Can asteroid-mass PBHDM be compatible with catalyzed phase transition interpretation of PTA?

Primordial black holes (PBHs) can catalyze first-order phase transitions (FOPTs) in their vicinity, potentially modifying the gravitational wave (GW) signals from PTs. In this study, we investigate the GWs from strong PTs catalyzed by PBHs. We consider high PBH number densities, corresponding to asteroid-mass PBH dark matter (DM) when the GWs from FOPTs peak in the nanohertz band. We calculate the PBH-catalyzed FOPT GWs from both bubble collision GWs and scalar-induced gravitational waves (SIGWs). We find that while low PBH number densities amplify the GW signals due to the formation of large bubbles, high PBH number densities suppress them, as the accelerated phase transition proceeds too rapidly. This suppression renders the signals unable to explain pulsar timing array (PTA) observations. By conducting data fitting with the NANOGrav 15-year dataset, we find that the PBH catalytic effect significantly alters the estimation of PT parameters. Notably, our analysis of the bubble collision GWs reveals that, the asteroid-mass PBHs (10-16-10-12M⊙) constituting all DM is incompatible with the PT interpretation of PTA signals. However, incorporating SIGWs alleviates this incompatibility for PBHs in the mass range 10-14-10-12M⊙.