What molecules are produced in carbon arc lamp and how do they produce light? I am curious about the chemistry of the arc lamp (an indirectly for the incandescent bulbs) thus I would like to ask the following.

It is a common understanding that the electrons pushed inside an arc lamp -- let's assume a carbon one, that is with electrodes in graphite -- will collide on the atoms of the carbon crystal and increase their kinetic energy rising those in the cathode to about 3600 degrees and those in the anode to 4200 degrees. My questions are:


Why is the cathode, where the electrons arrive first and at full energy, cooler than the anode?
What kind of molecules are produced at the electrodes? It is said that carbon evaporates at the electrodes when the current is allowed to flow between them. What is the vapour of carbon? From wikipedia, dicarbon is listed, but what would be the reaction from graphite (pure carbon) to dicarbon?
If dicarbon is produced by evaporation on the arc lamp, would that be produced also in the old incandescent lamps that used carbon filaments, such as that made by Edison?
Does dicarbon react with oxygen? Does it oxidise to carbon dioxide or monoxide?
And finally, how does dicarbon produce light? I imagine that it must be at a high energy state and photons are released with the decay of the electrons to their ground levels, is that correct? Is there some kind of quantitative measure of why arc lamps are more luminous than incandescent or halogen lamps?


Thank you
Answers:


Consider the mass and kinetic energy of an electron or of an ion of nitrogen or oxygen, and the reactivity with carbon.
Good question! It would be interesting to see the relative abundance of allotropes of carbon deposited from a filament in vacuo. There is a metallic glisten to the deposit, so there might be graphite, carbon nanotubes or buckminsterfullerene. $\ce{C2}$ would not be there for long, though.
There are a great many chemical species produced by an arc lamp operating in air. Depending on the gases in which it operates, an arc can produce complex organic molecules. Even something as ornate as a buckyball can be made!
I've not seen the relative abundance of products of an arc lamp, but I assume carbon oxidizes rapidly to the monoxide and dioxide, depending on abundance of oxygen. Charcoal briquets oxidize at a far lower temperature.
Most of the light is black-body radiation, though there would also be some spectral lines produced by recombination, such as from nitrogen. With a spectroscope, you'd see a continuum with a few bright lines added (or dark lines from absorption, as the gases cool).