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When reading the question about the first use of the term exoplanet (about which Giordano Bruno and Isaac Newton already speculated but they didn't use that term for them, I think), I searched a surfed a bit along and found this on Wikipedia:

An exoplanet or extrasolar planet is a planet outside the Solar System. In several cases, multiple planets have been observed around a star. About 1 in 5 Sun-like stars have an "Earth-sized" planet in the habitable zone.

I'm not sure how this estimate is made. Is it based on observation? Is there one Earth-like planet observed for every five stars? That is, planets with more or less the same mass as the Earth, orbiting at about the same distance from the star as we orbit the sun? Is it based on a calculation?
Are planets that have a higher mass and circle around a higher mass star considered as Earth-like too (the "only" difference being that a higher gravity is present)?

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Exactly what is meant by "Earth-like" or "habitable zone" can vary from paper to paper. So the exact number of 1 in 5 depends on what those definitions are.

The basic statistic comes from analysis of observed exoplanets discovered by the transiting method - mainly by Kepler. The definition of "Earth-like" will be based on the radius of the exoplanet inferred from the depth of the transit (e.g. it might be $0.5 < r/r_{\rm Earth} < 2$).

Of course, transiting planets are rare, so the fraction of stars for which a transiting "Earth-like" planet has been found in the "habitable zone" is far lower than 1 in 5 - given that Kepler found a few thousand exoplanetary candidates from a target list of a few hundred thousand stars, the observed "Earth-like" exoplanet fraction is $<1$%.

The key point is that the observational biases against the detection of such "Earth-like" planets are reasonably well understood and involve quite reasonable assumptions - e.g., we assume that the orientation of exoplanet orbital planes is random in space, so you can estimate what fraction of such exoplanets would actually transit.

As long as you have some sensitivity to the region of parameter space that you are interested in then you can apply some sort of forward-modelling approach, whereby you simulate a population of exoplanets with particular parameters, observed with the particular instrument you have (including all the sensitivity, noise properties, observation cadence etc.) and then see what fraction of the exoplanets are detected (or "recovered"). Hence you can then correct your raw observed frequency to a true frequency.

Relevant: https://physics.stackexchange.com/questions/633661/is-our-solar-system-really-that-odd/633693#633693

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  • $\begingroup$ You seem to know everything! :) Won't the orientations of the orbits lie in the plane of the galaxy (if the galaxy is flat)? $\endgroup$ – Methadont Jun 10 at 16:35
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    $\begingroup$ @Berbierium our solar system doesn't and there isn't any evidence for non-randomness. I believe there is a Q about this somewhere. See astronomy.stackexchange.com/questions/40277/… astronomy.stackexchange.com/questions/21191/… $\endgroup$ – ProfRob Jun 10 at 16:40
  • $\begingroup$ Thanks for the links. I understand that only a small fraction of planes will make it possible for us to detect the planets. The bigger the stars the more chance of seeing a planet pass between us and the star. Doesn't that mean we should observe no planets around most stars (assuming all planets to orbit in the same plane)? $\endgroup$ – Methadont Jun 10 at 16:52
  • $\begingroup$ @Barbierium Yes. There are a few thousand exoplanetary candidates in the Kepler dataset. Kepler observed a few hundred thousand stars. So the fraction of stars with an observed exoplanet is something like 1%. $\endgroup$ – ProfRob Jun 10 at 16:55
  • $\begingroup$ So that observation confirmes the idea that most planetary systems don't "spin" in alignment with the spin of the entire milky way? (I don't think planets outside the milky way have been found) $\endgroup$ – Methadont Jun 10 at 17:00

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