What is the critical escape speed needed to hold atmosphere, and how
will it depend on the temperature?

Let us take the major Solar System examples, from outside in:

Pluto: 1,18 km per second, approaches to 30 a. u.. Appreciable nitrogen
atmosphere restricted by freezing.
Triton: 1,45 km per second, orbits at 30 a. u.. Appreciable nitrogen
atmosphere restricted by freezing.
Titan: 2,64 km per second, orbits at 10 a. u.. A nonfreezing nitrogen
atmosphere, the inventory being 160 000 Pa.
Io: 2,57 km per second, orbits at 5,2 a. u.. Not much atmosphere.
Europa: 2,03 km per second, orbits at 5,2 a. u.. Not much atmosphere.
Ganymede: 2,73 km per second, orbits at 5,2 a. u.. Not much atmosphere.
Callisto: 2,44 km per second, orbits at 5,2 a. u.. Not much atmosphere.
Mars: 5,03 km per second, orbits at 1.52 a. u.. A freezing carbon
dioxide atmosphere, contains nonfreezing nitrogen inventory of 20 Pa.
Moon: 2,38 km per second, orbits at 1 a. u.. Not much atmosphere.
Earth: 11,2 km per second, orbits at 1 a. u.. Nitrogen atmosphere of
approximately 80 000 Pa.
Venus: 10,4 km per second, orbits at 0,72 a. u.. Carbon dioxide
atmosphere with nitrogen inventory of about 300 000 Pa.
Mercury: 4,44 km per second, orbits at 0,39 a. u.. Not much atmosphere.

I wonder if there is any rule between the nitrogen contents of the
three dense nitrogen atmospheres?