  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.
