# What proportion of planetary systems have been found with 'Hot Jupiters'

According to the NASA website "The strange attraction of Hot Jupiters", one of the main types of exoplanets that have been detected are Hot Jupiters, which are

These are behemoth worlds that orbit close to their parent stars, blocking a fraction of the star’s light when it transits in front.

Planets that are from as large as Saturn through to far larger than Jupiter, orbiting in a matter of days very close to their parent star. Something our solar system does not have.

What proportion of star systems have Hot Jupiters within their systems? Is it a case that Hot-Jupiter-less systems such as our own are unusual?

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In 2011, about 20% of the exoplanets found were hot Jupiters. That is a lot, but it is strongly biased simply because there are the easiest planets to detect. You can detect exoplanets by transit (that means that the planet passes in front of its host star which decreases the luminosity of the observed star during the transit), hot Jupiters being closer to their host star and bigger than smaller planets will therefore be easier to detect. You can detect exoplanets by radial velocity, which means that you detect variation of the position of the host star due to planet's gravity. The closer and the heavier the planet is, the larger the variation will be, and therefore the easier to detect.

That's why it is important to say "In 2011"; as our detection techniques (and telescopes) improve, the proportion of hot Jupiters should decreases.

Edit: To put that in perspective, you can read this article from Jason Wright in which he tries to estimate the "real" ratio of hot Jupiters orbiting around "normal" stars (F, G and K type stars). This ratio is actually much smaller than the currently observed ratio, about 1.2%.

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three-quarters? that's a lot more than I expected. Do you have any references that you can include in your answer? –  user8 Sep 25 '13 at 8:47
Sorry, I got the number wrong (I mistook it with earlier estimates). I putted a more reliable numbers with a good reference; I also add some details about the "real" ratio one should expect. –  MBR Sep 25 '13 at 9:21
No apologies needed - this is an excellent answer and answers both questions I had very nicely. –  user8 Sep 25 '13 at 9:49

I completely agree with the answer from MBR. The number is actually $1.20\pm 0.38$ per cent, is published by Wright et al. (2012) and is the fraction of F, G, K stars that have a hot Jupiter defined as being larger than 0.1 Jupiter masses and having an orbital period less than 10 days. Table 2 of that paper summarises results from other workers, who obtain between 0.5 and 1.5 per cent. The paper also discusses observational biases, including metallicity.

It has log been known that close-in planet incidence is higher around more metal-rich stars. There is also a bias whereby it is easier to find planets around metal-rich stars, whereas the average star in the solar neighborhood is slightly metal-poor compared with the Sun.

A study by Gonzalez (2014) accumulates our current knowledge of exoplanetary systems and their metallicities, dewriving a planetary incidence rate $$P_{planet} = \alpha 10^{\beta[Fe/H]},$$ with $\alpha= 0.022 \pm 0.007$ (i.e. 2.2 per cent), $\beta=3.0\pm 0.5$ and where [Fe/H] is the usual logarithmic ratio of the metallicity of the star to the metallicity of the Sun. (i.e. the Sun has [Fe/H]=0).

This calculation is done for giant planets with orbital periods less than 4 years, so not all of them would be classed as hot Jupiters. Bottom line, the number given by Wright et al. is about right on average, but it is higher for higher metallicity stars.

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