Observations and three-dimensional photoionization modelling of the wolf-Rayet planetary nebula NGC 1501

Deep optical spectra of the high-excitation planetary nebula NGC 1501 and its W04 central star are presented. A recombination line abundance analysis of the emission-line spectrum of the central star yields He C: O mass fractions of 0.36:0.48:0.16, similar to those of PG 1159 stars. A detailed empirical analysis of the nebular collisionally excited line (CEL) and optical recombination line (ORL) spectrums are presented, together with fully three-dimensional photoionization modelling of the nebula. We found very large ORL-CEL abundance discrepancy factors (ADFs) for O ²⁺ (32) and Ne ²⁺ (33). The mean value of∼5100 K for the T _e derived from Her recombination lines ratios is 6000 K, lower than the value of 11 100 K implied by the [O III] line ratio. This result indicates the existence of a second, low-temperature nebular component, which could account for the observed ORL emission. Electron temperature fluctuations (t ²) cannot account for the high ADFs found from our optical spectra of this nebula. A three-dimensional photoionization model of NGC 1501 was constructed using the photoionization code MOCASSIN, based on our new spectroscopic data and using the three-dimensional electron density distribution determined from long-slit echellograms of the nebula by Ragazzoni et al. The central star ionizing radiation field is approximated by a model atmosphere, calculated using the Tübingen non-local thermodynamic equilibrium model atmosphere package, for abundances typical of the W04 nucleus of NGC 1501 and PG 1159 stars. The nebular emission-line spectrum was best reproduced using a central star model with an effective temperature of T _eff = 110 kK and a luminosity of L* = 5000L ⊙ The initial models showed higher degrees of ionization of heavy elements than indicated by observations. We investigated the importance of the missing low-temperature dielectronic recombination rates for third-row elements and have estimated upper limits to their rate coefficients. Our single-phase, three-dimensional photoionization model heavily underpredicts the optical recombination line emission. We conclude that the presence of a hydrogen-deficient, metal-rich component is necessary to explain the observed ORL spectrum of this object. The existence of such knots could also provide a softening of the radiation field, via the removal of ionizing photons by absorption in the knots, thereby helping to alleviate the overionization of the heavy elements in our models.