Stellar Evolution

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after contraction onto the main sequence, a star shines by converting hydrogen into helium in its core.

the Vogt-Russell theorem: the properties of a star are entirely determined by mass (M) and chemical composition (X, Y, Z)

but as hydrogen is converted into helium, X & Y change -- the star must evolve with time!
 

Timescales:

H --> He releases 0.007mc² of energy

converting inner 10% of the sun's mass from hydrogen into helium will produce

(0.007)(0.1 M_sun)(c²) = 1.25x10⁵¹ ergs of energy

if the Sun is radiating energy at 1 L_sun = 4x10³³ erg/s, it can do this for a time

t=1.25x10⁵¹ erg / 4x10³³ erg/s = 3.3x10¹⁷ s ~ 10¹⁰ years ~ 10 billion years

What happens?

• as H --> He, the mean molecular weight (i.e., mass per particle) in the core rises.
• to stay in hydrostatic equilibrium, the core must contract. Remember the ideal gas law:
mu drops, so P drops. if P drops, the core contracts, and density rises.
• as the core contracts, the virial theorem says that half of the gravitational energy released by contraction must go into heating up the star.
• As the core heats up, energy generation goes up: E_pp ~ T⁴
• The star becomes gradually becomes more luminous:

Eventually, the hydrogen content of the core becomes so depleted that it cannot continue burning H --> He in the core. Big changes in store...