Theory and Diagnostics of Hot Star Mass Loss
  Massive stars have strong stellar winds that direct their evolution through
the upper Hertzsprung-Russell diagram and determine the black hole mass
function. Secondly, wind strength dictates the atmospheric structure that sets
the ionising flux. Thirdly, the wind directly intervenes with the stellar
envelope structure, which is decisive for both single star and binary
evolution, affecting predictions for gravitational wave events. Key findings of
current hot-star research include:
  * The traditional line-driven wind theory is being updated with Monte Carlo
and co-moving frame computations, revealing a rich multi-variate behaviour of
the mass-loss rate dM/dt in terms of M, L, Eddington Gamma, Teff , and chemical
composition Z. Concerning the latter, dM/dt is shown to depend on the iron (Fe)
opacity, making Wolf-Rayet populations, and gravitational wave events dependent
on host galaxy Z.
  * On top of smooth mass-loss behaviour, there are several transitions in the
Hertzsprung-Russell diagram, involving bi-stability jumps around Fe
recombination temperatures, leading to quasi-stationary episodic, and not
necessarily eruptive, Luminous Blue Variable and pre-SN mass loss.
  * Moreover, there are kinks. At 100 Solar Masses, a high Gamma mass-loss
transition implies that hydrogen-rich very massive stars have higher mass-loss
rates than commonly considered. At the other end of the mass spectrum, low-mass
stripped helium stars no longer appear as Wolf-Rayet stars, but as
optically-thin stars. These stripped stars, in addition to very massive stars,
are two newly identified sources of ionising radiation that could play a key
role in local star formation as well as at high-redshift.
