Observations and 3 D photoionisation 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 central star's emission-line spectrum yields He:C:O mass fractions of 0.36:0.48:0.16, similar to those of PG1159 stars. A detailed empirical analysis of the nebular collisionally excited line (CEL) and optical recombination line (ORL) spectrum is presented, together with fully three-dimensional pho-toionisation 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 He I recombination lines ratios is 6000 K lower than the value of 11100 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 photoionisation model of NGC 1501 was constructed using the photoionisation code MOCASSIN, based on our new spectroscopic data and using the three-dimensional electron density distribution determined from long-slit echellograms of the neb-ula by Ragazzoni et al. (2001). The central star ionising radiation field is approximated by a model atmosphere, calculated using the Tübingen NLTE Model Atmosphere Package (Rauch 2003), for abundances typical of the W04 nucleus of NGC 1501 and PG1159 stars. The neb-ular emission line spectrum was best reproduced using a central star model with effective temperature T eff = 110 kK and luminosity L * = 5000 L ⊙. The initial models showed higher degrees of ionisation 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 photoionisation model heavily under-predicts 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 ionising photons by absorption in the knots, thereby helping to alleviate the over-ionisation of the heavy elements in our models.