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KOBE: The Hunt for Habitable Zone K-dwarf Planets

From the standpoint of producing interesting life, K-dwarf stars look intriguing. Our G-class Sun is warm and cozy, but its lifetime is only about 10 billion years, while K-dwarfs (we can also call them orange dwarfs) can last up to 45 billion years. That’s plenty of time for evolution to work its magic, and while G-stars make up only about 6 or 7 percent of the stars in the galaxy, K-dwarfs account for three times that amount. We have about a thousand K-dwarfs within 100 light years of the Solar System.

When Edward Guinan (Villanova University) and colleague Scott Engle studied K-dwarfs in a project called “GoldiloKs,” they measured the age, rotation rate, and X-ray and far-ultraviolet radiation in a sampling of mostly cool G and K stars (see Orange Dwarfs: ‘Goldilocks’ Stars for Life?). Their work took in a number of K-stars hosting planets, including the intriguing Kepler-442, which has a rocky planet in the habitable zone. Kepler-442b is where we’d like it to be in terms of potential habitability, but it’s twice as massive as Earth, and it also raises the question of why it seems rare.

In other words, why do we have so few habitable zone planet detections around K-dwarfs? A new paper from astronomers with the European Southern Observatory points out that we have only a small number of such worlds at present. Have a look at the table below to see what I mean. Here we’re looking at known planets, which means either confirmed or validated, that are found within the ‘optimistic’ habitable zone of K-dwarfs with an effective temperature between 3800 K and 4600 K. ESO’s Jorge Lillo-Box and his fellow researchers go so far as to declare this lack of habitable zone worlds ‘the K-dwarf habitable zone desert’ in the paper, which has just appeared in Astronomy & Astrophysics (citation below).

Image: This is Table 1 from the paper, showing confirmed or validated K-dwarf planets in the habitable zone known as of May 2022.

A few points about all this. First of all, note the distinction above between ‘confirmed’ and ‘validated’ planets, two terms that are all too often conflated but mean different things. With the original Kepler mission (before the K2 extended mission), a planet candidate was a transit signal that passed various false-positive tests. A ‘validated’ planet is one that has been studied in follow-up observations and determined quantitatively to be more likely an exoplanet than a false positive. Thus ‘validated’ means a planet about which confidence of its existence is higher than a simple ‘candidate.’ Confirmation, as for example through radial velocity study of the transiting planet’s mass, is the final step in turning a validated planet into a confirmed one.

So what’s happening in the K-dwarf desert, or more to the point, why is the desert there in the first place? Expectations are high, for example, that a K-dwarf like Centauri B might host a planet in the habitable zone, such orbits being allowed even in this close binary system. The authors point out that the reason may simply be lack of observation. There is understandable emphasis on G-class stars because they are like the Sun, while M-dwarfs are highly studied because planets there are more readily detectable. What is needed is a dedicated program of K-dwarf observations.

Image: This infographic compares the characteristics of three classes of stars in our galaxy: Sunlike stars are classified as G stars; stars less massive and cooler than our Sun are K dwarfs; and even fainter and cooler stars are the reddish M dwarfs. The graphic compares the stars in terms of several important variables. The habitable zones, potentially capable of hosting life-bearing planets, are wider for hotter stars. The longevity for red dwarf M stars can exceed 100 billion years. K dwarf ages can range from 15 to 45 billion years. And, our Sun only lasts for 10 billion years. Red dwarfs make up the bulk of the Milky Way’s population, about 73%. Sunlike stars are merely 6% of the population, and K dwarfs are at 13%. When these four variables are balanced, the most suitable stars for potentially hosting advanced life forms are K dwarfs, sometimes called orange dwarf stars. Credit: NASA, ESA, and Z. Levy (STScI).

Enter KOBE, standing for K-dwarfs Orbited By habitable Exoplanets. This is a survey, introduced by Lillo-Box and team, that monitors the radial velocity of 50 pre-selected K-dwarfs using the CARMENES spectrographs mounted on the 3.5m telescope at the Calar Alto Observatory in southern Spain. Given the capabilities of the instruments and planet occurrence expectations, the team believes it will find 1.68 ± 0.25 planets per star, with about half of these likely to be planets in the habitable zone.

The choice of K-dwarfs is interesting in various ways. I’ve focused on this class of star recently because while G-class stars like the Sun offer obvious analogies to our own Solar System, their size puts habitable zone orbits far enough from the star that a radial velocity campaign to detect them takes years. Bear in mind as well that, as I learned from this paper, G-class stars produce a lot more stellar noise than K-dwarfs, making detections more problematic, even with instruments like ESPRESSO.

With M-dwarfs as well, we run into intrinsic problems. They tend to be active stars, so that working at the levels needed to detect habitable zone planets likewise means extracting data from the noise (not to mention the effect of flares on potential habitability!) We’ll continue to put a lot of emphasis on M-dwarfs because with habitable zones closer to their smaller stars, any planets there are quite detectable, but given the advantages of K-dwarf detection, an effort like KOBE is well justified.

The authors make the case this way:

K-dwarfs have their HZ located at longer periods (typically 50–200 days), where planets can have their rotation and orbital periods decoupled, thus allowing the planet to have day-night cycles. Stellar activity and magnetic flaring is dramatically diminished for stars earlier than M3 and specially in the late K-type domain… Consequently, habitability is not threatened by these effects as much as it is in the HZ planets around M dwarfs. Besides, unlike in M-dwarfs, we can derive, in a standard way, precise and reliable stellar parameters, as well as chemical abundances that are relevant to a proper characterization of the planets and the star-planet connection…

Indeed, K-dwarfs show UV and X-ray radiation levels 5 to 50 times smaller when they are young than early M-dwarfs, an interesting point re habitability prospects. And as the authors note, this type of star offers ‘the best trade-off’ to detect biosignature molecules through direct imaging using next-generation space observatories.

So I’m all for KOBE and similar efforts that may arise to populate our catalog of habitable planets around this interesting kind of star. Because it focuses on the detection of new worlds in the habitable zone, KOBE rules out stars that have already had exoplanets discovered around them or are highly monitored by other surveys. The effort runs through 2024, and if things go according to expectation, we should wind up with about 25 new planets in the so-called K-dwarf habitable zone desert.

Image: The 3.5m telescope at Calar Alto Observatory under the Milky Way. Credit: CAHA.

It’s always useful to delve into anomalies that seem to be the result of observational biases in getting a more accurate picture of the systems in the stellar neighborhood. And while it’s a southern sky object and thus out of range of KOBE’s efforts at Calar Alto, I still have high hopes for Centauri B, the closest K-dwarf to Earth…

The paper is Lillo-Box et al., “The KOBE experiment: K-dwarfs Orbited By habitable Exoplanets Project goals, target selection, and stellar characterization,” Astronomy & Astrophysics Vol. 667 (15 November 2022) A102. Full text.

{ 22 comments… add one }
  • Alex Tolley November 18, 2022, 13:12

    Our G-class Sun is warm and cozy, but its lifetime is only about 10 billion years, while K-dwarfs (we can also call them orange dwarfs) can last up to 45 billion years. That’s plenty of time for evolution to work its magic (…)

    Ever since I wrote up Prof. Tyrrell’s work on simulating planetary climate evolution and the result suggesting planets remaining habitable were rare, I have wondered if the idea that long-term habitability (i.e. a planet remaining in the CHZ) is a naive interpretation and that this longevity does not increase the probability of extant life on a world.

    Whether random events can cause runaway freezing or heating, or whether life can initiate these runaway instabilities, if these events are random and appear with some average frequency, then the chance that a planet has extant life will not increase with time. We assume that the length of the time in the CHZ will increase the time abiogenesis and evolution have to produce life and complex life too. We also assume that the Gaian homeostasis is powerful enough to increase climate stability allowing evolution to continue (although humans are doing a good job proving this may be wrong). If either or both these assumptions are wrong, then planets in the HZ of K-dwarfs will either be Venuses, or frozen worlds, more like Mars, or Earth in its snowball state. Living worlds, especially verdant ones, may be extremely rare, rather than common even if initial conditions would suggest otherwise.

    The Case for a Gaian Bottleneck: The Biology of Habitability

    Are Planets with Continuous Surface Habitability Rare?

    • Mike Serfas November 20, 2022, 8:02

      See https://www.science.org/doi/10.1126/sciadv.adc9241 for the most recent take on silicate weathering. One reassuring conclusion is that there is negative feedback homeostasis on time scales up to a million years or more. Nonetheless… for fluctuations over 1-20 million years, varying up to 3 K (rms), the results appears to favor a random walk without a stabilizing mechanism. What happens beyond that … is not on their graph.

      • Alex Tolley November 20, 2022, 22:17

        Thanks for the link to the Arnscheidt and Rothman paper. This from the discussion section is most salient:

        (…) the key question is: Are there any mechanisms in the Earth system that prevent these kinds of fluctuations from eventually driving surface temperature into an uninhabitable regime? If there are none, it would follow that chance may have played a nonnegligible role in Earth’s continued habitability, and that other Earth-like planets with an active carbonate-silicate cycle and in the conventional habitable zone may not necessarily be as accommodating to life over long periods of time as has previously been expected.

        Long-term randomness seems to indicate that long-term habitability might indeed be due to luck, rather than stabilization.

        I’m reminded of David Raup’s “Extinction: Bad Genes or Bad Luck?” where he tried to discern from the evidence whether extinctions were due to Darwinian competition (bad genes) or due to accidents like meteor impacts (bad luck). IHO, neither was compelling. The KT event was recently explained, and others were trying to find direct causes of other major extinctions, especially the Permian. Statistical analysis could not separate the reasons, as a random walk could explain the major extinction events. (The consensus is very much more in the “bad luck” camp as new discoveries have been made, although not just meteor impacts.

  • Mike November 18, 2022, 13:50

    Thanks for this article, Paul.

  • David November 18, 2022, 16:27

    According to the paper (which I only took a quick look through), they rule out stars in binary systems, which leaves out many nearby orange dwarfs such as 61 Cygni A/B. These would be good targets once more sensitive instruments are available and more time can be dedicated to surveys.

    Overall, I’m looking forward to hearing about their discoveries over the next couple years. From their paper, it doesn’t look like they expect to find any ‘Earth sized’ planets in the HZ, only ones greater than 3 Earth masses, which also leaves open the possibility of followup surveys for smaller worlds that could be missed in this project.

  • henry cordova November 18, 2022, 16:55

    It appears we’ve visited this terrain before…


    Yes, M dwarfs are more numerous, but they have narrow habitable zones. Statistically, there is just less of a chance to find a planet there, all else being equal. Having said that, big worlds orbiting very close to small stars are easier for our planet-detecting technology locate.

    Once again, the astronomer’s old bugaboo, ‘selection effect’, distorts our observations, and the conclusions we derive from them..

    Perhaps Sol-like stars and red dwarfs are outliers, and all these effects resonate at the K dwarfs.

  • Michael C Fidler November 18, 2022, 23:35

    “Statistically, there is just less of a chance to find a planet there, all else being equal.”
    Not so fast, habitable zone planets are much more common around M dwarfs. Just take a look;

    This table shows 95% of habitable zone planets within less then 600 light years are around M dwarfs, many of which have multi planets in the habitable zone. Best example being Trappist 1 with four habitable planets. The other 5 percent are 2 K dwarfs, the first G dwarf is at 635 light years.

    This study will help mesh the area between G dwarfs, K dwarfs and M dwarfs, helping understand the significance K dwarfs and our own bias for G dwarfs. The problem is the numbers are there and there is no question M dwarfs dominate.

    • hc November 19, 2022, 11:33

      You keep missing the point, Michael. Its a selection effect. That’s where the bias is.

      The reason so many planets are being found in the habitable zones of M dwarfs is that the HZs of those stars are very close to the stars. A planet there would be able to gravitationally affect the star very profoundly, especially for detection methods that rely on gravitational shifts imposed by a nearby planet. It also helps that the M-dwarfs are all low-mass stars, and easily gravitationally perturbed. For the same reason, radial velocity shifts are much easier to see when planets are very close to very low-mass stars. Just because planets are easier to see there does not necessarily mean they are more common.

      In transit surveys, a planet orbiting a star very closely might also cast a larger shadow on its celestial sphere, meaning a transit would have a much higher probability of being observed by a distant astronomer.

      For every one of those planetary discoveries, if we replace the primary with a brighter, more massive, and physically larger star, the resulting HZ would be pushed much further out and the gravitational perturbation, the radial velocity shift, and the chance of seeing a transit would all diminish to the point where they might not be detectable with our level of technology. Since we can’t see these effects, we cannot make any judgements as to how they alter the results of our surveys.

      I will concede that M stars are very common, and because of their long lifetimes often much older than other stars, which does statistically increase the number of potential astrobiologically interesting planets orbiting them (all else being equal). The age makes a difference since any given M dwarf is much more likely to be a very old, stable star because they evolve so slowly. But we have no knowledge of how planetary formation and solar system architecture is a function of spectral class, or of overall mass. In fact, there may be none: the number of planets formed may very well be totally independent of the mass (or brightness) of the primary.

      The one interesting factoid we can glean from these surveys is the large number of planets found in red dwarf HABITABLE ZONES. As I mentioned in our earlier discussions of this topic,


      the habitable zones of these stars are extremely narrow. The fact that we are finding any planets there at all is astonishing. Perhaps it is a clue as to how planets form. Perhaps, as you implied, all planetary systems for all stars are simply dimensionally scaled up or down as a function of the primary’s mass. But we have no way of knowing that.

      The chances of finding a planet in any particular HZ depends on the size of the HZ, which is greater for bright, short-lived, massive stars. But the chance of that planet evolving life depend on the number of stars, their average age, and their stability, all parameters which favor the red dwarfs. It is the combination of these two functions that will resonate at a particular stellar mass, somewhere in between. Exactly where, we don’t know for sure, although the authors of this article seem to favor spectral class K.

      • Michael C Fidler November 20, 2022, 5:09

        I’m not missing anything, I’m well aware of the selection effect and I understand that we have not found enough planets around G class stars to make a complete argument one way or the other. The TESS cameras is suppose to be looking for planets around the brighter stars like ours. I would like to see the information from both the candidates and confirmed planets to see if there is any trend.

        One problem with your view that has not been discussed in literature yet, is the stability of M dwarf systems compared to G dwarfs. The nearest star to earth The M dwarf Proxima Centauri has a density eight and a half times that of earth and gravity 162 times higher. Compared to the sun its density is 33 times that of the Sun and with a diameter of only 1.5 times that of Jupiter. What does this do to those planets that are much closer to the surface of M dwarfs then are much wider solar systems?

        It increases stability and even in giant impact collisions the planets do not get ejected from the M dwarf systems. It is a classic bound system, meaning it cannot lose mass but only gain mass. Binary system may not be bound because of the second star. Because of the higher gravity field and the planets being closer to the star more planets may be found to exist in the habitable zone then higher mass and larger stars.

        You are confusing the size of the star with the size of the habitable zone but the distances of the planetary orbits around the smaller stars are also smaller. The higher gravity of the denser M dwarfs cause the orbits to be closer and stability higher creating a denser planetary system with a higher number of planets in the habitable zone then around G dwarfs.

        • HC November 20, 2022, 13:44

          ‘Density’ is defined as mass divided by volume. Density has NOTHING to do with the shape or configuration of a star’s gravitational field. All spherical masses behave gravitationally as if their entire mass was concentrated at their geometrical center. In other words, when determining the acceleration at any point in a star’s gravitational field, all you need to know is the mass of the star, and the distance of that point from the star’s center of mass. Nothing else matters.

          As for the rather confusing relation between size, mass, age, luminosity, chemistry and temperature, there is a correlation between these properties, but only for stars on the Main Sequence (MS). In fact, it is precisely the correlation between temperature and luminosity (expressed as a line on the H-R diagram) that defines the MS.

          Low-mass MS stars are generally cooler, smaller, fainter and older. I say “generally’ because there are no doubt exceptions, but this is the rule. The age parameter is statistically skewed by the fact that massive stars evolve off the Main Sequence faster, and die sooner, so they may change luminosity, size, chemical composition, and temperature (but NOT mass) prematurely compared to red dwarfs. They are also prone to variability, planetary nebula outgassing, nova, supernova and other outbursts and catastrophes. Red dwarf’s, on the other hand, tend to be stable and long-lived. Once a star settles down to life on the Main Sequence, it tends to remain there until it evolves off the MS. And this is solely a function of the star’s initial mass, at birth. There may be circumstances when this is not the case, such as in close binary pairs, but in general, this is the rule.

          We know that low-mass stars are more likely to form from the interstellar medium than high-mass stars, and since they also tend to be much longer-lived, the snapshot we see at any one time shows that the majority of all stars are red dwarfs, and the majority of them are relatively older.

          None of this tells us anything about the formation or configuration of planetary systems. There very well may be a correlation between planetary architecture and stellar evolution and structure, but we do not know it. All we do know for sure is that since red dwarfs are generally older, and more stable, their planetary systems have had more time to dynamically evolve–as a rule. We also know that potential life-bearing planets have had more time to evolve a biosphere–as a rule.

          Unfortunately, since the red dwarfs are low-mass, it is much easier for our present planet detection techniques to see planets around these stars. But the resulting, biased observed statistics do not allow us to extend any conclusions to more massive stars, with wider and more distant habitable zones. This will have to wait until we develop the technology to detect less massive planets at greater distances from their primaries.

          There is no G spectral class bias among astrobiology researchers. In fact, any observation or reasoning that suggests the number of possible life-bearing, or civilization-forming worlds could be much greater is welcome news. I certainly rejoice at the inclusion of red dwarfs as potential sites, for that very reason–they’re older, they’re stable, and there’s so many of them. But there are also many reasons to be skeptical.

          • Michael C Fidler November 20, 2022, 21:50

            Density and size does matter. (Pun intended) Higher density in M dwarfs create a smaller star and planets that can orbit much closer to the center of gravity. The fastest orbiting exoplanets around main sequence stars orbit red dwarfs. The exoplanets orbiting around the M dwarf stars K2-137 and KOI -1843 orbit in 4.3 hours. By coincidence both are smaller then earth and denser and are iron-rich “cannonball” planets.

            I was trying to find a good illustration of the Sun’s habitable zone with all 8 planets, but nothing to be found (Another Bias?) to compare in an overlay of the Trappist 1 system to show how they compare. Trappist 1 habitable zone would reach clear out to URANUS! Now that’s what I mean by planets in M dwarf systems being pack in at a much higher orbital density then here.

    • Ron S. November 19, 2022, 15:23

      “habitable zone planets are much more common around M dwarfs”

      That’s selection bias. It’s too soon to say.

    • Mike Serfas November 21, 2022, 8:10

      Someone might be able to reverse engineer the observation bias, but in the meanwhile it would be interesting if someone here could directly address the question of planet formation, or at least the typical size of the protoplanetary disk. Intuition is misleading on this point – it’s easy for me to think that a tiny star should come with tiny planets in tiny orbits, but stars aren’t flowers! Looking at https://arxiv.org/pdf/2103.10465.pdf it seems like a star that can barely burn hydrogen might be forming a planet at 12 AU. But there are hundreds of relevant abstracts on ArXiv to look at – it would be enlightening to have an expert summarize the known and hypothesized rules of planet formation relative to stellar mass in an article.

      • Henry Cordova November 21, 2022, 12:07

        Well put.

        I don’t think anyone fully understands the planet forming process, and certainly not how it may vary across a spectrum of stellar masses that spans several orders of magnitude. We simply don’t have the data, and what we do know is heavily biased to very small stars with very nearby planets.

        It does appear that red dwarfs seem to have a lot of planets, and many of them are crowded into very narrow habzones. But these stars form the bulk of stellar populations, they can be extremely old, and our planetary discovery techniques are tuned to find exactly that. Its a classic example of the ‘ looking for the lost car keys near the streetlights’ problem. Either we develop observational methods for finding planets at greater distances from their primaries, or we come up with better theoretical descriptions of planetary system formation, preferably both,

        What we are seeing now is exactly what you’d expect, regardless of the underlying reality.

  • Edwin November 19, 2022, 6:23

    Another good read

    I feel like I have even more research papers to follow up and read now, and I can only wounder how Hycean or Ocean planets do around K stars.

    Thanks for the great comments everyone too.

    Cheers Edwin

  • Michael November 21, 2022, 14:14

    There may be plenty of K and M dwarfs and they could have life in orbit around them, but is it wise to go there. We may come in peace but our microbial baggage would act otherwise as would theirs. Perhaps we could go off to more sterile stars like Sirus to occupy. Sirus for instance puts out more energy than the nearest 200 hundred star systems and that white dwarf would allow us to use millions of solar gravity lens to observe and communicate from great distances. That white dwarf gravity lens starts at around 0.05 AU.

  • wdk November 21, 2022, 23:09

    Chou En-Lai was once asked ( in the 1970s?) what he thought were the consequences of the French Revolution? “Too early to tell”, he succinctly remarked. He might have observed our beauty contest of Main Sequence stars and habitable exoplanets similarly: Numerous M red dwarfs, but narrow nominally habitable zones awash with charged particle storms; the larger G stars occurring less frequently and not registering many planets; hence, the K stars looking like a compromise case.

    Looking at the offered Wikipedia list of HZ exoplanets detected, however, I do see some other detection biases, however. It’s not that the list saws the limb out from under the Mdwarf argument’s feet, but…

    1. For example, in the case of Trappist-1, only one planet is indicated as in the HZ ( Trappist 1 d) and the rest are not mentioned. Presumably it is the best of the lot because it is centered in the habitable zone, but the zone is still considered a ring of some width with fuzzy limits. For my own estimates, I would say that given a BB surface temperature for a star, assume the equivalent thermal expansion of the sun to about 1 AU or 400 K as a reference point. From there you can play any type of handicap games you want, compensating for the peak flux, planetary albedo or rotation rate. My guess is that Trappist 1 should have at least 3 habitable zone candidates since we still no little about each planet’s composition, history or response.

    That’s one case. But I suspect that the list, largely of Kepler candidates, has more identified multi-planet systems that could provide more than one HZ exoplanet candidate. Because the worst in such system might be better than the single one identified in another. Largely among M dwarfs, of course.

    2. Except for the solar base case of 365.24 days ( Us) the list has only one orbital period that’s longer.

    Now is that really because exoplanets of near terrestrial mass do not frequent the HZs of K or G stars as much as dwarfs – or is that because detection becomes more difficult with the detection methods available?

    For transits, if you have to wait for a year for a transit event vs. 10-20 days, noise increases, repeats opportunites might exceed spacecraft lifetime and the dip in luminosity is one part in ten thousand vs. as little as 1 part in 100. If you use doppler or astrometric measures, the ratio is not good either. The Earth is 1/330,000th of the sun in mass; for 1/10 mass red dwarf, it’s 1/33,000th. Which means transit is still your best chance. Imaging would be another possibility but you need a very good solar/stellar coronagraph setup to detect the infrared spectrum separate from the primary’s glare.

    Mulling these cases over, it is also worth examining the satellites of Neptune or Jupiter planets. When I look at the detection methods just mentioned, it would be hard to distinguish a terran size moon in orbit around a jovian prime with stellar doppler or astrometric measure.

    Perhaps this is a simpler explanation for other efforts to catch terrestrial moons of larger planets in other systems already described in detail. But I think I can give a simple rundown:

    Transit might work for detection of a moon even if the moon were not in the orbital plane if it transits the larger planet from time to time, forward or back.

    But this would take many passages and increased sensitivity or less
    background (light) noise in the stellar transit. Almost the same thing as
    a lead or lag on the transit passage of the primary. If the binary system were similar to the Earth-moon system, the effective area of the satellite would be about a quarter of the primary. For Jupiter and the Galilean moons the ratio is not as favorable. But were the Earth in orbit with a Neptune, that would work out about the same. Thus, an areal variation of about 1/16th would show up in some fashion.

    More massive planets are easier to detect with less massive stars, and there does seem to be a thinning out of Jupiters with red dwarfs. But if they did transit red dwarfs they would likely blank them out entirely or nearly. Depending on the monitoring algorithms for transits, I have wondered if such an event would be thrown out or retained. Most likely it would be detected. Nonetheless…. Should one be found, a precursor dip in the luminosity might mean something as described above.

  • wdk November 21, 2022, 23:21

    A correction on my post about Trappist 1 exoplanets above:
    I said “d” was the one included; it was “g”.
    Elsewhere, it is asserted that “e”, “f” and “g” are candidates.

    • Michael C Fidler November 22, 2022, 11:07

      The List of potentially habitable exoplanets has a nice sort option at the top of the list for all the columns. Hitting the up/down arrow will sort the object column so that all Trappist 1 planets that are habitable will be together or the distance also works great.
      You have to remember with Red dwarfs we a dealing with a completely different type of star at M4 on down to M9, they are fully convective and rotate very fast when young <3 billion years. There are indication that flares on these stars develop closer to the poles and that x-ray production is lower then earlier M dwarfs and K dwarfs. Planet formation may follow a different route then the more massive stars because of their full convection and fast rotation.

  • wdk November 21, 2022, 23:45

    Tempted to examine or illustrate satellite transit of stars further: with the Earth, sun and moon.

    Given the sun’s radius ~700,000 km and the Earth-Moon separation of up to 400,000 km, the latter would be the maximum separation for a transit taking the sun’s surface as akin to a projection sheet. With the ratio of areas, the Earth is about 1/10,000th of the sun’s and the moon is about 1/16th of that. This poses a significant problem of filtering if the sun’s luminous “signal” has any noise in it. It does. But the transit would take about a day – and the separation of the Earth and moon would vary for the observer. Not much in magnitude, but when you got the leading or trailing dip from the moon. At 30 km/sec an equatorial transit for the Earth would take about 12.9 hours. At max separation there would be about 3.7 hours between Earth and moon transit.

    One might expect something like this as the summary report transmitted among LGM Earth – Moon transit observers if they do not mistake us as sunspots. But my estimate, with the sun rotating in about 30 days, sunspot equatorial velocities would be about 1.7 km/sec across a fixed observer’s field of view.

  • wdk November 21, 2022, 23:50

    One more comment and calling it a night.
    With a thirty day rotational period, the sunspots at the equator
    are moving across the FOV twelve times faster than the Earth.
    Rotation rates vs. km/sec.

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