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Could we say that an individual star is almost a closed system?, as many of the stars like the sun don't exchange significant amount of their mass with their environment (except solar flares & other material ejections)

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Mass loss is one of the most important features of stellar evolution! I suppose much depends on what you mean by "until its death".

It is true that most of the mass loss occurs during the last 10-20% of their lives - either in the asymptotic giant branch phase for stars less than about 10 solar masses or the supergiant and Wolf-Rayet phases for massive stars. During these phases the star could easily lose more than half its mass in powerful, radiatively driven winds. It is because of this that stars of initial masses up to 8 solar masses leave behind white dwarfs of a solar mass or less, and why even stars of 20-30 solar masses may end up producing 1-2 solar mass neutron star remnants. Without mass loss there would be many more (and more massive) black holes.

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    $\begingroup$ It's a really great question of scale right? The energy loss by the Sun during normal Hydrogen burning is minimal but actually sustains life on this planet! Closed system indeed! $\endgroup$ – levitopher Oct 14 '16 at 23:18
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    $\begingroup$ It is important to distinguish between the conversion of mass to thermal and neutrino energy in fusion (which is quite a minor matter compared to the stellar mass) and the loss of gas and dust migrating off the surface under the influence of the star's own radiation pressure which is what Rob is referring to here. Also, cue the beautiful picture of the SN1987a shockwaves interacting the the shells of earlier ejected mass. $\endgroup$ – dmckee Oct 14 '16 at 23:56
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It does not exchange mass directly, but it radiates energy.

From equation $E^2 - (pc)^2 = m^2c^4$, you can see that the mass of the star decreases if energy is radiated.

So, the mass of the star does not remain constant.

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    $\begingroup$ The asker said "...exchange significant amount..." - how significant is the mass lost due to radiation? $\endgroup$ – Johnny Oct 15 '16 at 6:30
  • $\begingroup$ "Significant" is open to interpretation. It's significant enough to power all life processes on this entire planet. $\endgroup$ – Lightness Races in Orbit Oct 15 '16 at 12:17
  • $\begingroup$ I have sugegsted an edit of Your answer. if you wrap text in (double) dollars it will be rendered using $\TeX$ interpreter. $\endgroup$ – Crowley Oct 15 '16 at 12:43

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