Ionizing radiation of [WR] stars: atmospheres and photoionization models

Abstract: The radiation field of central stars of planetary nebulae (CSPNe) is crucial for determining the physical conditions of planetary nebulae (PNe). Many studies in the literature model PNe using the blackbody approximation (bb) or plane-parallel (p-p) atmospheres as the ionizing source. However, these approaches become inconsistent when the central star is a Wolf-Rayet ([WR]) type. These objects are hydrogen-deficient and exhibit intense stellar winds, similar to classical massive WR stars. Their accurate description therefore requires sophisticated NLTE expanding atmosphere models. In this work, we selected [WR] NLTE expanding-atmosphere models spanning a range of temperatures and mass-loss rates and compared them with bb and p-p models. We examined differences in the spectral energy distribution and ionizing photon fluxes for H I, He I, and He II to assess the impact of stellar winds on the nebula-star interaction. Using CLOUDY, we also evaluated how each ionizing source affects predicted line ratios (I$<em>λ$/I$</em>β$) for a sample of PNe with [WR] nuclei. Model performance was measured through the rms deviation between observed and predicted ratios. For temperatures below 100,000 K, the EUV spectrum differs strongly among the three model types. Stellar winds introduce substantial opacity, reducing log Q(He II) significantly relative to no-wind models. For hotter [WR] stars, wind effects on ionizing fluxes are much smaller. For nebulae hosting late-type [WR] stars, models including winds provide much better agreement with observed line ratios than bb or p-p models, whereas for early-type stars the choice of ionizing source has only a minor influence. Our results indicate that bb and p-p approximations should be avoided when modelling PNe with [WR] central stars, especially those of the [WCL] subtype, because they fail to reproduce the strong wind-modified ionizing spectra.