To determine the photons arriving from the Sun-like star (henceforth, for the sake of convenience, referred to as Pegasi, for a somewhat similar system), one need only repeat the process used for the dwarf, but for a higher temperature. Being Sun-like, Pegasi has a temperature of about 5800 K. So, using the Wein Displacement Law, we get
This is about 500 nm, which corresponds to green light. As a side note, this does not make the star appear green to the human eye (which is good, since it's supposed to be Sun-like, and the Sun is not green). Though the intensity peaks at 500 nm, the high-output portion of Pegasi's emission spectrum covers a wide range of wavelengths, and the visible spectrum is very narrow. This means that there are also plenty of blue and yellow and red photons produced, and when all of the wavelengths of visible light are produced together, you get white light. So, when viewed in the visible spectrum, Pegasi will appear white, not green.
So, with the maximum wavelength in hand, we can now use the specific intensity formula, the solid angle, and the equation for the energy of a photon to find the number of photons arriving from Pegasi per second per area. Using 2*pi for the solid angle (again assuming the observer receives half the photons), we have
Okay, cool. So, what's the flux ratio of the Y Dwarf to Pegasi? Flux is given in units of energy per time per frequency per area, so unlike specific intensity, it does not depend on the solid angle. To get to this from the values we have now, we need to convert photons back to energy. Which we can do with this equation:
So, after converting our values back into terms of energy per time per area and then dividing to get the ratio, we get
for the ratio of the Y Dwarf's flux to Pegasi's.
Once again, this was worked out in collaboration with Mee and David.
I think I'm actually following this, as long as I trust your math, and don't try to do it myself. As usual, however, I got a little distracted when you talked about the peak of the light emitted being green light, but the star light appearing white because there is still light emitted across the visible spectrum. Some questions that are off your original topic - does the light reflected from the moon look white because the light it is reflecting is white?
ReplyDeleteIs it possible to know if a moon's composition (or something else) could ever cause it to reflect light in a different color than the sun emits?
Are there suns whose emitted light would appear reddish to us?
So, yeah, all matter reflects, transmits, or absorbs different wavelengths of light depending on its composition (specifically, on the electron configurations of the elements and compounds and how they interact with photons). The color we perceive in the optical spectrum reflects (ha ha) which wavelengths of visible light are absorbed and which are reflected or transmitted.
ReplyDeleteSo yes, it is possible to see how an object's composition can affect the reflected light; in fact, that's the major determining factor. For example, Mars receives the same wavelengths of light from the Sun that the Moon does, but Mars appears red. This is due to the high quantities of iron oxide on its surface, which reflects red wavelengths.
And yes, there are stars that appear red, and there are stars that appear blue. Good examples are Betelgeuse and Rigel, both in Orion.
Think about what would happen if the peak wavelength occurred in the infrared or ultraviolet spectrum. We can't see the maximum wavelengths, but some of the higher-output ones will occur in red or blue. Because they can't be overpowered by the peak wavelength (since we can't see it), we see a mostly red or blue star.
It's really just a function of the boundaries of our vision. If we perceived light from 500 to 100 nm, green would be on the lower end of the visible spectrum, and we could see green stars. Make sense?
yes, thanks. I was partly just curious, and partly wondering whether one of my favorite sf/fantasy authors got her science right... :)
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