[Larry]

Looking at the photo I would say that the device is unlikely to be a flame thrower or smoke layer as a much smaller tube could have been fixed to the fuselage underside to branch out either side of the tail, like the Ju88 flame thrower photo (which I think I saw in 'Modell magazin- War Album' 1-5).

I doubt it was a launch rail for a missile, as the underside is U shaped which does not correspond to the usual flat launch rails of the period, and the rail is not parallel with the line of flight and unusually is very close to the forward fuselage at the point the missile would leave the rail. The idea that it was a Hurricat type rail has already been discounted.

If it was a refueling arm (and ahead of its time) it would make no sense in it being connected to a tanker flying below the Bf 109 and working against gravity! And why would the LW use a Bf 109 as the tanker when larger aircraft were available?

If the device does not show a clear operational benefit to the Bf 109, the only explanation left, is that it was flight testing something for another aircraft design. It was quite common at the time for bits of a proposed aircraft to be attached to other for aerodynamic trials. Someone I hope will recognise the device as a strut of a large aircraft, a proposed 'Mistel' or even a leading edge of a wing / strut etc.