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Gravitational-wave evolution of newborn magnetars with different deformed structure

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.