Astro2020: From Stars to Compact Objects: The Initial-Final Mass
  Relation
  One of the key phases of stellar evolution that remains poorly understood is
stellar death. We lack a predictive model for how a star of a given mass
explodes and what kind of remnant it leaves behind (i.e. the initial-final mass
relation, IFMR). Progress has been limited due to the difficulty in finding and
weighing black holes and neutron stars in large numbers. Technological advances
that allow for sub-milliarcsecond astrometry in crowded fields have opened a
new window for finding black holes and neutron stars: astrometric gravitational
lensing. Finding and weighing a sample of compact objects with astrometric
microlensing will allow us to place some of the first constraints on the
present-day mass function of isolated black holes and neutron stars, their
multiplicity, and their kick velocities. All of these are fundamental inputs
into understanding the death phase of stellar evolution, improving supernovae
models, and interpreting LIGO detections in an astrophysical context. To
achieve these goals, we require large area surveys, such as the WFIRST
exoplanet microlensing survey, to photometrically identify long-duration (>120
day), un-blended microlensing events as candidate compact objects. We also
require high-precision astrometric follow-up monitoring using extremely large
telescopes, equipped with adaptive optics, such as TMT and GMT.
