Friday, January 22, 2016

Rogue Planets – Numbers

Do we have any clues whatsoever about how many rogue planets there are in the galaxy? Unless the numbers are much larger than that for stars, there is no significant peril from their existence. The distance they would have to come to, relative to a star, in order to disturb the planets there is the ratio of the square root of the mass ratio, which is something like a thousand to a million. That is 30 to a thousand. So, there would have to be rogue planets at many times the density of stars.

Since they are invisible, is there any way to get an upper bound on the density of rogue planets? Recall, an upper bound says there cannot be more than this quantity. If the upper bound is 10 times the number of stars, then it’s no prize for rogue planets. They would be relegated to being a minor contributor to galactic perils.

One way to look is to address the total mass of the galaxy. Everybody knows the galaxy is missing mass. It is possible to measure the rotation rate of the stars in the disk, and compare that to the centripetal force caused by the stars, plus clouds and anything else we can see. Much of the mass is missing, and astronomers have come up with many ideas about what it consists of. Rogue planets is one of those ideas. If rogue planets make up the same amount of mass as the stars do, the numbers are of the order of some thousands of times more rogue planets than stars. This is plenty to qualify as a galactic peril.

We haven’t directly seen any rogue planets in the neighborhood of our solar system. If one drifted through, even out at the orbit of Neptune, the gravitational effects would be noticeable. But our solar system is so small compared to the galaxy, and we have only had astronomers for such a short time compared to anything else in the galaxy, that we can’t come up with a better upper bound than the missing mass one.

How about Kepler? That planet hunting satellite is looking for planets orbiting stars which have transits, meaning they exactly have an orbital plane aligned with the direction to Earth, and we see the obscuration caused when they pass in front of Kepler’s eyes. To think about it, if a rogue planet passed through the cone stretching from Kepler to a star, there would be obscuration there also. So, Kepler could detect a rogue planet crossing, if only the data was checked for that. Kepler’s data looks for periodic reductions in the light hitting Kepler’s scopes, as only an orbiting planet would produce a periodic signal. All the other things which lead to changes in the light output, such as sunspots or flares, are not periodic. Kepler’s data hounds like to find three or four or ten orbits to confirm that there is some potential planet candidate.

A rogue planet happening to go by between Kepler and a star it was observing would lead to a light reduction, but so would a sunspot. Only if the rogue planet were much closer to Kepler would the blocking of light be significant. If it were close enough, then the data hounds might just notice it. It would have a characteristic shape, mainly, flat for a long period. Out at 50 light years, with a star at 500 light years, G-sized star, Neptune-sized rogue planet, the time is of the order of a couple of hours. That might just be detectable.

But alas, nothing like that has been noticed. There was a big news flair recently when some reduction in light was noticed on a particular star, but the light curve reduction wasn’t flat, and SETI enthusiasts thought it might be some giant structure around the star made by aliens, but astronomers put their mind to it and said it was just comets. Since nothing has been noticed at all, if we assume somebody, somewhere, would have seen it if it did happen, we can use this result to put an alternate upper bound on rogue planets. Later data led to them not thinking it was comets, but no conclusions yet and nobody thinks it is relevant to the rogue planet count.

Unfortunately, using reasonable assumptions on star size, rogue planet size, closeness of rogue planet to Earth, velocity comparable to the average non-rotational speed of stars in the galaxy, 100,000 stars observed for five year by Kepler, the upper bound is still well above the one found by the missing mass argument. This is too bad, but it does mean that Kepler’s tremendous achievements do not extend to excluding large numbers of unobserved rogue planets in the galaxy.

This means that alien civilizations, lasting many millennia, might have to do something about a rogue planet drifting in toward their solar system. Regrettably, we don’t know much about what happens if one were to show up, even for our own solar system. If the rogue planet came into the inner solar system, and it was large, it would change the orbit parameters. How much remains to be calculated. One thing that helps is that there are balancing effects in some ways. If the rogue planet slowly came by, on an orbit like a comet but hyperbolic, the inner planets might make multiple orbits while it was present. It cannot be too slow, as the star’s gravitation will speed it up temporarily, but even a few orbits means that the gravitational pull to expand the orbit on the closer side of the orbit would be balanced by the gravitational pull of the rogue planet when it was on the other side, the farther side, or the orbit. Balanced, but certainly not exactly, as the closer side gets more gravity outward than the opposite side gets gravity inward. This is red meat for those who like to calculate planetary orbits.

The effect on outer planets, or indeed inner planets, would be huge if the trajectory of the rogue planet came anywhere near to it. This is exceedingly unlikely, as there is such vast spaces in a solar system, and the cross-section of large gravitational disturbance is small in comparison. Having it come to within 1% of the orbital radius of a planet would certainly qualify for large gravitational perturbation, but that is only a one in ten thousand chance for a random trajectory of the rogue planet. It might be more likely to pass either to the solar system north or south of the planetary plane, meaning that planets might gain some axial tilt from its passage. It is the integrated effect of the gravitation that controls the magnitude of the effect, so such a passage by would have an amplified effect if the speed of the rogue planet was close to the orbital speed of a planet.

All in all, rogue planets are still on the list of possible galactic perils, meaning that they could be a reason some alien civilization has to leave its home planet, since it was pushed out of the habitable zone or some other miserable orbital change happened, and they would be on the lookout for nearby replacements. Hopefully, this doesn’t happen in the nice galactic neighborhood we live in.

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