Plasma and Stars
Are there stars not made of plasma?
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Plasma is an electrically neutral medium of unbound positive and negative particles (i.e. the overall charge of a plasma is roughly zero). It is important to note that although the particles are unbound, they are not ‘free’ in the sense of not experiencing forces. When a charged particle moves, it generates an electric current with magnetic fields; in plasma, the movement of a charged particle affects and is affected by the general field created by the movement of other charges.
For more details see this link too.
A basic effect of the motion of charges is that electromagnetic radiation is created, i.e. light and thus stars certainly have plasma because they are called stars for being stationary sources of light in the night sky, in contrast to planets. The sun in the center of the solar system is a star and allows us to study the composition of stars, including the evident plasma.
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Our Sun, and all of the other stars, are made of plasma, much of interstellar space is filled with a plasma, albeit a very sparse one, and intergalactic space too.
[note that "all other stars is not really correct in this wiki link. see below]
Stars that are not wholy plasma are neutron stars:
A neutron star is the collapsed core of a large (10–29 solar masses) star. Neutron stars are the smallest and densest stars known to exist.1 With a radius on the order of 10 km, they can, however, have a mass of about twice that of the Sun. They result from the supernova explosion of a massive star, combined with gravitational collapse, that compresses the core past the white dwarf star density to that of atomic nuclei.
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Neutron stars that can be observed are very hot and typically have a surface temperature around 6×10^5 K.
They are complex stars.
Also very large stars that become supernovae, and in general the whole spectrum in the evolution of stars has stars which are not wholly plasma.
To be visible stars, they have to emit light so that their outer shell must be plasma.
So plasma in the outer atmosphere is necessary for a star to be visible in the night sky, but there do exist stars that are not wholly plasma. Thanks to DrunkenCodeMonkey for catching it.
you ask:
In what percentage stars are made of plasma?
They are mostly plasma, i.e neutral ionized matter, even the core, because of the very large kinetic energies acquired in the formation from the primordial plasma due to the gravitational attraction .
The core of the Sun extends from the center to about 20–25% of the solar radius. It has a density of up to 150 g/cm3 (about 150 times the density of water) and a temperature of close to 15.7 million kelvins (K). By contrast, the Sun's surface temperature is approximately 5,800 K.
This very high temperature does not allow nuclei and electrons to stabilize into neutral atoms, and even at that high density the core is a plasma. The temporary formation of neutral nuclei gives spectral lines detectable in the star's spectrum, but the temperatures are so high that no solid core can result. The amount of neutral atoms in a plasma is very small, and is controlled by the relevant equations, as was pointed out in the comments.
The planetary masses cooled off enough to acquire a solid core.
No, I think what is meant here is that in addition to containing lots of plasma, all stars also include a bit of neutral gas near their edges (this is where absorption lines in their spectra come from). This is an ambiguity in English - "things are mostly this" can either mean "most things are all this" or "all things are mostly this".
Hard to give a value, as it varies based on type of star, environment, and point in its life, but you can't really go wrong assuming that neutral gases are only a tiny fraction of the total mass.