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 subhorizon regions in the early Universe. We adopt a model-independent approach, where we parametrize 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 curvature 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 subhorizon formation is a change in the PBH mass function and formation redshift, which, in turn, affects gravitational wave (GW) observables. We find that subhorizon PBH formation in general enhances the isotropic SGWB energy density and the absolute angular power spectrum. However, the quasimonotonic 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. We find that despite the significant enhancement from subhorizon collapse, the resulting signal in the anisotropy power spectrum will not be detectable by planned future gravitational wave detectors such as LISA.