# Floating free

Recent results from planet-hunting surveys suggest that there is a sizeable population of planets which are not bound to any star. The origin of these free-floating planets is not yet understood. Did they form in protoplanetary discs like other planets, later to be removed by some dynamical process? Or were they created directly from the collapse of gas clouds, in the same way as stars?

A leading hypothesis to explain their origin postulates that they were formed in systems of several giant planets. After the damping effect of the protoplanetary disc ended when the disc disappeared, the planets interacted with each other strongly, throwing some out of the system and into interstellar space. This scattering process explains the distribution of exoplanet eccentricities, as well as explaining the existence of some planets on highly inclined orbits.

A recent paper by Veras & Raymond asks how effective such scattering can be at creating free-floating planets. The central problem is that there are, on average, two free-floating giant planets for every star in the Galaxy, while less than half of stars appear to have even one gas giant planet orbiting them. This suggests that each scattering event must throw out several planets to account for this discrepency in numbers.

Veras & Raymond quantify this more thoroughly as follows. The ratio of free-floating planets to stars must be equal to the fraction of stars that host giant planets, multiplied by the fraction of those that undergo scattering events, multiplied by the average number of planets ejected in each scattering event. All of these numbers can be quantified.

According to Sumi et al’s microlensing results, there are $1.8^{+1.7}_{-0.8}$ free-floating giant planets for every star. While the errors on this estimate are large, it is clear that the number of such planets is at least comparable to and probably greater than the number of stars.

The fraction of stars hosting giant planets is not known for certain, but radial velocity surveys (sensitive to planets close to their stars) suggest at least 15% of Sun-like stars host giant planets, while microlensing results suggest the fraction may be higher. Note however that not all of these stars will either currently or in the past have hosted more than one planet, which would be required for scattering to take place.

The fraction of planetary systems undergoing scattering events has been estimated at around 75%, in order to reproduce the large numbers of eccentric giant planets in the radial velocity surveys.

Putting these together allows the average number of planets ejected from each system to be estimated. Taking mid-range values from the above estimates, Veras & Raymond find that around twelve Jupiter-mass planets must have been ejected from each planetary system, an astonishingly high number. Assuming extreme values gives a range of between 2 and 50 ejections per system. Even the lower bound may be too large to credit: our own Solar System currently contains only two gas giants.

How many planets can be ejected from a system? There must to at least as many planets initially as are later ejected, so the authors answer this by performing numerical simulations of systems containing up to 50 gas giant planets. The results are shown below. Typically, between 20% and 70% of the total number of planets are ejected. Hence, to explain the figure of 12 ejections per system, systems of giant planets must form with on average several dozen planets.

Fraction of planets ejected from multiple planet systems, assuming all the planets have the same mass (left) or different masses (right). From Veras & Raymond (2012).

Forming this many planets seems implausible, because there is simply not enough space in a typical planet-forming disc to form them all. The maximum number of planets that might be formed is estimated by the authors to be around 8–13, far lower than the number needed for 12 ejections.

Hence, it is likely that some other means of creating free-floating planets must be at work, as well as endogenous scattering. The authors postulate disruption by other stars coming close to planetary systems, effects on planets’ orbits when stars reach the ends of their lives, rare collisions between protoplanetary discs, and the effects of the Galaxy on planets’ orbits. However, all of these may meet with the same objection: that since there are more free-floating planets than stars, and not all stars form giant planets, each star must supply a large number of planets to the free floating population, by whatsoever means. Perhaps the most likely explanation is the authors’ final suggestion: that the free-floating planets form directly from interstellar gas clouds, in the same way as small stars. In which case, free-floating planets would be born free, rather than liberating themselves in violent instabilities.