Gravitational-wave evolution of newborn magnetars with different deformed structures

Weak and continuous gravitational-wave (GW) radiation can be produced by newborn magnetars with deformed structure and is expected to be detected by the Einstein telescope in the near future. In this work we assume that the deformed structure of a nascent magnetar is not caused by a single mechanism but by multiple time-varying quadrupole moments such as those present in magnetically induced deformation, starquake-induced ellipticity, and accretion column-induced deformation. The magnetar loses its angular momentum through accretion, magnetic dipole radiation, and GW radiation. Within this scenario, we calculate the evolution of GWs from a newborn magnetar by considering the above three deformations. We find that the GW evolution depends on the physical parameters of the magnetar (e.g., period and surface magnetic field), the adiabatic index, and the fraction of poloidal magnetic energy to the total magnetic energy. In general the GW radiation from a magnetically induced deformation is dominant if the surface magnetic field of the magnetar is large, but the GW radiation from magnetar starquakes is more efficient when there is a larger adiabatic index if all other magnetar parameters remain the same. We also find that the GW radiation is not very sensitive to different magnetar equations of state.

Figure 1

Period of a magnetar as function of time for given Skyrme Lyon (SLy) EOS, $B_0={10}^{15}\mathrm{G}$, and $\mathrm{\Lambda }=0.2$. The solid red, blue, and green lines are the accretion torque, GW radiation torque, and dipole radiation torque, respectively. The black curve is the total contribution from all three.

Figure 2

Evolution of GW radiation with fixed $\mathrm{\Lambda }=0.2$ and given SLy EOS for different magnetic field strengths ($B_0={10}^{14}\mathrm{G},5\times {10}^{14}\mathrm{G},{10}^{15}\mathrm{G}$).

Figure 3

Evolution of GW radiation with fixed $B_0=5\times {10}^{14}\mathrm{G}$ and given SLy EOS for different poloidal magnetic field components ($\mathrm{\Lambda }=0.2$, 0.35, 0.8).

Figure 4

Evolution of GW radiation calculated with different adiabatic indices ($\gamma =2,2.1,\infty$) for SLy EOS and fixed $B_0={10}^{15}$, $\mathrm{\Lambda }=0.2$.

Figure 5

Evolution of GW luminosity with different EOSs for given $B_0=5\times {10}^{14}\mathrm{G}$, $\mathrm{\Lambda }=0.2$, and $\gamma =2.1$.

Figure 6

Gravitational-wave strain evolution with frequency of magnetar for different EOSs at distance 10 Mpc (top) and 40 Mpc (bottom). The black dotted line is the sensitivity limits for ET, and the black and gray solid lines are the sensitivity limits for aLIGO-Hanford and aLIGO-Livingston, respectively. The data of the noise curve are taken from Ref. [66].