Small-scale shear: peeling off diffuse subhalos with gravitational waves

Abstract

Dark matter (DM) substructures at subgalactic scales (\(M\lesssim 10^7 M_\odot \) or \(k\gtrsim 10^3 \,{\rm Mpc}^{-1}\)) are pristine testbeds for DM. However, they remain unexplored yet, being typically too diffuse and dark to induce visible signals. We first show that such NFW subhalos can be detected individually with single-imaged diffractive lensing of chirping gravitational waves (GWs). Detection rates are expected to be \({\cal O}(10)\) per year at BBO and less at LISA, limited by small merger rates of heavy black-hole binaries and large required SNR \(\gtrsim 1/\gamma(r_0) \sim 10^3\). Remarkably, by developing a general formalism for weak diffractive lensing, we find that the frequency dependence of lensing, what is actually the measurable effect, is due to shear \(\gamma\) at the Fresnel length \(r_F\). It not only provides useful insights but also offers a new way to measure mass profiles; the chirping \(r_F \propto f^{-1/2}\) probes successively smaller length scales. Further, by completing the formalism with strong diffractive lensing, we generalize estimations for power-law profiles and demonstrate the idea of measuring profiles through small-scale shear.