When a starship is destroyed in a battle with another starship in deep space the resulting anti-matter warp core explosion can be detected by anyone within 5,000 LY. The explosion point will be plotted as a purple starburst (8 spokes) on the starchart. You will also receive a distress call from the ship with will give you the name and location of the destroyed ship. 

You are unable to determine the ID number or race that the ship belonged to. Ships using their Glory Device ships do not send a distress call, but their victims will if they are distroyed.