What percentage of gas giant exoplanets are in the habitable zone?

Question

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.

Answer 1

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:

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.

Answer 2

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).