This is an intriguing paper which has hit the news, see  Planet Nine Could Doom Our Solar System - If It Exists. If our solar system has a planet in a distant orbit, way beyond Neptune, such as the planet X candidates, it could lead to instability of our solar system far into the future. That's a rather unintuitive result - how could such a distant planet make any difference to our solar system's stability? It's not only intriguing, it might also provide the solution to a major puzzle about white dwarf stars.

It might explain why so many white dwarfs are surrounded by debris fields, when you'd expect them to have lost all nearby planets long ago. The results also suggest that our solar system very probably has an extra Planet X in the outer solar system, well beyond Neptune. For those who fear such things, this planet is not something to worry about in our time. If it exists, it's not going to do anything to our solar system for billions of years into the future.

The paper is here. I was intrigued to find out how it works. The paper includes several scenarios on page 10, section 5.2. The author briefly discusses effects of stellar flybys within 100 au which should happen on average at least once for a sun-like star. But the main focus is on the effects of galactic tides.

The basic idea here is that if we have a distant planet way beyond Neptune, then once the Sun's gravity is much weaker after it throws off half its mass and becomes a white dwarf, it becomes more susceptible to gravitational interactions with the galaxy tides. As a result it gets closer to the Sun at its closest and further away at its furthest. Eventually it gets so close to the Sun at its closest that it does gravitational flybys of the gas giants which can change their orbits.

Every time one of our spacecraft does a flyby of a planet, the planet changes the trajectory of the spacecraft, but the spacecraft also makes a much smaller change to the orbit of the planet - so small it's insignificant. If a large planet does a flyby of another planet it can change its orbit significantly and if it keeps doing that then it can change it a lot. Those repeated tugs can destabilize its orbit, but whether it does or not depends on details of the orbital periods of the planets, and whether they are in resonances with each other and what those resonances are. So, let's look at this in more detail.

This is the image the university of Warwick included with the press release

The galactic tidal effects are due to the vertical gravitational attraction towards the plane of the galactic disk - most of the mass of the galaxy is in the plane of the galactic disk so if anything moves above or below it it experiences a gravitational pull back into the disk. This causes all the stars of our galaxy to gradually bob up and down above and below the plane of the galaxy as they orbit the center. It also has subtle tidal effects.

The tidal effects are negligible for solar systems that are coplanar with the galaxy and most extreme for those that are inclined at 90 degrees. Our solar system is inclined at 60 degrees. The paper is an attempt to explain observations of many white dwarfs with either planets or planetary debris. He says

"The spectacular discovery of at least one minor planet disintegrating in real time within the white dwarf disruption radius (Vanderburg et al. 2015) has prompted a spate of observational follow-up studies"

His explanation is that if we have a large planet out in the Oort cloud, then galactic tides would cause it to become more and more eccentric in orbit - not now, but later, once our Sun goes red giant and then loses half its mass in planetary nebulae. With reduced mass, then the other planets move further out and are more liable to be disrupted, and meanwhile, galactic tides influence the less strongly bound outer planet into more elliptical orbits. This often causes it to become so elliptical that its pericentre (closest point to its host star) gets as close as the outermost of the planets in the solar system, in our case Neptune. If the object is massive enough, this perturbs the Neptune analogue's orbit which can then destabilize the other planets too. He explores various scenarios for ways this could happen in his section 5.2. Many are stable, for instance with the Neptune analogue in a new orbit, and others are unstable in various ways, ejecting or destroying one or more of the smaller gas giants, though none of them are able to nudge a Jupiter analogue out of its orbit around the star.

First let's look at an overview of their results. In these results, the η parameter is a measure of the extent of the mass loss during the red giant phase. Higher η means more mass loss.

So now let's take a look at their overview figure. The main thing to notice in this figure is that there's a scattering of stable and unstable outcomes throughout the diagrams. Only the top left one has a region that seems totally stable from their simulations - that's for a low mass planet, and the closer it is to the sun, the higher mass it can be and not destabilize the system.The orange line marks out regions that are predominantly stable.

By this time in the future, the inner planets Venus and Mercury are gone, Earth is either gone or roasted, Mars is roasted but still there, the giant planets are hardly perturbed at all, though they move to double the current distance from their host star, and they still have all their moons. The destruction of the rest of our solar system, if it happens, would happen long after that, typically 13 or 14 billion years from now. That's about three times the length of time our planet has existed, and more than 25 times the time it took for humans to evolve from the smallest multicellular micro-organisms.

At this point, before the disruption, he gives a survey of existing understanding of what happens with many cites (I've removed the cites from this quote for readability). I'll include it in its entirety as it's an excellent overview of this field. 

In summary, only Mars and just possibly Earth remain of the terrestrial planets, asteroids spin up and disintegrate, the gas giants however are hardly affected, remain in more or less circular orbits with the orbit doubled in radius, and their moons are even more tightly bound than before because the white dwarf's gravitational effect is so much reduced while the Oort cloud loses most of its comets which hurtle through the solar system or are ejected. In detail:

"The Sun will leave the main sequence in about 6.5 Gyr,and undergo drastic changes. Its radius will increase by a factor of about 230, it will lose almost half of its current mass, and its luminosity will reach a peak value which is about 4000 times its current value. The Sun will become so large that its radius will extend just beyond where the Earth currently sits. These major changes will occur in two phases. The red giant branch phase will last about 800 Myr. In this time span,the Sun will gradually lose about a quarter of its mass.The second phase, when the Sun becomes an asymptotic giant branch star, is quicker: lasting just 5 Myr. Another quarter of the Sun’s mass will be lost during this period. During both phases, the radius of the Sun will extend out to nearly the Earth’s distance.The consequences for the inner Solar system will be profound. The terrestrial planets, which are likely to remain in stable orbits until the end of the main sequence at the approximately 99% level will be in danger. Mercury and Venus will be engulfed,and the Earth will be on the edge of survivability. Mars will be roasted, but should survive, because it will escape being ensnared by the tidal reach of the Sun. Asteroid belt constituents between 100 m and10 km in radius will be spun up to breakup speed, creating a sea of debris, some of which may be water-rich.

"The consequences for the giant planets, however, will be more benign. Jupiter, Saturn, Uranus and Neptune will increase their semimajor axes by a factor of about two each, and not undergo scattering nor instability, even though the chemistry of at least Jupiter’s atmosphere will be fundamentally altered. The giant planet eccentricities will remain effectively fixed because they reside within the adiabatic limit, beyond which stellar mass loss changes both eccentricity and semimajor axis. The present-day “adiabatic” limit for the Solar system specifically lies between about 103 and 104 au. Further, even though mass loss changes stability limits, this change will not be large enough to affect the giant planets. I perform some simulations here also to back up this statement.

"Moons, the Kuiper Belt, scattered disc and Oort Cloud will also be affected. Moons of planets will become more entrenched in the Hill spheres of the host planets, and would stay there in the absence of a planetary scattering event (Payne et al. 2016a,b). Although known Kuiper Belt and scattered disc objects are within the adiabatic limit, many are likely to become unstable as the stability limits between Neptune and Kuiper Belt objects change as the Sun’s mass decreases and its luminosity increases . The Oort Cloud will be both excited and decimated, which will alter the influx of comets into the inner Solar system, and these comets can be subsequently perturbed by radiation from the Solar white dwarf..."

In all his simulations the heavy Jupiter analogue's orbit remains stable. The lightest gas giants are the ones most affected, and the most common effect of the instability was ejection of a planet, but 3% of the time the unstable planets were torn apart by approaching too close to the host star ("engulfment).

"Other trends from the ensemble of plots include details of the instability: 97 per cent of all unstable simulations featured ejections. The remainder were engulfments (defined to occur when a planet intersected the star’s Roche radius). In no case did the Jupiter-like planet become unstable. The analogues of Saturn, Uranus and Neptune and the distant planet were either ejected or engulfed 8, 53, 24 and 15 per cent of the time, respectively. This result makes sense given that in almost every simulation, the analogue of Uranus was the least massive planet. Veras et al. (2016a) showed that scattering amongst unequal-mass planets across all phases of stellar evolution will preferentially eject the least massive planet (just as along the main sequence alone)."

He gives a few example scenarios to show how it works. This is one of the unstable ones

When interpreting these plots, and when reading the paper, you need to know that

• q_pl is the pericenter - the distance for the closest point in its orbit to its host star. So when the q for the distant planet (purple in the plots) is lower than the pericenter of the other planets, that means that it is intersecting their orbits to such an extent that it comes closer to the Sun (or host star) than they do.
• e _pl is the eccentricity - the closer this is to 1, the more eccentric its orbit, where 1 means a straight line orbit back and forth. 0 here means a circular orbit.
• a _pl is the semimajor axis - the radius if it is a circular orbit and otherwise, half the longest diameter of an elliptical orbit. This increases for all the planets 8 billion years from now when our Sun loses half its mass. Sometimes it increases further as a result of the perturbing planet's effects
• The simulations stop when any of the planets is ejected and you sometimes need to read the description to find out which one was ejected.

These symbols q, e and a are the standard symbols used for these orbital elements in this topic area.

As you see the outermost purple planet's orbit gets increasingly eccentric, eccentricity close to 1, and its semimajor axis and so its largest diameter increases. The last diagram shows how its q or pericenter evolves, with it eventually dipping inside the orbits of the other planets. It sometimes gets so close to the host star that it would get disrupted - so causing the "white dwarf pollution" they talk about. Eventually the outermost (red) Neptune gets ejected - you can't see this in the plot though, they just say so in its description, because the simulation stops when any planet gets ejected.

Here is another scenario, one which he says is unusual,

In this case, the eccentricity and pericenter change in cycles under the influence of the galactic tides, sometimes bringing the planet inside of Neptune and even closer. The Neptune planet gets pulled out into more distant orbits, eventually ending up orbiting at around 10,000 au from the white dwarf with eccentricity and pericenter changing in huge cycles lasting for several billion years each time.

He plots several other possible outcomes.

His conclusion is:

"I demonstrated that a distant planet with an orbital pericentre under 400 au could pose a serious danger to the stability of Solar system analogues during a Sun-like star’s giant branch and white dwarf phases. This statement holds true for a distant planet which is at least as massive as Jupiter and harbours a semimajor axis beyond about 300 au, or for a super-Earth when its semimajor axis exceeds about 3000au.

... "The consequences for other planetary systems are profound. Multiple planets beyond about 5 au (such as analogues of Jupiter, Saturn, Uranus and Neptune) may be common, but are so far unfortunately effectively hidden from detection by Doppler radial velocity and transit photometry techniques, the two most successful planet-finding techniques..."

Interesting. Perhaps this is indirect evidence for planet X in our solar system as well. Given that most white dwarfs are "polluted white dwarfs" with orbital debris or planets close to the host star, and if distant planets are the best explanation of this effect, it suggests that most stars that evolve into white dwarfs, such as our Sun, have distant planets beyond the orbit of Neptune. So perhaps that makes it likely that our Sun does as well. It also suggests that many white dwarfs as well as younger Sun like stars have distant planets in similar orbits, but they are too far away to spot easily with most existing planet detection techniques.

I'd just like to add for those that worry about such things (such as the readers of my Nibiru debunking articles here), that this is for events billions of years into the future. Our solar system was unstable when it first formed, with many embryo planets in intersecting orbits colliding with each other or doing close flybys of each other and it may well have ejected at least one large gas giant from the solar system, or if the Planet X candidate which has been labeled "planet 9" exists, it may be a planet ejected from the region occupied by the other gas giants in our solar system, but was slowed down by the gas and dust and didn't quite escape our solar system.

This study suggests our solar system might become unstable again in the future when the Earth goes red giant, though again it might not as there were many stable end points in the simulations too.  But this is the distant future, well beyond the stage when Earth would become uninhabitable anyway without mega technology due to the expanding Sun as it goes red giant.

Jupiter though remains bound to our solar system in all the simulations and it typically retains its moons as well. So perhaps Europa and other moons of Jupiter will remain habitable for ocean life by then. As for beings with technology, there will be lots of material they can make into space habitats or they may be able to protect and occupy one of the many moons or even move planets around by using repeated flybys of other asteroids. Or they could migrate to another star. Whatever happens then, it's not of any immediate relevance for us - this is a very distant event.

I wrote this because the news stories I read didn't go into any detail about this intriguing result and I thought the details were fascinating. So I wanted to read the paper myself and in the process of doing so, thought I might as well write it up as a Science20 blog post.

This should be enough background to read the paper yourself, if you are of a scientific bent, especially, take a look at some of the other example scenarios in his section 5.2. See The fates of Solar system analogues with one additional planet, by Dimitri Veras (University of Warwick, England).