Question Wired shadows on particle System

I got a shield bubble for my spaceship in the asset store. It consists of multiple particle systems stacked on top.
However, I get wired shadows on top of it, see screenshot:

I played around with all kinds of render parameters, disabled cast shadows on the Game object itself, nothing helped.
The only way they go away is to enable post-processing on the main camera, which costs performance and does not make any sense to me.

Any idea what is going on here?