MD83 First Officer describes compass system anomalies during descent resulting in map display failure and autopilot disengagement. Captain assumes the flying duties while the First Officer attempts to reset the system unsuccessfully. Radar vectors to a visual approach are requested and received.

Narrative

While on FISEL 2 arrival at intersection FATHR with First Officer flying and autopilot engaged; we got a heading comparator indication on both FMA's. Shortly there after the First Officer map failed and displayed HDG in red. The autopilot kicked off and I hand flew the aircraft. The heading flag and map reset only to fail within a few minutes and not reset. We had decided that the Captain should fly the remainder of the leg due to the First Officer map and heading malfunction being intermittent. I transferred control of the aircraft to the Captain and ATC gave us proceed direct to JALOP. At this time the Captain had no fail indications but no waypoints or data were on his MFD after the positive transfer of controls. The Captain advised ATC of the situation and asked for heading vectors off the arrival and ATC complied with our request. All other indications were normal. While the Captain flew the aircraft; I ran the appropriate QRC checklist which led us to attempt a reset on the Number 2 gyro. The HDG flag remained and as directed by the QRC; I attempted to transfer Captain's data to my MFD without success. At this time the Captain's MFD map and way points had reset. We proceeded to a visual approach to Runway 27R and my HSI was approximately 100 degrees off from the Captain's HSI and the stand-by compass when it displayed a compass rose. While on final the Captain's FD command bars stowed themselves all with a positive ID on LOC 27 right in both NAV radios. The Captain shot a raw data visual approach and landed without further incident.