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The AUGUST 13, 2020 Phys.org article Results from Hubble suggest that Betelgeuse's recent dimming was due to material ejected from the star says:

...the star's unexpected and significant dimming periods in late 2019 and early 2020 were most likely caused by the ejection and cooling of dense hot gases

and links to Spatially Resolved Ultraviolet Spectroscopy of the Great Dimming of Betelgeuse in Ap.J.

I assume that the blue shift caused by the convection cells moving outward was detected because it was directly in our line of sight to the star, if a similar event occured at right angles to us, Hubble wouldn't detect it so easily.

My question is how likely is it that Betelgeuse is continually experiencing events like this that are not visible to us because the opaque material is not between the Earth and the star?

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    $\begingroup$ It might be doing it again: cfa.harvard.edu/news/2020-17 $\endgroup$
    – user34599
    Commented Aug 13, 2020 at 23:17
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    $\begingroup$ All red giants throw out a lot of gas & dust, in irregular or semiregular cycles that are not well understood. Wikipedia says that Betelgeuse may be ejecting up to 1 solar mass of material per 10,000 years. That's over 33 Earth masses per year. $\endgroup$
    – PM 2Ring
    Commented Aug 13, 2020 at 23:43

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