Factors affecting Fusion Rate

• Density– Since protons are closer together, the mean free

path between collisions will be smaller

• Temperature– At higher temperatures a larger proportion of

protons are moving fast enough to overcome the Coulomb Barrier

– Faster protons take less time to cover the distance between collisions

The Effect of Mass

• Higher mass condensing into the star means– More hydrogen fuel to fuse– Higher pressure leading to higher density and

temperature in the centre of the core– Much higher nuclear energy generation rates– So higher mass stars have much higher

luminosities• e.g. a 10 Solar Mass Star generates 10,000 times

more luminosity than the Sun

Star Formation

Mass –Luminosity

Main Sequence Masses

Lifetime

High mass stars have more hydrogen to fuse

BUT

They fuse this hydrogen much faster

SO

They run out sooner

Mass-Lifetime

Main Sequence Lifetimes

Cluster Formation

Red green and yellow dots represent post main sequence stars

Clusters

1 Solar Mass Evolution

Approach to Main sequence

Core is always contracting and heating up, in vertical track heat is transported by convection so the increase in core temperature doesn’t show on the photosphere

Approach with time scales

Approach for different Masses

Vertical & Horizontal tracks

Protostar TracksProtostars are always getting smaller and hotter

• Vertical Track <> Convective envelope

– Convection requires larger temperature difference between the core and the photosphere

– Although the core is getting hotter , the temperature of the photosphere stay relatively constant

– Luminosity falls because the star is shrinking

• Horizontal Track <> Radiative Envelope

– Radiation results in smaller temperature difference between the core and the photosphere

– Photosphere temperature rises but contraction results in luminosity staying nearly constant

MS Structure

1 Solar Mass Evolution5. Vertical track

6. Horizontal trrack

7. Main Sequence

8. Red Giant Branch

9. Helium Flash

10. Horizontal Branch

11. Asymptotic Giant Branch

12. Planetary Nebula

13. White Dwarf

14. Brown Dwarf

Core Degeneracy

Heat energy goes into nuclei but density is controlled by the electrons

Degenerate Gas

If you push the electrons closer together, the energy levels all get farther apart , in a non degenerate gas some electrons will jump to lower energy levels

Evolution to Red Giant

Red Giant

1 Solar Mass Evolution

Helium Flash

• Ash dumped from shell raises core Temp to 100 Million K,

• Helium to Carbon Fusion

• Degenerate gas has no safety valve, He fusion proceeds explosively

• Most of the energy goes into making the core expand, lifting degeneracy

• In a non-degenerate core…1. More reactions Higher Temp2. Higher Temp Higher Pressure3. Higher Pressure Expansion4. Expansion Lower Temp5. Lower Temp Less Reactions

– In a degenerate core step 2 doesn’t happen because heat energy goes to lifting the degeneracy rather than raising the pressure

Safety Valve ?

Helium to Carbon Fusion

Core and Shell Fusion

Post Main Sequence HR

Asymptotic Giants

Descent to White Dwarf

Cooling Embers

Mass-Radius for Degenerate Stars

Mass-Radius for White Dwarfs

Multiple Shell Burning

Iron catastrophe

Timescales to Supernova

Heavy element synthesis

Cosmic Abundance

Open Cluster

Globular Cluster

Cluster HR Diagram

Cluster Turn-off