How Stars End Their Lives

While the basic evolution of stars has been understood for many decades, there are still major uncertainties in our overall understanding of how stars end their lives, both in the context of low- and intermediate-mass stars (including the Sun) and massive stars. I will first review some of key principles that govern the structure and evolution of stars and then present recent progress that has been made for both groups of stars. I will argue and present numerical simulations that show that all stars become dynamically unstable when they become large giant stars, which leads to sporadic, dynamical mass ejections. Low- and intermediate-mass stars may lose all of their envelopes as a consequence, leaving white-dwarf remnants. More massive stars experience core collapse, leaving a neutron-star or black-hole remnant, possibly associated with a supernova explosion. I will show how the dramatic recent progress on understanding the core-collapse process, for the first time, allows us to connect the late evolution of massive stars with the resulting supernova explosions and the final remnants and discuss how observations with current gravitational-wave detectors (such as LIGO) will allow us to test this theoretical connection.