Wave-Tide Locking in Thin Stellar Streams: A Phenomenological Mass Spectrometer for an Intermediate Ultralight Axion
We propose a phenomenological mass estimator for an intermediate ultralight axion dark-matter component using thin stellar streams. The central observation is an analytic relation linking three length scales in a fuzzy-dark-matter stream progenitor: the tidal radius of a bound dark core, its gravitational Bohr radius, and the axion de Broglie wavelength evaluated at the stripped-star velocity scale. If the stream width is (w=C_w r_{\rm t}), with (C_w=O(1)), then [ \frac{r_{\rm t}}{r_{\rm B}} =========================== \frac{4π^2}{C_w^2} \left(\frac{w}{λ_{\rm dB}}\right)^2 . ] Thus (λ_{\rm dB}\sim w) automatically implies (r_{\rm t}/r_{\rm B}\sim25)--(40): the dark wave core survives well inside the tidal boundary while the extended stellar envelope is stripped into a thin stream. This wave--tide locking gives a no-simulation axion-mass estimator, [ m_a \simeq 2.69\times10^{-19},{\rm eV} \left(\frac{\sqrt{2}}{q_κ}\right) \left(\frac{R}{10,{\rm kpc}}\right) \left(\frac{38,{\rm pc}}{w}\right)^2 \left(\frac{w}{\ell_{\rm ripple}}\right) \left(\frac{220,{\rm km,s^{-1}}}{v_c}\right). ] In the simplest locked case (\ell_{\rm ripple}\sim w), a homogeneous first-pass set of narrow stream widths points to (m_a) of a few (10^{-19},{\rm eV}) and hidden-core masses of a few (10^3)--(10^4M_\odot). This is not a detection claim; it is a falsifiable phenomenological test for an ultralight axion component that can be sharpened by homogeneous stream catalogs and Schrödinger--Poisson simulations.