Sub Woofer Hum... This One Puzzles Me

i've got a low level hum coming from my subwoofer, and this one has got me scratching my head. the sub is a vandersteen 2w that's connected via high level inputs (the only option on this sub) from a separate amp channel (instead of piggy-backing off the mains). here's what i've found...

when the system is up and running, there's no hum. so, all the following applies only to when the amp that is sending signal to the sub amp is turned off.
as soon as i turn off the amp that is connected to the sub, the hum starts.
the level of the hum increases and decreases as i adjust the level of the sub (sensitivity on the vandy plate amp).
disconnecting the preamp from the amp does not eliminate the hum.
disconnecting one of the speaker leads at the sub amp does eliminate the hum.
unplugging the sub from the AC receptacle results in the hum getting appreciably louder.
using a cheater plug to lift the ground results in a similar increase in hum loudness as when the sub is unplugged.

any ideas?

the amps are plugged into a running springs audio ac conditioner, the sub is plugged directly into the wall. i was curious about plugging the sub into the running springs unit, but it's too far away.

is this just a normal ground loop? i thought in those cases a cheater plug diminishes the hum - in this case the cheater plug, or simply disconnecting the AC to the sub, resulted in the hum getting quite a bit louder.

any inputs would be appreciated.