How far from Betelgeuse is its habitable zone?

Betelgeuse is a red supergiant or hypergiant in the constellation Orion. It is one of the biggest and brightest stars seen from the Earth, and is expected to soon go supernova. The habitable zone, or Goldilocks zone, is the distance from the parent star where the temperature allows for liquid water to exist on a planet's surface (in case the planet has an atmosphere of at least ~0.0061 atm (triple point of water)). How far is the habitable zone of Betelgeuse, in astronomical units? For comparison, the Sun's habitable zone is at about 0.7-1.7 astronomical units (other than Earth, Venus and Mars are on its rims).

Nobody knows the limits of the Sun's habitable zone, or how broad or narrow it is.

Here is a link to a list of various estimates of the inner, or outer, or both, edges of the circumstellar habitable zone of the Sun:

https://en.wikipedia.org/wiki/Circumstellar_habitable_zone#Solar_System_estimates

Note that one well known estimate, that of Hart et al. in 1979, makes the habitable zone very narrow, while another well known estimate, that of Kasting et al in 1993, produces a conservative habitable zone that is several times as wide as Hart's and an optimistic habitable zone that is wider still.

And there are other estimates with the inner edge of the habitable zone closer to or farther from the Sun than Kasting's and with the outer edge of the habitable zone closer to or farther from the Sun than Kasting's.

So if you study all of the original papers where those limits of the habitable zone were proposed, you can decide which ones are most convincing to you, and then use the habitable zone for the Sun to compare with Betelgeuse to determine Betelgeuse's habitable zone.

Taking the safe route, I will assume that a planet would have to receive exactly as much radiation from Betelgeuse as Earth receives from the Sun in order to be habitable.

According to Wikipedia, Betelgeuse has a luminosity about 126,000 times that of the Sun.

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

Since the square root of 126,000 is 354.96, a planet orbiting about 354.96 AU from Betelgeuse should receive the same amount of radiation from Betelgeuse as Earth receives from the Sun and thus should be within the circumstellar habitable zone of Betelgeuse, no matter how broad or narrow that habitable zone is.

But Betelgeuse is a variable star. Its luminosity varies between about 90,000 to 150,000 times the luminosity of the Sun, so the distance from Betelgeuse where a planet would receive exactly as much radiation from Betelgeuse was Earth receives from the Sun would vary between 300 AU and 387.298 AU.

Possibly a planet could orbit Betelgeuse with a somewhat elliptical orbit so it was closest to Betelgeuse when Betelgeuse was least luminous and farthest from Betelgeuse when Betelgeuse was most luminous and so constantly receive the same amount of radiation as Earth receives from the Sun.

Betelgeuse is classified as a semiregular variable star, indicating that some periodicity is noticeable in the brightness changes, but amplitudes may vary, cycles may have different lengths, and there may be standstills or periods of irregularity. It is placed in subgroup SRc; these are pulsating red supergiants with amplitudes around one magnitude and periods from tens to hundreds of days.[8]

https://en.wikipedia.org/wiki/Betelgeuse#Variability

The semiregular nature of Betelgeuse's variability means that nobody could even begin to design an orbit around Betelgeuse that would enable a planet to constantly receive the same amount of radiation as Earth receives from the Sun.

So planets in the habitable zone of Betelgeuse would receive significantly varying amounts of radiation from Betelgeuse as the star varied. Whether that would make life impossible on those hypothetical planets is unknown.

I may add that there are still more problems with having a planet with conditions suitable for life orbiting Betelgeuse; the answer by antispinwards mentions some of them.

So the probability that there will be lifeforms on any planets orbiting Betelgeuse when Betelgeuse becomes a supernova and destroys all its planets seems to be very, very, very low.

I note that humans can not survive in the majority of the biosphere of Earth. Humans can't survive in most places where other Earth lifeforms can survive.

A discussion of the conditions necessary for humans or similar beings to survive can be found in Habitable Planets for Man Stephen H. Dole, 1964, 2007.

https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf

Here is a link to a list of the nearest stars and brown dwarfs to the Sun, stars within a distances of 5 parsecs or 16.3 light years:

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

There could be worlds with some kind of life in some of those star systems.

And what would happens to those hypothetical worlds with life orbiting stars within 5 parsecs or 16.3 light years of the Sun if the Sun became a supernova? The Sun will never become a supernova, but if it did the planets of those nearby stars would probable receive so much radiation during the supernova event that their oceans and atmospheres would boil away and their surfaces turn to red hot lava, and all life on them would die.

And a supernova might be deadly to life on worlds at a much greater distance. I am not very familiar with the distances at which a supernova would wipe out all life on a planet.

Betelgeuse is expected to have a supernova explosion in less than 100,000 years. During that time many stars will get closer and closer to Betelgeuse and then start to get farther and farther from Betelgeuse, as those stars and Betelgeuse orbit around the center of the galaxy.

Here is a link to a list of stars which, according to the calculations of astronomers, have passed within 5 light years of Earth in the past three million years or will pass within 5 light years of Earth in the next three million years.

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

And it seems to me that any alien astronomers on a planet orbiting a star near Betelgeuse would be very displeased to learn that their star is getting closer and closer to Betelgeuse and is likely to be only a few light years from Betelgeuse when Betelgeuse supernovas.

• It's a fact that Mars is in the habitable zone, at least during its perihelion, because the temperatures on its surface allow for liquid water to exist. At certain times of the Martian year the conditions on certain locations on Mars allow for liquid water. Therefore, those who exclude Mars from the habitable zone are wrong. But Venus and Mars are indeed close to the inner and outer rim of the zone. While on Venus' surface liquid water can't exist, it could in its upper atmosphere if it got there somehow. – Ioannes Jul 19 '20 at 5:18
• Unfortunately, we don't know the mass of Betelgeuse, so it's not possible to give a precise estimate of the orbital period of a planet in its habitable zone. Wikipedia gives recent estimates ranging from 11 to 19 $M_\odot$. Combining that data with your habitable zone radius estimates, the orbital period of a body in that zone is somewhere in the range of 1160 to 2300 years. – PM 2Ring Jul 19 '20 at 5:46
• @PM2Ring Where did I claim that? I only wrote "in case of". That doesn't mean it's likely. Also, if it has no crust it's obviously a lava ocean planet rather than a terrestrial planet. :-) – Ioannes Jul 19 '20 at 6:46
• @PM2Ring I just was curious where Betelgeuse's habitable zone is. I know that from an evolution point of view it is unlikely to have Earthlike planets. – Ioannes Jul 19 '20 at 6:51
• – PM 2Ring Jul 19 '20 at 7:14

The concept of a habitable zone really doesn't apply to a star like Betelgeuse. In addition to being a highly unstable and variable supergiant, it's a runaway star, suggesting that it was formerly a member of a multiple star system with a companion star that went supernova. Its relatively rapid rotation is difficult to explain via single star evolution, suggesting that it has undergone a stellar merger (Wheeler et al. 2017, Chatzopoulos et al. 2020). These events do not bode well for the survival of orbiting planets, even if planets could form in the environment around the progenitor system containing multiple early-B or O-type stars. Any terrestrial planets would at best still be in the magma ocean stage and would not have time to cool before Betelgeuse itself undergoes a supernova.

The environment of Betelgeuse is strongly affected by stellar variability and eruptions of substantial amounts of material from the star itself, creating a wind environment that would strongly affect habitability (e.g. via atmospheric erosion) even if you somehow magicked the right kind of planet into existence at a vaguely appropriate distance.

• And that wind isn't just gas / plasma, it contains substantial amounts of abrasive dust. Wikipedia says: "Assuming the Jovian orbit of 5.5 AU as the star radius, the inner [dust] shell would extend roughly 50 to 150 stellar radii (~300 to 800 AU) with the outer one as far as 250 stellar radii (~1,400 AU)". – PM 2Ring Jul 19 '20 at 5:58

Habitable zones, defined in terms of equilibrium temperature, scale with the square root of the luminosity of the star. So whatever the habitable zone limits $$[a_{inner},a_{outer}]$$ are for the Sun, for another star a good starting guess is $$\sqrt{L/L_\odot}$$ times those limits*.

For Betelgeuse the simple-minded square root model gives a time-varying habitable zone 300 to 387 times further out. A planet could stay in it, assuming a similar width as the habitable zone in the question scaled up by this factor.

As the other answers rightly point out, there are many reasons why Betelgeuse likely doesn't have any habitable worlds around it, but these reasons are (with the exception of variability) unrelated to its luminosity. The problem of actually defining the habitable zone (even in the solar system) is that other planetary properties like atmospheric composition, water surface area, pressure, rotation etc. can affect it in nontrivial ways: the limits are not exact. To further complicate things one might demand that a planet remain in the zone "long enough" to develop life, which requires that stellar evolution does not shift the zone beyond the planet over the suitable (unknown) time-span.

[* Why the square root relationship? A planet at distance $$a$$ receives $$P_{in}=(\pi r^2)( L / 4\pi a^2)=r^2L/4a^2$$ Watt of starlight. Emitting like a blackbody it radiates $$P_{out}=4\pi r^2 \sigma T^4$$ Watt. Since $$P_{in}=P_{out}$$ we get $$a^2=L/16\pi \sigma T^4$$, or $$a\propto \sqrt{L}$$ for some fixed habitable temperature $$T$$. Obviously this is complicated by greenhouse heating, for starters.]

• Of course, but there's a zone too close to a star where there is no way liquid water can exist on the surface (like in case of Mercury even if it had an atmosphere) and one too far from the star where it is too cold for liquid water to exist (unless the air pressure is as high as in gas planets but liquid water can't be there for other reasons). – Ioannes Jul 19 '20 at 9:03
• @Greenhorn - Yes, and the star distance of these zones roughly scale with the square root of luminosity. The inner and outer edges just correspond to different T. – Anders Sandberg Jul 19 '20 at 18:50