Missing Mass, the Absent Planet X and Yet More Comments on Trujillo & Sheppard and Batygin & Brown

Since my two previous posts attempting to debunk the idea of “Planet X” – a supposed large planet in the outer reaches of the Solar System – the occasional media reference has informed me that teams of researchers and various items of multi-million pound equipment are apparently employed chasing the wild Planet X goose.  Indeed, as I go to press, Scientific American has just emailed me a link to an article reporting the latest developments in the search.  Then, yesterday, New Scientist reported on speculation as to where Planet X (or “Planet Nine” as they call it) might have come from.  A paper New Scientist refer to has a bearing on my own conclusions so I’m adding a note about it at the end of this piece.

I had some further thoughts some weeks ago, and, it’s time I cleared away a loose end by writing them up.

My Original Proposed Explanation

Let’s recap.  The story so far is that, based on certain characteristics of the orbits of Sedna and a dozen or so other distant minor planets – often referred to as trans-Neptunian objects or TNOs – several groups of researchers have proposed a “Planet X” or sometimes “Planet Nine”, Pluto, the ninth planet for a certain generation, having been relegated to mere “minor planet” status. As I consider the demotion of Pluto to be utterly ridiculous, I’m going to stick to the terminology “Planet X” for the hypothetical distant planet.  You can take “X” to be the Roman numeral if you want.

I was immediately sceptical about the existence of Planet X.  Some other explanation for the TNO orbits seemed more probable to me.  Planet X would be exceptional, compared to the eight (or nine) known planets, not only in its distance from the Sun, but also in the plane of its orbit.  To explain the strange features of the orbits of the minor planets by the known “Kozai mechanism” of gravitational “shepherding” of smaller objects by a large body, Planet X would have to orbit perpendicular to the plane of the Solar System, within a few degrees of which the planes of the orbits of all the other planets lie.

Some weeks ago then, in my first post on the subject, I reviewed what had been written on the subject of Planet X.  I think now that I was perhaps overly influenced by the Scientific American article on the subject and considered much the most important aspect of the minor planets’ orbits to be their near 0˚ arguments of perihelion (AOPs).  That is, they cross the plane of the Solar System roughly when they are nearest the Sun.

On reflection, I was perhaps wrong to be so dismissive of the eccentricity of the minor planets’ orbits.  All orbits are eccentric, I pointed out.  But the minor planets orbits are really quite eccentric.  There may be a cause of this eccentricity.

I also think it is important that the minor planets’ orbits are highly inclined to the plane of the Solar System compared to those of the inner planets, but they are nevertheless less inclined than random, i.e. in most cases somewhat less than 30˚.

I went on to suggest that perhaps something (other than Planet X) was pulling the minor planets towards the plane of the Solar System.   I suggested it was simply the inner planets, since there would be a component of the gravitational attraction of the minor planets perpendicular to the plane of the Solar System.  I included a diagram which I reproduce once again:

160205 Planet X slash 9In my second post about Planet X a few days later, I looked more closely at the original scientific papers, in particular those by Trujillo & Sheppard and Batygin & Brown.  I wondered why my suggestion had been rejected, albeit implicitly.  To cut a long story short, the only evidence that the minor planet orbits can’t be explained by the gravity of the inner eight planets (and the Sun) is computer modelling described in the paper by Trujillo & Sheppard.  I wondered if this could have gone wrong somehow.

Problems with Naive Orbital Flattening

Let’s term my original explanation “Naive Orbital Flattening”.  There are some issues with it:

First, if the minor planets are “falling” towards the plane of the Solar System, as in my figure, as well as orbiting its centre of gravity, they would overshoot and “bounce”.  They would have no way of losing the momentum towards the plane of the Solar System, so, after reaching an inclination of 0˚, their inclination would increase again on the opposite side of the plane as it were (I say “as it were” since the minor planets would cross the plane of the Solar System twice on each orbit, of course).

Second, mulling the matter over, there is no reason why orbital flattening wouldn’t have been detected by computer modelling.  Actually, I tell a lie; there is a reason.  The reason is that the process would be too slow.  Far from bouncing, it turns out that the minor planets would not have had time for their orbital inclinations to decline to 0˚ even once.  I did some back of the envelope calculations – several times in fact – and if you imagine the minor planets falling towards the plane of the Solar System under the gravity of the component of the inner planets’ orbits perpendicular to the plane and give yourself 4 billion years, the minor planets would only have fallen a small fraction of the necessary distance!

Third, we have this issue of the AOP.  The AOPs of the inner planets precess because of the gravitational effect of the other planets as they orbit the Sun (with some tweaks arising from relativity).  It’s necessary to explain why this precession wouldn’t occur for the minor planets.

Missing Mass

However you look at it, explaining the orbits of the minor planets must involve finding some mass in the Solar System!  One possible explanation is Planet X.  But could there be another source of missing mass?

Well, trying to rescue my theory, I was reading about the history of the Solar System.  As you do.

It turns out that the Kuiper Belt, beyond Neptune, now masses only a fraction of the Earth.  At one time it must have had at least 30 times the mass of the Earth, in order for the large objects we see today to form at all.  Trouble is, the consensus is that all that stuff either spiralled into the Sun, or was driven into interstellar space, depending on particle size, by the effect of solar radiation and the solar wind.

The science doesn’t seem done and dusted, however.  Perhaps there is more mass in the plane of the Solar System than is currently supposed.  Stop Press: Thanks to New Scientist I’m alerted to a paper that suggests exactly that – see the Addendum at the end of this piece.

It seems to me a likely place for particles to end up is around the heliopause, about 125 AU (i.e. 125 times the Earth’s orbit) from the Sun, because this is where the Solar wind collides with the interstellar medium.  You can imagine that forces pushing particles – of a certain range of sizes – out of the Solar System might at this point balance those pushing them back in.

Sophisticated Orbital Flattening

OK, there’s a big “if”, but if there is somewhat more mass – the remains of the protoplanetary disc – in the plane of the Solar System than is generally assumed, then it might be possible to explain the orbits of Sedna and the other TNOs quite neatly.  All we have to assume is that the mass is concentrated in the inner part of the TNOs orbits, let’s say from the Kuiper Belt through the heliopause at ~125 AU.

First, the AOPs of around 0˚ are even easier to explain than by the effects of the inner planets.  As for the inner planets, the mass would have greatest effect on the TNOs when they are nearest perihelion, so would perturb the orbits most then, as discussed in my previous posts.  The improvement in the explanation is that there is no need to worry about AOP precession.  Because the mass is in a disc, and therefore distributed relatively evenly around the Sun, its rotation has no gravitational effect on the minor planets.  And it is the rotation of the other planets that causes each planet’s AOP precession.

Second, we need to observe that there is a trade-off between orbital inclination and eccentricity as in the Kozai effect, due to conservation of angular momentum in the plane of the Solar System.  Thus, as the inclination of the TNOs’ orbits is eroded, so their orbits become more eccentric.  This could have one or 3 possible consequences:

  • it could be that, as I concluded for the effects of the inner planets alone, there has not been time for the TNOs’ orbits to flatten to 0˚ inclination in the 4 billion or so years since the formation of the Solar System.
  • or, it could be that the TNOs we observe are doomed in the sense that their orbits will be perturbed by interactions with the planets if they stray further into the inner Solar System – assuming they don’t actually collide with one of the inner planets – and we don’t observe TNOs that have already been affected in this way.
  • or, it could be that the TNOs’ orbits eventually reach an inclination of 0˚ and “bounce” back into more inclined orbits.  The point is that the eccentricity of the orbits of such bodies would decline again, so we may not observe them so easily, since the objects are so far away we can only see them when they are closest to the Sun.

Which of these possibilities actually occurs would depend on the amount and distribution of the proposed additional mass I am suggesting may exist in the plane of the Solar System.  My suspicion is that the orbital flattening process would be very slow, but it is possible different objects are affected in different ways, depending on initial conditions, such as their distance from the Sun.

Now I really will write to the scientists to ask whether this is plausible.  Adding some mass in the plane of the Solar System to Mercury symplectic integrator modelling would indicate whether or not Sophisticated Orbital Flattening is a viable hypothesis.

Addendum: I mentioned towards the start of this post that the search continues for Planet X.  I can’t help remarking that this doesn’t strike me as good science.  What research should be trying to do is explain the observations, i.e. the characteristics of the minor planets’ orbits, not trying to explain Planet X, which is as yet merely an unproven hypothetical explanation of those observations.  Anyway, this week’s New Scientist notes that:

“…the planet could have formed where we find it now. Although some have speculated that there wouldn’t be enough material in the outer solar system, Kenyon found that there could be enough icy pebbles to form something as small as Planet Nine in a couple of hundred million years (arxiv.org/abs/1603.08008).”

Aha!  Needless to say I followed the link provided by New Scientist and it turns out that the paper by Kenyon & Bromley does indeed suggest a mechanism for a debris disc at the right sort of distance in the Solar System.  They focus, though, on modelling how Planet X might have formed.  They find that it could exist, if the disc had the right characteristics, but it also may not have done.  It all depends on the “oligarchs” (seed planets) and the tendency of the debris to break up in collisions.  This is from their Summary (my explanatory comment in square brackets):

We use a suite of coagulation calculations to isolate paths for in situ production of super-Earth mass planets at 250–750 AU around solar-type stars. These paths begin with a massive ring, M0 >~ 15 M⊕ [i.e. more than 15 times the mass of the Earth], composed of strong pebbles, r0 ≈ 1 cm, and a few large oligarchs, r ≈ 100 km. When these systems contain 1–10 oligarchs, two phases of runaway growth yield super-Earth mass planets in 100–200 Myr at 250 AU and 1–2 Gyr at 750 AU. Large numbers of oligarchs stir up the pebbles and initiate a collisional cascade which prevents the growth of super-Earths. For any number of oligarchs, systems of weak pebbles are also incapable of producing a super-Earth mass planet in 10 Gyr.

They don’t consider the possibility that the disc itself could explain the orbits of the minor planets.  And may indeed be where they originated in the first place.  In fact, the very existence of the minor planets could suggest there were too many “oligarchs” for a “super-Earth” to form.  Hmm!