*4.5. Are LBV's Relevant?*

As noted at the end of Section 3.1 above, the most critical mass-loss episode may conceivably occur just before the LBV stage of evolution. If so, then LBV outbursts may have little in common with continuum-driven giant eruptions. The following remarks and conjectures may be pertinent.

The fast region in any LBV wind (usually 100 to 300 km s<sup>−</sup>1) is transparent in the visual-wavelength continuum. This fact was noted before 1990 [71], and later motivated the static atmosphere models [25,88–91]. But it might not apply to the inner, slow, denser part of the outflow during a major LBV event. The following remarks concern major LBV1 eruptions with *T*1 < 10,000 K, not the states above 15,000 K that are emphasized in most analyses since 2010.

Recall the analogy between a stellar wind and flow through a transonic nozzle, with *V* = *w*, the speed of sound, at radius *rw* [92,93]. The subsonic region *r* < *rw* resembles an atmosphere constrained by gravity, while the flow dominates outside *rw*. Imagine such a hybrid model of AG Car's major eruption around 1994, when *T*1 declined to about 9000 K while *M* ˙ rose to about 10−<sup>4</sup> *M* y<sup>−</sup><sup>1</sup> [23]. At that time *w* ∼ 20 km s<sup>−</sup><sup>1</sup> in the photosphere, and the photospheric outflow speed was of the order of 1 or 2 km s<sup>−</sup>1. The sonic point was thus two or three scale heights above the photosphere, much closer than in a normal stellar wind. According to Figure 4,a3× larger value of *M* ˙ would have moved the photosphere to the sonic point – so a flow model rather than a static atmosphere would have become appropriate if *M* ˙ had grown above that amount. In this order-of-magnitude sense the major eruption was "almost" opaque.

A normal stellar wind has only an indirect relation to the continuum photosphere, with *V* < 0.01 *w* in the photosphere. The much larger *V*/*w* in major LBV eruptions, along with proximity to the Eddington Limit, suggests that their outflows are more directly related to their continuum photospheres. This line of thought—or rather, of surmise—motivates a three-step conjecture:


This is an empirical hypothesis, not a theoretical prediction. There are semi-theoretical methods of predicting LBV mass loss rates, far more elaborate than this reasoning, but their developed versions have been applied mainly to the hotter states above 15,000 K [94]. Anyway, the above expression is consistent with estimated values for major LBV1 eruptions.

If we portray LBV outbursts as quasi-static inflated states [88–91], then unfortunately we de-emphasize the mass outflow. Since the latter is probably more consequential, the "eruption" aspect expresses a broader significance than the inflation. On the other hand, it is conceivable that most of the cumulative LBV mass loss occurs in rare giant eruptions à la P Cygni, not merely major eruptions. In any case the static 1-D models do not answer the main questions, Section 5.1 below.

### **5. Physical Causes of the Eruptions**

The Eddington Limit turns out to be wonderfully subtle and complicated. Relevant instabilities were recognized after 1980 (see many refs. in [1]), but they are difficult to analyze or even to describe. Practically all of our knowledge of eruption parameters, post-eruptive structure, timescales, and long-term mass loss is still empirical.

Two classic high-mass stellar instabilities were naturally suspected when giant eruptions and LBV events attracted notice in the 1980's: The Eddington mechanism or Ledoux-Schwarzschild instability energized in the stellar core [95], and radial dynamical instability which occurs if the average adiabatic index falls below 4/3 [96]. But they proved unsuitable [97], and have been replaced by newer ideas which are generally non-adiabatic, involve radiation pressure, and resemble each other. Three regions in the star merit special attention: the photosphere, the "iron opacity bump" region with *T* ∼ 200,000 K, and the stellar core, broadly defined.

Details of the instabilities are too lengthy to explore here. Instead, this overview lists a set of essential considerations, including some that have seldom been discussed in research papers. Here rotation does not ge<sup>t</sup> the attention that it deserves, because that would greatly lengthen the text. Interacting or merging binary scenarios are omitted because there is no clear need for them at this time, see Section 6.
