the number of habitable planets & moons...
A planetary Drake equation
The Drake equation [1] is a formula first proposed by the astronomer Frank Drake in order to estimate the number of intelligent, communicating civilizations in the Galaxy. The equation essentially multiplies the number of stars in the Galaxy by the probability of each star having a habitable planet with intelligent aliens on it. The intelligent aliens part is the largest unknown in the equation. How likely is it that an intelligent species will really evolve on such planets?
There really is no way of knowing until we start to detect them or prove they do not exist. But one thing we can do much more reliably is use the same kind of reasoning to work out the number of habitable planets in the Universe. If we use our definition of habitability from the previous article and assume we only care about environments which can support complex life rather than simple microbial organisms, then we may proceed to estimate this number. We will perform this calculation for planets initially, and then look at moons.
Firstly, consider that estimates of the number of stars in our galaxy vary from around 200-400 billion [2, 3] and so we will use 300 billion as an average in what follows. In general, it is believed that main sequence stars offer the best chance for life since they are stable for long periods of time and do not exist in some exotic form like a black hole or a pulsar. Fortunately, around 90% of all stars are main sequence [4].
The number of habitable moons
In the previous article, we discussed how exomoons could also be habitable worlds. Running through the planetary Drake equation again, we need to make a few small changes for the case of exomoons. The same constraints on the host star still exist and so nothing needs to be changed there.
Let us consider a suitable host planet being anything from an Earth to a Super-Jupiter. There is no reason why a captured large moon could not be stable around a Super-Earth object for billions of years from a dynamical point-of-view [14]. We therefore boost Mayor’s 30% figure (for Neptune-mass or less) to 50% (for any kind of planet). Let us also assume that the habitable zone for exomoons is extended by around 50% due to the possibility of tidal heating maintaining temperate conditions in traditionally cold-zones. This means that 15% of all planets can host a habitable exomoon.
But how many planets have large moons in the first place? To this end we have very little information but looking at our Solar System there are at least two planets, out of eight, where a moon has been formed through a capture/impact origin, which seems to be a requirement for a large moon. So let us roughly take the figure that 10% of planets host a large moon. Running through the planetary Drake equation again yields:
25 million habitable-exomoons in the Milky Way
So our calculation suggests that there are roughly half the number of exomoons than exoplanets. One important thing to realize is that these calculations are based on many guesses but many of the assumptions underlying each calculation are the same. Whether the ratio is 0.5, 1, 2 or 5 is not very reliable right now, but what does seem perhaps more persuasive is that if we talk about ‘order of magnitude’ kind of figures, the number of habitable exoplanets and exomoons is ball-park equal.
In a previous version of this calculation I relaxed the M-dwarf constraint on exomoons which predictably gives about 10 times more habitable moons than planets, due to the large number of M-dwarf stars out there. I wanted to revise the figure to present a more conservative approach and to emphasise how we are really only able to speculate about ‘orders of magnitude’ and not specific numbers or even ratios.
The important thing seems to be that there are many millions of both habitable planets and habitable moons out there in our galaxy.
Photo credit: NASA, ESA, RAS, UCL, G. Bacon (STScI), BSN, Andy McLatchie and Sylvain Girard
The Greater Universe
In the last two sections we estimated that there are ~50 million habitable exoplanets and ~25 million habitable exomoons in the Milky Way alone. Let us therefore choose ~100 million habitable environments per galaxy as our order of magnitude estimate i.e. our galaxy is not special. What does this mean for the whole Universe?
The numbers are staggering.
With 100 billion galaxies estimated to exist [15], perhaps many more, we are looking at the total of number of habitable environments exceeding:
10 000 000 000 000 000 000 worlds
= 10 million trillion
10 million trillion, take a moment and just say to that yourself. It is colossal.
What are the consequences? Read the next article for my take on what this number implies...
references
[1] Frank Drake’s presentation, Green Bank meeting, West Virginia, USA, 1960
[2] Sanders, Robert (January 9, 2006). "Milky Way galaxy is warped and vibrating like a drum". UCBerkeley News. http://www.berkeley.edu/news/media/releases/2006/01/09_warp.shtml. Retrieved on 24-05-2006.
[3] Frommert, H.; Kronberg, C. (August 25, 2005). "The Milky Way Galaxy". SEDS. http://www.seds.org/messier/more/mw.html. Retrieved on 09-05-2007.
[4] Vik Dhillon (29th September, 2008), “Detailed stellar models”, http://www.vikdhillon.staff.shef.ac.uk/teaching/phy213/phy213_detailed.html. Retrieved 24-05-09
[5] LeDrew, G.; The Real Starry Sky, Journal of the Royal Astronomical Society of Canada, Vol. 95, No. 1 (whole No. 686, February 2001), pp. 32–33. Note: Table 2 has an error and so this article will use 824 as the assumed correct total of main sequence stars
[6] Michel Mayor’s presentation, JENAM conference, Hatfield, London, 21-04-2009
[7] Lineweaver, C. H. & Grether, D. 2003, ApJ, 598, 1350
[8] The Extrasolar Planet Catalogue, Retrieved 24-05-2009
[9] Gonzalez, G., Brownlee, D. & Ward, P. 2001, Icarus, 152, 185
[10] Prantzos, N. 2008, Space Science Reviews, 135, 313
[11] Lineweaver, C. H., Fenner, Y. & Gibson, B. K. 2004, Science, 303, 59
[12] Bond, A. & Martin, A. R. 1978, Journal of the British Interplanetary Society, 31, 411
[13] Boss, A. 2009, The Crowded Universe, Basic Books, ISBN-13: 978-0465009367
[14] Barnes, J. W. & O'Brien, D. P. 2002, ApJ, 575, 1087
[15] Mackie, Glen (2002-02-01). "To see the Universe in a Grain of Taranaki Sand". Swinburne University. http://astronomy.swin.edu.au/~gmackie/billions.html. Retrieved on 20-12-2006.
trackbacks
[1] Centauri Dreams - 16/03/2010 - [link]
[2] Where the Sun Hits the Sky - 10/03/2010 - [link]
Out of the main sequence stars, 22.7% are F, G and K-type stars [5] which should be capable of supporting habitable planets. Go lower than a K-type and you find yourself with M-dwarfs which have habitable zones so close to the star that planets become tidally locked and may experience atmospheric collapse or instability (see the previous article for more details on this). Go higher than an F-type star and the stars burn for less than a billion years which seems too short for complex life to evolve based upon our own planet.
From this sample of stars, recent work by Michel Mayor and his team at Geneva have used the HARPS telescope to measure the fraction of stars with planets [6]. They find around 30% +/- 10% of F, G and K-type stars harbour Super-Earth or Neptune mass planets. Using 30% as a fixed value and assuming that very roughly half of this sample correspond to rocky planets and half to Neptune-like gas giants then we may write down that 15% of all F, G and K-type stars have rocky planets around them. It should be noted that this value is very likely an underestimate due to fact planets of Earth mass are currently below the detection threshold. (This value also agrees with planetary models, e.g. see [7]).
Of these planets, how many exist in the habitable zone? Of the 330+ exoplanets so far found [8], around 30 are in the habitable zone of their host star suggesting a rough fraction of 10% would be a very good estimate based on current knowledge (incidentally, this also works well for Solar System).
The final thing to consider is the Galactic habitable zone (GHZ), which proposes only certain regions of the Galaxy itself may harbour habitable planets [9]. The GHZ is quite a controversial idea and is currently under-fire from some quarters [10]. But let us assume the GHZ exists and therefore any value we arrive at will also be an underestimate rather than an overestimate. This means that only 5% of stars can harbour habitable planets [9]. (This value is doubled to 10% according to a more recent study, see [11]).
Put all of these fractions together and you end up with:
50 million habitable-zone exoplanets in the Milky Way
For comparison, in 1978, Bond & Martin [12] made highly conservative assumptions and estimated 10 million habitable exoplanets in the Galaxy. Our figure is larger, and more empirical, as a result of including the results from exoplanetary science, which has only been in existence since 1992. In contrast, Alan Boss predicts that there are 10 billion habitable exoplanets in the Milky Way [13].
The Universe is big... Here is Earth’s humble place within the observable Universe
Sizes of main-sequence stars from spectral type M to O. Our Sun is a G-type.