How big can a gas giant become before it's considered a star?
How does the theoretical maximum compare the observed maximum?
[Physics] When does a planet become a star
astronomyastrophysicsstars
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In answer to your question of "What happens to the neighboring star?", according to the Johns Hopkins folks, it gets blown away:
(Credit Johns Hopkins)
I would be a little skeptical of the certainty of this claim only because we have not been able to observe any of these Type Ia explosions up close while it is happening. That's why the Type Ia SN 2011fe is so important to us. It is merely 21 million light years away, instead of a billion.
The nuclear fusion that powers stars has little to nothing to do with electrons. In the cores of stars, temperatures are high enough that all the electrons are stripped from the nuclei, leaving a pure plasma.
As stars contract and condense out of interstellar dust, their gravitational potential energy is converted to heat faster than this heat can be radiated away. Once the temperature reaches roughly $10^7\ \mathrm{K}$, protons (hydrogen nuclei, stripped of their electrons) have a nonnegligible chance of sticking together when they colide, with one of them converting to a neutron along the way: $$ {}^1H + {}^1H \to {}^2H + e^+ + \nu_e. $$ This is the first step of the PP chain, and it releases energy. There are more steps that ultimately turn four protons into a helium-4 nucleus. In more massive stars than the Sun, there are other ways (e.g. the CNO cycle) to catalyze this process with the help of carbon, nitrogen, and oxygen.
In any event, there is nothing extreme about the gravity. It just happened to pull matter from a huge distance close together. If you took infinitely spread apart particles totaling mass $M$ and formed a uniformly dense sphere of radius $R$, the gravitational potential energy released would be $$ \frac{3GM^2}{5R}, $$ about half of which you expect to go into heating the material. Once hot, hydrogen naturally forms helium in exothermic processes.
Stellar reactions are self-regulating in the sense that if the rate of fusion increases, the additional luminosity would push the outer layers of the star, causing the star to expand and cool, thus reducing the reaction rate. Thus as long as there is hydrogen in the core, stars more or less burn at a steady rate once ignited.
Best Answer
You mean like Arthur C. Clarke's 2010 when Jupiter turns into a star? We often turn to Jupiter's mass ($M_j$) when thinking about this problem.
It turns out there's a whole class of stars that fuse so faintly that we can only see them well in infrared. Brown dwarfs (which are still called "stars") turned out to be so cool that only new infrared technologies could find them. We now know they are very common, so common that new classes, L and T (cooler than M) had to be made for them. Surprisingly they turn out to be about the same diameter as Jupiter. Between 0.073 solar masses (78 Jupiter-masses) and 13 Jupiter-masses, brown dwarfs do fuse their natural deuterium (heavy hydrogen, with an extra neutron) to helium. Below 13 Jupiters (0.0124 solar masses), fusion stops altogether.
The brighter stars like our sun begin above 0.073 solar masses where they are hotter and emit more visible radiation.
So you need at least 13 Jupiters to get it going and the theoretical limits are still being refined by observations of Brown Dwarfs. There is a fussy line between planets and brown dwarfs. Small brown dwarfs can still be considered stars and not planets even if they are not fusing because they probably burned off all their deuterium (form of hydrogen).
From Wikipedia: