There is no atmosphere for comets to get hot and burn and show tails but they still have tails. Why do they?
Edit: Isn't the answer "acceleration"?
A simplistic answer according to the article "Comets: Formation, Discovery and Exploration" (Choi, 2010) is as the comet (which is a lump of 'dirty ice') approaches the sun, the radiation emitted causes the ice to melt into a 'coma', and then blown out into a tail in the solar wind.
Going further, from the webpage "Why do some comets have two tails?", it is noted that the formation of the tail is actually in two parts, from the website:
The reason for two tails that you see there is