Probing supermassive black hole scalarization with Pulsar Timing Arrays

Scalar-tensor theories with a scalar field coupled to the Gauss-Bonnet invariant can evade no-hair theorems and allow for non-trivial scalar profiles around black holes. This coupling is characterized by a length scale $\lambda$, which, in an effective field theory perspective, sets the threshold below which deviations from General Relativity become significant. LIGO/VIRGO constraints indicate $\lambda$ is small, implying supermassive black holes should not scalarize. However, recent work suggests that scalarization can occur within a narrow window of masses, allowing supermassive black holes to scalarize, while leaving LIGO/VIRGO sources unaffected. We explore the impact of this scenario on the stochastic gravitational wave background recently observed by Pulsar Timing Arrays. We find that scalarization can alter the characteristic strain produced by circularly inspiralling SMBH binaries and that current data shows a marginal preference for a non-zero $\lambda$. However, similar signatures could arise from astrophysical effects such as orbital eccentricity or environmental interactions, emphasizing the need for improved modeling and longer observations to discriminate among the different scenarios.