Not the same thing. The plasma sheath surrounding the Sun is not in glow mode, a red giant's plasma sheath would be in glow mode, hence the appearance as a very large reddish star. The reason that a red giant's plasma sheath is glowing red is that it is starving for electrons.The "Sun" as we perceive it, is just the center of a red giant star
Low-mass electrons carry most of the electric current in space plasma. Galaxies and the stars within them seem to be “born” electron deficient by an efficient charge separation process observed in laboratory plasma discharges. Stars operate as positive anodes in a galactic glow discharge. I wrote about red giant stars in Twinkle, twinkle electric star, “Red stars are those stars that cannot satisfy their hunger for electrons from the surrounding plasma. So the star expands the surface area over which it collects electrons by growing a large plasma sheath that becomes the effective collecting area of the stellar anode in space. The growth process is self-limiting because, as the sheath expands, its electric field will grow stronger. Electrons caught up in the field are accelerated to ever-greater energies. Before long, they become energetic enough to excite neutral particles they chance to collide with, and the huge sheath takes on a uniform ‘red anode glow.’ It becomes a red giant star.
The electric field driving this process will also give rise to a massive flow of positive ions away from the star, or in more familiar words—a prodigious stellar ‘wind.’ Indeed, such mass loss is a characteristic feature of red giants. Standard stellar theory is at a loss to explain this since the star is said to be too ‘cold’ to ‘boil off’ a stellar wind. And radiation pressure is totally inadequate. So when seen in electric terms, instead of being near the end point of its life, a red giant may be a ‘child’ losing sufficient mass and charge to begin the next phase of its existence— on the main sequence.”
Internal heating doesn’t cause the giant red glow of Betelgeuse. It is an electrical plasma glow like that seen in a neon tube. And like a neon or fluorescent light tube it is relatively cool. In fact, measurements of temperature (random motion) of a plasma in an electric field (directed motion) will be misleading because the electric field tends to align motions in one direction. Radio measurements of the temperature distribution in Betelgeuse’s atmosphere give readings that decrease with distance from the photosphere and are lower than those derived from the optical and ultraviolet (UV), where the temperature is calculated from theoretical model atmospheres. The radio astronomy findings could be explained by current flowing in radial filaments in the extensive, diffuse envelope of Betelgeuse, like the red sprites seen stretching up to the ionosphere above earthly thunderstorms.
Betelgeuse’s size, seen in the more energetic UV light, is double its already gigantic dimensions in visible light. The existence of high-energy UV light at large distances above the star fits an external power source like that producing the superhot solar corona. What we are seeing is the same kind of plasma sheath effect that turns insignificant rocks in our solar system into comets like the recent Comet Holmes whose glowing electrical coma exceeded the size of the Sun. The visible disk of Betelgeuse tells us nothing about the physical size of the central condensed body. And like a cometary coma’s changing size as it races toward and away from the electrified Sun, red giant stars alter their size in adjusting to their electrical environment.
The UV image of Betelgeuse is smooth apart from the occasional hotspot. This is quite distinct from the UV image of the Sun, which typically has a mottled appearance due to many active regions. This smoothness of the light from Betelgeuse is a result of the quite different mode of plasma discharge of dim red stars from that of bright main sequence stars. It is the difference between the diffuse voluminous glow of a neon tube and the pinpoint light from an arc lamp.
The electric model of bright stars shows that there is an exquisitely simple control mechanism introduced by a bright photosphere. The photosphere acts like a junction transistor to regulate the current flow between the star and its environment. It results in a remarkably steady output of light and heat radiation despite a varying power supply. For example, the Sun, viewed in X-rays, is a variable star. X-rays are generated high above the photosphere and are a measure of electrical power input. They reveal the variability of the Sun’s power source. The photosphere generates the radiant output, which is stabilized by its transistor effect.
Dim red stars like Betelgeuse do not have the same power control mechanism. They respond to variation in their power supply instead by varying the surface area of their glowing plasma sheath—in other words, their visible size. Our own Sun varies slightly in size, much to the puzzlement of astrophysicists. However, what is called “the photosphere” of Betelgeuse is physically and electrically nothing like the photosphere of bright stars.
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