Pulsar timing arrays are now setting increasingly tight limits on the gravitational wave background from binary supermassive black holes .
But as upper limits grow more constraining , what can be implied about galaxy evolution ?
We investigate which astrophysical parameters have the largest impact on strain spectrum predictions and provide a simple framework to directly translate between measured values for the parameters of galaxy evolution and PTA limits on the gravitational wave background of binary supermassive black holes .
We find that the most influential observable is the relation between a host galaxy ’ s central bulge and its central black hole , M _ { \bullet } - M _ { bulge } , which has the largest effect on the mean value of the characteristic strain amplitude .
However , the variance of each prediction is dominated by uncertainties in the galaxy stellar mass function .
Using this framework with the best published PTA limit , we can set limits on the shape and scatter of the M _ { \bullet } - M _ { bulge } relation .
We find our limits to be in contention with strain predictions using two leading measurements of this relation .
We investigate several possible reasons for this disagreement .
If we take the M _ { \bullet } - M _ { bulge } relations to be correct within a simple power-law model for the gravitational wave background , then the inconsistency is reconcilable by allowing for an additional “ stalling ” time between a galaxy merger and evolution of a binary supermassive black hole to sub-parsec scales , with lower limits on this timescale of \sim 1 - 2 Gyr .