Six planet system is perfectly tuned

A rare system of six exoplanets, all smaller than Neptune but larger than Earth, has been found with orbits that are all resonant with each other. The system was discovered by astronomers led by Rafael Luque of the University of Chicago, who suggest that the planets have remained undisturbed in this configuration since their formation a billion years ago.

The planetary treasure trove also provides one of the best opportunities for characterizing “mini-Neptunes”, which are a mysterious class of planet that are absent from the Solar System.

The planets orbit an orange star called HD 110067, which lies about 100 light–years away. The innermost two planets, dubbed b and c, were discovered by NASA’s Transiting Exoplanet Survey Satellite (TESS) mission. Luque and colleagues then noticed that the orbits of planets b and c were in resonance. This is because their orbital periods of 9.114 days and 13.673 days have a ratio of 2:3. There was also something else in the data – rogue transits that could not be attributed to planet b or c.

Given the resonant orbits of b and c, it stood to reason that if there were other transiting planets in the HD 110067 system, then they might share orbital resonances. Using the rogue transit events as starting points, and guessing that any third planet called d might also have a 2:3 orbital ratio with planet c, allowed the team to predict when planet d might transit next. They followed this up with the European Space Agency’s CHEOPS telescope and discovered the planet as predicted.

From the orbital period of planet d, which is 20.519 days, Luque’s team were then able to predict a fourth planet called e, with a 30.793-day orbit that is in 2:3 resonance with planet d, and which matched one of the unassigned transits seen by TESS.

Laplace angles

There were still several unexplained transits in the TESS data. To figure out what planets these transits belonged to, Luque’s team took advantage of the complex rules of resonant orbits as laid down by the eighteenth century mathematician Pierre-Simon Laplace, who studied the resonant orbits of some of Jupiter’s moons.

Like Jupiter’s moons, HD 110067’s planets “always have to be within certain angles of each other in order that any perturbations they exert on each other can’t grow,” says team member Andrew Collier Cameron of the University of St Andrews, who focused on measuring the masses of the planets with the radial-velocity technique.

The angles that Cameron alludes to are referred to as Laplace angles, and they provide stable configurations of orbits. Any deviations from them would result in the gravitational perturbations growing over time. The result would be the planets being thrown out of resonance and quite possibly sent into orbits that cross each other, where they might collide.

By estimating what the Laplace angles should be, Luque’s team were able to predict that planets f and g would have orbital periods of 41.0575 and 54.7433 days respectively. These matched the two remaining unexplained transits in the Kepler data. The pairs of planets e and f, and f and g, each have a 3:4 orbital resonance.

There is the possibility that there are even more planets orbiting HD 110067 on wider orbits within the star’s habitable zone. However, if there are more planets, neither TESS nor CHEOPS has recorded a transit. This means that an attempt to find a seventh or eighth planet would be a “blind search”, says Luque. “But if we did get lucky and found an extra planet, then certainly it would be very interesting due to its potential prospects for habitability.”

However, there is no prospect of searching for more planets any time soon. If there was a planet on a 75-day orbit, for example, CHEOPS would have to observe HD 110067 for at least that time to observe one transit. However, observing time is very precious, as Luque explains; “We prefer to invest observing resources in refining the parameters of the known planets in the system”.

Characterizing the planets

Further work on the system will instead involve refining the parameters of the known planets – which is dependent upon measuring their masses. The radius of each planet is determined from how much starlight they block when they transit in front of the star – they range in size from 1.9 to 2.85 Earth radii. Masses are determined by radial velocity measurements, which look at how the planets cause the star to wobble. Once both their radius and mass are known, the densities of the planets can be calculated. Whether the planets have thick atmospheres could be determined by the James Webb Space Telescope.

So far, masses have only been obtained for three of the planets, specifically planets b (5.69 Earth masses), d (8.52 Earth masses) and f (5.04 Earth masses). This was done using the HARPS-North instrument on the Galileo National Telescope in the Canary Islands and the CARMENES spectrograph on the 3.5-metre Calar Alto Observatory in Spain.

“The remaining three planets are still flying slightly under our detection capabilities,” says Cameron. In particular, stellar activity can mask the radial velocity signals of the planets. “So the next thing to do is to push deeper with the radial velocities so that we can determine the masses of the planets.”

Transit-timing measurements provide another way of measuring the planetary masses. As the planets orbit their star, their gravity can pull each other back, or speed each other up, resulting in slight discrepancies in when the planets are seen to transit. The size of the discrepancy is determined by the gravitational pull, and hence their mass.

Regardless of what these planets are like, their existence in resonant orbits alone is notable. Theory suggests that the planets formed in these resonances. Ordinarily these resonances are then destroyed by gravitational perturbations from passing stars or marauding giant planets, but around HD 110067 this doesn’t seem to have happened.

“Given a dynamically stable environment this idealistic kind of planetary system could form and even more remarkably it can actually survive for a very long time,” says Cameron.

As such, HD 110067 may provide a window through time, retaining the configuration that the planets had immediately after their formation.

The findings are described in Nature.