After some testing, it appears that the starglow texture brightness level does not have an effect on the central part of the star model. Overbrightness seems to come from the corona. I've made a series of screenshots to determine what a good level of brightness would be.
For reference, this is a stock star:
stock
Each of these is labeled with the pixel level brightness of the star glow:
200
180
160
140
120
Note that I did not try to capture all images with the solar flares on the same animation frame. I might have to increase the star glow effect size a little for the lower brightness levels, if I go with one of them.
The question is, what level do you prefer? What is too bright? Just right?