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

TL;DR

The paper investigates how the ionizing radiation from Wolf–Rayet central stars in planetary nebulae shapes nebular emission, focusing on the role of dense stellar winds. It contrasts blackbody, plane-parallel NLTE, and NLTE expanding-atmosphere WR models (CMFGEN, Keller 2011) and quantifies their EUV output via ionizing-photon counts, then tests these spectra in Cloudy-based photoionization models for five WR-PNe. The results show wind-attenuated EUV fluxes strongly affect He II ionization, especially for cooler [WCL]-type stars, while hotter [WCE] stars exhibit smaller wind effects; for cooler WR PNe, wind-inclusive atmospheres yield substantially better agreement with observed nebular lines than simpler approximations. The study highlights the importance of incorporating wind-modified spectra in PN modeling and underscores limitations due to geometry, dust, and abundance assumptions, pointing to future multi-dimensional, wind-aware, and chemistry-resolved models. Overall, the paper advances the reliability of photoionization analyses for WR-hosting PNe by demonstrating when and why wind effects cannot be neglected.

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$_λ$/I$_β$) 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.

Figures (15)

• Figure 1: Comparison of the theoretical spectra in the ultraviolet region. For [WR] models, the mass-loss rate is displayed. The vertical axis represents the flux on a logarithmic scale, while the horizontal axis displays the wavelengths in angstroms. In the lower panel, we highlight the EUV region. Solid vertical lines indicate the wavelengths that correspond to the photoionization of H I (912 Å), He I (504 Å), and He II (228 Å). Note the differences between the models in the EUV despite having the same temperature, luminosity, and log g. [WR]-A refers to the [WR] models labeled "A" in keller2011new.
• Figure 2: Same as Fig. \ref{['fig:fluxA50']}, but for T$_{*}$ = 80000 K, log g = 5.3 and v$_{\infty}$ = 1000 km $s^{-1}$. [WR]-A refers to the [WR] models labelled "A" in keller2011new.
• Figure 3: Same as Fig. \ref{['fig:fluxA50']}, but for T$_{*}$ = 100000 K, log g = 6.0 and v$_{\infty}$ = 2500 km $s^{-1}$. [WR]-A refers to the [WR] models labelled "A" in keller2011new.
• Figure 4: Same as Fig. \ref{['fig:fluxA50']} and \ref{['fig:fluxA100']}, but for T$_{*}$ = 150000 K, log g = 6.0 and v$_{\infty}$ = 2000 km $s^{-1}$.
• Figure 5: Same as Fig. \ref{['fig:fluxA50']} and \ref{['fig:fluxA100']}, but for T$_{*}$ = 165000 K, log g = 6.3 and v$_{\infty}$ = 2000 km $s^{-1}$.