What is causing these strings in the overhangs?
While this looks a lot like stringing, it's not what I would call stringing. I usually reserve that term for material that should never have left the nozzle to begin with, due to insufficient or missing retraction or excessive compression of the filament between the extruder and the nozzle. The "strings" you've shown look like desired wall extrusions that did not adhere to the adjacent walls in the same layer or to the previous layer.

This is common when printing concave perimeters that are overhanging, due to a combination of minimal-to-no contact with previous layer and acceleration of the nozzle away from the previous wall in the current layer. Sometimes under-extrusion can also be a factor.

You can often mitigate this by:


using thinner layers (for the whole print, or "adaptive layer height" that will dynamically adjust as needed). For a given wall slope (fixed rise over run), this will reduce the "rise", and thereby place the walls of the next layer such that they overlap more with the previous layer. Sometimes this makes the difference as to whether they overlap at all.
increasing hotend temperature. This will improve bonding with adjacent wall and with previous layer, if there's any contact with it.
decreasing print speed, especially for outer walls. This will reduce the effect of the nozzle pulling the wall away from the adjacent wall it's supposed to bond to, and will also deliver more heat to the adjacent wall and previous layer wall you want to bond to.


All three of these will also help if under-extrusion is part of the underlying cause.

If you can't get any of this to work, using supports is always an option, but spherical (as opposed to flattened) domes generally "shouldn't" need support to print.