You have already been told, it is a circumstantial case.
In case you are not already aware, an important general point to understand is that circumstantial evidence and forensic evidence are not opposites. It seems to be very common for people to think they are, but they aren't. Forensic evidence can be direct or can support a circumstantial case.
A case based on circumstantial evidence alone - i.e. without any direct evidence - will always be inferior and prompt residual doubts and questions where the convicted person protests his innocence on some credible basis. That said, in general principle, I have no problem with a conviction based on a circumstantial case, especially as nowadays it is expected that such a case would be supported by forensic evidence - including forensic evidence that, one would hope, eliminates other probable suspects.
This brings me to the central problem we have in discussions here: without key case papers such as the pathology report, DNA evidence and so on, it is difficult to truly assess the weight of the case against Luke. We're scratching around in the dark.