Towards Nebular Spectral Modeling of Magnetar-Powered Supernovae

Many energetic supernovae (SNe) are thought to be powered by the rotational-energy of a highly-magnetized, rapidly-rotating neutron star. The emission from the associated luminous pulsar wind nebula (PWN) can photoionize the SN ejecta, leading to a nebular spectrum of the ejecta with signatures possibly revealing the PWN. SN 2012au is hypothesized to be one such SN. We investigate the impact of different ejecta and PWN parameters on the SN nebular spectrum, and test if any photoionization models are consistent with SN 2012au. We study how constraints from the nebular phase can be linked into modelling of the diffusion phase and the radio emission of the magnetar. We present a suite of late-time (1-6y) spectral simulations of SN ejecta powered by an inner PWN. Over a large grid of 1-zone models, we study the behaviour of the SN physical state and line emission as PWN luminosity ($L_{\rm PWN}$), injection SED temperature ($T_{\rm PWN}$), ejecta mass ($M_{\rm ej}$), and composition (pure O or realistic) vary. We discuss the resulting emission in the context of the observed behaviour of SN 2012au, a strong candidate for a PWN-powered SN. The SN nebular spectrum varies as $T_{\rm PWN}$ varies, as the ejecta become less ionized as $T_{\rm PWN}$ increases. Low ejecta mass models at high PWN power obtain runaway ionization for O I and, in extreme cases, also O II, causing a sharp decrease in their ion fraction over a small change in the parameter space. Certain models can reproduce the oxygen lines luminosities of SN 2012au reasonably well at individual epochs, but we find no model that fits over the whole time evolution; this is likely due to the simple model setup. Using our derived constraints from the nebular phase, we predict that the magnetar powering SN 2012au had an initial rotation period $\sim$ 15 ms, and should be a strong radio source (F > 100 $\mu$Jy) for decades.