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

TL;DR

This paper develops a formalism for using gravitational wave lensing to detect and analyze small, diffuse dark matter subhalos at subgalactic scales, revealing new ways to probe dark matter structures beyond current observational limits.

Contribution

It introduces a complete formalism for weak and strong diffractive lensing of gravitational waves, enabling detection of subhalos with sizes comparable to the GW Fresnel length, and highlights the frequency-dependent shear as a key measurable effect.

Findings

NFW subhalos can be detected individually at low rates with future GW detectors.

Lensing sensitivity is higher for lighter subhalos due to scale radii matching the GW Fresnel length.

Frequency dependence of weak lensing is due to shear at the Fresnel scale, offering a new probe of mass profiles.

Abstract

Subhalos at subgalactic scales ($M\lesssim 10^7 M_\odot$ or $k\gtrsim 10^3 \,{\rm Mpc}^{-1}$) are pristine test beds of dark matter (DM). However, they are too small, diffuse and dark to be visible, in any existing observations. In this paper, we develop a complete formalism for weak and strong diffractive lensing, which can be used to probe such subhalos with chirping gravitational waves (GWs). Also, we show that Navarro-Frenk-White(NFW) subhalos in this mass range can indeed be detected individually, albeit at a rate of ${\cal O}(10)$ or less per year at BBO and others limited by small merger rates and large required SNR $\gtrsim 1/\gamma(r_0) \sim 10^3$. It becomes possible as NFW scale radii $r_0$ are of the right size comparable to the GW Fresnel length $r_F$, and unlike all existing probes, their lensing is more sensitive to lighter subhalos. Remarkably, our formalism further reveals that the frequency dependence of weak lensing (which is actually the detectable effect) is due to shear $\gamma$ at $r_F$. Not only is it consistent with an approximate scaling invariance, but it also offers a new way to measure the mass profile at a successively smaller scale of chirping $r_F \propto f^{-1/2}$. Meanwhile, strong diffraction that produces a blurred Einstein ring has a universal frequency dependence, allowing only detections. These are further demonstrated through semianalytic discussions of power-law profiles. Our developments for a single lens can be generalized and will promote diffractive lensing to a more concrete and promising physics in probing DM and small-scale structures.