Living on an edge: how much does a planetary system’s tilt screw up our measurements?

Journal Juice: summary of the research paper, 'On the Inclination and Habitability of the HD 10180 System',  Kane & Gelino, 2014. (Shared also on Google+)

This animation shows an artist's impression of the remarkable planetary system around the Sun-like star HD 10180. Observations with the HARPS spectrograph, attached to ESO's 3.6-metre telescope at La Silla, Chile, have revealed the definite presence of five planets and evidence for two more in orbit around this star.

HD 10180 is a sun-like star with a truck load of planets. The exact number in this ‘truck load’ however, is slightly more uncertain. The problem is that we haven’t seen these brave new worlds cross directly front of their star, but have found them by looking at the wobble they produce in the star’s motion. As a planet orbits its stellar parent, its gravity pulls on the star to make it move in a small, regular oscillation as the planet alternates from one side of the star to the other. By fitting this periodic wobble, scientists can estimate the planet’s mass and location. 

The problem is that when there is a truck load of planets, there are multiple possible fits to the star’s motion, and each of these yield different answers for the properties of the planetary system. 

In 2011, a paper by Lovis et al. determined that there were 7 planets orbiting HD 10180, labelled HD 10180b through to HD 10180h. However, they were uncertain about the existence of the innermost ‘b’ planet and their model made a number of inflexible assumptions about the planet motions.

In this paper, authors Kane & Gelino revisit the system. One of the constraints they remove from the Lovis model is the insistence that a number of the planets sit on circular orbits. Rather, the authors allow the planets to potentially all follow squished elliptical paths around their star. In our own Solar System, the Earth has an almost circular orbit around the sun, but Pluto does not, moving in a squashed circle of an orbit. 

The result of this new model is a six planet system, where the dubious planet ‘b’ is removed. Two other planets, ‘g’ and ‘h’, also have their orbits changed, with ‘g’ now moving on a more elliptical path. This is particularly interesting since planet ‘g’ was thought to be in the habitable zone: the region around the star where the radiation levels would be right to support liquid water. How does g’s new orbit change things?

Before charging off in that direction, the authors ask a second important question: what is the inclination of the planetary system? Are we looking at it edge-on (inclination angle, i = 90 degrees),  face-on (i = 0) or something in between (i = ??) ?

This question is important since it affects the estimated mass of the planets. The more face-on the planetary system is with respect to our view on Earth, the larger the mass of the planets must be to produce the observed star wobble. Unfortunately, inclination is devilishly hard to determine without being able to watch the planets pass in front of their star. 

While it was not possible to view the inclination directly, the authors ran simulations of the planet system’s evolution to test out different options. Since the planets’ masses change with the assumed inclination, the gravitational interactions between the worlds also changes. Some of these combinations are not stable, kicking a planet out of its orbit. Unless we got very lucky with regards to when we observed the planets, the chances are these unstable configurations are not correct. This allows scientists to limit the inclination possibilities. The simulations suggested that an angle less than 20 degrees was not looking at all good for planet ‘d’. 

With the new model and a set of different inclinations, the authors then returned to the most exciting (from the point of view of a new Starbucks chains) planet ‘g’. Even with its new squished-circle orbit, planet ‘g’ spends 89% of its time in the main habitable zone. The remaining 11% is within the more optimistic inner edge for the habitable zone, whereby the temperatures might be able to support water for a limited epoch of the planet’s history. This is a pretty promising orbit, since there is evidence that a planet’s atmosphere might be able to redistribute heat to save it during the time it spends in a rather too toasty location.

However, planet ‘g’ has other problems.

If the planet system is edge-on, the mass of planet ‘g’ is 23.3 x Earth’s mass with a rather massive radius of 0.5 x Jupiter. Tilting round to face-on at i = 10 degrees (bye bye planet ‘d’) increases that still more to 134 Earth masses and the same radii as Jupiter. 

All options then, suggest promising planet ‘g’ is not a rocky world like the Earth, but a gas giant. The best hope for a liveable location would therefore be an Ewok-invested moon. Yet, even here the authors have doubts. Conditions on a moon are affected both by the central star and also heat and gravitational tides from the planet itself. Normally, these are small enough to forget compared to the star’s influence, but with the planet skirting so close to the star for 11% of its orbit, this may be sufficient to give a moon some serious dehydration problems. 

The upshot is that the inclination of the planetary system’s orbit is vitally important for determining the masses of the member planets and that HD 10180g is worth watching for moons, but probably not ready for a Butlins holiday resort.