Measuring the electric dipole moment of the neutron using neutron star spin-down
The neutron electric dipole moment (nEDM) is a sensitive probe of CP violation beyond the Standard Model. We develop a source-specific framework for constraining CP-odd neutron structure using the nearby millisecond pulsar PSR J0437-4715. Mass and radius measurements are used to construct a stellar-structure model and estimate the polarized inner-crust neutron reservoir. Wideband radio polarimetry provides a propagation-informed surface-field posterior that is not obtained from the conventional $P\dot P$ magnetic-field estimate, while published NICER hot-region constraints are used to test low-order surface-field geometries and isolate the dipolar component entering the electromagnetic torque. These inputs are propagated through a present-day spin-down budget including electromagnetic and gravitational-wave losses. The remaining positive residual is first interpreted as an unscreened electric-dipole-radiation benchmark. Crustal and magnetospheric screening then motivate an effective CP-odd magnetic-quadrupole channel. Conditional on the adopted screening, coherence, and effective-mode-frequency prescriptions, the positive-residual branch gives a 90th-percentile bound $|M_n^0|<7.47\times10^{-38}$ e cm$^2$. With the adopted QCD conversion coefficients, this corresponds to $|\barθ|<2.99\times10^{-9}$ and an equivalent $|d_n|<4.42\times10^{-25}$ e cm. Although weaker than laboratory nEDM limits, the result demonstrates how source-specific neutron-star structure, radio propagation, magnetic geometry, and spin-down energetics can be combined to test nonstandard CP-odd radiation channels.