On the Anisotropy of the Stochastic Gravitational Wave Background from Sub-Horizon-Collapsed Primordial Black Hole Mergers

We study the properties of the stochastic gravitational wave background (SGWB) resulting from the mergers of primordial black holes (PBH) that formed from the collapse of sub-horizon regions in the early universe. We adopt a model-independent approach, where we parameterize the fraction $f_H$ of the wavelength of the perturbation mode in units of the horizon radius when the patch starts to gravitationally collapse. Assuming a monochromatic spectrum of isocurvature perturbations and spherically-symmetric density perturbations, we investigate the isotropic SGWB energy density and angular power spectrum at various frequencies, PBH masses, and horizon size fractions. The key effect of sub-horizon formation is a change in the PBH mass function and formation redshift, which, in turn, affects gravitational wave (GW) observables. We find that sub-horizon PBH formation in general enhances the isotropic SGWB energy density and the absolute angular power spectrum. However, the quasi-monotonic increases in both quantities as $f_H$ decreases cease when the chirp mass of the binary PBHs reaches a mass threshold determined by the frequency of observation; the isotropic SGWB energy density spectrum significantly drops above the corresponding cutoff frequency.