**1. Super-Eddington Events in Massive Stars**

Very massive stars lose much—and possibly most—of their mass in sporadic events driven by continuum radiation. This fact has dire consequences for any attempt to predict the star's evolution. After four decades of research, the instability mechanism has not ye<sup>t</sup> been established; maybe it occurs in the stellar core, or else in a subsurface locale, or conceivably at the base of the photosphere. Without concrete models of this process, massive-star evolution codes can generate only "proof of concept" simulations, not predictive models, because they rely on assumed mass-loss rates adjusted to give plausible results. Even worse, eruptions may illustrate the butterfly effect— the time and strength of each outburst may depend on seemingly minor details, and the total mass loss may differ greatly between two stars that appear identical at birth. And an unexpected sub-topic, involving precursors to supernova events, arose about ten years ago. Altogether, the most luminous stars cannot be understood without a greatly improved theory of radiative mass-loss events. No theorist predicted any of the main observational discoveries in this subject.

Most of the phenomena explored here are either giant eruptions (including supernova impostors, supernova precursors, and shrouded supernovae) or LBV outbursts. They have four attributes in common:


Giant eruptions are presumably driven by continuum radiation. They carry far too much kinetic energy to be "line-driven winds." Gas pressure is quite inadequate, blast waves are either absent or

inconspicuous, and there is no evidence for sufficient MHD processes. Individual events have peak luminosities ranging from 10<sup>5</sup> *L* to more than 10<sup>8</sup> *L* while ejecting masses ranging from 10−<sup>3</sup> *M* to 10 *M* or more. Note that driving by continuum radiation (i.e., a super-Eddington flow) is not the root "cause" of an eruption. Logically the cause must be some process or instability that either increases the local radiation flux, or increases its ability to push a mass outflow.

This review does not include eruptions with *L* < 105.5 *L*, such as "red transients" and nova-like displays. Those lower-luminosity cases generally involve stars with *M* < 20 *M* or even *M* < 10 *M*, which are vastly more numerous than the very massive stars ( *M*ZAMS > 50 *M*) that most likely produce giant eruptions. The relatively low-luminosity outbursts may be highly abnormal phenomena (e.g., stellar mergers) that occur in only a tiny fraction of the stars. In some cases they might not be above the Eddington Limit, or might not be opaque, or might be accelerated by non-radiative forces. Giant eruptions, by contrast, are highly super-Eddington, tend to look like each other regardless of their causative instabilities, and may occur in a substantial fraction of the most massive stars. Much of Section 4 and part of Section 5 may apply also to the lower-luminosity eruptions, however.

This article is a descriptive review like a textbook chapter, not a survey of publications. It outlines the basic physics and theoretical results with only a minimal account of the observational data. It also includes comments about some of the quoted results, with a few personal conjectures. Some of the generalities sketched here have been unfamiliar to most astronomers, even those who work on supernovae. They are conceptually simple if we refrain from exploring technicalities. One important topic—rotation—is mostly neglected here, because it would greatly lengthen the narrative and there is not ye<sup>t</sup> any strong evidence that it is required for the chief processes. Binary systems are also neglected, except the special case of *η* Car; see remarks in Section 6.
