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Approximately what percent of exoplanet gas giants discovered so far are in the habitable zones of their stars? I hear that most of them are "Hot Jupiters", orbiting so close to their stars that the heat causes them to swell up like a hot air balloon.

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Of the gas giants, the number of "hot Jupiters" is about the same as the number of "hot Neptunes." A little under 9% of known gas giants are in the habitable zones.

An article by John Wenz has the discoveries thus far collated into a chart:

All the Exoplanets We’ve Discovered in One Small Chart

The claim, "most of them are "Hot Jupiters", orbiting so close to their stars that the heat causes them to swell up like a hot air balloon," is at best a bit of a stretch - the only reference that I found for this was a Gizmodo article about Kelt-9b. The Nature paper, A giant planet undergoing extreme ultraviolet irradiation by its hot massive-star host, that discusses Kelt-9b says,

The planet is also extremely inflated relative to theoretical models, with a radius of $\sim 1.9\ R_J$. Poor redistribution of heat and radius inflation (both of which are also observed in WASP-33b), have been linked to high stellar insolation, although the exact physical mechanisms remain uncertain.

So they did observe that Kelt-9b had a larger radius than is normally expected from a planet of that mass, and it receives massive amounts of radiation from its star, but it cannot be concluded from that that it is the same as putting a balloon filled with air near a heat source.

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I was curious about the figure given in Mick's answer (~9%), so I did some data-crunching of my own. I looked at the NASA Exoplanet Archive, in particular the table of confirmed planets. I was interested in four parameters:

  • $a$, the planet's semi-major axis
  • $M\sin i$, the planet's minimum mass
  • $T$, the temperature of the star
  • $R$, the radius of the star

From the final two, I could approximate the luminosity of the star by the Stefan-Boltzmann law: $$L=4\pi\sigma R^2T^4$$ I downloaded the dataset (3774 exoplanets) including only those parameters, then filtered out all the planets that lacked all four (leaving 932). I then created lists of all four parameters. Going back through this list, I removed planets of less than $\sim0.05$ Jupiter masses (i.e. Neptune-mass or less) and objects of more than $\sim20$ Jupiter masses (which are really essentially brown dwarfs - the cutoff's fuzzy). This left me with 751 probable giant planets, including ice giants.

I estimated the habitable zone by using a black body approximation for the surface temperature of a planet: $$T_p=\left(\frac{L(1-a)}{16\pi\sigma d^2}\right)^{1/4}$$ where $a$ is albedo and $d$ is the mean distance to the star. I set $a\approx0$, for simplicity. Then, for each planet, I calculated the orbital radii at which water would freeze and boil, and finally compared the measured semi-major axis to see if it fit inside the two. I ended up with 72 giant planets in the habitable zone - a total of 9.6% of the giant planets I considered, similar to the result given in Mick's answer.

In summary, according to the NASA data I looked at, around 10% of giant planets lie in the habitable zone, although uncertainties in planetary and stellar parameters could change this.

Notes:

  • Increasing the minimum mass even up to $1M_J$ changed my result by no more than 1% of the population; lowering it down to $0.01M_J$ also changed it by only about 1% of the population.
  • Varying the albedo from $0.1$ to $0.9$ changed the results by about 1.5% of the population, going in both directions.
  • I assumed no greenhouse effect when calculating the effective surface temperature.
  • Removing the lower mass restriction entirely (i.e. including terrestrial planets) brought the result down by about 1% of the population.
  • I used Python after downloading the .csv file from the Archive (code available on GitHub).
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