Lecture 15: The Main Sequence

Key Ideas:

Main Sequence stars "convert" Hydrogen into Helium in their cores.

The Main Sequence is a Mass Sequence:

• Lower M-S: M < 1.2 M_sun
• Upper M-S: M > 1.2 M_sun

Lifetime depends on the Mass:

• Larger Mass = Shorter Lifetime

Main Sequence Membership

For a star to be located on the Main Sequence in the H-R diagram:

• must "convert" Hydrogen into Helium in its core.
• must be in a state of Hydrostatic Equilibrium.

Relax either of these and the star will no longer be on the Main Sequence.

The Main Sequence is a Mass Sequence

The location of a star along the M-S is determined by its Mass.

• Low-Mass Stars: Cooler and Fainter
• High-Mass Stars: Hotter and Brighter

Follows from the Mass-Luminosity Relation: Luminosity ~ Mass^3.5

Internal Structure

Nuclear reaction rates are very sensitive to core temperature:

• P-P Chain: rate ~ T⁴
• CNO Cycle: rate ~ T¹⁸ !

Leads to:

• differences in internal structure.
• divides M-S into Upper and Lower parts by mass.

Upper Main Sequence

Upper Main-Sequence stars have

• M > 1.2 M_sun
• T_Core > 18 Million K

Generate Energy by the CNO Cycle

Structure:

• Convective Cores
• Radiative Envelopes

Lower Main Sequence

Lower Main-Sequence stars have

• M < 1.2 M_sun
• T_Core < 18 Million K

Generate Energy by the Proton-Proton Chain

Structure:

• Radiative Cores
• Convective Envelopes

Lowest Mass Stars

Mass Range: 0.25 < M_* < 0.08 M_sun:

• Generate energy by the P-P Chain

These stars have Fully Convective Interiors:

• Convective Core and
• Convective Envelope

Main Sequence Lifetime

How long a star can burn H to He depends on:

1. Amount of H available = MASS
2. How Fast it burns H to He = LUMINOSITY

Time to exhaust the available fuel is the lifetime:

Lifetime = Mass / Luminosity

Recalling the Mass-Luminosity Relationship for M-S stars:

Luminosity ~ Mass^3.5

We combine these to derive the Main-Sequence lifetime:

Lifetime ~ 1 / M^2.5

In Words: The higher the mass, the shorter its life on the Main Sequence.

Examples:

• Sun: ~10 Billion Years
• 30 M_sun O-star: ~2 Million years
• 0.1 M_sun M-star: ~3 Trillion years

Consequences:

• If you see an O or B dwarf star, it must be young as they only live for a few Million years.
• You can't tell how old an M dwarf is because their lives can be so long.
• The Sun is ~5 Billion years old, so it will last only for ~5 Billion years longer.

Summary:

Main Sequence stars convert H into He in their cores.

The Main Sequence is a Mass Sequence.

• Lower M-S: p-p chain, radiative cores & convective envelopes
• Upper M-S: CNO cycle, convective cores & radiative envelopes

Lifetime depends on Mass: Larger Stars have Shorter M-S Lifetimes