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:

In 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!

 

Is Planet X Needed? – Further Comments on Trujillo & Sheppard and Batygin & Brown

In my last post, Does (Brown and Batygin’s) Planet 9 (or Planet X) Exist?, I ignored the media squall which accompanied the publication on 20th January 2016 of a paper in The Astronomical Journal, Evidence for a Distant Giant Planet in the Solar System, by Konstantin Batygin and Michael E Brown, and discussed the coverage of the issue in New Scientist (here [paywall] and here) and in Scientific American (here [paywall]).

The idea that there may be a Planet X is not original to the Batygin and Brown paper.  It was also proposed in particular by Chadwick A. Trujillo and Scott S. Sheppard in a Nature paper A Sedna-like body with a perihelion of 80 astronomical units dated 27th March 2014.  The New Scientist and Scientific American feature articles were not informed by Batygin and Brown.  Scientific American explicitly referenced Trujillo and Sheppard (as well as a paper by C and R de la Fuente Marcos).

A key part of the evidence for a “Planet X” is that for the orbits of a number of trans-Neptunian objects (TNOs) – objects outside the orbit of Neptune – including the minor planet Sedna, the argument of perihelion is near 0˚.  That is, they cross the plane of the planets near when they are closest to the Sun. The suggestion is that this is not coincidental and can only be explained by the action of an undiscovered planet, perhaps 10 times the mass of the Earth, lurking out there way beyond Neptune. An old idea, the “Kozai mechanism”, is invoked to explain how Planet X could be controlling the TNOs, as noted, for example, by C and R de la Fuente Marcos in their paper Extreme trans-Neptunian objects and the Kozai mechanism: signalling the presence of trans-Plutonian planets.

I proposed a simpler explanation for the key finding.  My argument is based on the fact that the mass of the inner Solar System is dispersed from its centre of gravity, in particular because of the existence of the planets. Consequently, the gravitational force acting on the distant minor planets can be resolved into a component towards the centre of gravity of the Solar System, which keeps them in orbit, and, when averaged over time and because their orbits are inclined to the plane of the Solar System, another component at 90˚ to the first, towards the plane of the orbits of the eight major planets:

My suggestion is that this second component tend will gradually reduce the inclination of the minor planets’ orbits. Furthermore, the force towards the plane of the Solar System will be strongest when the minor planets are at perihelion on their eccentric orbits, not just in absolute terms, but also when averaged over time, taking into account varying orbital velocity as described by Kepler. This should eventually create orbits with an argument of perihelion near 0˚, as observed.

Has such an effect been taken into account by those proposing a Planet X?  The purpose of this second post on the topic is to look a little more closely at how the two main papers, Batygin & Brown and Trujillo & Sheppard tested for this possibility.

Batygin & Brown

The paper by Batygin and Brown does not document any original research that would have shown AOPs tending towards 0˚ without a Planet X by the mechanism I suggest.  Here’s what they say:

“To motivate the plausibility of an unseen body as a means of explaining the data, consider the following analytic calculation. In accord with the selection procedure outlined in the preceding section, envisage a test particle that resides on an orbit whose perihelion lies well outside Neptune’s orbit, such that close encounters between the bodies do not occur. Additionally, assume that the test particle’s orbital period is not commensurate (in any meaningful low-order sense—e.g., Nesvorný & Roig 2001) with the Keplerian motion of the giant planets.

The long-term dynamical behavior of such an object can be described within the framework of secular perturbation theory (Kaula 1964). Employing Gauss’s averaging method (see Ch. 7 of Murray & Dermott 1999; Touma et al. 2009), we can replace the orbits of the giant planets with massive wires and consider long-term evolution of the test particle under the associated torques. To quadrupole order in planet–particle semimajor axis ratio, the Hamiltonian that governs the planar dynamics of the test particle is [as close as I can get the symbols to the original]:

Η=-¼(GM/a) (1-e²)^-3/2 Σ⁴_i=1(m_ia_i²)/Ma²

In the above expression, G is the gravitational constant, M is the mass of the Sun, m_i and a_i are the masses and semimajor axes of the giant planets, while a and e are the test particle’s semimajor axis and eccentricity, respectively.

Equation (1) is independent of the orbital angles, and thus implies (by application of Hamilton’s equations) apsidal precession at constant eccentricity… in absence of additional effects, the observed alignment of the perihelia could not persist indefinitely, owing to differential apsidal precession.” [my stress].

After staring at this for a bit I noticed that the equation does not include the inclination of the orbit of test particle, just its semimajor axis (i.e. mean distance from the Sun) and eccentricity.  Then I saw that the text also only refers to the “planar dynamics of the test particle”, i.e. its behaviour in two, not three dimensions.

Later in the paper Batygin and Brown note (in relation to their modelling in general, not just what I shall call the “null case” of no Planet X) that:

“…an adequate account for the data requires the reproduction of grouping in not only the degree of freedom related to the eccentricity and the longitude of perihelion, but also that related to the inclination and the longitude of ascending node. Ultimately, in order to determine if such a confinement is achievable within the framework of the proposed perturbation model, numerical simulations akin to those reported above must be carried out, abandoning the assumption of coplanarity.”

I can’t say I found Batygin & Brown very easy to follow, but it’s fairly clear that they haven’t modeled the Solar System in a fully 3-dimensional manner.

Trujillo & Sheppard

If we have to discount Batygin & Brown, then the only true test of the null case is that in Trujillo & Sheppard.  Last time I quoted the relevant sentence:

“By numerically simulating the known mass in the solar system on the inner Oort cloud objects, we confirmed that [they] should have random ω [i.e. AOP]… This suggests that a massive outer Solar System perturber may exist and [sic, meaning “which”, perhaps] restricts ω for the inner Oort cloud objects.”

I didn’t mention that they then referred to the Methods section at the end of their paper.  Here’s what they say there (and I’m having to type this in because I only have a paper copy! – so much for scientific and technological progress!):

“Dynamical simulation. We used the Mercury integrator to simulate the long-term behaviour of ω for the Inner Oort cloud objects and objects with semi-major axes greater than 150AU and perihelia greater than Neptune.  The goal of this simulation was to attempt to explain the ω clustering.  The simulation shows that for the currently known mass in the Solar System, ω for all objects circulates on short and differing timescales dependent on the semi-major acis and perihelion (for example, 1,300 Myr, 500 Myr, 100 Myr and 650 Myr for Sedna, 2012 VP113, 2000 CR105 and 2010 GB17, respectively).”

In other words their model reproduced the “apsidal precession” proposed in Batygin & Brown, but since Trujillo & Sheppard refer to ω, the implication is that their simulation was in 3 dimensions and not “planar”.

However, could the model used by Trujillo and Sheppard have somehow not correctly captured the interaction between the TNOs and the inner planets?  The possibilities range from apsidal precession being programmed in to the Mercury package (stranger things have happened!) to something more subtle, resulting from the simplifications necessary for Mercury to model Solar System dynamics.

Maybe I’d better pluck up courage and ask Trujillo and Sheppard my stupid question!  Of course, the effect I propose would have to dominate apsidal precession, but that’s definitely possible when apsidal precession is on a timescale of 100s of millions of years, as found by Trujillo and Sheppard.

Does (Brown and Batygin’s) Planet 9 (or Planet X) Exist?

What exactly is the evidence that there may be a “Super-Earth” lurking in the outer reaches of the Solar System?  Accounts differ, so I’ll review what I’ve read (ignoring the mainstream media storm around 20th January!), to try to minimise confusion.

New Scientist

If you read your New Scientist a couple of weeks ago, you’ll probably have seen the cover-story feature article Last Great Mysteries of the Solar System, one of which was Is There a Planet X? [paywall for full article – if, that is, unlike me, you can even get your subscription number to give you access].  The article discussed the dwarf planets Sedna and 2012VP113.  The orbits of these planetoids – and another 10 or so not quite so distant bodies – according to New Scientist and the leaders of the teams that discovered Sedna and 2012VP113, Mike Brown and Scott Sheppard, respectively, could indicate “there is something else out there”.

Apparently, says NS:

“[the orbits of Sedna and 2012VP113] can’t be explained by our current understanding of the solar system…  Elliptical orbits happen when one celestial object is pushed around by the gravity of another.  But both Sedna and 2012VP113 are too away from the solar system’s giants – Jupiter, Saturn, Uranus and Neptune – to be influenced.”  Something else must be stirring the pot.”

“Elliptical orbits happen when one celestial object is pushed around by the gravity of another.”  This is nonsense.  Elliptical orbits are quite usual, beyond the 8 planets (i.e. for “trans-Neptunian objects”) which is where we’re talking about.  The fact that the orbits of Sedna and 2012VP113 are elliptical is not why there may be another decent-sized planet way out beyond Uranus (and little Pluto).

I see that the online version of New Scientist’s article Is There a Planet X? has a strap-line:

“Wobbles in the orbit of two distant dwarf planets are reviving the idea of a planet hidden in our outer solar system.”

Guess what?  The supposed evidence for Planet X is nothing to do with “wobbles” either.

The New Scientist article was one of several near-simultaneous publications and in fact the online version was updated, the same day, 20th January, with a note:

Update, 20 January: Mike Brown and Konstantin Batygin say that they have found evidence of “Planet Nine” from its effect on other bodies orbiting far from the sun.

Exciting.  Or it would have been, had I not been reading the print version.  The link is to another New Scientist article: Hints that ‘Planet Nine’ may exist on edge of our solar system [no paywall]. “Planet Nine”?  It was “Planet X” a minute ago.

Referencing the latest paper on the subject, by Brown and Batygin, this new online NS article notes that:

“Brown and others have continued to explore the Kuiper belt and have discovered many small bodies. One called 2012 VP113, which was discovered in 2014, raised the possibility of a large, distant planet, after astronomers realised its orbit was strangely aligned with a group of other objects. Now Brown and Batygin have studied these orbits in detail and found that six follow elliptical orbits that point in the same direction and are similarly tilted away from the plane of the solar system.

‘It’s almost like having six hands on a clock all moving at different rates, and when you happen to look up, they’re all in exactly the same place,’ said Brown in a press release announcing the discovery. The odds of it happening randomly are just 0.007 per cent. ‘So we thought something else must be shaping these orbits.’

According to the pair’s simulations, that something is a planet that orbits on the opposite side of the sun to the six smaller bodies. Gravitational resonance between this Planet Nine and the rest keep everything in order. The planet’s high, elongated orbit keeps it at least 200 times further away from the sun than Earth, and it would take between 10,000 and 20,000 Earth years just to complete a single orbit.”

Brown and Batygin claim various similarities in the orbits of the trans-Neptunian objects.  But they don’t stress what initially sparked the idea that “Planet Nine” might be influencing them.

Scientific American and The Argument of Perihelion
Luckily, by the time I saw the 23rd January New Scientist, I’d already read The Search for Planet X [paywall again, sorry] cover story in the February 2016 (who says time travel is impossible?) issue of Scientific American, so I knew that – at least prior to the Brown and Batygin paper – what was considered most significant about the trans-Neptunian objects was that they all had similar arguments of perihelion (AOPs), specifically around 0˚.  That is, they cross the plane of the planets roughly at the same time as they are closest to the Sun (perihelion).  The 8 (sorry, Pluto) planets orbit roughly in a similar plane; these more distant objects are somewhat more inclined to that plane.

Scientific American reports the findings by two groups of researchers, citing a paper by each.  One is a letter to Nature, titled A Sedna-like body with a perihelion of 80 astronomical units, by Chadwick Trujillo and Scott Sheppard [serious paywall, sorry], which announced the discovery of 2012 VP113 and arguably started the whole Planet X/9/Nine furore.  They quote Sheppard: “Normally, you would expect the arguments of perihelion to have been randomized over the life of the solar system.”

To cut to the chase, I think that is a suspect assumption.  I think there may be reasons for AOPs of bodies in inclined orbits to tend towards 0˚, exactly as observed.

The Scientific Papers

The fact that the argument of perihelion is key to the “evidence” for Planet X is clear from the three peer-reviewed papers mentioned so far.

Trujillo and Sheppard [paywall, still] say that:

“By numerically simulating the known mass in the solar system on the inner Oort cloud objects, we confirmed that [they] should have random ω [i.e. AOP]… This suggests that a massive outer Solar System perturber may exist and [sic, meaning “which”, perhaps] restricts ω for the inner Oort cloud objects.”

The Abstract of the other paper referenced by Scientific American, Extreme trans-Neptunian objects and the Kozai mechanism: signalling the presence of the trans-Plutonian planets, by C and R de la Fuente Marcos, begins:

“The existence of an outer planet beyond Pluto has been a matter of debate for decades and the recent discovery of 2012 VP113 has just revived the interest for this controversial topic. This Sedna-like object has the most distant perihelion of any known minor planet and the value of its argument of perihelion is close to 0 degrees. This property appears to be shared by almost all known asteroids with semimajor axis greater than 150 au and perihelion greater than 30 au (the extreme trans-Neptunian objects or ETNOs), and this fact has been interpreted as evidence for the existence of a super-Earth at 250 au.”

And the recent paper by Konstantin Batygin and Michael E Brown, Evidence for a Distant Giant Planet in the Solar System, starts:

Recent analyses have shown that distant orbits within the scattered disk population of the Kuiper Belt exhibit an unexpected clustering in their respective arguments of perihelion. While several hypotheses have been put forward to explain this alignment, to date, a theoretical model that can successfully account for the observations remains elusive.

So, whilst Batygin and Brown claim other similarities in the orbits of the trans-Neptunian objects, the key peculiarity is the alignment of AOPs around 0˚.

Is There a Simpler Explanation for ~0˚ AOPs?

Let’s consider first why the planets orbit in approximately the same plane, and why the Galaxy is also fairly flat.  The key is the conservation of angular momentum.  The overall rotation within a system about its centre of gravity must be conserved.  Furthermore, this rotation must be in a single plane.  Any orbits above and below that plane will eventually cancel each other out, through collisions (as in Saturn’s rings) and/or gravitational interactions (as when an elliptical galaxy gradually becomes a spiral galaxy).  Here’s an entertaining explanation of what happens.

This process is still in progress for the trans-Neptunian objects, I suggest, since they are inclined by up to around 30˚ – Sedna’s inclination is 11.9˚ for example – which is much more than the planets, which are all inclined within a few degrees of the plane of the Solar System.  What’s happening is that the TNOs are all being pulled constantly towards the plane of the Solar System, as I’ve tried to show in this schematic:

Now, here comes the key point: because the mass of the Solar System is spread out, albeit only by a small amount, because there are planets and not just a Sun, the gravitational pull on each TNO is greater when it is nearer the Sun (closer to perihelion) than when it is further away. There’s more of a tendency for the TNO (or any eccentrically orbiting body) to gravitate towards the plane of the system when it’s nearer perihelion.

This is true, I believe, even after allowing for Kepler’s 2nd Law, i.e. that the TNO spends less time closer to the Sun.  Kepler’s 2nd Law suggests the time an orbiting body spends at a certain distance from the centre of gravity of the system is proportional to the square of that distance, which you’d think might cancel out the inverse square law of gravity.  But the mass of the Solar System is not all at the centre of gravity.  The nearest approach of Neptune to Sedna, for example, when the latter is at perihelion is around 46AU (astronomical units, the radius of Earth’s orbit) but about 476AU when Sedna is at aphelion.

The most stable orbit for a TNO is therefore when it crosses the plane of the Solar System at perihelion, that is, when its argument of perihelion (AOP) is 0˚.  Over many millions of years the AOPs of the orbits of Sedna and co. have therefore tended to approach 0˚.

I suggest it is not necessary to invoke a “Super-Earth” to explain the peculiarly aligned arguments of perihelion of the trans-Neptunian objects.