Fifth Day

On the fifth day of Christmas, my true-love gave to me,
Five solar flares.
Four chickadees,
Three mammoths,
Two ptarmigan,
And a spruce hen in a spruce tree.

What Would an Alien Sun Look Like?

#scifi Now that we’ve discussed the role of water in affecting albedo, as a greenhouse gas and in moving energy around a planet, let’s go back to that alien planet we’re building. What will its sun look like?

In the first place, we do not need to consider all stars, or even all main-sequence stars. Massive stars have rather short lifetimes. Our sun has a projected lifetime of some 10 billion years. A star three times its mass would stay on the main sequence only half a billion years. Further, such massive stars are much rarer than sun-sized stars, and put out a very large fraction of their energy in ultraviolet (dangerous) wavelengths.

 

Apparent size of a star in the sky of one of its planets as a function of its color. The sun has a size of 1.

 

 

(In fact, named stars are almost all poor candidates for having livable planets. If they are named, they are relatively bright. Almost all bright stars are either very massive or are in the later, helium-burning stage of their existence.)

What about smaller stars? Lifetime is not a problem, nor is finding one—less massive stars are far more numerous than those of sun size. They are harder to find in the night sky because unless they are extremely close they are too dim to see. However, a planet would have to be quite close to a very small star to keep warm, and smaller stars are dangerous at that distance.

If we want an earth-like planet, with temperatures that allow water in liquid, solid and gaseous phases, we could take as a first approximation that the energy received from the star at the planet’s distance would be equal to that received by the earth from the sun—the solar constant. Let’s assume this in determining how the star’s color will affect its apparent size in the sky and the year length of the planet.

 

The length of a planet's year, in earth-years, as a function of the color of its sun.

 

First, we need to define color. Any star will look white, because our eyes automatically adjust to the color of any light containing a continuum of wavelengths in the visible part of the spectrum. But different stars have their light peaking in different parts of the spectrum. Our sun, for instance, peaks at a wavelength of about .5, which is green. Red is .7 and blue-violet is about .4, so the left side of each chart is ultraviolet and the right side is red—but all of the stars will look nearly white.

The difference is in the non-visible light. A star toward the left—blue—end of the chart will be putting out a lot of energy in the ultraviolet. We don’t see that part of the spectrum, though some other organisms can see in the near ultraviolet. But aside from a small amount needed to make vitamin D, ultraviolet is generally not good for living things.

Stars at the right—red—end of the spectrum again will look white to our eyes—they are in fact less red than an incandescent light bulb. But they will put out much more infrared radiation, and less ultraviolet. They would feel warmer than they looked, but human beings living under such a sun might well need to take supplemental vitamin D, and would probably evolve toward fair skin, just as Europeans have. Plant growth might also be slow.

If we assume a solar constant matching Earth’s, we can predict the apparent size of the sun in the sky and the length of the planetary year as functions of the star’s color. The charts show this, with the apparent size being scaled to that of the sun and the year lengths being scaled to ours. From this it is apparent that a redder star than our sun will appear larger in the sky and be associated with a shorter year, while a bluer star will appear smaller in the sky and the planet will have a longer year.

Next time: the sky color and the effect of the atmosphere on how things look.

Planet Building and Astrophysics Part 2

Once hydrogen burning is well established,  a star settles to a remarkably consistent relationship between temperature, luminosity, diameter and mass known as the main sequence.  It will then very gradually increase its luminosity while decreasing its temperature, but the change is extremely slow.  Our sun has been on the main sequence for about four and a half billion years, and will remain on the main sequence for another 5 billion years.  During that first four and a half billion years, its luminosity increased by about 40% – enough that the early radiative equilibrium temperatures of its planets were about 9% below present values.  Observationally, the temperature of earth has remained in a range that allowed the presence of liquid water throughout this period, so the change in solar output was offset by changes in the Earth’s atmosphere or surface reflectivity.

More generally, stars spend most of their lifetimes, and by far the most stable part, on the main sequence.  A planet stable enough to support life, and especially one on which life has evolved, is most likely orbiting around a main sequence star.

How long a star remains on the main sequence again depends on its mass.  Very massive stars are prodigal of their energy, and exhaust their hydrogen fuel quickly.  A star five times the mass of the sun has ten thousand times the luminosity, and will exhaust its fuel in  fifteen million years – a mere eye-blink in geological and evolutionary terms.  A star half the mass of the sun would have a main-sequence lifetime of two hundred billion years – considerably more than the age of the universe.  It would also, however, have a luminosity a mere 3% of the sun’s.  A planet would have to be very close – and have a very short year – to get the amount of energy from that star that we do from the sun.

The end of life on the main sequence is catastrophic for any earth-like planets.  The star becomes both brighter and cooler – which means a very considerable increase in its diameter.  The sun, for instance, will expand to include the orbits of Mercury and Venus, and approach that of Earth.  The core temperature will rise until it reaches roughly a hundred million degrees Kelvin, at which point two other fusion reactions become possible – the combination of three helium nuclei to make carbon, and the collision of an additional helium nucleus with the carbon to make oxygen.  The resulting ed giants are elderly stars, either in the initial expansion phase or in the core helium burning stage   The transition to helium burning is again disastrous for any planets in the vicinity, and may cause part of the star’s mass to be blown off into space.  The star may go through a phase of periodic changes in luminosity.  In general a red giant is far less hospitable to planets than a main-sequence star – but it does have a very important role in that it produces heavier elements than helium – elements that did not exist shortly after the big bang.

Eventually, the star runs out of helium in its core.  Again it becomes unstable, often ejecting up to half its mass and thus adding two newly produced elements – oxygen and carbon – to the interstellar medium from which the next generation of stars will be born.  For a star with a mass less than four times that of the sun, there is no other possible fuel, and the star shrinks to a white dwarf – a dead star.

For larger stars, the core temperatures may rise high enough (600 million degrees Kelvin) that fusion reactions involving carbon atoms are possible, producing neon and magnesium as well as additional oxygen.  If the star has more than nine solar masses, the temperature may rise even higher, to a billion degrees Kelvin, at which point neon burning begins, producing still more magnesium and oxygen at the expense of neon, while at 1.5 million degrees oxygen burning begins.  Oxygen burning produces silicon, sulfur and phosphorous, as well as more magnesium.  Finally, at around 3 billion degrees Kelvin, silicon fusion begins, producing iron.  Iron is the most stable element with regard to nuclear reactions, and no further thermonuclear reactions are possible once all the other elements are burned to iron “ash”.

The star goes through these stages with increasing speed.  If it spent 7 million years on the main sequence, it will then spend 700 thousand years burning helium, 600 years burning carbon, a year burning neon, 6 months fusing oxygen, and a mere day to use up its silicon.

Without further fuel to keep up its temperature, the star is doomed.  It will either become a supernova or collapse into a black hole.  In the former case it returns a cornucopia of new elements to the interstellar medium for the production of the next generation of stars and planets, as well as sending out a shock wave that may well trigger the birth of new stars.

The elements returned to the interstellar medium are not only the ones produced by the primary reactions given above.  Some of the reactions produce neutrons, and these neutrons can interact with the elements produced earlier to produce new isotopes and elements.  In addition, the heat and pressure of the supernova explosion itself produces additional elements, some of which are intensely radioactive and no longer exist in the local part of our universe. But every element in our universe, except hydrogen and helium, is produced by the thermonuclear processes in stars.

Next week–planetary atmospheres.

Why Planets have Seasons

Why do planets have seasons?

The chance that a planet will rotate in exactly the same plane as its orbit is pretty remote.  So is the chance that its orbit will be exactly circular. (I have a planet in the sequel to Homecoming that is seasonless because its equator is in its orbital plane, but that’s fiction.)

The direction of the axis of rotation, the planet’s pole, plays a large role in its weather, and especially in the planet’s seasons.  Seasons on Earth are controlled primarily by the tilt of the earth’s equator relative to the plane of its orbit.  This tilt for the earth is 23 degrees and 27 minutes.

An increase in the tilt would enhance the contrast between the seasons, but reduce the difference in the total annual solar heating between the equator and the poles.  (If the tilt is greater than about 60 degrees, the poles actually get more annual average incoming energy than the equator, as is the case on Uranus.)

In contrast, if the equator were closer to being in the same plane as the planet’s orbit, there would be less difference in the seasons and more in the difference of the average annual energy budget between the equator and the poles.

In general the oceans, which hold heat and release it slowly, will be most influenced by the average annual energy budget, while the land areas are more influenced by the seasonal energy input.  Thus the progression of the seasons will be strongly influenced both by the distribution of land and water on the planet and by the inclination of its axis.

Water, by the way, is not a rare substance in the universe.  It is the simplest possible chemical compound of the most abundant element in the universe, hydrogen, and the third most abundant, oxygen.  (The second most abundant, helium, does not usually form chemical compounds and can be ignored for this purpose.)

Water is going to be lacking on a real planet only if it has been removed at some point in the planet’s history.  In our system, the near lack of water on Mercury and its scarcity on Venus is probably due to the fact that water, being relatively volatile, was blown out of the inner Solar system by the tantrums of the early sun.  Mars also seems short of free water, but that is likely due to its small size and correspondingly weak gravitational field and ice is still a possibility.

Getting water in liquid state is largely a function of planetary temperature and atmospheric pressure. Making the planet the right size (gravity) and putting the planet at the right distance from its sun are probably the critical factors here.

Solstices are defined as the dates when the planet’s axis points most nearly directly at the planet’s sun. In one hemisphere the sun will be at its highest in the sky and the days will be at their longest. In the opposite hemisphere the sun will be at its lowest and the days will be shortest. Close to the poles, the sun may appear to be above or below the horizon for 24 hours at a time. Summer and winter are defined as starting at the solstices.

Equinoxes are defined as the dates when the planet’s axis is at right angles to the line between the planet and its sun. At this time the difference in the radiation received at the pole and at the equator is at its maximum, but there is no difference between the northern and southern hemispheres. Spring and fall are defined as starting at the equinoxes.

There is another way of getting seasons on a planet, minor but perceptible on Earth, but possibly major on a planet whose equator is close to the plane of its orbit.  This is the ellipticity, or elongatedness, of its orbit.  The ellipticity of the Earth’s orbit is only about 0.016 at the present, though it has been as high as 0.06 in the past.  But ellipticity influences both the energy received from a planet’s sun, with maximum energy coming at perihelion (planet closest to sun) and the length of the seasons, since the planet moves fastest in its orbit when it is closest to its sun.  Seasons controlled by the orbital eccentricity differ from those due to axial tilt in several ways.

Firstly, pure tilt-controlled seasons are opposite in the two hemispheres, while pure perihelion-controlled seasons are the same in the northern and southern hemispheres.

Secondly, pure tilt-controlled seasons are equal in length–the summer half-year is the same length as the winter half-year, counting the equinoxes (when the sun is 90 degrees from its midsummer position relative to the stars) as the dividing points.  Perihelion-controlled seasons have a long winter and a short summer.

Thirdly, the length of time the sun is above the horizon each day varies markedly over a tilt-controlled seasonal cycle, as does the direction of sunrise and sunset at medium to high latitudes.  Tilt-controlled seasons at the equator have a double cycle, with the most incoming energy at the equinoxes.  In pure perihelion-controlled seasons, there is no change in the apparent path of the sun in the sky, and the equatorial seasons follow those nearer the poles.

Fourthly, in pure tilt-controlled seasons, there is no change in the apparent size of the sun in the sky.  In perihelion-controlled seasons, the sun appears larger in summer and smaller in winter.

Most real planets have both kinds of seasonality at once, with one dominating.  On Earth, tilt dominates, but summer is slightly longer than winter because Earth is at perihelion around January 4.  (This is why the number of days between the spring and fall equinoxes is slightly more than the number between the fall and spring equinoxes—or more simply, why February is the shortest month, while July and August are the only two adjacent months with 31 days.)

Since tilt, perihelion date and eccentricity are the variables that can change in a multi-body system (and if fact do change slightly over a few thousand to hundreds of thousands of years on Earth, just due to the other planets in our system) the seasons in a multiple star system are likely to be rather variable and not really conducive to earthly life.  Even on Earth, the slight variations in orbital elements produced by the other planets are thought to be enough to account for the alternation between ice ages and interglacials.

The Science behind “Homecoming”

Real planets come in all sizes, geographies, climates, geologies, and probably ecologies. They circle a wide variety of stars. But they do all follow certain physical laws, and these laws constrain how the various aspects of a planet work together. Orbital mechanics and the physics of how stars work do provide some limits. In inventing a planet, you need first to consider what you require of that planet. Is it to be a carefully chosen object for colonization by human beings? The site of an accidental colonization? An uninhabitable world with something worth exploiting? The home of a non-human and totally alien species? A base for scientific exploration? For Homecoming I invented three planets. Two are intended to be fully livable, Earthlike planets, the results of long-ago modification. Both circle sun-like stars and have climates, year lengths, day lengths and axial inclinations similar to Earth’s. The ecology of Central is assumed to be a mixture of species imported from Earth and the home planet of the R’il’nai, and differences from Earth ecology are unimportant for this story, though they do exist. That of Riya is a combination of a native ecology with that from R’il’n. In the native Riyan ecology, land animals with internal skeletons have six, rather than four, limbs. This allows for four-legged animals with wings, like the little lizard-like animals that act as pollinators for the native vegetation. Photosynthesizers also differ from Earth’s, with a growth structure based on expanding sheets (with holes) rather than branches. Both planets have components—like the tinerals on Riya—brought in from planets other than the primary sources. On the third planet, Mirror, I let my imagination go. This is not a comfortable planet for human beings, nor is it intended to be. It is, however, modeled on the early stages of evolution on Earth, with an interesting twist—both left-handed and right-handed biochemistry co-exist. Is this possible? I don’t know, and neither do my characters. But every scientist I know would agree that this is a planet to be preserved for study, not colonized. Mirror circles a star much like our sun at a distance that allows water to be liquid, so as real planets go it’s pretty tame. Its atmospheric pressure is high—like that of early Earth—with a significant fraction of the pressure coming from carbon dioxide, which contributes to its hot climate. There is nothing surprising about a planet having lots of water and carbon dioxide. Hydrogen, carbon, oxygen and nitrogen are the four most common reactive elements in the universe, so we expect their compounds to be common. Water is just hydrogen and oxygen, while carbon dioxide is carbon and oxygen. What is unusual is to have free oxygen, as on Earth, and pressure and temperature that allow water to be liquid. On Mirror the process of combining carbon dioxide and water to produce carbohydrates and free oxygen, using sunlight as an energy source, is just getting started. There is oxygen in the air, but not enough to support much in the way of land dwellers. My castaways are quite reasonable in wanting to get away as soon as possible—they’re not properly equipped for the scientific study they recognize the planet needs. Besides, they want to get home! I’ll have more to say on planet building later. For now, welcome to my blog and I hope you surf on over to my website and find out what Homecoming is all about (www.sueannbowling.com).