Universality of gravitational radiation from magnetar magnetospheres

TL;DR

This work shows that gravitational waves from magnetar magnetospheres exhibit universal behavior: the magnetospheric GW signal is largely determined by the near-surface field and stellar compactness, with only modest dependence on the detailed twist or multipolar structure due to a maximum stable energy excess. Using 3D GR force-free magnetosphere models solved via physics-informed neural networks for dipole and dipole-plus-quadrupole geometries, the authors compute the magnetospheric quadrupole moment $Q^{22}$ and the corresponding strain $h_0$, then compare to interior hydromagnetic contributions. They find that the magnetospheric contribution remains a robust floor to the GW luminosity and that its amplitude scales with $B_0^2 R^5$, leading to marginal detectability by DECIGO for Galactic magnetars but enhanced prospects for strong near-surface multipolar fields, potentially observable out to a few kpc. The results offer a pathway to constraining near-surface magnetic fields and current distributions in magnetars, and highlight the value of future space-based GW observations in multimessenger contexts with X-ray activity and timing anomalies. A key limitation is the static, non-rotating formulation, suggesting future work to incorporate rotation and time-dependent twists to refine detectability and waveform predictions.

Abstract

The intense magnetic fields inferred from magnetars suggest they may be strong gravitational-wave emitters. Although emissions due to hydromagnetic deformations are more promising from a detection standpoint, exterior fields also contribute a strain. However, numerical evidence suggests that the free energy of stable magnetospheric solutions cannot exceed a few tens of percent relative to the potential state, implying that the magnetospheric contribution to the gravitational-wave luminosity cannot differ significantly between models. This prompts 'universality', in the sense that the strain provides a direct probe of the near-surface field without being muddied by magnetospheric currents. Using a suite of three-dimensional, force-free, general-relativistic solutions for dipole and dipole-plus-quadrupole fields, we find that space-based interferometers may enable marginal detections out to $\lesssim$ kpc distances for slowly-rotating magnetars with fields of $\gtrsim 10^{15}$ G independently of internal deformations.

Figures (7)

• Figure 1: Magnetic field lines for $\alpha_{0} = 1.5 R^{-1}$, $\theta_{1} = \pi/4$, and $\sigma = 0.2$ near the stellar surface (top) and at larger radii (bottom) for a star with $\mathcal{C} = 0.17$. The colour bars show the position-dependent value of $\alpha(\bm{x})$ itself.
• Figure 2: Comparison of the GR-boosted mass-quadrupole moment for an untwisted dipole relative to the Newtonian case, using either the perturbative expansion \ref{['eq:q22']} (dashed) or direct integration (solid).
• Figure 3: Magnetospheric quadrupole moments \ref{['eq:massquadnaxi']} for compactness $\mathcal{C} = 0.17$, normalised to the untwisted dipole, for varying base twist ($\alpha_{0}$; left), spot scale ($\sigma_{0}$; middle), and coronal-loop latitude ($\theta_{1}$ in degrees; right) as defined by expression \ref{['eq:alphaexpression']}.
• Figure 4: Mass quadrupole moments of twisted GR magnetospheres, normalised by the current-free value \ref{['eq:q22']}, as a function of $\alpha_0$ for $\mathcal{C} = 0$ (blue squares), $\mathcal{C} = 0.17$ (yellow stars), or $\mathcal{C} = 0.25$ (green circles).
• Figure 5: Variation of the (absolute value of the) quadrupole moment \ref{['eq:quadquadmom']} for untwisted, dipole-plus-quadrupoles with $\mathcal{C} = 0$ (blue squares), $\mathcal{C} = 0.17$ (orange crosses), or $\mathcal{C} = 0.25$ (green circles) where we fix $R =10$ km and the surface field strength maximum to $\tilde{B} = 2 \times 10^{15}$ G.