When is aggregate demand high

This question puzzled me: If aggregate demand is so low, why are profits so high?
If I remember what's left of my economic knowledge correctly, aggregate demand is simply C+I+G (in a closed economy) and this in turn equals Y or GDP.

So is Tyler asking why are profits so high when output is so low? This doesn't really make sense and I decided that it has to be the output gap that is high (that makes aggregate demand low).

From FRED the picture for corporate profits:



And from FRBSF a picture of the output gap (I wish these folks would make their data available for download):



The questions I would have are (and bearing in mind that output gap measures can be vastly different, e.g. see here for example):

1. Is the cyclical component of profits pro- or counter-cyclical to the output gap?
2. Same question vis-a-vis unemployment and profits.