# How much mass would my hot Jupiter lose?

Having done a bit of research lately, I learnt that hot Jupiters are often victim to having their atmospheres gradually stripped away by their parent stars. That got me thinking:

Assuming a planet of roughly Jupiter's mass and composition, and a parent star similar to the Sun, how much of the planet's mass would be lost over the lifetime of the planet?

Would it depend on the distance from the star?

• Yes, it depends on distance. Hot Jupiters are hot because they are close to their sun, which is also why they may lose atmosphere. Dec 1, 2020 at 23:43

### Jupiter at 0.02AU will lose about 5%-7% via hydrodynamic escape

From Wikipedia (source)

If the atmosphere of a hot Jupiter is stripped away via hydrodynamic escape, its core may become a chthonian planet. The amount of gas removed from the outermost layers depends on the planet's size, the gases forming the envelope, the orbital distance from the star, and the star's luminosity. In a typical system, a gas giant orbiting at 0.02 AU around its parent star loses 5–7% of its mass during its lifetime, but orbiting closer than 0.015 AU can mean evaporation of a substantially larger fraction of the planet's mass. No such objects have been found yet and they are still hypothetical.

• The fact that to even be a hot jupiters they need to be very close to the host star anyway, leads credence to this lower bound. Dec 1, 2020 at 16:09

## The planet will lose 0.2% - 19% of its mass.

Zendejas et al. discussed mass loss of planets around low-mass stars, but we can adapt their basic tools to our situation. They found that a planet with a radius $$R_p$$ orbiting at a distance $$D$$ from a star with a stellar wind of density $$\rho$$ and speed $$v$$ will lose mass at a rate $$\dot{M}_p\approx2\pi R_p^2\alpha\rho v$$ or $$\dot{M}_p\approx\left(\frac{R_p}{D}\right)^2\frac{\dot{M}_*\alpha}{2}$$ with $$\dot{M}_*$$ the mass-loss rate of the star and $$\alpha$$ an efficiency parameter. In the worst-case scenario, the winds remove the entirety of the star's mass (impossible, in reality), and if we set $$\alpha=1$$, then for a $$1M_{\odot}$$ star, a Jupiter-mass planet orbiting at $$D=0.02\text{ AU}$$ (as Ash considered) would lose 29% of its mass (where the mass lost is $$\dot{M}_p\Delta t$$, so $$\dot{M}_*\Delta t=M_{\odot}$$, with $$\Delta t$$ the star's lifetime). In reality, $$\alpha$$ should be closer to $$1/3$$, at least for terrestrial planets, and if we assume that the star loses more like half of its mass (still quite high), we find that it would lose 4.8% of its mass.

This is in close agreement with the numbers Ash cites. Note that $$\dot{M_p}$$ is proportional to the square of the radius of the planet and the inverse square of its orbital radius. At $$D=0.01\text{ AU}$$, we find that the planet should lose 19% of its total mass; at $$D=0.1\text{ AU}$$, we get 0.2%. A typical hot Jupiter lies within those two extremes, so that gives us some rough bounds.

• This is very informative, thank you. Do you think I should publish this question on Astronomy SE? Dec 1, 2020 at 17:52
• @NFrancis I'm glad it's helpful. I would advise against cross-posting; we typically discourage it, and your question's certainly on-topic here on Worldbuilding. Dec 1, 2020 at 17:54
• Noted. Thanks again Dec 1, 2020 at 19:03
• Bit of a while later, but I had a few questions. Equations aren't my strong suit... 1) What units of measurement do are the radius, diameter etc. given in? 2) Is the p in Rp the same as the individual P? Dec 14, 2020 at 1:21
• @NFrancis The units can be anything you want, so long as you convert them appropriately at the end. For instance, you could write $R_p$ in km and $D$ in AU, then convert $D$ to km. 2) Which do you mean by "individual P"? If you mean the $\rho$, then no, that's different. But all of the subscripts do refer to the planet. Dec 14, 2020 at 15:52