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Constraining the ellipticity of strongly magnetized neutron stars powering superluminous supernovae

Superluminous supernovae (SLSNe) have been suggested to be powered by strongly magnetized, rapidly rotating neutron stars which are often called magnetars. In this process, rotational energy of the magnetar is radiated via magnetic dipole radiation and heats the supernova ejecta. However, if magnetars are highly distorted in their geometric shape, rotational energy is mainly lost as gravitational wave radiation and thus such magnetars cannot power SLSNe. By simply comparing electromagnetic and gravitational wave emission timescales, we constrain upper limits to the ellipticity of magnetars by assuming that they power the observed SLSNe. We find that their ellipticity typically needs to be less than about a few 1e-3. This indicates that the toroidal magnetic field strengths in these magnetars are typically less than a few 1e16 G so that their distortions remain small. Because light-curve modelling of SLSNe shows that their dipole magnetic field strengths are of the order of 1e14 G, the ratio of poloidal to toroidal magnetic field strengths is found to be larger than ~ 0.01 in magnetars powering SLSNe.