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 long 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, deriving 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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Just for fun I did a limited analysis of Jupiter size planets found using radial velocity or astrometry (mostly the former) techniques with the following criteria: 1) Data from the on-line sources http://exoplanet.eu/catalog/bd%2B15_2375_b/ and http://www.exoplanets.org/ giving planets discovered through Apr. 2016. 2) Msini: 0.5-10 M(J) 3) Distance to star less than 58 parsecs 4) Planets out to 5200 day periods (or 6AU) 5) Only data from K,G or F dwarfs on main sequence (V or IV/V). This was an attempt to minimize observational bias. I still found a pronounced peak in Jupiters with periods less than 50 days, but less pronounced if plotting against distance (sma). However, I also found peaks in numbers of Jupiters at slightly farther out than Earth and at a distance about the same as the beginning of the asteroid belt in the solar system.The Earth peak is much wider and goes away in the period histogram. This data is dominated by planets orbiting G stars 89 of 139 (107 of 171 planets). Interestingly (or not) there is a peak in Jupiters that are in "multiple Jupiter systems" around the orbit of Venus that "washes out" the Earth peak. The percenatage of "hot Jupiters" depends on definition, but 22 of 171 have period less than 50 days and 13 have orbits less than 0.1AU. If anyone is interested in more detail of my results please e-mail me.

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@RobJeffries See above comment. Could there still be some "observational bias" that I am missing? – Jack R. Woods Apr 19 at 19:18
Yes, there are enormous biases favouring the detection of hot Jupiters and your procedure has not minimised those at all. – Rob Jeffries Apr 19 at 22:27
@RobJeffries I apologize for my ignorance. My question to you would be do you think that it is possible that the HARPS project, which has been monitoring stars less than 58pc for over 10 years now, may have missed some Jupiter size planets, with periods about that of Jupiter or less, orbiting stars they have been watching? There has been a fall off in discoveries (out of 107 "Jupiters" found in this range orbiting G stars only 18 have been found since Jan 2012/ 2 of those were in the same system and three were found in systems that already had a closer in "Jupiter" detected). – Jack R. Woods Apr 24 at 13:37
And I may have to apologise for mine. I had assumed you were dealing with a parent sample that was incomplete. If the HARPS project have surveyed every F,G,K star within 58pc with uniform sensitivity and sampling for 10 years, then yes, they should be highly complete for all Jupiters with periods of less than say 5 years, except for those around young stars. If however they have been observing selected samples, with instruments with varying (increasing) sensitivity then I suspect a bias towards hot Jupiters is still present, especially amongst the K-dwarfs. – Rob Jeffries Apr 24 at 14:27