Analog SFF, November 2005

by Dell Magazine Authors

  Let's look more closely at such “bad” stars. I've collected data for three nearby “red” dwarfs (hereafter “RDs") in Table 1. As you can see, their temperatures range from about 3000 kelvins to 3300 kelvins—that is, from the filament temperature of a very bright “white” incandescent light, like those used for projectors or stage lights, to even hotter. Close up, these stars will hardly look red!

  To be sure, most of the light they put out does lie in the infrared, with a wavelength at the peak intensity of around one micron. (For comparison, the reddest light you can see, at the threshold of perception, has a wavelength of about 0.7 microns or 700 nanometers). In fact, only a few percent of the radiation such stars put out lies in the visible; their light is mostly infrared (Table 1). Again, that's how they justify their name of “red” stars: their light does mostly lie toward the red, even though that's not perceptible to the eye.

  By the way, this also is why ordinary incandescent lamps are so energy-inefficient. Just like these “red” stars, they shine just through being hot, so they put out lots more infrared than visible light. Which is completely wasted: not only can't you see it, but it heats up the surroundings, which often means that extra cooling is needed—and sometimes all that extra heat even starts fires.

  Also because of that big infrared component, we have to be careful when talking about these stars’ “luminosities.” Their total, or “bolometric,” luminosity ranges up to a few thousandths of the Sun's, but their visible luminosity is a ten-thousandth or less (Table 1). The reason is simply that so much of an RD's output lies in the infrared. For comparison, the difference between the Sun's bolometric and visual luminosities is only about 15%. Most of the Sun's output lies in the visible.

  Bolometric magnitudes are hard to measure, too, and you'll find several different answers in the literature for how to correct the observed visible luminosity to the true luminosity. I estimated the bolometric luminosities in Table 1, as well as the actual stellar temperatures, using the results of the study by Kirkpatrick et al. (1993). These differ a bit—but not grossly so—from the correction values I quoted in my book World-Building. There are two reasons it's hard to measure bolometric magnitudes. First, for best results the spectrum needs to extend into the infrared, but IR spectra haven't been common till recently. Second, the atmosphere of an RD is cool enough that lots of hardy molecules can form, things like carbon monoxide (CO), titanium monoxide (TiO), and so on. The absorption bands from such molecules add a lot of complexity to the spectrum. (In fact, such oxide bands define spectral type “M.") They tend to hide the “blackbody” radiation from the star itself; that is, the radiation that the star puts off just because it is a hot body, and which we need to measure to get the temperature.

  A digression: some years back ("Carbonosis", March 1993) I proposed that planets forming in stellar systems with high ratios of carbon to oxygen were bad bets for technical intelligence. Briefly, if carbon atoms outnumber oxygen in the nebula from which planets are condensing, no iron gets oxidized—and so no iron ends up in a planet's crust. It all ends up in the core instead, as iron metal. At the very least, even if intelligence evolves, having no iron in the crust will make it difficult to stumble across metallurgy. Furthermore, the planet's mantle can act as a “ocean eater” over geologic time, because its chemistry is such that it breaks down subducted seawater. (Technically, the mantle is too “reduced.") The result is that hydrogen, instead of steam, will spew out of volcanoes, there ultimately to be lost to space. This would be even more awkward for an Earthlike planet!

  The sheer abundance of type M dwarfs shows that this extreme “carbonosis” scenario is rare. In an M dwarf, all the carbon combines with all the oxygen to form CO, but since there's oxygen left over we get those metal oxides. There are certain red dwarfs, called “carbon stars” (spectral types R, N, and S) in which carbon is more abundant than oxygen, and then you get molecules other than oxides in the atmosphere (and the spectral types R, N, S depend on which molecules.). Carbon stars, however, are quite rare.

  But a formal study has since appeared (Gaidos, 2000) that indicates that “carbonosis” can happen even if carbon atoms don't outnumber oxygen. And you saw it here first, in Analog!

  In any case, the alleged “lurid light” of a “red” star is no reason for ignoring them.

  There's a good reason not to ignore them, too: there are so many of them. Most of the stars in the Galaxy—in the universe—are red dwarfs. According to Heath et al. (1999), about 70% of the stars in the solar neighborhood are RDs. They extend from stars of about half a solar mass (Msun), with—6.0% solar luminosity and an effective temperature around 3,700 kelvins, to stars at the threshold of “stardom,” the minimum mass needed to initiate nuclear fusion reactions, about 0.08 Msun or 80 Jupiters.

  Tides and Locks

  A better reason for ignoring the “red” stars, both in SF and in SETI scenarios, has been “tidal locking.” Even though an RD is vastly less luminous than the Sun, its mass is not all that much less. It's still anywhere from about 10% to nearly 50% of a solar mass (see Table 1).

  To get an Earthlike level of illumination, then, a planet around an RD must be proportionately far deeper in the star's gravity well. And this means the planet's spin has been vastly slowed by tidal forces from the star, just as the Moon was long ago locked into synchronous rotation with the Earth. Look at Table 1 again, where I've calculated the distance a planet would need to be from each star to get an Earthlike level of illumination. (Note that we must use the bolometric luminosity, rather than the visible-light luminosity, when calculating how far from its “red” sun an Earthlike planet must be. Obviously, the planet's total heating comes from its total illumination, not just from the part that happens to be visible light! Just as with an ordinary incandescent lamp, those infrared rays are good at heating things up, even though you can't see them.)

  I've also shown the tide-raising force for a planet at that distance relative to the Moon around the Earth. As you can see, even an Earthlike planet around Barnard's Star, the biggest and brightest of the three listed, still “feels” over 4 times the tidal effect that Earth's Moon feels from Earth. So, all these planets will have been tidally braked; the conventional wisdom is certainly correct there.

  But the tidal locking is not necessarily a show-stopper. For one thing, an Earthlike companion of a giant planet that in turn circles a red dwarf could have a reasonable day length. What happens is that the Earthlike planet would be locked to the giant planet instead. So, just as the Sun rises and sets on our Moon, even though it always keeps one face to Earth, the red sun would rise and set on the Earthlike companion, even though the companion would always keep the same face to the giant planet. Sure, this won't happen very often, but there are so many red dwarf stars it doesn't need to happen very often to make a big difference in the number of Earthlike planets. And certainly, over the last decade lots of giant planets have been discovered in close orbits to their parent stars. (Over the very long term, such orbits are still unstable to tidal braking: the planet's orbit around its primary slowly decays, so that the planet is eventually torn apart when it approaches the primary too closely. This will happen to our Moon in a hundred billion years(!) or so. The process is an issue for RDs simply because they are so extraordinarily long-lived, as I describe below.)

  Robert L. Forward used another option in Timemaster, based on the case of Mercury in our own System. Although Mercury was once thought to show the same face always to the Sun (a setting used by lots of classic SF stories), it's in fact in a “3/2 lock"; it rotates thrice for every two revolutions around the Sun. So the Sun does rise and set on Mercury. (Synchronous rotation like the Moon's is a “1/1” lock; it rotates once for every revolution around the Earth, so that it always keeps the same face toward Earth.)

  Presumably a Mercury-like situation could arise for an otherwise Earthlike world around a small RD. What's necessary for the 3/2 rather than the 1/1 lock to be stable is a modestly elliptical
orbit, which Mercury has, and which is hardly an unlikely possibility for a near-in planet of another star. Again, this won't always happen, but it doesn't have to happen too often to make a significant difference in potentially Earthlike planets in the Universe. However, I've treated this scenario already in some detail in World-Building, so there's no point in belaboring it again here. [Well, get a copy!]

  Life and the Dark Side

  Let's instead look again at that 1/1 lock. Such a state, with one face permanently facing the star and the other facing away, has seemed a very bad situation for a planet to be Earthlike. In fact, it's tended to get dismissed out of hand. It's been used in SF, though, right here in Analog. Stanley G. Weinbaum envisioned a tidally locked Venus in the 1930s ("Parasite Planet,” February 1935, and “The Lotus Eaters,” April 1935), and Poul Anderson ("Trader Team,” July/August 1965) even envisioned a planet tidally locked to a red dwarf (or at least it's clear that's what he meant, although at one point the star is described as of spectral type K0.)

  Weinbaum and Anderson, in fact, may have been on to something. A recent academic study suggests that planets in 1/1 locks (what these authors call “synchronously rotating planets,” or SRPs) can support a roughly Earthlike environment under certain conditions (Heath et al., 1999). “Atmosphere collapse"—the freeze-out of all atmosphere onto the dark side, the way a cold trap in a laboratory vacuum line pulls out residual gases—turns out to be more easily forestalled than you'd figure. (Remember when Mercury was supposed to have oceans of such things as nitrogen on its dark side?) Heath et al.'s models indicate that a mere 100 millibars (mb) pressure of CO2—a tenth of an atmosphere, near enough—ensures enough heat transport to the dark side to preserve the atmosphere. With 1500 mb of CO2, and a total insolation of 0.8 Earth's, parts of the sunlit side can even support liquid water. Surprisingly, too, the surface winds are not extreme between the Day Side and the Dark Side, averaging only 5-10 m/s (about 10-20 mph), even near the terminator (the day-night boundary). Most of the exchange occurs in the jet streams aloft. (Airplane rides could be bumpy!)

  For comparison, however, Earth's present atmospheric CO2 level is about 350 parts per million (ppm), or a bit more than a third of a millibar, so it's substantially less than these values. On the Earth, too, the CO2 content over geologic time is regulated by weathering of surface rocks, in the so-called “carbonate/silicate cycle.” The overall stoichiometry is:

  CO2 + CaSiO3—SiO2 + CaCO3.

  CaCO3 is calcium carbonate, the main component of limestone. This is why Earth has as much CO2 as Venus does; ours, however, is nearly all safely locked away in limestone (see “On Building an Earthlike Planet,” July 1989). So at least on an Earthlike planet it's not possible to add arbitrary amounts of CO2 to the air. Over geologic time it just gets drawn down again.

  Rather than worry about how to get a much higher CO2 content on an active, Earthlike planet, though, Heath et al. noted that in any case the main greenhouse gas in the Earth's atmosphere is just water vapor. According to them, Earth's water-rich atmosphere is nearly equivalent to a pure 1000 mb CO2 atmosphere, and so they do their models on that basis. They find that the temperatures at the subsolar point—um, substellar point, the point directly underneath the unmoving sun—exceed 50 degrees C (122 degrees F), which is warm, but not unreasonably so. The temperatures fall away from the substellar point to reach 0 degrees C somewhere around the terminator. So there will be a good-sized temperate zone.

  What might such a planet be like? Well, there are no seasons, at least in an Earthly sense. Our seasons, of course, come from the Earth's axial tilt: when one pole is tilted toward the Sun, it's summer in that hemisphere, while it's winter when the pole is tilted away. However, the pole of a synchronously rotating planet will be upright, so that unmoving sun will always be shining from the same point in the sky. Of course, if the orbit's at all elliptical, there will be some variation in heating over the course of the planet's “year"—but the year is only a week or two long (Table 1)! That hardly counts as a season.

  Nonetheless, all is not so boring as it seems. Obviously the star will be a lot larger in its sky than our Sun—around 2 degrees across, versus half a degree for the Sun (Table 1). So equally obviously, area for area, the surface is dimmer than is our Sun. When you then consider that most of the radiation coming off each square centimeter of the star's surface is infrared, the sun is very dim indeed—at least by comparison with our Sun. You could look directly at (say) Proxima from an Earthlike orbit, at least briefly.

  And that's interesting because the star itself is going to be much more interesting to look at than the Sun. Sunspots are (proportionately) much bigger and could even cause a significant dimming in the brightness, perhaps as much as 40% over periods of weeks. Because the star is (relatively speaking) so cool, the molecules in its outer layers might even condense locally, clouds of refractory oxides freezing out like ice crystals in the Earth's atmosphere. You might be able to see brighter and darker areas across the stellar surface due to the changing “cloud cover."

  Most spectacularly, many RDs are “flare stars.” Every now and then they shoot off a huge flare and increase their luminosity by as much as 100 times—which, of course, could be awkward indeed for a habitable planet. The planet will need a thick atmosphere and ocean as a buffer to moderate such occasional pulses of heat—but it needs that anyway to forestall atmosphere collapse. Flares could be particularly threatening for local life forms because they put out much more ultraviolet than the star radiates normally.

  Flaring seems to be related to rapid stellar rotation, though, so as the rotation rate decays over geologic time, it may no longer be an issue by the time higher life forms evolve. Nonetheless, “stellar weather” is going to be a major source of climatic variability on an RD's planet. Perhaps an indigenous priesthood observes the star continually for hints as to what the future holds, for crops, floods, and so on. Poul Anderson used much this idea in another of his Polesotechnic League stories ("Territory,” June 1963).

  Over geologic time, assuming active plate tectonics like Earth's, massive extinction events—and spectacular recoveries therefrom—will occur as the continents move in and out of the dark side. In fact, a continent's transit through the dark side will look like an “ultra-glaciation.” At least for a while, the geothermal heat leaking out of the planet will keep the oceans from freezing all the way to the bottom during such transits. Ultimately, though, as the planet loses its internal heat its tectonics will stop—and then the oceans will freeze up completely. Trillions of years is ample time for all the original complement of long-lived radioactive elements, which play such an important role in driving tectonics on the Earth, to decay away completely (see “Refueling a Rundown Planet,” August 1991).

  But that's a long way off yet. Maybe a trip to Barnard's Star or Wolf 359, instead of (say) Tau Ceti, is not such a dismal alternative after all. (I'll sign up!)

  Only a Trillion Years....

  RDs have a huge advantage if you take the long view, too. They're extremely long-lived. That's, of course, a consequence of their low luminosity. They're exceedingly miserly with their hydrogen fuel, with the upshot that they'll last far longer than the Sun—even, for the smallest, over ten trillion years. That's over 650 times the present age of the Universe. Moreover, for most of their lives RDs are “completely convective” in their internal structure. That means the star stays thoroughly mixed, with the result that a much higher fraction of a star's hydrogen content will be available as nuclear fuel than for the Sun. When all the bright stars have long since dwindled to unprepossessing white dwarfs, the RDs will still be calmly shining, scarcely changed.

  Or rather, maybe a bit changed. At present, hydrogen fusion in a very-low-mass star isn't quite the same as in a more massive star like the Sun. To be sure, it starts out the same: two protons (hydrogen nuclei, 1H) fuse into a deuteron (deuterium nucleus, 2H):1H + 1H = 2H + e+ + energy where the “e+” is a positron—an antielectron—that carries awa
y the extra positive charge. Sooner or later it mutually annihilates with an electron to release even more energy. Later, this deuteron acquires another proton to become a nucleus of helium-3 (3He):

  2H + 2H = 3He + n (neutron) + energy or,

  2H + 2H = 3H + 1H + energy

  Since tritium (3H) decays to 3He with a half-life of only about a dozen years, the end result is the same.

  In stars like the Sun, one more step occurs: two 3He's fuse into a 4He, with a couple of protons left over:

  3He + 3He = 4He + 2 1H.

  Present-day RDs, though, stop at 3He; their cores aren't hot enough to go on to 4He. The reason is that electrostatic repulsion between the two 3He nuclei requires a lot more energy to overcome than that between two protons.

  (As an aside, 3He fusion has attracted interest as a potential fusion power source on Earth, because it's in theory a lot cleaner. Note that the by-product is 2 protons, which won't tend to make the surroundings radioactive the way by-product neutrons will. Unfortunately, 3He is almost completely absent on Earth; the helium out of gas wells is nearly pure 4He, because that helium originated as alpha particles from uranium and thorium decay. Helium-3 is slightly enriched on the Moon's surface from solar-wind implantation, and that's a proposed incentive for lunar development. Unfortunately, even if we had a source of 3He, we still don't know how to do controlled fusion with it.)

  So, as an RD shines away, 3He accumulates in it ... and you might expect that that 3He will eventually “burn.” Stars tend to burn hotter and hotter over their lifetimes, because as the more massive fusion products accumulate in the core they raise the pressure. In turn, the raised pressure causes the nuclear reactions to proceed more efficiently. The Sun's luminosity, for example, has increased about 30% since its formation, according to current astrophysical models. Eventually, too, the Sun will become a “red giant": conditions in its core will become intense enough that it will become able to fuse three He-4's into a carbon-12. At that point, some 5 billion years from now, the Sun will have swollen greatly and cooked out the inner System completely.