# How hot can the surface of a planet be?

I just read this article https://edition.cnn.com/2018/07/02/world/newborn-planet-image-study/index.html and noticed that the astronomers estimates the surface temperature of the planet to 1000 °C. This made me wonder how hot can the surface of planet be? Slightly depending on definitions the highest known melting points for any material seem to be in the range 3500-4000°C.

What would happen if the surface temperature of an Earth like planet was (significantly) higher than that? Or is that impossible?

It's not entirely clear how do you define a planet being "Earth-like" (to me, a planet with a surface as hot as 1000K is nothing Earth-like!), but I'll try to give a general idea what makes a planet a planet instead of a diffuse gas cloud.

A planet does not hold together because it's a piece of solid rock. On the contrary, a pretty solid planet (or a smaller piece of rock, like the recently imaged Ultima Thule) will fly apart in pieces if it rotates too fast. The main point to note is that it's practically unimportant what a celestial body is made of. It can be a pile of loose sand, or a huge ball of liquid. It can be even a ball of hot plasma, just like stars are, provided they are massive enough that the matter—the hot gas—doesn't escape the gravity well of the object too quickly.

So, if the planet temperature is high enough that it melts as a whole, this lump of liquid lava will still be a whole normal planet, spherical if it doesn't rotate on its axis, or geoidal if it does; the faster is the rotation, the more flattened is the shape along the rotation axis.

1000°C is not even close to the point where a rocky planet starts losing mass due to evaporation, assuming that its composition is close to that of the Earth. Earth constantly loses H₂ and He, the light gasses, to space. Hot vaporised rock also has the high kinetic temperature and is prone to escape the gravity well.

As the temperature grows, you'll get more material in a gaseous form. The loss of mass (simply speaking, the gradual evaporation of the molten planet) requires that a significant portion of gas molecules posses enough energy to overcome the gravity of the body. The effect will be dampened if the planet has atmosphere: hot gas rising and trying to escape will inevitably "bump into" colder gas of upper atmosphere (if you prefer more physical lingo, it will exchange kinetic energy with the cool gas, so it's temperature evens out as convection goes on). Here we assume that (1) the atmosphere is transparent enough (so that it's cooler as we go farther up and away from the hot surface, and doesn't absorb a lot of starlight itself), and the major heating of evaporating material happens at the body surface, which absorbs the most star's radiative energy; (2) the atmosphere does exits at all, instead of being completely blown out (or significantly rarefied) by the stellar wind of highly energetic particles.

If these two assumptions hold, the planet can exist for millions of years as a molten ball of whatever it's made of without dissipating, and, back of the envelope check, the temperatures up to many a thousand K do not seem to imply that the body becomes gravitationally unbound due to material evaporation, when gas kinetic energy overcomes the gravitational potential energy of the planet.

• How does evaporation lead to mass loss? Imagine that Earth was molten so rock boiled away. Wouldn't the resulting gas just rise a bit and then be pulled back by gravity? Similar to if you cook water at the stove at home with a lid on the pot, the steam is stuck in the lid and falls back? Thank you for your answer.
– d-b
Commented Jul 14, 2019 at 11:38
• A good question! The Earth atmosphere is blown off by solar wind, and Earth is a calm place far away from its home star. But these hot planets sometimes have an orbital period of a few days, they are very close to their star. At this distance, everything that can be blown off by the stellar wind, likely will--we are speaking of a smaller planet with defined surface and temperature. If the planet is a gaseous heavy super-Jupiter brown dwarf type, then I do not really know. This thing may even probably steal stellar wind and gain total mass. This all becomes handwavy without a computable model. Commented Jul 14, 2019 at 14:49
• I'm reading @Buttonwood's link to Wikipedia article on "hot Jupiters", and it has not a bad overview of possible scenarios. Commented Jul 14, 2019 at 14:54