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Of the exoplanets found so far, is there one that can exchange material with its host? How could we prove that?

Io might be a good example, but it is not a planet.

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I believe WASP-12b, a hot Jupiter, is a good example of what you're looking for. Li et al. (2010) first predicted that there should be gas transfer - easy, because the planet has a semi-major axis of only about 3 times the radius of WASP-12. Aside from the mass loss, extreme temperatures and distortion from tidal heating make the planet stand out.

The gas should be transferred into a small disk around the planet, which could reach temperatures of 3,000-4,000 K. Eventually, there should be significant angular momentum transfer between the star/disk and the planet. However, the authors note that certain assumptions of their model mean that this angular momentum transfer may not be as significant. There is also the possibility that a super-Earth in the disk could influence the interaction.

Follow-up observations by Hubble showed that there is in fact mass transfer between WASP-12b and the star, with gas reaching peak velocities of around 100-200 km/s.


The mass loss rate $\dot{M}$ should be approximately $$\dot{M}\sim\frac{\dot{E}_tR_p}{2GM_p}$$ where $R_p$ and $M_p$ are the radius and mass of the planet, and $\dot{E}_t$ is the tidal heating rate, given as $$\dot{E}_t\sim\frac{e^2GM_pM_*}{a\tau_e}$$ for stellar mass $M_*$, semi-major axie $a$ and characteristic eccentricity damping timescale $\tau_e$.

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