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A Tight Fit: Planets in the Habitable Zone

How many habitable planets should we expect in the average stellar system? One sounds like a good number to me, even an optimistic one. But it’s a tough question because we don’t exactly know what an ‘average’ stellar system is, there being such a wide range currently being discovered.

There was a time less than a century ago when the idea that there might be three habitable planets — i.e., habitable by humans — in the Solar System was current. Imagine Venus as something like French Polynesia, or maybe what was then the Belgian Congo. Imagine Mars with a thicker atmosphere and ancient seas, Edgar Rice Burroughs territory.

Today we think of multiple habitability here in the Solar System as perhaps including ocean life under the ice of the moons of giant planets, but we’ve ruled out anything a human could walk around on in relative comfort. The question of what makes our Solar System able to support just one planet in the human habitability range bothered Stephen Kane (UC-Riverside) because of examples like the seven planets around TRAPPIST-1, three of which seem to be in that planet’s liquid water habitable zone. Why so many? Why so few around our own star?

Image: The Trappist-1 planetary system has three planets in its habitable zone, compared to our Solar System, which has only one. (NASA/JPL/Caltech).

Out of such speculations came a way to analyze the question. Kane and team simulated gravitational interactions as planets at various distances from each other orbited their stars for millions of years. The upshot is that according to these calculations, a star like the Sun could support as many as six planets in liquid water habitable zone orbits. The fact that we do not see anything like this may just be the result of Jupiter and its ability to disrupt orbits because of its mass. Another needed trait of habitable zone planets: Their orbits need to be circular.

Kane’s team looked at the width of the habitable zone depending on spectral type and considered the dynamical constraints on stable orbits within the habitable zone, noting that “…dynamical constraints allow ~6 HZ Earth-mass planets for stellar masses ≿0.7M, depending on the presence of farther out giant planets.”

To examine these matters further, Kane has taken particular interest in Beta Canum Venaticorum (Beta CVn), a scant 27 light years away in the northern constellation Canes Venatici. This is a G-class star a bit more metal-poor than the Sun, although in most other respects it stands as a pretty fair double to our star in terms of mass and age. Maggie Turnbull (SETI Institute), a co-author on this paper, singled Beta CVn out as long as 12 years ago as one of the stars of possible astrobiological interest within 10 parsecs.

No planets are currently known here, but the very fact that there is no attendant gas giant makes Kane interested in looking for multiple smaller worlds. This is a nearby star that may yield transit results, based on the probabilities Kane calculates, and it offers the opportunity to test habitable zone packing scenarios. Finding nearby G-class stars without gas giants can be a profitable way to assess planetary orbital architectures, and to weigh how common our own Solar System’s might be:

Even though giant planets are more common around solar analogs than later-type stars (Zechmeister et al. 2013; Wittenmyer et al. 2016), they are still relatively rare, with an average occurrence rate of 6.7% beyond orbital periods of 300 days (Wittenmyer et al. 2020). Consequently, the solar system may not be representative of orbital architectures, and it is useful to directly compare with another nearby solar-type star, such as Beta CVn.

The paper presents 20 years of radial velocity data on Beta CVn from HIRES (Keck/High Resolution Echelle Spectrometer) as well as the Automated Planet Finder (APF) instrument, ruling out planets more massive than Saturn anywhere within 10 AU of the star. The potential packing given orbital dynamics around this star — numerous terrestrial-class worlds could exist here — show that relatively nearby targets like Beta CVn may also be interesting for space-based direct imaging missions of the future like HabEx and LUVOIR, as we begin to drill down toward smaller worlds in hopes of eventually characterizing their atmospheres.

Thus far we have primarily studied low-mass stars with transiting planets, which has revealed the phenomenon of compact, tightly packed systems. The paper goes on:

Some of these systems, such as TRAPPIST-1, have been found to have multiple terrestrial planets in the HZ, causing speculation as to whether such dynamical packing in the HZ is normal or rare. Our analysis presented here demonstrates that in fact the dynamical limitations to the packing of HZ terrestrial planets is ∼5 planets for most spectral types, and ∼6 planets for stellar masses ≳ 0.7M. Packing 7 planets in the HZ is possible within certain specific stellar mass and architecture regimes, but becomes vulnerable to MMR [mean motion resonance] perturbations that compromise the dynamical stability of such configurations. The 20 years of RV data for Beta CVn presented here rule out a large range of giant planet masses and orbital parameters, providing an excellent candidate for complex terrestrial architectures.

A few thoughts on earlier work:

Highly packed stellar systems like TRAPPIST-1 also caught the attention of Alysa Obertas (University of Toronto). Obertas tackled the question in 2016, but a key unknown remained whether or not there is enough mass in the planet-forming disk to produce systems packed up to the limits allowed by computer simulations. The resulting paper looked at simulations involving up to 10 billion orbits, focusing largely on M-dwarf stars, of which TRAPPIST-1 is an example. “Applying the outcomes of our simulations, we show that isolated systems of up to five Earth-mass planets can fit in the habitable zone of a Sun-like star without close encounters for at least 109 orbits,” said the paper, making orbital stability unproblematic.

We’ve also talked about the implications of tightly orbiting planets in terms of astrobiology. 1530 light years away in Cygnus, Kepler-36 is orbited by a ‘super-Earth’ and a ‘mini-Neptune’ in orbits that differ by 0.013 AU, producing transit timing variations for both planets. Here we have a 7:6 orbital resonance, and presumably spectacular views from the molten surface of the super-Earth as the larger planet moves across its sky.

The system inspired work by Jason Steffen (UNLV) and Gongjie Li (Harvard-Smithsonian Center for Astrophysics), who extended it into speculations on the transmission of life between close planets in habitable zones. For that one, see Habitable Planets in the Same System.

Image: A gas giant planet spanning three times more sky than the Moon as seen from the Earth looms over the molten landscape of Kepler-36b. Credit: Harvard-Smithsonian Center for Astrophysics.

The Kane et al. paper is “Dynamical Packing in the Habitable Zone: The Case of Beta CVn,” Astronomical Journal Vol. 160, No. 2 (27 July 2020). Abstract / Preprint. Also see Steffen and Li, “Dynamical considerations for life in multi-habitable planetary systems,” Astrophysical Journal Vol. 816, No. 2 (14 January 2016). Abstract / Preprint. The Obertas paper is “The stability of tightly-packed, evenly-spaced systems of Earth-mass planets orbiting a Sun-like star,” Icarus Volume 293 (1 September 2017), pp. 52-58 (abstract / preprint).

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{ 31 comments… add one }
  • Bruce D Mayfield August 4, 2020, 11:53

    This study bodes well, not just for the number of liquid water bearing worlds, but even for the shear numbers of smaller planets of hot and cold temperature ranges as well. The more the merrier. Ever more worlds to explore, galore!

    I wonder if it could even be that Sol’s system might prove to be below average as to total planet count among single star systems.

  • henry cordova August 4, 2020, 12:42

    The more luminous a star is, the wider its habitable zone, as normally defined (orbits where planetary surface water is in liquid form). Bright giants have extremely wide habzones, red dwarfs have extremely narrow ones. But many of the potentially habitable exoplanets we have discovered recently are near to low luminosity dwarfs. Is this purely a selection effect (massive planets near small stars are easy for our planet detection technology to find) or does it have to do with the mechanics of planetary system formation (low mass stars have planets closer to them, as a rule, than high mass ones)?

    This question has profound astrobiological consequences. Luminous, massive stars may have many planets in their generous habzones, but these stars are very rare, usually short lived and evolve too quickly for biological processes to lead to intelligent life. The dwarfs, on the other hand, are very common and extremely old and stable, but their habzones are so narrow that it is unlikely that any planet will form there.

    These two processes work at cross-purposes to each other, and our technology is much better at detecting very big planets very close to very small stars, which further complicates our assays. Does anyone know if these parameters have been carefully studied and their relative weights considered?

    I.E., is our Sun truly representative of life-bearing worlds, or are smaller, later spectral types a better place to look?

    • Ronald August 4, 2020, 19:15

      “These two processes work at cross-purposes to each other”.
      Exactly! Plus tidal locking and superflares, for the small ones.
      I guesstimate, that the optimum (for higher life) will be somewhere around late G, earliest K, having a wide enough ánd long-term stable HZ, and at the same time not bothered by tidal locking.

      • David Sims August 11, 2020, 21:10

        K3 stars have main sequence lifetimes that are most commensurate with the spindown times for terrestrial planets in the habitable zone. (From an 8h initial period to a 1:1 spin orbit tidal lock.)

    • Brett P Bellmore August 4, 2020, 19:23

      That’s just a side effect of how we’re looking for the planets; They’re easier to detect if the star is small relative to the planet.

    • Michael Fidler August 4, 2020, 19:59

      Now that is not true if anything the M dwarf system scale the same as any other and are more likely to have planets in their habitable zone. The example Trappist 1 turned the idea that M dwarfs are not a good place to look for life around. We are still early in understanding planetary systems and how they are made up. I would like to spend some time looking up the results of exoplanet list to see what holds in the secrets of Planets in the Habitable Zone:

      Exoplanet Catalog.
      https://exoplanets.nasa.gov/exoplanet-catalog/

      NASA EXOPLANET ARCHIVE.
      https://exoplanetarchive.ipac.caltech.edu/

      https://en.wikipedia.org/wiki/List_of_potentially_habitable_exoplanets

      https://en.wikipedia.org/wiki/List_of_exoplanets_discovered_in_2020

      Remember that most of the research has been looking for systems like ours; G2V when red dwarfs are dim, they are still finding new ones near to the sun!!! They are the most over 75% of all stars and have the highest land and sea available for the longest time for life and ET to develop. I am glad to hear that our system is not a freak of nature but our biases are overwhelming against the idea of life anyplace but on earth! Long live the mighty RED DWARF!

  • Brett August 4, 2020, 12:59

    They’d have stable orbits with each other, but would any of these hypothetical six Earth-mass planets be able to hold on to moons? Or would they lose them to gravitational interaction?

    • Bruce D Mayfield August 4, 2020, 17:22

      Maybe small, close in moons (like Mars has), but larger moons on large orbits would be out in tightly packed systems.

      • Ryan Carthy August 5, 2020, 1:02

        What about really large moons with close in orbits? There’s a rare possibility there. If the moon is large enough, much larger than our moon, then both bodies could tidally lock to each other early on in their history, preventing further tidal acceleration and leaving them orbiting at just a few multiples of the roche limit. The formation of “binary planets” has been simulated (https://ui.adsabs.harvard.edu/abs/2014DPS….4620102R/abstract) and is expected in a very small number of grazing collisions.

        This is also the kind of thing that would happen more often if you started with a packed system. It’s expected that packed systems would have larger hill reduction factors for moons, but if two almost equal mass planets orbit each other tidally locked at only 5 radii apart then they should be able to persist longer than smaller moons that cannot lock their planet soon enough to avoid being spun outwards to face the influence of the other planets, or inwards to collide. A habitable planet could have a habitable moon in this way, even in an otherwise tightly packed system (though they would behave to the other planets more or less as an object with their combined mass)

        If you did see a binary planet/double planet like this, perhaps it would be exceedingly hard to detect as such.

        • Bruce D Mayfield August 5, 2020, 15:37

          Double planet configurations are an interesting possibility Ryan.
          I suppose that very long orbital stability would depend on just how close a doubles’ neighboring planets are.

    • Harold Shaw August 5, 2020, 8:57

      A planet’s axial tilt is affected by other planets in the system. Would a moon be more or less necessary for maintaining a stable tilt for a planet in a tightly packed system?

  • Eniac August 4, 2020, 15:19

    Here it might be appropriate to once again recall that, currently, none of our planets would be detectable if they were around another sunlike star. The fact that we see so many stars with more detectable planets (bigger planets or tighter orbits) means that our system, if anything, contains an unusually small number of planets. If we assume that there is nothing unusual about our planets, we have to assume that there are similar ones around most stars, undetected, in addition to those we have detected. So, plenty of planets out there, more than we can see, and the unseen ones are bound to be more like ours than those we can see.

    I can’t wait for us to finally get equipment up there that can actually see planets like ours. I think it is just one more generation of instruments, maybe a decade or so.

    • Bruce D Mayfield August 4, 2020, 17:34

      Good points Eniac.

      I’m hoping (as a temperate rocky planet dweller) that the average exoplanetary mass will drop as our detection abilities improve. Gas bags may disagree, but they’re just full of hot air.

  • Alex Tolley August 4, 2020, 17:26

    Could the hypothesized Mars-sized Theia that collided with Earth have been an example of another planet in our HZ that expired due to the collision, or was the orbit too eccentric?

    In another post there was an example of 2 planets that could occupy very similar orbits that periodically swapped positions. This was stable, I think. Unusual perhaps, but would that help close packing?

    • FrankH August 5, 2020, 16:41

      But Theia, being Mars-sized, would not have been massive enough to be habitable in the Sun’s HZ.

      As for moons in a crowded solar HZ, that would depend in part on each planet’s Hill sphere. As long as there isn’t an overlap, large moons are probably OK.

  • Ronald August 4, 2020, 19:07

    Excellent post again, and intriguing topic, very encouraging also. This kind of paper makes me glad.
    As I have argued before, this would imply that lower metallicity solar type stars, without the greedy giants, might be the best candidates, possessing a whole series of terrestrial planets.
    And a later spectral type of solar type star might better, in order to have a more long-term stable HZ.

    This is also my only doubt about Beta CVn: it is a G0 star, somewhat hotter than the sun ánd somewhat older, 5.3 gy orso. This means that the HZ moves outward faster than ours, and that any planets that were in the HZ for the first 4 gy orso, have left it, on the inner side (hot!). And planets that are now inside the HZ, weren’t so for those first 3 or 4 gy.

    It might be (even) better to study later type solar stars, around G6 – G8, such as: Tau Ceti, 82 Eridani, 61 Virginis, Alpha Mensae, etc.
    Alpha Mensae has no detected (giant) planets.

  • Geoffrey Hillend August 4, 2020, 23:25

    Alex Tolley, Theia would be in our habitable zone today, but a Mars like planet in the HZ zone would still loose it’s atmosphere and end up like Mars today due to it’s smaller mass and lower gravity. Mars has an escape velocity of only 3.1 miles per second and Earth 7 miles a second. A planet with a lower escape velocity will loose an atmosphere faster due to the principles of atmospheric escape. Also the iron core of Theia supposedly went into the Earth and what was left over became the Moon. It’s probably not good to have two planets relatively at the same distance because the odds are high for a collision.

    Earlier in my life liked to imagine what it would be like to have more than one habitable planet in our solar system or at least one with a comfortable surface a person would not need to have a space suit. It would help if Mars was the size of Venus or larger. If Venus was further away from the Sun like 87 million miles or maybe 89 that would be comfortable. The odds are against having more than one Earth like planet with a Moon and a magnetic field in the same solar system because of the need to have what Alex Tolley mentioned, for two planets have to be in nearly the same orbital distance to collide and with three Earth like planets, we would need three Mars like planets in approximately their same orbits to collide with them. More favorable odds would include a G class star system with three Earth like planets in the habitable zone, but only one of them with a moon and a magnetic field which would produce humanoid life.

    Henry Cordova, I do think intuitively that the size and mass of the star really does matter like Trappist-1 planetary system, which an M dwarf has all it’s planets close together as the result of the star having a smaller mass and lower gravity than a G class star. A Smaller star therefore must have a smaller accretion protoplanetary disk. In my opinion the migration of planets to produce the close orbit of planets in the Trappist-1 case is dubious for more than one reason.

  • Ross Turner August 5, 2020, 1:01

    An article was done goldilocks stars – the best stars with the best stars to find habitable planets. It turns out they are the K-dwarf stars, not the M or G. They are more numerous and have longer lives than the G stars, and have a lot less radiation and habitable zone issues than the M-dwarfs.

    There are about 1000 of these stars within 100 ly of the sun.

    Here is the article:
    https://www.nasa.gov/feature/goddard/2020/goldilocks-stars-are-best-places-to-look-for-life

    • Paul Gilster August 5, 2020, 6:24

      See, for example, “Orange Stars: ‘Goldilocks’ Stars for Life?”

      https://www.centauri-dreams.org/2020/01/13/orange-dwarfs-goldilocks-stars-for-life/

      • Ronald August 8, 2020, 9:58

        I have a somewhat related question for Ashley Baldwin, or anyone here who can answer it;

        In the post linked by Paul, Mr. Baldwin makes an intriguing statement:
        “Ironically spectral class isn’t just determined by mass. K0.5 40 Eridani has 5% more mass than Tau Ceti whilst G6 82 Eridani has about 9% less and is still significantly more luminous.”

        To which I replied:
        “I have been wondering about that.
        The correlation is (logically) rather sturdy, but not perfect.
        (…) Alpha Mensae, for instance, has an estimated mass about 10% greater than our Sun, but spectral type G6, B-V color index 0.72, temperature about 5580 K.
        I find that all rather remarkable for such a heavier star.”

        This question was never answered. Generally, stellar mass determines temperature, and hence spectral type.
        What could be the explanation for some stars being such outliers in this?

        Particularly, 82 Eridani and Alpha Mensae have been puzzling me in this respect.
        As for Alpha Mensae: could the mass calculation be wrong (10% more than solar! Should be G0 or so)?

    • Ronald August 7, 2020, 9:47

      Exactly, the goldilocks stars, See Paul’s referenced post plus referenced paper.
      And the concept of super-habitability.
      I think that the optimum is probably somewhere around late G and early K, because at or beyond K3, corresponding with a HZ midpoint around 0.5 AU, the problem of tidal locking starts kicking in. Tidal locking time correlates with the 6th power of distance, so it goes down really fast with decreasing orbital distance. Hence, beyond K2/3 you loose the added advantage of increased stable stellar lifetime.
      And below G0/F9 stellar evolution and the outward movement of the HZ goes so fast that the wide HZ is no longer an compensating advantage. In other word: the HZ may be wide, but the continuous HZ (CHZ) becomes very narrow. This is something I miss in the otherwise excellent paper.
      Humbling thought that we may be well beside the optimum, rather close to the hot end of ‘stellar habitability’.
      Even we, with our middle-aged G2 star, have a window of opportunity for higher life of only about 1 gy, through which we are about half-way. Again, a humbling thought.
      At or below about F9 this window of opportunity decreases to close to zero.
      The was a fascinating post here on CD about this window of opportunity for complex life, a few years ago, but I would have to look it up.

      • Paul Gilster August 7, 2020, 16:20

        I think you’re talking about this one, Ronald:

        G-Class Outliers: Musings on Intelligent Lifehttps://www.centauri-dreams.org/2012/11/01/g-class-outliers-musings-on-intelligent-life/comment-page-1/

    • Ronald August 7, 2020, 10:17

      Ok, the referenced paper by Cuntz & Guinan says it all, I looked it up again, fascinating must-read, the concept of the Continuous HZ, CHZ, is also in there:
      “Another intriguing aspect that also tends to support our main conclusion is the onset of tidal locking, which for planets located in the CLI-HZ (both CHZ and GHZ), pertaining to a timescale of 4.5 Gyr, occurs for stars with effective temperatures close to 4800 (±200) K (i.e., for K3 V stars).”
      And the earlier CD post about WoO for complex life is also mentioned there, in one of my comments:
      https://www.centauri-dreams.org/2012/11/01/g-class-outliers-musings-on-intelligent-life/comment-page-1/#comments

  • Laintal August 5, 2020, 4:47

    Hi All

    Thanks for the post Paul and everyone great comments

    Sure is interesting and now to read the paper (also Larrys review to)

    Cheers Laintal

  • Michael Fidler August 5, 2020, 5:30

    Take a look at this list on Wikipedia:

    List of multiplanetary systems.

    https://en.m.wikipedia.org/wiki/List_of_multiplanetary_systems

    This list has many G and F dwarfs systems on the list but not many in the habitable zone. It seems the large gas giants make it more difficult for the smaller planets to form in the habitable zone of these stars. The M and K dwarfs make up 90% of stars and are prone to make earth like planets. That is where the real dirt/soil will be found and life will develop.

  • andy August 5, 2020, 7:57

    Venus is an interesting case: some of the climate modelling predicts that thanks to the slow rotation rate, it should be able to maintain habitable conditions until the present. This is due to the prediction that slowly-rotating planets would build up a large reflective cloud cover on the day side, which would be disrupted on a planet with faster (Earthlike) rotation.

    A recent suggestion by Way & Del Genio (2020) is that habitable conditions on Venus were ended not by increasing insolation but by the eruption of large igneous provinces (LIPs) similar to the Siberian and Deccan Traps that erupted at the end of the Permian and the Cretaceous respectively (which both happen to be significant times in the history of life on Earth). These may have output sufficient carbon dioxide to trigger the runaway greenhouse.

    It is likely that the eruption of LIPs throughout Earth’s history (Ernst, 2014; Ernst et al., 2019) is a random stochastic process. This may imply that multiple large scale LIPs have not occurred simultaneously on Earth by purely random chance, which is fortuitous for life as we know it today. Venus may not have been as fortunate.

    So maybe we are in a system with multiple habitable zone planets, but one of them got killed by an unfortunate geological accident.

  • Geoffrey Hillend August 5, 2020, 16:30

    I will agree that a gas giant does decrease that chances of the formation of Earth like rocky inner planets, but only in smaller stars with less mass that formed from smaller accretion disks like K and M dwarf stars which is why I am sticking to the idea that that intelligent life is most probable around a G class star with gas giants and a solar system similar if not an exact match to our own with four, outer gas giants and nine planets.

    We still have one example of a solar system with intelligent life which is our own that is better than no examples or something different. If it worked here, then it will have to work somewhere else based on physics.

  • Adam Crowl August 6, 2020, 3:27

    Hi Paul
    Sean Raymond has blogged on this very question, as well as the speculative question of just how many planets can stably share a common orbit – it’s surprisingly many. Of course, in the latter scenario, the planets need to be deliberately placed in such shared orbital configurations. Given how many loose planets are likely near the Galactic Core, a side-effect of crowded star formation, one wonders if there’s not such artifacts already in existence.

  • Gary Wilson August 6, 2020, 19:46

    This is such a fascinating topic, the idea of determining how many planets can be stacked in orbits in the HZ of various types of stars. I look forward to learning much more about this in my lifetime :)! I’m at 19,500 scans evaluated for TESS in my personal search for exoplanets by the way. I’m quite proud of that. Keep on giving us such amazing articles Paul.

  • Joy August 7, 2020, 19:28

    My star! The traditional name Chara was originally applied to the “southern dog”, but it later became used specifically to refer to Beta Canum Venaticorum. Chara (χαρά) means ‘joy’ in Greek. – Joy

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