Studies on the spin and magnetic inclination evolution of magnetars Swift J1834.9-0846 under wind braking

TL;DR

This work develops a unified spin-down framework for magnetars that jointly models magnetic-dipole radiation, gravitational-wave emission, and wind braking to explain the anomalously low braking index of Swift J1834.9-0846. By constraining the wind torque via nebular energetics and tracking coupled evolution of the dipole field and magnetic inclination, the authors find wind braking accounts for a substantial fraction of the current spin-down and that a toroidally-dominated internal field best reconciles the observations. Bayesian inference indicates the current geometry and wind-coupled evolution are robust, but the birth spin remains strongly prior-dependent, with an inferred age around a few thousand years and a precession-damping parameter ξ in the range $10^4$–$10^5$, compatible with crust-core coupling. Gravitational waves from the present epoch are undetectable with current instruments, but early-time signals at birth could have approached next-generation detector sensitivity under favorable conditions, linking magnetar interior physics to multi-messenger observables and offering a framework applicable to other low-braking-index neutron stars.

Abstract

The magnetar Swift J1834.9-0846 presents a significant challenge to neutron star spin-down models. It exhibits two key anomalies: an insufficient rotational energy loss rate to power its observed X-ray luminosity, and a braking index of $ = 1.08\pm 0.04$, which starkly contradicts the canonical magnetic dipole value of $n=3$. To explain these anomalies, we develop a unified spin-evolution model that self-consistently integrates magnetic dipole radiation, gravitational wave emission, and wind braking. Within this framework, we constrain the wind braking parameter to $κ\in [13, 37]$ from the nebular properties, finding it contributes substantially (17%-51%) to the current spin-down torque. Bayesian inference reveals that the birth period is poorly constrained by present data and is prior-dependent, indicating a millisecond birth is allowed but not required. Furthermore, we constrain the number of precession cycles to $ξ\sim 10^{4}$--$10^{5}$, and our analysis favors a toroidally-dominated internal magnetic field configuration as the most self-consistent explanation for the low braking index. Finally, we assess the continuous gravitational-wave detectability. The present-day signal is undetectable. However, the early-time signal might have reached the projected sensitivity of next-generation gravitational-wave observatories, such as the Advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO) and the Einstein Telescope (ET), although a confident detection would require exceptionally stable rotation, an assumption considered highly optimistic for a young magnetar. This work establishes a unified framework that links magnetar spin-down with their interior physics and multi-messenger observables, providing a physically consistent interpretation for Swift J1834.9-0846 and a new tool for understanding similar extreme neutron stars.

Figures (8)

• Figure 1: The $\kappa$--$\chi$ relation for Swift J1834, obtained from Equation (\ref{['eq:dew']}) and (\ref{['eq_eta']}) under the assumption that the wind luminosity equals the rotational energy-loss rate.
• Figure 2: Evolution of angular velocity $\Omega$ with time for Swift J1834. Dashed lines: toroidal-dominated (TD) internal magnetic configuration. Solid lines: poloidal-dominated (PD) configuration. Red and blue lines correspond to initial inclination angles $\chi_0 = 10^\circ$ and $45^\circ$, respectively. The black dot marks the current observed position of Swift J1834. Back symbols represent other magnetars with supernova remnant age constraints (data from Gao2016MNRAS).
• Figure 3: Time-dependent evolution of the magnetic inclination angle $\chi$ for Swift J1834. Dashed lines: TD case, evolving toward orthogonality ($\chi \rightarrow 90^\circ$). Solid lines: PD case, trending toward alignment ($\chi \rightarrow 0^\circ$). Colors indicate initial values: red for $\chi_0 = 45^\circ$, blue for $\chi_0 = 10^\circ$.
• Figure 4: Posterior distributions of the inferred parameters for Swift J1834 under two different priors on the initial spin period $P_0$. Left: log-normal prior on $P_0$; right: log-uniform prior on $P_0$. The diagonal panels show the marginalized one-dimensional posteriors with the median and 68% credible intervals, while the off-diagonal panels display the two-dimensional joint posteriors.
• Figure 5: Evolution tracks of Swift J1834 in the $P$--$\dot{P}$ diagram, derived from Bayesian posterior samples. The blue (orange) curve shows the median track obtained with a log-normal (log-uniform) prior on the initial period $P_0$, and the corresponding shaded regions indicate the pointwise $68\%$ credible intervals. The red star marks the current observed position of Swift J1834. Different markers indicate various neutron star populations: high-energy pulsars (HE, yellow circles), normal radio pulsars (black dots), non-radio active pulsars (NRAD, cyan triangles), rotating radio transients (RRATs, red squares), X-ray isolated neutron stars (XINSs, green diamonds), and magnetars (MAG, blue stars). These data are taken from Manchester2005AJ and Olausen2014ApJS.