How does rogue planet PSO J318.5-22 stay 800ºC?

Question

According to this article, the rogue planet (meaning a planet which does not orbit a star) PSO J318.5-22 has a surface temperature of 800ºC and weather that features molten iron rain. Without a star pumping energy into its atmosphere, how does it maintain these temperatures? The linked article doesn't explain, nor does its wikipedia page. Is this typical for rogue planets? I had assumed a planet with no star would be more cold and barren than Pluto.

Answer 1

I'm not an expert but I believe the following is correct.

The object PSO J318.5-22 is referred to as a "young L dwarf." An L dwarf is a type of brown dwarf, meaning a mass of hydrogen and other elements that is not large enough to fuse hydrogen. PSO J318.5-22 is Jupiter-sized, but I guess there is no particularly important difference between "failed stars" and "rogue planets" other than size, so I think astronomers use the same term (brown dwarf) to refer to both.

Now, brown dwarfs are formed from clouds of (mostly) hydrogen gas. As the gas cloud collapses, it loses gravitational potential, and by the first law of thermodynamics that energy has to go somewhere. Much of it becomes heat, and so when a brown dwarf is formed it is hot. (This is also the main reason why the core of the Earth is hot, though in that case nuclear fission also plays a role.) The only way the object can lose that thermal energy is by radiating it into space, and that can take a long time, although it will generally be quicker for smaller objects, due to their small thermal mass and higher surface-area-to-volume ratio.

Another important thing to note is that gravitationally bound objects can actually have negative heat capacities, meaning that their temperature goes up as they lose energy. This is because taking energy out of the gas means the gas contracts, which means that it loses yet more gravitational potential energy, and this can turn into even more heat than was lost in the first place. This isn't perpetual motion - gravitational potential is being used up, and eventually the object will condense and switch to having a positive heat capacity again - but it does mean that the temperature of a ball of gas can stay high for a long time as it radiates.

Thus, I conclude that the reason PSO J318.5-22 is hot is that it is young. (About 10-30 million years old according to Liu et al. 2013; compare this with the Earth's 4 billion years and you'll see that it's really very young indeed.) It has plenty of heat left over from its formation, and is still radiating it away, so it will become cooler over time. I don't know what the time scale for this is, but I assume that the age figure above is calculated from the temperature, along with knowledge of how rapidly the object loses heat. (Gaseous objects radiate as black bodies to a good approximation, so the Stefan-Boltzmann law can be used to calculate this.)

Answer 2

The plot below shows a model of how an isolated mass of gas (planet, brown dwarf) cools down with time, taken from Baraffe et al. (2003). The cooling tracks are labelled with mass in Jupiter masses. The time axis is logarithmic in years, the luminosity axis is lograrithmic in units of solar luminosities.

Young brown dwarfs and giant planets are governed by an equation of state similar to that in the Sun. They are born with large radii and then begin to contract because they lose heat from their surfaces as radiation. But as they contract they also release gravitational potential energy. The virial theorem tells us that half of that energy gets radiated and half goes into making the interior of the brown dwarf hotter. Larger brown dwarfs have more potential energy and are able to stay luminous for longer.

The effective temperature at the surface is simply obtained from Stefan's law. It turns out that whilst the luminosity decreases, the radius decreases and $L/R^2$ also decreases, but not that quickly. Hence brown dwarfs and giant planets can stay quite hot for a considerable time, as shown in the diagram.

There is a couple of other wrinkles to the story though. The object you are talking about has an arguable age. In their discovery paper, Liu et al. (2013) used the luminosity of the object ($10^{-4.4}\ L_{\odot}$) and an age of 12 Myr to claim this was a giant planet (you can place it on the diagram below yourself and see it falls at around the 5 Jupiter mass track. However, subsequent work has suggested that the beta Pic moving group that this object may belong to is older - about 24 +/3 Myr. This means that the inferred mass of this object is bigger, probably $>10$ Jupiter masses. EDIT: Just noted tha the new paper by Biller et al. (2015),that triggered your question, uses the revised age and arrives at 8.3 Jupiter masses.

The wrinkle here is that at around these masses ($\sim 12$ Jupiter masses) the core of the brown dwarf gets hot enough to ignite deuterium. This provides an additional source of energy that keeps the brown dwarf hot. It can be seen clearly as a plateau in the luminosity plots below for the 20 Jupiter mass track, and a shallower gradient over the first 100 Myrs for the 12 Jupiter mass track. So it may not be just gravitational contraction that is keeping this object hot.

Second wrinkle is the difference between "hot start" and "cold start" models. The models plotted above are "hot start" models. The brown dwarf/planet starts off as a collapsing gas cloud. However, the cold start models might be more appropriate for a genuine planet that forms by accretion onto a rocky core. The gas cools a lot during the accretion process, so these planets start off colder. I show below plots from Spiegel & Burrows (2012) with both hot- and cold-start variants.

The luminosity and temperature ($\sim 1200-1500$ K) found the Liu et al. (2013) (or 1160 K by Biller et al. 2015) looks too big to be anything below 10 Jupiter masses in the cold-start models. So if it is a giant planet, then it seems unlikely to have formed by core-accretion. From that point of view it looks like it's a low-mass brown dwarf to me.