If you want to do some work finding out, here's a long answer for you:
How Well Can Persistent Contrails Be Predicted
"There are two atmospheric conditions necessary for persistent contrails. First, the so called Schmidt-Appleman criterion must be fulfilled, which is a pure thermodynamic criterion that rules whether contrail formation is possible in a given situation or not. This criterion covers both short-term (lifetime seconds to a few minutes) and persistent contrails. Thus a second condition is required for persistent contrails: the ambient air must be in a state of ice supersaturation, that is, the relative humidity with respect to ice, RHi must exceed 100%"
Although there are other articles that cover the same topic