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I'm writing a sci-fi novel and I have an some astrophysics questions. First, is it possible for a binary system to be made up of a large gaseous planet and a dwarf star?

I know it's possible to have two stars orbit each other, and a planet around those (since there is still a center of mass that the system orbits) but could one of the stars be replaced with a planet of sufficient mass without the planet becoming a star itself?

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The mass of Jupiter is around $\approx 10^{-4} M_{sun}$.

A super-jupiter type of planet, is roughly $80$ times the mass of Jupiter, so, $\approx 10^{-2} M_{sun}$.

The least massive white dwarf star, is roughly $\approx 0.17 M_{sun}$.

So we are talking about a mass ratio of roughly $5\%$. According to wikipedia, the Charon-Pluto orbit in the solar system is considered a binary system, and Charon has $12\%$ the mass of Pluto.

So, I didn't do any calculations to locate the center of mass, in order to make sure it is located outside the bodies, and thus claim it as a binary system, but, looking at these data, it looks promising, and it seems to indicate it is possible to have a binary system made of a star and a planet [a very small dwarf star, and a super-jupiter planet].

However.. It might not look like a binary system, even if it is. For instance, this is Charon-Pluto:

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