Astronomy Without A Telescope – Forbidden Planets


Binary star systems can have planets – although these are generally assumed to be circumbinary (where the orbit encircles both stars). As well as the fictional examples of Tatooine and Gallifrey, there are real examples of PSR B1620-26 b and HW Virginis b and c – thought to be cool gas giants with several times the mass of Jupiter, orbiting several astronomical units out from their binary suns.

Planets in circumstellar orbits around a single star within a binary system are traditionally considered to be unlikely due to the mathematical implausibility of maintaining a stable orbit through the ‘forbidden’ zones – which result from gravitational resonances generated by the motion of the binary stars. The orbital dynamics involved should either fling a planet out of the system or send it crashing to its doom into one or other of the stars. However, there may be a number of windows of opportunity available for ‘next generation’ planets to form at later stages in the evolving life of a binary system.

A binary stellar evolution scenario might go something like this:

1) You start with two main sequence stars orbiting their common centre of mass. Circumstellar planets may only achieve stable orbits very close in to either star. If present at all, it’s unlikely these planets would be very large as neither star could sustain a large protoplanetary disk given their close proximity.

2) The more massive of the binaries evolves further to become an Asymptotic Giant Branch star (i.e. red giant) – potentially destroying any planets it may have had. Some mass is lost from the system as the red giant blows off its outer layers – which is likely to increase the separation of the two stars. But this also provides material for a protoplanetary disk to form around the red giant’s binary companion star.

3) The red giant evolves into white dwarf, while the other star (still in main sequence and now with extra fuel and a protoplanetary disk) can develop a system of orbiting ‘second generation’ planets. This new stellar system could remain stable for a billion years or more.

4) The remaining main sequence star eventually goes red giant, potentially destroying its planets and further widening the separation of the two stars – but it also may contribute material to form a protoplanetary disk around the distant white dwarf star, providing the opportunity for third generation planets to form there.

How a binary system might give birth to generations of planets: a) First generation planets - small and close-in - might be possible while both stars are on the main sequence (MS) and in close proximity to each other; b) Eventually one star evolves from the main sequence to the Asymptotic Giant Branch (AGB) - in other words, it goes red giant. c) The two stars spread further apart while stellar material blown off from the red giant builds a protoplanetary disk around the other star and second generation planets form; d) the second star eventually goes red giant giving the first star (now a white dwarf - WD) a protoplanetary disk which could create a third generation of planets. Credit: Perets, H.B.

The development of the third generation planetary system depends on the white dwarf star sustaining a mass below its Chandrasekhar limit (being about 1.4 solar masses – depending on its rate of spin) despite it having received more material from the red giant. If it doesn’t stay below that limit, it will become a Type 1a supernova – potentially lobbing a small proportion of its mass back to the other star again, although by this stage that other star would be a very distant companion.

An interesting feature of this evolutionary story is that each generation of planets is built from stellar material with a sequentially increasing proportion of ‘metals’ (elements heavier than hydrogen and helium) as the material is cooked and re-cooked within each stars’ fusion processes. Under this scenario, it becomes feasible for old stars, even those which formed as low metal binaries, to develop rocky planets later in their lifetimes.

Further reading: Perets, H.B. Planets in evolved binary systems.

15 Replies to “Astronomy Without A Telescope – Forbidden Planets”

  1. The early paragraphs of this article is highly misleading.

    “Binary star systems can have planets – although these are generally assumed to be circumbinary” “Planets in circumstellar orbits around a single star within a binary system are traditionally considered to be unlikely due to the mathematical implausibility of maintaining a stable orbit through the ‘forbidden’ zones”

    A wide array of planets are known in binary and multiple star systems where the planet orbits one of the stars, instead of both. I won’t name them all, as there’s quite a lot, but examples include 55 Cancri, Gliese 676, Gliese 777, Gliese 86, Epsilon Reticuli, Gamma Cephei, 83 Leonis, 79 Ceti, HD 41004, 16 Cygni, 30 Arietis, 91 Aquarii, BD-10 3166, Gliese 667, Upsilon Andromedae, etc. Among what we’ve found, circumbinary planets are in a very small minority.

    The maintaining of stable orbits applies to systems that undergo post-MS evolution and mass transfer. This is where the rest of the article comes into play.

    1. Sirius_Alpha said;

      The maintaining of stable orbits applies to systems that undergo post-MS evolution and mass transfer.

      Eh? Sorry I don’t get it.

      Do you mean here that this is the primary “condition” for planets around binary stars?

      As for “Among what we’ve found, circumbinary planets are in a very small minority.” I thought there was only four known examples, including this one around this pulsar. The key issue is they orbits are less than 3 AU from these stars, and the binaries in question are also very close contact binaries. I.e. They are all eclipsing binaries, too.

      Also the short list you have given of binary stars have unlike undergone any “…post-MS evolution and mass transfer…” Nearly all the examples are fairly wide double stars at 100 to 1000 AU, where formation of planets can occur and are unlikely not disrupted by the companion. Only three or four, including Gamma Cephei, are less than 20AU. These latter planets theoretically occur by so-called core–accretion.

      Most theorists really seem to think that these systems might differ quite significantly from when the stars were formed or the accretion of the disk.

      I don’t think “The early paragraphs of this article is [are] highly misleading” at all. I just think Steve Nerlich has just really micro-surmised the current situation for the general readership here. (I’ve also given a wider explanation on the points you’ve objected too, below.)


      Note: There is an excellent paper by F. Marzari (2008) in Astrophysical Journal and arXiv that discusses some of these issues you have raise.

  2. The whole article is about how you can have circumstellar planets in binary systems.

    I am not convinced that it is misleading to say that a ‘traditional’ view existed (based on mathematical modelling, not observation) that this wasn’t possible – but happy to acknowledge that Universe Today readers don’t ‘generally assume’ anything without evidence. Good for you.

    1. I think both the “mathematical modelling” AND observational evidence from binary and multiple stars is almost overwhelming, Studies on this interesting subject date back to the 1980s or earlier, and little, as far as I know, has changed in our “traditional” view.

  3. I think, planets may safely orbit a system of double stars, as long as the radius of their orbit is much larger than the distance between the two partner stars. In this case, the respective planet “sees” the two stars as one object and orbits the common center of gravity of the two. There a many examples of close binaries that orbit each other in a couple of days or less. Thus, their distance from each other is just some ten million kilometers. If such a system had a planet like e. g. Neptune, orbiting the system at a distance of 4,6 billion kilometers, the binary quality of the core star system would not impede the planet´s orbit in any way.

    Planets may orbit one star in a double star system safely, as long as the distance between the partner stars is very much larger than the radius of the planet´s orbit.

  4. Steve wrote ;

    Planets in circumstellar orbits around a single star within a binary system are traditionally considered to be unlikely due to the mathematical implausibility of maintaining a stable orbit through the ‘forbidden’ zones – which result from gravitational resonances generated by the motion of the binary stars. The orbital dynamics involved should either fling a planet out of the system or send it crashing to its doom into one or other of the stars.

    Whilst this is interesting and likely true, is this not the same very principle applying to all multiple stars?
    Really, there should be no difference between stars and planets in such gravitational systems. As an estimated 35% of binary systems are multiple stars, it would be logical to assume the same applies to planets too.
    The biggest celestial mechanical problem (not said here in exact detail) is the accepted concept that planets condense out the disk in ring-like rotation plane. From this planets are slowly gathered up within the sweeping debris field. The origin of the “orbit instability” in binaries is that this disk is easily disrupted by the motions of the stars, quickly ripping apart the disk and ejecting the material well away from the system.
    For triple stars, the disk is more easily destroyed by the third companion, which (from statistical studies on triples) does not (and cannot) orbit in the plane of the main binary, but is preferentially aligned at a steeper angle. (I.e. Preferentially 35 to 55 degrees) Again, the significant variable gravitational field cause enough disruption so planets cannot form. (Also the motion of the third star can be either planar or coplanar; the later meaning the orbit of the inner binary is opposite the orbital motion of the third star. Such co-planar systems are more unstable than planar ones [by about 31%, as theorised by W.D. Heintz in 1970. I’d asume this would apply for planets too.])
    Yet multiple star systems are even more complicated as they can form the trapezia (where there is no central binary) and the four stars orbit around some common centre. Else, they are arranged in hierarchal orders (first formallyb investigated by D.S. Evans “Stars of Higher Multiplicity”; QJRAS., 9, 3, 88 (1968), where there is a central binary with most of the angular momentum and (a larger combined mass), and the other lesser mass components simple orbit around that centralised mass.
    Trapezia are the really interesting systems here, being the definite example of the ejection of components. (Crashing components are highly unlikely unless hit straight on, as any deviation just slingshots one star out of the system.) When trapezia breakdown (they cannot survive more than 100000 years) from four to three components, they will do sow from a unstable system to a stable one. Calculations show each of the four stars have a variable gravitational energy over time. Under some circumstance the gravitational energy of three stars exceed the gravitational energy of one component, and so “gang up” to make the single component exceed the escape velocity of the system. Normally this has a number of significant effects. It ejects one of the components. Two of the stars form a closer binary star, which now has increased its angular momentum, a tighter binding energy, and shorter orbital period. The solitary third component now orbits the central binary in a much longer and more stable period. Together, this makes a positive energy system into a negative stabile one. (This neatly explains the larger number of triples, with a close binary and a more distant companion.)
    Theoretical experiments done in the 1980s show the ratio of the orbits in trapezia go roughly from 8:1, increase in the resultant triple between 20:1 and 500:1 or more.
    This same principle should also apply to planets, but due to the higher ratio of masses, are likely to suffer catastrophic changes to the orbit in shorter periods of time.
    As a final comment, with globular star clusters, the number of encounters is greatly enhanced compared to the Milky Way fields. Stars are constantly being buffered by the varying (dynamical) gravitational field, where capture and release is happening all the time. Key to all clusters (open and globular) is the orbits are mostly hyperbolic. Energies from the orbital motion is controlled by the so-called hard and soft binaries, which act like sinks in holding the angular momentum. This holds the cluster together, but can also cause continuous ejections over time — throwing stars out that exceed the cluster’s escape velocity. (This explains why open and globular clusters gradually lose or evaporate their membership.)

    NOTE : Known triples are far less numerous in open clusters or globulars than the general field. In the last two decades, though, the existence of triples and quadruples in clusters has been known. Observational support for this is often made by high-dispersion spectra or by astrometry. In 1996 only eleven systems were known. The first triple system in either a open or globular cluster was discovered in 1994, being this same millisecond pulsar of PSR B1620-26 within globular cluster M4 (NGC 6121).

  5. Universe Today readers don’t ‘generally assume’ anything without evidence. Good for you.

    To take that OT subject further:

    One can read a “useful skepticism, but a red herring” theme into the discussion. I agree on both counts.

    It is useful to make assumptions for the sake of the discussion and/or theory, and they will promptly and/or eventually be removed when no longer useful/harmful for the subject.

    Another red herring, sort of, is the flagging of topics. This is my current pet peeve problematic however, since it can be misleading.

    As an example, when in astrobiology one frequently sees the claim that cells “are far from equilibrium” it seems one really want to flag that cells are interesting chemical systems. But if taken at face value the claim quickly falls apart AFAIU.

    Cells, which may come as spores or rapidly (oh, so rapidly!) dividing bacteria, are when considered as slowly growing nearly steady state systems not much further from equilibrium than Earth steady state over a diurnal cycle. This is realized by considering the temperature difference characterizing quasi steady state deviations from thermodynamical equilibria.

    Or one can look at the time constants for returning to steady state, at which point “far” becomes ambiguous. Is a methane explosion, which quickly returns to equilibrium, more or less away in time from equilibrium than the same mass (and nearly equal energy) of an eukaryotic cell wasting away at ~ 0.5 % day if not fed? Or an iron meteorite slowly rusting the same mass (and nearly equal energy) away over more than 100 years before returning to equilibrium in its new environment? And why should we care about _that_?

    [Btw, a possible UT topic, perhaps?]

    To add harm to injury I suspect that the flag, which is misleading to outsiders and false as stated, is mostly a crutch for the superstitions of vitalism and creationism both, especially in their symbiosis in religions of the day. Instead of making the forthright statement on chemistry as pertaining biology one wants to go a roundabout way over irrelevant physics to hide the unveiling of the cell machinery and keep a place to put mystery in (a “gods gap”). This makes a big fish to fry out of a red herring.

    Finally as mentioned there is always the problem beyond red herrings of unnecessarily unstated or untested claims; which couched in algorithmic terms ‘makes it useful [“good”] for us to peek and poke at every bit of science’.

    1. If you mean biological systems obey the 2nd law of thermodynamics (the entropy one) – well, sure. If you were clearer what the ‘possible UT topic’ was may be someone would take a punt?

      1. One frequently sees the claim that cells “are far from equilibrium”:
        “What is life? … In general, we are bound to define life by properties that we ascribe to it, that is, to a complex system that is far from equilibrium and that follows the laws of thermodynamics (Elitzur 1994).” [From “Lectures in Astrobiology”, Vol II, ch 8 “Habitability: the Point of View of a Biologist” by P. López-Garcia; my bold.]

        As I mentioned, the issue isn’t thermodynamics, which we know cells & evolution obeys each. But that this claim, “far”, is a, I believe questionable lead in. (For the chapter in question, to a discussion of cells and their environmental requirements.) I haven’t tracked down Elitzur yet, and maybe the claim (of “far”, not the application of thermodynamics as such) is defensible.

        But as I described above, I can’t see how it is defensible. The mission for someone taking a punt would be, should you choose to accept it, be open to trace any history of the claim (as I said, it is frequent), why it is used (is it a flag for “life has interesting chemistry”?), if it is correct, et cetera.

        I mentioned rather obliquely why the claim _taken at facial value, mind,_ may be incorrect, and I could decompress my notions for what its worth (not much, likely). But I rather want an astrobiologist/biologist to pitch in and explain why one would make such a claim. Beyond want, I would likely be thrilled! 😀

      2. Actually biology is the only science in which I have a qualification of substance (which may explain my bodgy astronomy reporting). Living systems strive for homeostasis – but need to do so in the context of the environmental niche they occupy. (For example, the recently discovered bacteria using arsenic instead of phosphorus). There are aspects of equilibrium here – but really homeostasis is a constant battle against temperature and osmotic gradients. In most contexts, a cell would die if it achieved equilibrium with its environment.

        That said, I don’t know biologists who would use a term like ‘far from equilibrium’. What the heck does far mean? What is the measurement scale that determines what is far vs. close?

      3. Thanks, that was my point, what does it mean. No, I don’t know if biologists say that, nor what it would mean at face value (if that is the intent).

        If clarifying its use, that may not be all that pervasive if you haven’t encountered it before, is interesting or can be made so for UT readers I don’t know.

        [Btw I don’t think your reporting is bodgy.

        Some stuff has been far out IIRC, but that is a way to keep things interesting for all, if one doesn’t mind the calling out that will happen.

        As an example, it is often claimed by theoreticians that they make a few conservative papers and then mix with a speculative to keep on their feet. (IIRC Tegmark has said exactly that, ~ 4 conservative/1 speculative.) I think one should do that, I certainly let myself loose now and then. (But prefer to speculate on what I perceive as sound if not always most likely basis.)

        Of course, the difference is that theoreticians may place their respective categories in different interest papers or on arxiv, and that commenters have little to none authority to loose. It may be more of a conundrum for reporters.]

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