Signatures of $10-10^4\,{\rm M}_{\odot}$ Dark Matter halos in LISA via Stochastic Diffraction
Cold Dark Matter predicts a population of low-mass halos which are sensitive to its fundamental nature and the primordial power spectrum, yet remain undetected. Although elusive, their discovery may be possible thanks to wave-optics lensing of gravitational waves (GWs) by the superposition of many halos along the line of sight. We study the statistical properties of stochastic diffractive lensing, which imprints correlated fluctuations on the amplitude and phase of the original waveform. The stochastic distortions can be described by an orthogonal basis that captures the dominant ''tones'' associated with the dark matter properties, or dark timbre, which is not degenerate with binary source parameters. LISA is most sensitive to halos of $O(10\text{--}10^4\,M_\odot)$, and because the imprint recurs in every source, stacking $\sim(50,500)$ loud binaries could confirm them at the $(2,5)\sigma$ level ($\sim0.2$ to $\gtrsim4\sigma$ for realistic merger rates and different concentration estimations). The per-event signal is only $O(10^{-3})$ in cold dark matter, demanding major advances in waveform accuracy and data analysis. Even short of that reach, stochastic diffraction places stringent bounds on models that enhance small-scale structure, such as axion miniclusters and primordial black holes.