Stellar Interiors

Physical Astronomy

Professor Lee Carkner

Lecture 10

Kelvin-Helmholtz Timescale

Very roughly, the amount of gravitational energy in a sphere of mass M and radius R is

E ~ -(3/10)(GM2/R)

Also for non-fusion objects like planets and brown dwarfs

Can only provide solar luminosity for ~107 years

Fusion

Fusion of lighter elements into heavier ones

u = 1 atomic mass unit = 1.66053873X10-27 kg

E= mc2 = 26.731 MeV per reaction Enough energy to power the sun for ~1010 years

Fusion and Mass

Stars fuse elements in order of mass

Only massive stars can fuse heavier elements

More massive reactions are faster H burning phase long, each subsequent

phase shorter and shorter

Proton-Proton Chain

4 H → 4He + 2e+ + 2e +2

No heavier catalysts involved

Dependant on T4

Three Chains

In PPI chain, 2H and 3He formed as intermediate products

In PPII chain, 8B and 8Be formed as intermediate products

CNO Cycle

Temperature dependant as T20

Only available in stars with CNO present Does not work for first generation stars

Triple Alpha

4He + 4He → 8Be8Be + 4He → 12C +

8Be decays rapidly back into 4He, so three

alpha particles have into collide almost simultaneously

Heavier Elements

12C + 4He → 16O + 16O + 4He → 20Ne +

Other reactions can occur at higher mass

Even more super massive stars can fuse oxygen into silicon, phosphorus, and sulfur

Limits of Fusion

Fusion of elements up to atomic mass 56 can liberate energy

Elements heavier than iron produced in supernovae

Fusion and The Main Sequence

Stars that burn hydrogen don’t change much since hydrogen burning is slow

Since H burning rate depends on core temperature, high mass stars have the shortest main sequence lifetime

Radiation Pressure

For a star of temperature T, the radiation pressure at the surface can be written as:

Prad = (4/3c)T4

Note that Prad is strongly temperature dependant

Eddington Luminosity

Occurs at the Eddington Luminosity:

LEd = (4GcM/)

~0.034 for very luminous stars

Puts upper limits on stellar size and accretion

events

Main Sequence Evolution

This increases the fusion rate and the luminosity

Faint young Sun problem

Solar Interior

60% of mass is inside 1/3 radius

Inner 25% of sun generates almost all energy

Outer ¼ of Sun is convective

Next Time

Read 11.2-11.3 Homework: 10.21, 11.5a, 11.12, 11.15