On the Formation of the W-shaped O <sc>ii</sc> Lines in Spectra of Type I Superluminous Supernovae

H-poor Type I superluminous supernovae (SLSNe I) are characterized by O II lines around 4000-4500 & Aring; in pre-/near-maximum spectra, the so-called W-shaped O II lines. As these lines are from relatively high excitation levels, they have been considered a sign of nonthermal processes, which may provide a hint of the power sources of SLSNe I. However, the conditions for these lines to appear have not been well understood. In this work, we systematically calculate synthetic spectra to reproduce the observed spectra of eight SLSNe I, parameterizing departure coefficients from the nebular approximation in the supernova ejecta (expressed as b neb). We find that most of the observed spectra can be well reproduced with b(neb) less than or similar to 10, which means that no strong departure is necessary for the formation of the W-shaped O II lines. We also show that the appearance of the W-shaped O II lines is sensitive to temperature; only spectra with temperatures in the range of T similar to 14,000-16,000 K can produce the W-shaped O II lines without large departures. Based on this, we constrain the nonthermal ionization rate near the photosphere. Our results suggest that spectral features of SLSNe I can give independent constraints on the power source through the nonthermal ionization rates.