• For stars on the main sequence, luminosity is proportional to the star’s mass to the 3.5th power (L α M^3.5)
• For the Sun: original composition about 30% helium in mass –> today – 65% helium –> 5 billion years later: 100% helium
• The total amount of hydrogen “fuel” in a star is proportional to the star’s mass; the rate of fuel use is proportional to luminosity; lifetime α mass α 1/L
• The Sun’s main sequence lifetime is 10¹º years; its entire lifetime is 10¹º + 1/M2.5 years, where M = the star’s mass in solar masses

How Lifetime, Luminosity, and Mass Compare Among Various Spectral Types

Spectral Type  Mass (M☉)   Luminosity (L☉)  Lifetime (years)

• O5                        60                          800,000                        3 million
• A5                         3                                55                              4 million
• G2                        1                                  1                             10 billion
• M0                      0.5                           0.08                             70 billion
• M5                      0.2                           0.01                           190 billion

Stars with masses below 0.8 M☉ have never left the main sequence and have lifetimes longer than the current age of the Universe.

Post- Main Sequence

• Core can’t maintain its balance between gravity and pressure; gravity compresses the star to a much smaller size
• Electron Degeneracy Pressure: halts collapse of the star
• Core’s radius swells to several thousand km, or about the size of Earth
• Hydrogen converts to helium at  a very rapid rate; luminosity more than 1000 times greater than before; star swells to enormous size

Red Giants: 50x Sun’s radius, 1000x Sun’s luminosity

• H –> He in a shell
• Helium core swells to the size of Earth; no fusion anymore
• Non-burning hydrogen atmosphere
• Helium fusion needs higher velocities and energy to overcome repulsion
• At 100 million K, helium atoms yield carbon atoms, also known as “helium flash”
• “Triple-Alpha Process“: ⁴He + ⁴He –> ⁸Be; ⁴He + ⁸Be –> ¹²C
• In half an hour, half the helium yields carbon in the core

• Horizontal Branch Star: after the core expands and the star enters a steady phase (50-100 million years) of helium burning and becomes less luminous
• Core contracts again, He –> C in a shell around the core; hydrogen burning shell around that layer
• “Asymptotic Giant Brand“: star moves upward toward the H-R Diagram “Red Giant” area, exceeds 10,000 L☉

*Blue-Stragglers: stars in a dense environment; when two stars collide, the core could be “rejuvenated,” giving the star extra lifetime

Planetary Nebulae

• The outer layers, about 20% of the star’s mass, are ejected in a strong wind
• Gas is ionized by UV protons from hot, exposed stellar core
• Star shines for 50,000 years before gases disperse and fade
• About 1,000 in the Milky Way Galaxy
• Have many shapes and sizes because of binary star systems’ different orbits, temperature, rotation, luminosity, mass

White Dwarfs:  (0.6 – 0.7 M☉) bare core of a star often all fusion reactions ended, supported against gravity by electron degeneracy pressure; density at 1 million grams/cm³

• e.g. Sirius A: Main Sequence, A1, -1.5; Sirius B: white dwarf, 8.5

End States: Initial Mass and White Dwarf Composition

• >0.45 M☉: helium
• 0.45-4 M☉: carbon, oxygen –> (Sun)
• 4-8 M☉: oxygen, neon, magnesium