Abbadon Exotic machine gun
The Abbadon is the Solar variant of the Thunderlord heavy exotic and you can only begin the quest chain for it once you've got the Nova Mortis.
Talk to Commander Zavala to initiate the Hymns of Fire quest.
He'll send you to Banshee-44 who wants you to get out there and get 100 kills with Solar abilities.
After the slaughter is complete, pop back to Banshee-44 and he'll send you off on another strike. Boot up the Shield Brothers strike on the Dreadnaught and get some more killing done.
Return to Commander Zavala and the Abbadon is yours.