are generally dominated by the continuum opacity of the H-minus atom (a neutral H atom with one additional bound electron, making it a negative ion with a single very weakly bound state-- indeed emission by the formation of this state is mostly where sunlight comes from). The opacity of this ion depends on temperature and density in a way that works to keep the surface T rather "red", so even though the energy transport over the entire interior of the star is predominantly convective, the final radiative escape from the surface regulates the surface T. Since the surface T is rather fixed, the luminosity L depends mostly on the radius of the protostar, which is simply a function of its history of contraction (i.e., its age).

III. Mostly Radiative Stars and the Henyey Track

Given the above, as the R drops, so does L. Eventually this convective L drops so low that it would fall below the L from radiative diffusion (which you may recall depends mostly on the mass M of the star, so is rather fixed for any given star). Since radiative diffusion is always happening, the L cannot drop below the radiative L, and at this point the star shifts from having a nearly constant surface T (a vertical path on the H-R diagram, yes?), to having a nearly constant L (a horizontal path on the H-R diagram, yes?). This "right turn" is called the Henyey track, and is where the star begins to obey the celebrated "mass-luminosity relation." (For red dwarfs, which are low-mass main-sequence stars, core fusion initiates before the star reaches the Henyey track, but it is conventional to include these stars in what gets called the mass-luminosity relation anyway.)

IV. The Main Sequence

Of course the main sequence is when core fusion initiates, and the stellar evolution slows dramatically because the heat being lost by radiative diffusion is replaced by self-regulated fusion. With no net heat loss, contraction slows, and actually reverses into a very slow expansion (a small enough effect it is often neglected from the story). I will include this, because its physical origin is instructive-- it comes from the fact that core fusion reduces the number of particles in the star. This in turn implies that to obey the virial theorem at a nearly fixed core T (self-regulated by the fusion), the star must expand. An expanded star is a larger leaky bucket of light at similar core T, so L rises some, though it is a fairly small effect. (And unfortunately for our understanding, this reduction in particle number only happens in the core, so there is a helium gradient, which means the high He content in the core actually causes the core to contract-- leading many textbooks to claim that the L rise comes from core contraction, which leads to faster fusion, and again we see the false preoccupation with fusion rate causing L.