Star Formation (DP IB Physics): Revision Note

Conditions for Fusion

• For nuclear fusion to occur, both nuclei must have sufficiently high kinetic energy to overcome the electrostatic repulsion between protons

• The conditions required to achieve this are:

  • Very high temperature (on the scale of 100 million Kelvin)

  • Very high pressure and density

• Four hydrogen nuclei (protons) are fused into one helium nucleus, producing two gamma-ray photons, two neutrinos and two positrons

  • Massive amounts of energy are released

  • The momentum of the gamma-ray photons results in an outward acting pressure called radiation pressure

Nuclear fusion of hydrogen nuclei to form helium nuclei

Equilibrium in Stars

• Once the core temperature of a star reaches millions of degrees kelvin and the fusion of hydrogen nuclei to helium nuclei begins

  • The protostar’s gravitational field continues to attract more gas and dust, increasing the temperature and pressure of the core

  • With more frequent collisions, the kinetic energy of the particles increases, increasing the probability that fusion will occur

  • Eventually, when the core becomes hot enough and fusion reactions can occur, they will begin to produce an outward radiation pressure which balances the inward pull of gravity

• The star reaches a stable state where the inward and outward forces are in equilibrium

  • As the temperature of the star increases and its volume decreases due to gravitational collapse, the gas pressure increases

  • The gas pressure and the radiation pressure act outwards to balance the gravitational force (weight, F = mg) acting inwards

Equilibrium in stars occurs when the outward radiation pressure is balanced with the inward gravitational force

• If the temperature of a star increases, the outward pressure will also increase

  • If outward pressure > gravitational force, the star will expand

• If the temperature drops the outward pressure will also decrease

  • If outward pressure < gravitational force, the star will contract

• As long as these two forces are balanced, the star will remain stable