BACK TO Week 4 ASSIGNMENTS

BROWN DWARF (B.D.) FORMATION

* REMINDER - IN STAR FORMATION, NUCLEAR FUSION STOPS CONTRACTION WHEN CENTRAL TEMPERATURE HITS ABOUT 6 MILLION KELVIN

* BIG QUESTION - WHY CAN'T CONTRACTION OF B.D. GET TO 6 MILLION KELVIN?

* BELOW 0.08 SOLAR MASS, CONTRACTING OBJECT WILL HIT A CRITICAL VALUE OF CENTRAL DENSITY BEFORE THE TEMPERATURE CAN GET TO 6 MILLION KELVIN

* AT THIS CENTRAL DENSITY, GRAVITATIONAL CONTRACTION CAN NO LONGER CONTINUE TO FORCE ELECTRONS INTO A SMALLER VOLUME

*THROUGHOUT A B.D. (OR ANY STAR) THERE ARE AS MANY ELECTRONS AS THERE ARE PROTONS (INCLUDING PROTONS IN NUCLEI HEAVIER THAN HYDROGEN) AT ANY TIME.

* IDEA COMES FROM QUANTUM PHYSICS - PAULI EXCLUSION PRINCIPLE STATES THAT IDENTICAL ELECTRONS CANNOT OCCUPY THE SAME SPACE AT THE SAME TIME

* FOR FREE ELECTRONS, THIS RESTRICTS ELECTRON ENERGIES WHEN THEY GET TOO CLOSE TO EACH OTHER - AND INCREASING COMPRESSION WOULD MEAN TRYING TO INCREASE ELECTRON ENERGIES; BUT ALL AVAILABLE ENERGIES ARE ALREADY OCCUPIED BY OTHER ELECTRONS.

* THIS EFFECT GOES BY THE NAME "ELECTRON DEGENERACY PRESSURE", AND WILL APPEAR AGAIN IN UNIT 5 WHEN WE DISCUSS POST-MAIN SEQUENCE EVOLUTION OF LOWER MASS STARS, AND AGAIN IN THE PHYSICS OF WHITE DWARF REMNANTS.

* MATTER IN THIS DEGENERATE STATE DOES NOT HAVE A PRESSURE - TEMPERATURE THERMOSTAT: TEMPERATURE CAN INCREASE HUGELY WITHOUT AN INCREASE IN PRESSURE - AN INCREASE IN TEMPERATURE RESULTS IN MORE ENERGY FOR THE NUCLEAR PARTICLES, BUT NOT THE ELECTRONS, WHICH DOMINATE THE TOTAL PARTICLE PRESSURE AT MILLIONS KELVIN (AS WELL AS LOWER TEMPERATURES).

* IN SUMMARY:  FOR THE MORE MASSIVE BROWN DWARFS, ELECTRON DEGENERACY PRESSURE IN THE 'CORE' HALTS COLLAPSE AT TEMPERATURES BELOW THE 5-6 MILLION KELVIN REQUIRED FOR NUCLEAR FUSION OF PROTONS.