Pulsar timing arrays ( PTAs ) are designed to detect the predicted gravitational wave ( GW ) background produced by a cosmological population of supermassive black hole ( SMBH ) binaries .
In this contribution I review the physics of such GW background , highlighting its dependence on the overall binary population , the relation between SMBHs and their hosts , and their coupling with the stellar and gaseous environment .
The latter is particularly relevant when it drives the binaries to extreme eccentricities ( e > 0.9 ) , which might be the case for stellar-driven systems .
This causes a substantial suppression of the low frequency signal , potentially posing a serious threat to the effectiveness of PTA observations .
A future PTA detection will allow to directly observe for the first time subparsec SMBH binaries on their way to the GW driven coalescence , providing important answers of the outstanding questions related to the physics underlying the formation and evolution of these spectacular sources .