Node-locked phase of annual modulations from the gravitational chiral anomaly in the solar Kerr field

Abstract

The leading parity-odd mass--spin curvature invariant of the solar exterior, $P_{\odot }\equiv {}^{\ast }RR\simeq 288G^2{M}_{\odot }^2{a}_{\odot }\cos \theta /c^4{r}^7$, changes sign when the Earth crosses the solar equatorial plane and acts as the geometric source of the gravitational chiral anomaly. We study two minimal phenomenological responses to this structure: a long-memory reservoir $Q\propto \int (P_{\odot }-⟨P_{\odot }⟩)dt$ and the local worldline derivative $D=u^{\mu }{\nabla }_{\mu }{P}_{\odot }$. Both have an annual Fourier phase fixed by ephemerides, $t^{\ast }=158.7$~d (June 7--8) or the opposite branch $t^{\ast }=341.4$~d, with a calculable secular drift of $+0.014$~d\,yr${}^{-1}$ and an energy-independent geometric input phase, while predicting different semiannual fractions, $3.75\%$ and $15\%$, respectively. The response amplitudes and their microscopic origin are not predicted; the phase is. Single-amplitude fits to the digitized DAMA/LIBRA--phase2 1--3~keV residuals give ${\chi }^2/\mathrm{dof}=62.7/51$ for the reservoir and $63.6/51$ for the derivative, against $60.9/51$ for the standard-halo cosine. The most precise published phase, $t^{\ast }=153.5\pm 3.8$~d, lies $0.3\sigma$ from the halo value and $1.4\sigma$ from the node-locked one; phase metrology at the two-day level ($\simeq 3\sigma$), together with the phase-locked semiannual component, discriminates between the two clocks.

4 pages, 2 figures