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Week 4 ASSIGNMENTS * 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 * 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. |