#scifi #writing At this point, we have a planet whose composition is similar to the universal elemental abundance (as modified by the process of early star formation, which involves a good deal of blowing away of volatile molecules), orbiting a main sequence star.  What more can we say about such things as the appearance of the “sun”?

This is where optics and even quantum mechanics come in.  Stars behave pretty much as black bodies—that is, the surface electromagnetic radiation at a particular wavelength (color) is determined only by the surface temperature.  (Note that color is generalized to include x-rays, far and near ultraviolet, visible light, near and far infrared, microwaves and radio waves.)  The blackbody radiation has a peak in the middle while falling off in intensity at very long wavelengths (radio or thermal infrared—IR) and at very short wavelengths (ultraviolet—UV—or x-rays.)

The exact position of the peak radiation, and thus the color of the light, is a function of temperature only.  In fact, the wavelength of maximum intensity, in micrometers, is given by 2900 divided by the Kelvin temperature.  For our sun, this is about 5800 degrees Kelvin, so the peak radiation from the sun would be expected to have a wave length of about half a micrometer, which is in the visible part of the spectrum. In fact, it’s green—so much for that green sun!  Since our eyes have evolved under a green sun, we would see it as white, simply because that’s the way our eyes work.

Color isn’t the only thing about starlight that depends on temperature.  The amount of radiative energy given off by a unit area of a star’s surface is also a function of temperature.  The energy per unit area per unit time is directly proportional to the fourth power of the temperature.

If a star’s absolute temperature were half that of the sun’s, 2900 degrees K, it surface would be only one sixteenth as bright as that of the sun.  The peak radiation would be shifted to 1 micrometer, in the thermal infrared—but we would still see it as a somewhat yellowish white.  In fact, it would be about the color of an ordinary incandescent light bulb.

If a star’s absolute temperature were twice that of the sun’s, 11, 600 degrees Kelvin, its surface would be sixteen times brighter than the sun’s.  It would also have its peak radiation shifted to about a quarter of a micron, which is in the ultraviolet region of the spectrum.    Interestingly, our eyes would probably notice only the increase in brightness, and perhaps a slightly bluer color—but we’ll talk about that later.  The fraction of the total radiation that was in the visible range would hardly change.  What would change would be the fraction of ultraviolet, which would increase by a factor of six, and the fraction of infrared, which would be less than half of that in sunlight.

On earth, we have  a considerable amount of free oxygen in the air, which is ionized by the shorter ultraviolet wavelengths to produce ozone, which absorbs the somewhat longer ultraviolet.  As a result, little of the really damaging UV radiation reaches the surface to ionize the molecules necessary for life.  We have developed physiological mechanisms, such as skin pigmentation, which responds to UV exposure by darkening, to protect us against the UV that does get through the ozone layer.  But remember that the presence of free oxygen, and thus of ozone, in the atmosphere is probably dependent on life.  Stars beyond some limiting temperature probably produce too much ultraviolet to allow life on their planets.  In any event, we know from looking at the stars in our sky that such hot stars are rare.

Luminosity—the total energy output of a star—is equal to the amount of radiation the start puts out per unit area times the surface area of the star.  Thus if we know both luminosity and temperature, we can calculate the radius of the star.  But both luminosity and temperature of main-sequence stars are surprisingly well-defined functions of the mass of the star—which means that the radius is, as well.  So if we know the mass of a star and that it is on the main sequence, we also know its color and size.  The only real variation comes from the fact that the star changes slightly with time while it remains on the main sequence, becoming more luminous and cooler (and thus larger) with age.  This change, however, is slight compared with changes before and after the portion of the star’s life spent on the main sequence.