Astronomy & Celestial Mechanics
the sky, computed
Concept

Giant planet — where it appears

A planet massive enough to have captured a thick envelope of hydrogen and helium, from roughly Neptune's mass up to about thirteen Jupiters. Giants form beyond the snow line and are far rarer round small stars than round large ones.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

How planet occurrence rises with the host star's iron, by kind of planet. Planet occurrence relative to its value at solar metallicity, on a logarithmic axis, against the host star's iron abundance [Fe/H] (zero is the Sun; one unit is a factor of ten). Each class is a power law, occurrence ∝ 10^(β[Fe/H]). Giant planets within a few astronomical units follow β = 2, the relation found in the first large radial-velocity survey to measure it: 12 per cent of stars at [Fe/H] = +0.3 have one, against 3 per cent at solar and under 0.3 per cent at −0.5 — a factor of 158 across the range drawn. The small planets found by transits rise far more gently; the slopes drawn, β = 0.5 for sub-Neptunes and 0.2 for super-Earths, are representative of published fits, which range from nearly flat to about a doubling across this interval depending on orbital period.

A threshold that makes iron matter only to giants

A star with twice the Sun's iron is four times as likely to have a giant planet, and barely more likely to have a small one. The steep law and the flat one look like two mechanisms. A core racing its disc, run over a spread of discs, produces both — steep where winning is rare, flat where it is common.

exoplanets · Occurrence rates Small planets and giant planets per star, against the mass of the star. Planets per star against the host star's mass, both on logarithmic axes, for small planets (one to four Earth radii, orbital periods under 200 days) and giant planets (above a third of Jupiter's mass, within 2.5 astronomical units). The small-planet rate is drawn as 1.1 per star at one solar mass rising as M^−0.6; the giant rate as 7 per cent at one solar mass falling towards small stars as M^1. Both are representative of published fits, not fits of their own. At 0.3 solar masses a star has 2.3 small planets and a 2.1 per cent chance of a giant; at one solar mass 1.1 and 7 per cent. The ratio of small planets to giants changes by a factor of 7 between the two, so a statement about how common planets are depends on which star it is about as much as on which planet.

More small planets round smaller stars

A red dwarf has about twice as many small planets as the Sun's kind of star and a third as many giants. The two populations move in opposite directions along the same axis, and the small planets were built from discs several times poorer.

exoplanets · Occurrence rates Giant planets per logarithmic interval of orbital distance, and who can see where. Giant planets (a third of Jupiter's mass to thirteen Jupiters) per star per unit of the natural logarithm of orbital distance, against distance, round Sun-like stars. The curve is a broken power law representative of the long radial-velocity surveys: rising as a^0.8 to a peak at 3 AU and falling beyond it as a^−1, which integrates to 2.7 per cent of stars inside 1 AU and 12 per cent in all. The shaded bands are where each method has the sensitivity to measure it: radial velocities out to about 7 AU, where two decades of monitoring cover one orbit, and direct imaging beyond about 10 AU, where a young giant can be separated from its star. The peak sits near the outer edge of the radial-velocity window, where a planet has completed one or two orbits in the data, and the fall beyond it lies entirely outside that window — so the peak's position is where the two methods have to be joined rather than a place either can measure alone.

A peak that neither survey can see alone

Giant planets become commoner with distance from their star out to a few astronomical units, and then rarer. The rise is measured by radial velocities and the fall by direct imaging, and the peak between them sits where neither method is comfortable.

exoplanets · Occurrence rates

Named alongside it

The objects these essays reach for when they reach for this one.

Occurrence rateProtoplanetary discRadial-velocitySelection effectStellar massConvective envelopeCore accretionDirect imagingExtrapolationHabitable zoneM dwarfMetallicity

All concepts