Chapter 12 Evolution of Low Mass Stars Sun won t remain a main sequence star forever eventually it will exhaust the hydrogen fuel source in its core relatively minor differences in the masses and chemical compositions of two stars can sometimes result in significant differences in their fates two main categories of stars are high mass and low mass luminous O and B stars follow a course fundamentally different from that of the cooler fainter less massive stars Low mass stars have masses less than 8 solar masses 12 1 The Life and Times of Main Sequence Star structure of the Sun is determined by a balance between the inward pushing force of gravity and outward force of pressure maintained by energy released by nuclear fusion in core more mass means stronger gravity stronger gravity means higher temp and pressure in star s interior higher temp and pressure mean fast nuclear reactions which mean more lumi nous star stars with higher masses live shorter lives because they burn their fuel faster it would be unlikely for life to evolve on a planet orbiting a massive star with a stable life of only a few million years with the proton proton chain ting smaller and denser When the sun formed 90 of its atoms were hydrogen then it converted them to helium As a protostar collapses its always in balance but it radiates away thermal energy get We can use the H R diagram to observe a star s evolutionary track as the protostars grow smaller and hotter until they reach their positions as stars on the main sequence as a main sequence star uses the fuel in its core its structure must continually shift in re sponse to changes in its core composition between the time the sun was born and the time it will leave the main sequence its luminosity will have doubled primarily during the last billion years of its life mass and luminosity of main sequence stars are related mass governs the rate at which nuclear reactions occur in the core the time a star spends on main sequence is determined by its mass less massive stars live longer at the temp found at the center of a low mass main sequence star atomic collisions are not energetic enough to overcome the electric repulsion between helium nuclei nonburning helium ash products of fusion accumulates most rapidly at the center of a star chemical composition changes most rapidly at the center of a star and less rapidly as we move outward when the sun formed it had a uniform composition of 70 hydrogen and 30 helium by mass but as hydrogen was fused into helium the helium in the core climbed now only about 35 of mass in the core of the Sun is hydrogen 12 2 A Star Runs Out of Hydrogen and Leaves the Main Sequence eventually a stars uses up its hydrogen fuel in the core the innermost core is composed entirely of helium ash thermal energy leaks out of the helium core into surrounding layers no more energy in generated in the core to replace it balance is broken main sequence life has ended matter we usually experience is empty space an atom is mostly empty except for space taken up by nucleus and electrons this is just like the Sun high temps strip electrons from nu clei through collisions gas is ionized a mix of electrons and atomic nuclei flying freely but most of gas is still empty space electrons and nuclei make up only a tiny fraction of volume when a low mass star like the sun uses all its hydrogen at its center the situation changes gravity begins to overcome pressure helium core is crushed smaller and denser finally reaches the limit of how many electrons can be packed in a given volume so dense that a cubic centimeter has a mass of 1 000 kg matter compressed to this point is electron degenerate once hydrogen is exhausted nuclear burning pauses in the core but continues outside of it called hydrogen shell burning because hydrogen now burns only in a shell surrounding a core of nonburning helium and degenerate electrons rules of electron degenerate matter as more helium ash piles up the core shrinks in size so the more massive it is the smaller it is due to the added mass that increases the strength of gravity and weights bearing down on the core so electrons can be smashed further together degenerate core triggers a chain of events that will dominate the evolution of our 1 solar mass star for the next 50 million years after the hydrogen runs out degenerate core means stronger gravity means higher pressure means faster nuclear burning producing greater and greater amounts of energy this heats the overlying star layers they expand to form a bloated luminous giant hundreds of times the luminosity of the Sun a radius over 50 solar radii yet the core is far more compact than the Sun s and mass is only a few times the size of Earth as it gets larger and more luminous it also gets cooler and redder due to the enormous ex panse of its surface which allows it to cool easily interior grows hotter surface temp begins to drop H R diagram helps keep track of changing luminosity and surface temperature as a star evolves away from the main sequence as soon as a star exhausts its core hydrogen it leaves the main sequence and moves upward and to the right on the H R diagram getting larger and cooler until progress ceases surface layers regulate how much radiation can escape and so pre vent it from getting cooler so it moves vertically on the H R diagram grower larger and more luminous but maintaining the same temperature it has become a red giant this path has been the red giant branch of the H R diagram change in structure is low at first but the star then moves up the red giant branch faster and faster takes about 200 million years to finish branch during first half the luminosity increases to about 10 times that of the Sun the second half it rises to almost 1 000 times like a snowball rolling down hill the bigger it is the faster it rolls but not exactly like a snowball because the helium core grows in mass not radius as hy drogen is converted to helium in the hydrogen burning shell increasing mass of helium core increases gravity pressure then the rate of nuclear burning core grows quicker 12 3 Helium Begins to Burn in the Degenerate Core in the degenerate core although as many electrons are packed as possible atomic nuclei are still able to move freely as far as nuclei are concerned the electron degenerate core of the star is still mostly empty space as the star evolves up the red giant branch the helium core grows not just smaller and more massive also hotter temp