Physics Question #3466
Gabriel, a 37 year old male from Winnipeg, MB asks on May 28, 2006,
What is the distance from the sun for each of the elements in the periodic table where they would condense or melt? The key word is distance, the insolation distances. Specifically, I am looking for a formula so that I can get a plot for a star of any mass. The reason for this is that it would be easier to predict were an Oxygen Gas Giant with habitable moons would form, but I am not looking for information on star formation, or gas giant formation, only the distance from the sun, for each individual type of element, at which it would condense/melt.
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You are asking the wrong question. Elements do not condense as elements, so their own melting temperatures are not relevant. Dust grains tend to form with silicon-based or carbon-based chemistries, in large part based on the carbon-oxygen ratio in the chemistry out of which a star is born -- because CO and CO2 are quite stable, you get carbon only as a gas when sufficient oxygen is present and then dust is dominated by silicate chemistry. When primordial stars contain less oxygen, carbon tends to come out in graphitic form in grains which are called polycyclic aromatic hydrocarbons (PAHs). All the other elements, present to a significantly less extent than C, N, and O, tend to precipitate with these grains. (There are notable exceptions in certain circumstances, like titanium oxide formation in the atmospheres of very cool red supergiants.) The thermal history and abundance ratios in these grains create a variety of mineraologies which are reflected in spectra of these grains -- which make notable imprints in the infrared spectra of objects where this dust plays a role.
There used to be a lab at NASA Ames research center in California that synthesized these minerals and recorded their spectra so as to compare with astronomical observations. We use their results all the time to understand the silicate dust and PAH dust, which is found in crystalline and amorphous types that we see in telescope observations.
I can't tell you the temperatures at which these condensations take place -- it depends on density and composition as well -- but these grains are essentially ceramic (when silicate dominated) or soot (when carbon dominated) so they are not affected by very high temperatures. I think every native element except carbon has melting temperatures below those of silica or graphite, with a few exceptions like platinum, tungsten and tantalum -- and of course these are exceptionally rare.
One can very quickly get the approximate distance from a star to a given "temperature zone" through a few scaling relationships. Let's call the temperature of the surface of the star = Tstar, and the temperature of the desired zone = Tzone. Assuming an emissivity of unity, the amount of energy lost per unit surface area scales as T^4, so the ratio of energy lost per area will be (Tstar/Tzone)^4. To balance, the star should appear from that zone as having that fraction of area of the entire sky. For example: on earth, the planet's mean temperature is roughly 300 K, and the sun's surface temperature is near 6000 K. So the ratio in temperatures is 20 and the ratio in emitted energy per unit area is about 160,000. So for the Earth to get as much as it radiates into space, per unit area, the Sun should subtend about 1/160000 of the whole sky's area. A sphere contains 41000 square degrees, so 1/160000 of that is about a quarter square degree. The Sun is a disk on the sky with diameter 0.5 degrees, so it has an apparent size in square measure of pi*0.25^2 or about 0.2 square degree.
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