What is the significance of the eagle which Herod had put up over the door of the temple?

In War 1.650ff, Josephus describes a confrontation between the Herod and the people over a statue of an eagle that he had put up over the entrance to the temple. What was the significance of this eagle? The eagle was a complex symbol in the ancient world. It was a Greek symbol of Zeus (an Egyptian religious symbol before that), appeared on lots of Ptolemaic coins and might have been a sort of dynastic symbol, but also a symbol of the Roman Empire. The eagle appears in relief on lots of temples of the time, but Josephus' description makes it sound like the eagle is fully 3D (rather than a relief), like those on the treasury at Petra. Why did Herod put up the eagle? It is the only animal representation we have evidence of in Herod's temple (or at any time in the Second Temple). He knew it would make the people mad, so what was he after? I'm interested in historical arguments based in academically credible source material.