  The light curve of many supernovae (SNe) and gamma-ray bursts (GRBs) can be
explained by a sustained injection of extra energy from its possible central
engine, a rapidly rotating strongly magnetic neutron star (i.e. magnetar). The
magnetic dipole radiation power that the magnetar supplies comes at the expense
of the star's rotational energy. However, radiation by gravitational waves
(GWs) can be more efficient than magnetic dipole radiation because of its
stronger dependence on neutron star spin rate Omega, i.e. Omega^6 (for a static
'mountain') or Omega^8 (for a r-mode fluid oscillation) versus Omega^4 for
magnetic dipole radiation. Here, we use the magnetic field B and initial spin
period P_0 inferred from SN and GRB observations to obtain simple constraints
on the dimensionless amplitude of the mountain of epsilon < 0.01 and r-mode
oscillation of alpha < 1, the former being similar to that obtained by recent
works. We then include GW emission within the magnetar model. We show that when
epsilon > 10^-4 (B/10^14 G) (P_0/1 ms) or alpha > 0.01 (B/10^14 G) (P_0/1
ms)^2, light curves are strongly affected, with significant decrease in peak
luminosity and increase in time to peak luminosity. Thus the GW effects studied
here are more pronounced for low B and short P_0 but are unlikely to be
important in modelling SN and GRB light curves since the amplitudes needed for
noticeable changes are quite large.
