Sure enough, RDs do something similar, but not nearly so spectacularly. A group of researchers (Laughlin et al., 1997) has modeled in some detail the evolution and ultimate fate of RDs ranging in mass from the lower stellar limit near 0.08 Msun to 0.25 Msun. According to their calculations, a 0.1 Msun star begins with a temperature of 2228 K and a luminosity some 0.04% of the Sun's, and not much happens for a trillion(!) years or so. At about 1.4 trillion years (Ty) of age, the mass fraction of 3He has risen to its maximum value, almost 10%. The star hasn't changed much outwardly, though: its temperature has risen to just under 2400 K and its luminosity to about 0.06% solar. For the next 2.5 trillion(!!) years, 3He is steadily consumed. By 3.05 Ty, 4He dominates the mass; the temperature is now about 2500 K and the luminosity has risen to some 0.1% of solar.
A “critical juncture” occurs at 5.74 Ty, when the temperature is 3450 K and the luminosity not quite 0.3% solar. Hydrogen now makes up only 16% of the star's mass, and the structure changes abruptly because now radiation can get out more easily (or, in the language of physics, “radiative transport” now dominates “convective transport.") By comparison to its languid youth, the star now starts living at a breakneck pace: it reaches a maximum luminosity of around 0.63% solar, and a temperature of 5400 K, only a matter of a few hundred billion years later. Its maximum temperature, 5800 K (hotter than the Sun!), when its luminosity is about half a percent of the Sun's, is reached a mere 400 billion years after that critical juncture. Now the star begins to cool off, eventually becoming a “helium white dwarf” after having converted nearly 99% of its original hydrogen into 4He—a remarkable efficiency. The total “hydrogen burning time” has lasted something over 6 trillion years. (The usual white dwarfs in the present Galaxy are composed of carbon-oxygen-nitrogen, the debris left behind by a red giant. A few He dwarfs are known at present, though; they're all part of a binary system, and have been prematurely aged by the companion star's stealing away much of their mass.)
* * * *
Red Giants and Late Bloomers
That last breakneck 400 billion years represents a curious kind of star, a type G that has only 1% or so of the Sun's luminosity. Such stars don't exist now, as there hasn't been nearly enough time for such highly evolved red dwarfs to evolve. Laughlin et al. suggested that such “late bloomers” might spawn life on their newly thawed outer planets, which had previously lain in deep freeze for trillions of years. There should be plenty of time: after all, the total duration of the star's “last gasp” is some 90 times that of the Earth's present age!
A problem these authors didn't mention, though, is that those newly thawed planets will be tectonically dead: no plate tectonics, no volcanoes, no nothing. Again, trillions of years is plenty of time for planets to lose all their internal heat sources. This makes them considerably less promising as “abodes of life"—at least for higher life forms.
Laughlin et al.'s calculations indicate that stars with masses somewhat greater than 0.1 Msun evolve similarly, except that the “late bloomer” stage is both more dramatic—i.e., hotter and more luminous—and happens sooner. In fact, in a transition region from about 0.16 to 0.2 Msun, the “bloomer” phase starts to look more and more like a red giant, in that there's a sizable increase in luminosity and swelling of the star, although helium fusion never occurs. The minimum mass for a red-giant phase to occur seems to be about 0.25 Msun—after a trillion or so years of fusing hydrogen. Barnard's Star seems to lie right at this limit (Table 1).
Retirement Homes of the Gods ...
All in all, then, that overwhelming multitude of type M dwarf stars just might be good real estate after all. If nothing else, they'll be retirement sites for long-lived civilizations. (Humans can hope they're among them.) n
References:
Gaidos, Eric J., “A Cosmochemical Determinism in the Formation of Earth-Like Planets,” Icarus, 145, 637-40, 2000.
Gillett, Stephen L., World-Building, Writer's Digest Books, 1996.
Heath, Martin J.; Doyle, Laurance R.; Joshi, Manoj M.; Haberle, Robert M.; “Habitability of Planets Around Red Dwarf Stars,” Origins of Life and Evolution of the Biosphere, 29, 405-424, 1999.
Kirkpatrick, J. D.; Kelly, Douglas M.; Rieke, George H.; Liebert, James; Allard, France; Wehrse, Rainer; “M Dwarf Spectra From 0.6 to 1.5 Micron—A Spectral Sequence, Model Atmosphere Fitting, and the Temperature Scale,” Astrophys. J., 402, 643-654, 1993.
Laughlin, Gregory; Bodenheimer, Peter; Adams, Fred C.; The End of the Main Sequence, Astrophys. J., 482, 420-32, 1997.
About the Author:
Till recently, Steve Gillett was a research professor at the Mackay School of Mines, University of Nevada, Reno, where he'd worked on Paleozoic paleomagnetism, lunar resources, and seismic risk at Yucca Mountain, Nevada, the proposed high-level nuclear waste repository. He also taught intro geology classes including one on planetary geology. He is now involved in several start-up ventures on applications of molecular nanotechnology in environment and resources. He has a white paper on this topic online at the Foresight Institute (www.foresight.org). Gillett has a B.S. in geology from Caltech and a Ph.D. from SUNY Stony Brook. Copyright (c) 2005 Stephen L. Gillett
Copyright (c) Stephen L. Gillett, Ph.D.
* * * *
TABLE 1
The Sun and some “red” dwarves compared.
Distance in Light Years
Sun: —
Proxima Centauri: 4.2
Bernard's Star: 6.0
Wolf 359: 7.8
—
Temperature (kelvin)
Sun: 5770
Proxima Centauri: 3050
Bernard's Star: 3300
Wolf 359: 3000
—
Spectral Type
Sun: G2
Proxima Centauri: dM5e
Bernard's Star: M5 V
Wolf 359: M5
—
Luminosity: Visual
Sun: 1.0
Proxima Centauri: 0.00006
Bernard's Star: 0.00044
Wolf 359: 0.00004
—
Luminosity: Bolometric
Sun: 1.15
Proxima Centauri: 0.00151
Bernard's Star: 0.00544
Wolf 359: 0.00082
—
Luminosity: Vis./Holo.
Sun: 87%
Proxima Centauri: 3.7%
Bernard's Star: 8.2%
Wolf 359: 2.5%
—
Peak Wavelength (microns)
Sun: 0.50
Proxima Centauri: 0.94
Bernard's Star: 0.87
Wolf 359: 0.97
—
Mass: (Sun * 1)
Sun: 100%
Proxima Centauri: 18.1%
Bernard's Star: 25.4%
Wolf 359: 15.4%
—
Average Distance of Earthlike Planet (Earth *1)
Sun: 1.0
Proxima Centauri: 0.036
Bernard's Star: 0.069
Wolf 359: 0.027
—
Period (Earth Days)
Sun: 365.24
Proxima Centauri: 5.92
Bernard's Star: 13.1
Wolf 359: 4.06
—
Solar Day (Earth Days): 3/2 lock, prograde
Sun: —
Proxima Centauri: 11.84
Bernard's Star: 26.2
Wolf 359: 8.13
—
Solar Day (Earth Days): retrograde
Sun: —
Proxima Centauri: -2.37
Bernard's Star: -5.24
Wolf 359: -1.63
—
Average Disk Size (degrees)
Sun: 0.5
Proxima Centauri: 2.1
Bernard's Star: 1.8
Wolf 359: 2.3
—
Average Disk Size (Implies radius w.r.t. Sun *)
Sun: 1.0
Proxima Centauri: 0.073
Bernard's Star: 0.119
Wolf 359: 0
.056
—
Tidal force (Earth on Moon =1)
Sun: 0.0056
Proxima Centauri: 21.5
Bernard's Star: 4.4
Wolf 359: 45.6
* * * *
[Back to Table of Contents]
* * *
Probability Zero: Keeping Track by Richard Foss
The high priest facing the giant stone disk made a hasty obeisance as a jaguar screamed in the distance, then turned back to the circle of sub-priests who sat next to the stonecutter. For a moment there was nothing but the chattering of monkeys in the forest below the pyramid. The high priest counted again on his fingers and toes, then looked at the waiting circle of men.
“So the day of the dog is followed by the day of the monkey in the month of the new sun in the great cycle of the Father God One Hunahpu?"
The chief calculator bobbed his head affirmatively and grinned, showing pointed teeth inlaid with jade. “Which will be repeated eighteen times twenty, times twenty, turnings of the Sun."
The high priest nodded with satisfaction. “Which is repeated thirteen times, and then all that is ends.” The assembled worthies looked at the glyph at the bottom of the outer edge of the giant stone calendar. “The last chisel marks were put in today. The work of years finally finished, tracking as day by day we approach that apocalypse.” There was a moment of sober contemplation, broken by a commotion from below. A small woman in a lavishly embroidered huipil was standing on the platform at the base of the pyramid, and her voice carried easily to the assembled group.
“Walks Straight Path, have you noticed what day it is?"
The high priest turned pale.
“All that time devising that thing, and you don't pay attention to it. Your daughter missed her appointment to have her teeth filed again, and now it will be weeks before we can get her another one! We'll owe him eight cacao pods for the missed appointment, too."
The chief calculator's eyes flicked to a point on the giant carved stone, where he noted a hieroglyphic-covered leaf glued with pond slime.
“Day of the snake already? Er, excuse me, guys, I gotta go ... If I hurry, I can catch the second half of my son's game on the ball court. Be a shame if he gets to behead the other team captain at the end of the game and I miss it."
The other men muttered and sidled toward the edge of the giant pyramid that towered over the Guatemalan jungle. The high priest sighed and covered his eyes. Every new invention had its drawbacks, after all. He had an eerie feeling that the day would come when people wished this thing had never been made.... Copyright (c) 2005 Richard Foss
Copyright (c) Richard Foss
[Back to Table of Contents]
* * *
EDITORIAL by Stanley Schmidt
DIFFUSE TYRANNY
The latest wrinkle to come to my attention in our country's current rush toward an “Inquisition” mentality is a growing tendency for pharmacists to refuse to fill prescriptions for birth control pills because of their personal religious or moral beliefs.
“Their,” in this case, meaning the pharmacists', not the patients'. In other words, pharmacists are taking it upon themselves to forbid patients to do things completely within their legal rights and not affecting the pharmacists at all. As I write this, some states are considering legislation to guarantee pharmacists their “right” to do this, while others are considering legislation requiring them to fulfill their “duty” to fill all prescriptions.
Another tendency on which I commented recently (October 2005) may at first glance seem unrelated, but is in important ways quite similar: the growing number of school teachers and officials who take it upon themselves to effectively remove evolution from the biology curriculum by refusing to teach it, even when the “official” curriculum says it's supposed to be taught.
There have been other examples, and I suspect we'll be seeing more as time passes. But where are we headed, if this goes on? What happens if we allow ordinary individuals rather than laws to dictate what products or services other people can get?
You might try to shrug off the problem by saying nobody has to do things that violate his or her conscience, and that if you insist on studying evolution you can do it on your own, and that if one pharmacist turns you away you can go to another. But the real world is not that simple.
Yes, you can study evolution on your own—if you know that you want to. But (a) most people in this country are not very good at studying things on their own (our educational and credentialing system actively discourages the belief that they can), and (b) many people will never suspect that they might want to learn something unless they've had at least a little exposure to it in school. Providing such exposure is, in fact, is one of the main functions of schools.
You can't write or fill your own prescriptions, so the “do it yourself” argument, weakly tenable as it is for evolution, fails completely here. If you want a prescription filled, you have no choice but to go to a pharmacist. If your local pharmacist has appointed him—or herself to overrule your physician, and you live in a small town in a sparsely populated area, going to another is not a realistic option. In such a case, a decision that should be made by you and your doctor is instead made unilaterally by your pharmacist, cutting both of you out of the loop.
This, I respectfully submit, is the height of arrogance. It's none of his or her business. He or she is employed to fill whatever legally written prescriptions are presented.
“But what of religious freedom?” you may ask. “That's one of the cornerstones of our country. Doesn't that mean the pharmacist is free to follow his own beliefs, even if that means refusing to dispense a medicine he believes to be immoral?"
Simple answer: No, it does not. The crucial point most people seem to find inordinately difficult to grasp about any kind of freedom is that it can never be absolute. If everyone is to be allowed as much freedom of as possible, that can only be achieved if everybody's freedom extends to, and not beyond, any point at which it begins infringing on somebody else's. Neither you nor I can reasonably be allowed to do absolutely anything we want; we can only be allowed to whatever we want that does not restrict somebody else's freedom to do the same.
A pharmacist whose religion frowns on birth control pills has no obligation to use them—and no right to interfere with someone else whose religion doesn't forbid them. A science teacher whose faith makes him or her unable to believe in evolution despite the scientific evidence is free to disbelieve, but is not excused from teaching what science says and why.
History has provided several thousand years of empirical evidence that human beings cannot agree about religion. Secular laws are the one body of guidelines that we all can and must agree on, however grudgingly. One of the most important of those guidelines says that those who hold one set of religious beliefs may not dictate the actions or beliefs of those who hold a different set (or none).
And that one is in serious danger right now.
The small-town woman who can't get her prescription filled may be in even worse shape than having to drive 90 miles to the next town. That town may be no different. We already have sizable areas where that narrow subset of Christians called “Fundamentalists” constitutes an increasingly aggressive majority. If all (or even most) of the pharmacists or teachers in a region quietly decide to do what they want rather than what the law says, then the protections nominally provided by the law have become meaningless. In such a situation, much of what people can do, and what is done to them, is determined not by constitutional law, even if such law exists on paper, but de facto by an unofficial and unregulated “diffuse tyranny” of people imposing their personal beliefs on others who do not share them.
Simple answers, of course, tend to be simplistic. No discussion of this problem would be complete without taking a look at things from the pharmacist's or teacher's point of view. When should somebody with a deeply ingrained sense of moral values do something that clashes with those values, such as dispensing medici
ne or a worldview he doesn't approve of? That's by no means a simple or trivial question. It's not enough to expect a person in such a position to just do it and shrug off personal responsibility by saying, “I was only following orders.” We didn't buy it at Nüürnberg, and I hope we're not ready to buy it routinely now—though I feel obliged to add that “following religious convictions” often amounts to following orders from religious leaders, and that's not necessarily a better excuse than following orders from political leaders.
Ultimately all such decisions will be made by weighing some combination of inputs from religion, law, personal conscience, and—we can at least hope—reason. And the process isn't necessarily easy. Some years ago (January 1987) I devoted a whole editorial to this “fundamental dilemma” of civilization: that our “real” government involves a system of “expanded checks and balances,” with official governments necessarily enforcing laws as they exist and people trying to get them improved, working within the system where possible and breaking laws when other means have failed.
In practice, my advice to the pharmacist would be to ask: does this really bother you so much, and are you so sure you deserve to dictate somebody else's highly personal decision, that you can't fill this prescription? If so, the honorable thing to do is to get out of pharmacy and leave it to people who can recognize that other people have as much right to their religion (or lack of it) as you do. Of course, if too many pharmacists do that, then there'll be a major shortage and we'll have a new problem to deal with—because practically everybody will need a pharmacist sooner or later.
Finding ways to solve that one just may force some of those who felt so righteous about imposing their personal views on others to take a fresh look at the rightness of that stance. And maybe a few more of them will come to realize that there are good reasons for constitutional protection of freedom of religion, and that in practice your freedom to practice your religion must end where it conflicts with somebody else's.
Analog SFF, November 2005 Page 22