# Temperature of a gas giant 23 AU from Fomalhaut

If a gas giant, weighing about 30 Jupiter masses, orbited the A-type star Fomalhaut at 23 AU, what would its temperature be? Would it be warm enough to have ammonia clouds like Jupiter or Saturn, or would it be too cold to support these and instead “condense” into an ice giant?

At this distance, radiation from the star is irrelevant to set the planetary temperature. Effectively, you are having a Brown Dwarf, fusing deuterium and at the age of Formalhaut (440 Myrs) still having some formation heat retained. While $$\rm NH_3$$ is certainly present in the atmospheres of those objects, you'd need to have a look at detailed models of BDs e.g. Mukherjee et al. 2022 to get a feeling for what clouds you would 'see' on the exterior, if that is the aim of your question.

I don't think anything that has 30 $$M_J$$ of mostly gas can 'condense' into an ice giant, ever.

The mass ranges of stars and planets are separated by the mass range of a third type of objects, brown dwarfs. Brown Dwarfs have a mass range from about 13 Jupiter masses (or about 4,131.4 Earth masses) to about 75 Jupiter masses (or about23,835 Earth masses.

An object with about 30 Jupiter masses (or about 9,534 Earth masses) would be a brown dwarf, not a planet.

If your planet is 23 AU from Fomalhaut the amount of radiation it receives from Fomalhaut would be 1 dived 23 squared, or 1 divided by 529, or 0.001890, as much as it would receive it if was 1 AU from Fomalhaut.

Fomalhaut A has a luminosity of about 16.63 plus or minus 0.48 that of the Sun.

16.63 times 0.001890 is 0.031436672. Thus a planet 23 AU from Fomalhaut A would receive about 0.031436672 as much radiation as Earth get from the Sun.

The semi-major axis of Saturn's orbit is 9.5826 AU. So Saturn receives about 1 divided by 9.5826 squared, or 1 divided by 91.82622276, or 0.010890135, as much radiation as Earth receives from the Sun.

So your brown dwarf would, if it was identical to Saturn, have a temperature slightly higher than that of Saturn. Of course your 30 Jupiter mass brown dwarf would be very different in many ways from Saturn, which would change its temperature.

I note that the star TW Piscus Austrini is also known as Fomalhaut B, since it is a companion star to Fomalhaut. And it is claimed that the star LP-876-10 is also a companion of Fomalaut.

https://en.wikipedia.org/wiki/TW_Piscis_Austrini

https://en.wikipedia.org/wiki/Fomalhaut_C

I also note that Fomalaut A is known to have several rings of dust surrounding it. And there have been a number of attempts to detect planets orbiting Fomalhaut A.

https://en.wikipedia.org/wiki/Fomalhaut

• "So your brown dwarf would, if it was identical to Saturn, have a temperature slightly higher than that of Saturn." you are stating the Equilibrium temperature here, not the effective temperature, which includes the internal one. This, young and massive object would be dominated by $T_{\rm int}$, hence $T_{\rm eq}$ is irrelevant. Feb 24 at 22:20