Here is the distribution map of mt-haplogroup J.
The origins of J are complicated. Although it hasn't been found yet in Mesolithic or Palaeolithic Europe,
it is possible that J was already in Europe before the Neolithic. Samples have been identified from various Neolithic sites, including Linear Pottery culture (LBK) in Central Europe, the Cardium Pottery culture in southern France, Megalithic cultures in northern Spain, and the Funnelbeaker Culture in Germany and Sweden.
During the Bronze Age, J has been found in the Urnfield and Corded Ware sites. However I would tend to think that it represent the maternal lineages inherited from the Neolithic rather than new lineages brought by R1a/R1b conquerors. Indeed, mtDNA J has never been found in Bronze Age sites linked with the Indo-Europeans in Russia, Ukraine, Central Asia, Siberia or Mongolia, although J is present in these regions today. The oldest J sample in North Asia are from the Iron Age Scytho-Siberian Pazyryk culture (6th to 3rd century BCE) and the Iron Age Xiongnu culture, and could have been brought by later migrations from southern Central Asia, notably by the Scythians.
It is hard to explain the various hotspots of J in Europe: the Western Isles of Scotland, Wales, Cornwall, Denmark, the French Pyrénées and Aragon...
In Denmark's case, J probably came through the LBK culture from Germany, and might have prospered due to a founder effect or some intrinsic evolutionary advantage. It has been claimed that carriers of haplogroup J have a greater resistance to cold, and that this may be why it was positively selected in Scandinavia. That could also apply for the British Isles, Estonia and the adjacent Pskov oblast in Russia. This would also make sense for the Arabian peninsula where night time temperature often fall very low.
The Pyrénées, Aragon and Sardinia could be seen as relatively isolated regions where Neolithic lineages survived better various invasions through the ages.