Air carrier First Officer reported the aircraft became disconnected from the tow bar during push back; and was rolling free for a few moments before the Captain brought the aircraft to a safe stop. There was reportedly no communication from the ground crew during the incident.

Narrative

During pushback; the Captain directed the start of the left engine. During the engine start; I heard a non-normal sound from the nose gear and tow bar area. I made the comment to the Captain '...that didn't sound good...' while I was monitoring the left engine start. ~10 seconds after I made this comment; the Captain said '...we are no longer attached to the tug; the airplane is moving; I have the airplane; brakes; and parking brake set...' He requested an update from the push crew; but we realized they were no longer on intercom with us. We waited for the push crew to re-connect while we ensured the jet was secure and not moving. After they re-connected; they explained the tow bar had become disconnected from the aircraft.Cause: The cause of this event was the tow bar becoming disconnected from the aircraft during push back.Suggestions: I do not have enough experience with tugs and tow bars to understand how to prevent this incident; but I do have input on that happens following an inadvertent tow bar disconnect. The immediate reaction from the push crew is they must signal to the pilots an inadvertent disconnect has occurred. This was the most disconcerting part of this incident; that there was no attempt to signal to the flight deck the tug was no longer attached to the aircraft. This is a critical step to ensure safety is maintained via positive control of the aircraft. We are very fortunate the Captain was able to realize quickly the aircraft had separated from the tug vehicle and reacted quickly to take control of the aircraft and safely stop prior to hurting anyone or damaging equipment.