Air carrier Captain reported a near mid air collision with a possible UAS while they were descending on arrival.

Narrative

While on the DFW BEREE 2 RNAV arrival; descending through ~12;800 ft. MSL (+/- 800 ft.) I suddenly noticed a large black object (approximately 5 to 8 feet in diameter); without any lighting; quickly pass our left wing with ~30 feet lateral and ~20 feet horizontal separation. (All information is estimated as total sight time was ~1/4 to 1/2 of a second; at most; due to the massive velocity differential between our aircraft and this object.) My First Officer also had visual contact with this object for a similar amount of time. We advised ATC within the next minute advising of either a 'large drone or bird' passing by our aircraft at or near 12;800 ft. MSL. We heard the approach controller warn the following aircraft who later reported a TCAS target; with no altitude; which then disappeared as they apparently approached this object. In reply; the approach controller advised; 'Well; it must be a drone then.' We were later transferred to another frequency and are unaware of other sightings.Cause: Speculation as drones are not within my general field of knowledge; but a lack of required ADS-B and/or transponder altitude transmission for drones may have been causal.Suggestions: Given the large size of this drone; we had an extremely high potential for sudden and catastrophic aircraft damage with this near collision. To our recollection; we had no TCAS traffic display of this drone; although without altitude data available; we; like the following aircraft; would also not have had a TCAS TA or RA. While not an area of my expertise; if not already required or regulated; the FAA should mandate ADS-B and/or onboard transponders for all drones capable of high altitude flight. We were profoundly lucky in this incident. The large size of this drone; combined with the dark; cloudy sky and the extremely high rate of closure; would have precluded any successful aircraft maneuvering prior to impact.