Gravitational Waves from Strongly Magnetized Eccentric Neutron Star Binaries

We study the imprint of magnetic fields on gravitational waves emitted during the inspiral phase of eccentric binary neutron star systems. While observations indicate that neutron stars typically exhibit strong magnetic fields in the range of $10^{14}$-$10^{15}\,\mathrm{G}$, theoretical models allow for fields as high as $ \sim 10^{17-18}\,\mathrm{G}$. In binaries, the fate of these fields depends on the formation pathway: in systems formed through isolated evolution, magnetic fields may decay over long inspiral timescales. In contrast, binaries formed via dynamical capture can retain substantial eccentricity and strong fields until merger, potentially altering the gravitational waveform. We consider two magnetic effects: magnetic interaction between the neutron stars and electromagnetic radiation from the system's effective dipole, and identify regimes where each dominates. Using a perturbative framework, we compute the associated energy loss and gravitational wave phase evolution. We find that for binaries with strong and comparable magnetic fields, $10^{14}\,\mathrm{G}$ fields may be detectable up to $\sim 10 \, \mathrm{Mpc}$ with DECIGO and the Einstein Telescope, while $10^{15}\,\mathrm{G}$ fields extend the reach to several hundred Mpc. For extreme fields of $10^{16}\,\mathrm{G}$, third-generation detectors could be sensitive out to Gpc scales. In contrast, LIGO is limited to galactic distances: $10^{15}\,\mathrm{G}$ fields are detectable only within $\sim 100\,\mathrm{kpc}$, and only ultrastrong fields ($\sim 10^{16}$-$10^{17}\,\mathrm{G}$) are potentially observable at Gpc distances. In highly asymmetric systems, where dipole radiation dominates, the gravitational wave dephasing is significantly suppressed, reducing the detection horizon. These findings suggest that current and future gravitational wave observatories may be capable of identifying magnetized binary systems.