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
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
Solar Interior
60% of mass is inside 1/3 radius
Inner 25% of sun generates almost all energy
Outer ¼ of Sun is convective
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