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A Path to Planet Formation in Binary Systems

How planets grow in double-star systems has always held a particular fascination for me. The reason is probably obvious: In my younger days, when no exoplanets had been discovered, the question of what kind of planetary systems were possible around multiple stars was wide open. And there was Alpha Centauri in our southern skies, taunting us by its very presence. Could a life-laden planet be right next door?

What Kedron Silsbee and Roman Rafikov have been working on extends well beyond Alpha Centauri, usefully enough, and helps us look into how binaries like Centauri A and B form planets. Says Rafikov (University of Cambridge), “A system like this would be the equivalent of a second Sun where Uranus is, which would have made our own solar system look very different.” How true. In fact, imagining how different our system would work if we had a star among the outer planets raises wonderful questions.

Could we have a habitable world around each star in such a binary? And if so, wouldn’t the incentive to develop spaceflight take hold early among the denizens of such a world? We used to imagine a habitable Mars, by stretching Percival Lowell’s observations of what Giovanni Schiaparelli described as ‘canali’ (‘channels’) to their limit. How much more would a green and blue world with clouds and oceans beckon?

Image: Artist’s impression of a hypothetical planet around Alpha Centauri B. Credit: ESO/L. Calçada/N. Risinger.

But back to Rafikov, whose paper with Silsbee (Max Planck Institute for Extraterrestrial Physics) has been accepted at Astronomy & Astrophysics. The two researchers have refined binary star planet formation through a series of simulations, with Alpha Centauri in mind as well as the tight binary Gamma Cephei, a K-class star with red dwarf companion and a planet orbiting the primary. Silsbee explains the problem they were trying to solve: How does the companion star affect the existing protoplanetary disk of the other? He adds:

“In a system with a single star the particles in the disc are moving at low velocities, so they easily stick together when they collide, allowing them to grow. But because of the gravitational ‘eggbeater’ effect of the companion star in a binary system, the solid particles there collide with each other at much higher velocity. So, when they collide, they destroy each other.”

Gamma Cephei is a case in point: The system yields planetesimal collision velocities of several kilometers per second at the 2 AU distance of the system’s known planet, which should be enough, the authors note, to destroy even planetesimals as large as hundreds of kilometers in size. This problem appears in the literature as the fragmentation barrier, and it looms large, even when taking into account the aerodynamic drag induced by the gases of the protoplanetary disk. We can expect high collision velocities here.

And there go the planetesimals, which should, according to core accretion theory, grow out of dust particles as they gradually begin to bulk up into larger solid bodies. Given that we now know about numerous exoplanets in binary systems, how did they emerge? Were they all ‘rogue’ planets that ambled into the gravitational influence of the binary pair? And if that idea seems unlikely, how then do we explain their growth?

Rafikov and Silsbee show through their simulations that given realistic processes and the mathematics to describe them, such worlds will emerge. Incorporated in the resulting model is a new look at the question of gas drag and its effects. They find that drag in the disk — Silsbee likens it to a kind of wind — can indeed alter planetesimal dynamics and can offset the gravitational influence of the nearby stellar companion.

For although a number of earlier studies included gas drag in their models, their calculations ignored the effect of disk gravity, which according to the authors changes the dynamics of the population of planetesimals. They are able to identify quiet zones in the disk in which planetesimals can grow into planets. And they believe their model fully accounts for planetesimal dynamics throughout the young system. Among their conclusions:

The gravitational effect of the protoplanetary disk plays the key role in lowering the minimum initial planetesimal size necessary for sustained growth by a factor of four. This reduction can be achieved in protoplanetary disks apsidally aligned with the binary, in which a dynamically quiet zone appears within the disk provided that the mass-weighted mean disk eccentricity ≲ 0.05…

And this:

For most disk parameters considered in this paper, planet formation in binaries such as γ Cephei can successfully occur provided that the initial planetesimal size is ≳ 10 km; however, for favorable disk parameters, this minimum initial size can go down to ≲ 1 km.

We should expect, then, that planets could form in systems like Alpha Centauri, where the hunt for worlds around the Centauri A and B pair continues. This can occur if the planetesimals can reach this minimum size, and it assumes a protoplanetary disk that is close to circular. Given those parameters, planetesimal relative velocities are slow enough in certain parts of the disk to allow planet formation to take place.

How to get planetesimals to the minimum size needed? The streaming instability model of planetesimal formation may be operational here, in which the planetesimals grow rapidly. In this model, drag in the disk slows solid particles and leads to their swift agglomeration into clumps that can gravitationally collapse. Streaming instability is a rapid alternative to the alternate theory of planetesimals growing steadily through coagulation alone. In fact, the paper cites a timescale of tens of local orbital periods, rapidly producing a population of ‘seed’ planetesimals.

Whether or not streaming instability does offer a pathway to planets is a question that is still unresolved, though the theory has implications for planet formation around single stars as well. It certainly eases formation in the binaries considered here.

The paper is Silsbee & Rafikov, “Planet Formation in Stellar Binaries: Global Simulations of Planetesimal Growth,” accepted at Astronomy and Astrophysics (abstract / preprint).

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{ 9 comments… add one }
  • henry cordova July 28, 2021, 14:19

    Orbital mechanics demands that planetary systems, as well as binary or multiple star systems, be hierarchical. That, is, one or more bodies orbit another, or additional bodies orbit the centers of gravity of some of the others, and so on. Examples of this can be found in our own solar system: planets orbit the sun, and 0ne or more satellites orbit some of those planets. It is even possible that perhaps the sun has unseen companion(s) (perhaps with their own retinue of planets and satellites) orbiting far out in the cold and dark. Or, as when the Apollo module orbited our own moon, a satellite can have its own satellite. However, these tertiary pairings are probably unstable and easily disrupted. Still, they are not dynamically impossible. Whether the ‘C’ component revolves stably about the ‘B’ component, or the center of mass of the A-B pair depends on the relative spacing and the resulting gravitational resonances and perturbations. Strictly speaking, body X does not orbit Y, they both orbit a common center of mass. However, when one is much much more massive than the other, the CM of the pair is much closer to the more massive body (or even inside it!)

    As far as I know, there is no known stellar triple system in which B and C both orbit the A component., the way our planets orbit Sol. What we usually see is the C component revolving about the center of mass of the A-B pair, as in the Alpha Centauri system. Whether this is a general rule, a result of mutual perturbations and resonances, or just the result of an observational selection effect, I do not know.

    We tend to think of binary stellar systems as being relatively close, even in physical contact with each other, their centers of mass actually within the Roche Lobes of their companions. But in other cases, they are separated by hundreds of astronomical units; so far apart they may be considered essentially independent systems in spite of their gravitational connection. I don’t even know how these separations are distributed in statistical space (Note: a great topic for a dissertation!). Then again, it is perfectly reasonable to describe the Sol-Jupiter system as a binary–the conceptual distinction between star/planet/and satellite being rather arbitrary.

    For SETI purposes, much more important than the orbital configuration of a system is the spacing and masses of the components. Presumably, members of a multiple star system were formed at the same time in the same molecular cloud, But the more massive members will evolve faster, and will have to be spaced far away from the star that is evolving life for any of that life to survive. If Jupiter had been born as a 5 solar mass giant, it would have evolved quickly into an obscure white dwarf by now but its not likely Earth would have become an abode of life.

  • Brett July 28, 2021, 15:20

    It’s good to read that they believe planets could form around the Alpha Centauri stars again, since I remembered that the recent modeling suggested it would be hard.

    It’d be quite striking if you were on a habitable planet around one of them. You’d see the stars migrate closer and closer together over the course of a year until they’re rising and setting together, then one of them would gradually get farther and farther away until eventually you have a couple days where the planet is between the two stars, and “night” as we know it disappears for a while.

  • Ron S. July 28, 2021, 16:07

    I quickly skimmed a few sections of the pre-print to find at what point the simulations begin. This is important to the ultimate findings. Section 2 has the model description, and is where I found this:

    “We assume the primary component of the binary to host a massive protoplanetary disk, coplanar with the binary orbit…”

    I have a problem with this as part of the initial conditions of the model. The nebula from which the two, gravitationally coupled proto-stellar systems has a somewhat homogeneous 3D structure. Since it has been disturbed (as it must have for the system to form), the influence of angular momentum, gravitation and gas/particle collisions are what cause the disk (disks in the case of binaries) to form.

    Those two segments of the nebula are interacting far earlier than the start of their model. As soon as the different angular momenta are established, the segments interact. This will constrain the shape, radius and mass of the forming stellar disks. Their assumption that the primary’s disk is coplanar with the binary orbit also strikes me as peculiar.

    Those interactions will cause potential disk material to be ejected from the system, move inward, or even accrete to the proto-star. The mass of the eventual disk will be greatly diminished, and that determines whether planets can form and what class of planets they can be.

    Beware of initial conditions in models.

    xx

  • Alex Tolley July 28, 2021, 17:29

    Given planets can form in binary star systems, how stable can those planets be over the long term? Will the ‘clockwork” suffer perturbations that eventually disrupt the orbits?

    Lastly, just what effect does a nearby star have on habitability? A companion G-type star as distant as Uranus will add .25% to the received illumination of the planet around teh primary. But this changes by about 22% depending on whether the companion is in conjunction or opposition. Not much, but perhaps enough to cause periodic climate changes. If the companion is larger, the effect will be greater, and over the long term, its luminosity will increase faster than the primary, creating possible long-term habitability issues.

    While papers have been published about HZs in binary star systems, I don’t recall if they consider long-term habitability rather than a temporary stable HZ for any planets.

  • Edwin July 29, 2021, 4:58

    Tanks Paul

    An interesting read with the comments too.

    I’ll look forward to reading the paper

    Cheers Edwin

  • Spaceman July 29, 2021, 9:46

    So, according to this study, under certain conditions which may or may not commonly occur during planet formation in binary systems, such as coplanarity and minimal planetesimal size, planets can form in close binary systems. I have a couple of questions related to the content of this study, including:

    1. How do the results of this paper compare with the observational results regarding the frequency of planets in binary systems?

    2. Does the study offer any additional predictive power above what we already know from existing theory regarding the frequency, the types planets (e.g. terrestrial vs gas giant), and what binary systems are more likely vs what binary system are less likely to form planets?

    The last question I have has to do with the searches for exoplanets in the Alpha Centauri system. Does anyone know what the current status of these searches is as of mid-2021?

  • wdk July 29, 2021, 15:41

    Some details of this study leap off the page, but others, I will have to
    look at more slowly.

    Despite thousands of transit cases, I suspect that potential transiting
    binaries similar to Alpha Centauri are still hard to come by, verifying the difficulty or giving hope by their example. My suspicion is that Alpha Centauri’s dynamic stability region would not extend more than a couple of AUs for either star and the lesser mass star would provide tighter binding in the HZ.

    Still, I would like to review some results I provided here about 2 years ago, using a dynamic simulation model.

    Since planetesimals will not perturb stellar motions individually, the approximations of restricted elliptic 3-body motions apply to a large degree, minus the atmospheric drag. What was observed in the 0.5 eccentricity 80 year period binary case of Alpha Centauri was that in the star A case HZ, initially zero eccentricity orbits obtained a maximum eccentricity of several percentage points and then cycled back to zero with a cycle time of 8000 terrestrial years. The line of apsides rotated in the celestial sphere along with this eccentricity amplitude. The orbit of particular interest had a period of about 425 days and a stellar distance of about 1.25 AUs based on Earth analog assumptions.

    Closer or further positioning would change the amplitude and the period. Closer proximity to parent star, lesser perturbation, but shorter period.

    Now one could suspect that if there were a cluster of planetesimals starting out at 1.25 AU and zero eccentricity, they could/would continue to fly like geese in formation. If they were to diverge, they would not necessarily all collide under the worst possible conditions.

    What’s more, observed that planets with some initial eccentricity would behave similarly, within a band about a higher eccentricity outside of the cycle described above.

    Circum-stellar disks for binaries of this nature will not be wide. There looks like no room for Jupiters and Neptunes outside, but the density of
    circum-stellar disks is not necessarily uniform from planet to planet.
    A Jupiter accumulates about 330 times as much mass as the Earth has
    remaining. So, to my view, the prospect of terrestrial planet formation is not entirely eliminated.

  • Geoffrey Hillend July 29, 2021, 19:00

    From what I recall reading it is the centrifugal force which causes the protoplanetary cloud to collapse from a volume into a flat disk because it is that centrifugal force keeps the dust and particles from moving towards the star or away from it which explains how the planets form. Kipppenhahn 1983. The dust is at relatively the same speed at a certain distance from the star where there is a higher concentration dust where a planet is. The planet’s size increases very quickly from the small dust particles and pebbles which accumulate and grow in size once it becomes large enough and the gravity becomes strong enough to have a high enough escape velocity and size to keep it from being destroyed and retain the material of the dust and pebbles which collide at high velocity.

    I like the egg better idea which occurs at the central point between the two stars which are a Uranus distance apart. The problem is that the egg beater effect will throw all the dust, gas and pebbles into further orbits and no planets can form around the two starts. By the time the two stars form, there is no disk of gas and dust, but a thin ring at the distance of the two stars. with nothing in most of the center. This is of course an intuitive speculation of what happens in the computer simulation of the double star ring idea by Rudolph Kippenhahn’s idea of why double stars can’t have planets in his 1983 book 100 Billion Suns. I actually don’t know the exact physics of it. Maybe some other astrophysicists know.

  • Geoffrey Hillend July 30, 2021, 16:10

    I was looking at Alpha Centauri article on Wikipedia. It says that these A and B stars have an eccentricity which means they don’t always stay the same distance apart over time. Their furthest distance is the apastron. Their closest distance, the periastron reoccurs every 80 years. Their closest distance is the distance between the Sun and Saturn and the furthest is the Sun Pluto distance. Also on I think I recall reading on Wikipedia, the Binary system, that the further two stars are away from each other the greater the eccentricity, so this would affect double star systems at a Sun Uranus distance apart maybe by pulling dust towards or away from the other star. I don’t know if that effect might be the main mechanics of the physics which resulted the dust ring model computer simulation by Kippenhahn and his team. It certainly would make planet formation more difficult.

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