Stellar Evolution: The Main Sequence

• Short revisit of main-sequence lifetimes.

  First, careful job of calculating the time for the Sun to use up 10% of its Hydrogen fuel gives a main-sequence lifetime of 10 billion years.

  Lifetime =	M	x LifetimeSun
  	L

  Stellar Mass	MS Lifetime
  40 MSun 15 MSun 3 MSun 1.5 MSun 0.5 MSun	1 x 106 years 12 x 106 years 400 x 106 years 3 x 109 years 2 x 1012 years

• So just what happens to "end" the main-sequence lifetime of a star?

  The sequences in the H-R Diagram were known long before stellar evolution was understood and there were thoughts that stars might evolve along the main-sequence. But, with stellar models it is possible to let the models "evolve" and see what happens to stars as they begin to use up their H fuel in the regions where it is hot enough for fusion.

• The Sun is changing its structure. It is building up a helium core.

  

• Does the He fuse together to form beryllium? No, for two reasons.
  1. Because He nuclei have 2 p⁺ each so the temperature needs to be even higher for fusion

  2. Beryllium nuclei have MORE mass than the sum of two He nuclei so energy is not released in this reaction -- it is absorbed.

• So, the Sun's central structure is now a small He core surrounded by a hydrogen fusion shell. The He core starts to contract under its own gravity.

  This contraction releases GPE which increases the temperature in the Hydrogen fusion shell and the total energy production goes up.

• So the Sun's core is getting hotter, Luminosity is increasing and the envelope begins to expand so the outer surface temperature decreases.

• The Sun is becoming a Red Giant.

• For the Sun, we think it is a little more than 1/2 of the way through its main-sequence lifetime and it will reach the base of the giant branch in about 4 billion years.

• At the tip of the giant branch, the Sun will have a radius about the size of the Earth's orbit. We will need a new home by the time this happens.

  As a red giant the Sun will have these properties:

  Luminosity	2000 LSun
  Radius	1 AU
  Surface Temp	3200 K

• Let's remember the equilibria and energy sources:
  1. Proto-star: Gravity is winning and this object is contracting. GPE is the energy source.

  2. Main-sequence Star: Here gravity is balanced by thermal pressure and we say these stars are in Hydrostatic Equilibrium. The energy is provided by hydrogen fusion in the core.

  3. Red Giant: Here, we say there is a quasi-static equilibrium with thermal pressure barely winning the battle in the envelope and gravity winning in the core. Red giants have two energy sources, GPE in the contracting core and H-fusion in a shell around the core.